MathMammoth_Grade2A
Short Description
Math practice...
Description
Copyright 2007-2010 Taina Maria Miller. EDITION 1.4 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, or by any information storage and retrieval system, without permission in writing from the author. Copying permission: Permission IS granted for the teacher to reproduce this material to be used with students, not commercial resale, by virtue of the purchase of this book. In other words, the teacher MAY make copies of the pages to be used with students. Permission is given to make electronic copies of the material for back-up purposes only.
Please visit www.MathMammoth.com for more information about Maria Miller's math books. Create free math worksheets at www.HomeschoolMath.net/worksheets/
2
Contents Foreword .....................................................................
5
Chapter 1: Getting Started Introduction ...................................................................
6
Some Review .................................................................
8
Adding and Subtracting Within 0-100 .........................
10
Ordinal Numbers ..........................................................
13
Fact Families .................................................................
15
Dividing to Two Parts - Halves ....................................
17
Fourths and Other Parts ..............................................
19
Chapter 2: Clock Introduction ...................................................................
21
Review - Whole and Half Hours ..................................
23
The Minutes ...................................................................
24
Five-Minute Intervals ...................................................
27
How Much Time Passes? ..............................................
31
Half and Quarter Hours ...............................................
33
The Calendar ..................................................................
35
Review .............................................................................
37
Chapter 3: Addition and Subtraction Facts Within 0-18 Introduction ...................................................................
38
Review: Completing the Next Whole Ten ...................
41
Review: Going Over Ten ..............................................
43
Adding with 9 .................................................................
45
Adding with 8 .................................................................
47
Adding with 7 .................................................................
49
Adding with 6 .................................................................
51
Review - Facts with 6, 7, and 8 .....................................
52
Subtract to Ten ..............................................................
54
Subtraction and the Difference ......................................
56
Number Rainbows - 11 and 12 ................................
58
3
Fact Families - 11 and 12 .......................................
60
Number Rainbows - 13 and 14 .....................................
62
Fact Families - 13 and 14 ..............................................
63
Fact Families - 15 ..........................................................
66
Fact Families - 16 ..........................................................
68
Fact Families - 17 and 18 .............................................
70
Review ...........................................................................
73
Chapter 4: Addition and Subtraction With Two-Digit Numbers Introduction ....................................................................
75
Adding with Whole Tens ..............................................
78
Subtracting Whole Tens ................................................
81
Carrying to Tens ............................................................
83
Going Over to the Next Ten ..........................................
86
Two-Digit Numbers Ending in 9 ...................................
89
Add in Columns Practice ..............................................
91
Two-Digit Numbers Ending in 8 or 7 ...........................
93
Addition Practice ...........................................................
95
Many Addends ...............................................................
97
Subtracting in Columns .................................................
100
Borrowing/Regrouping, Part 1 ......................................
101
Borrowing/Regrouping, Part 2 ......................................
104
Borrowing/Regrouping, Part 3 ......................................
107
Graphs and Problems ...................................................
109
Mental Subtraction Methods .........................................
112
Euclid's Game .................................................................
115
Mixed Review ................................................................
118
Chapter 5: Counting Money Introduction ...................................................................
120
Counting Coins Review ................................................
122
Change ...........................................................................
125
Dollars ............................................................................
128
Counting Change ..........................................................
131
4
Foreword The Math Mammoth Grade 2-A and Grade 2-B worktexts comprise a complete math curriculum for the second grade mathematics studies. The main topics during second grade, as in first grade, are the study of addition and subtraction and place value up to 1000. In the second grade, children learn to add and subtract two and three-digit numbers mentally and in columns (under each other). They learn to carry to tens and to hundreds (also called regrouping), and how to borrow either from the tens or from the hundreds. The topics of borrowing two times and borrowing over zero tens are in this curriculum left for the third grade. Mental math is very important, as it builds number sense and solidifies the understanding of place value. Children learn by heart the common addition and subtraction facts, and understand how to use them when adding two-digit numbers. They practice many kinds of mental math with three-digit numbers as well (in the 2B book). Other topics studied are reading the clock to the five-minute intervals; measuring length, weight, and volume; shapes and a few simple geometry concepts; and money topics. These topics are important as well, since they are everyday applications of mathematics. When you use these books as your only or main mathematics curriculum, they can be like a “framework”, but you still have liberty in planning your child's studies. While addition, subtraction, and place value topics are best studied in the order they are presented, you can choose to study clock, coins, and geometry topics in a different order. This does not totally apply to the chapter on measuring, as it uses 3-digit numbers. Changing the topic might even be advisable if your child is “stuck” on some concept. Sometimes the brain mulls it over in the background, and the concept they were stuck on becomes clear after a break. This curriculum aims to concentrate on a few major topics at a time and study them in depth. This is totally opposite to the continually spiraling step-by-step curricula, in which each lesson typically is about a different topic from the previous or next lesson, and includes a lot of review problems from past topics. This does not mean that your child wouldn't need an occasional review. However, when each major topic is presented in its own chapter, this gives you more freedom to plan the course of study and choose the review times yourself. In fact, I totally encourage you to plan your mathematics school year as a set of certain topics, instead of a certain book or certain pages from a book. For review, I have included an html page called Make_extra_worksheets_grade2.htm that you can use to make additional worksheets for computation or for number charts. You can also always simply reprint some pages that were already studied . I wish you success in your math teaching! Maria Miller, the author
5
Chapter 1: Getting Started Introduction The first chapter of the Math Mammoth Grade 2-A Complete Worktext has addition and subtraction review from the first grade, plus a few new topics that should be easy. The chapter starts out with review. Ordinal numbers are probably familiar from common language. The lesson Fact Families practices addition/subtraction connection, and introduces missing subtrahend problems such as __ − 5 = 4 where the total is missing. This is an early prelude to algebraic thinking. The last two lessons introduce some easy parts, such as one-half, one-fourth, two-fourths and threefourths. These lessons also practice finding half of a number or a fourth of a number. This is done for a good reason: First of all, the idea of finding part of a number is of paramount importance throughout elementary mathematics. Second, it prevents the fixation that half is “half of a pie” or that one-fourth is “one-fourth of a pie”, when halves and fourths apply to all kinds of “totals”. Third, the child will soon encounter the idea of a quarter of an hour when studying the clock, which is just one-fourth of an hour.
The Lessons in Chapter 1 page
span
Some Review ..........................................................................
8
2 pages
Adding and Subtracting Within 0-100 ...................................
10
3 pages
Ordinal Numbers ....................................................................
13
2 pages
Fact Families ..........................................................................
15
2 pages
Dividing to Two Parts - Halves .............................................
17
2 pages
Fourths and Other Parts .........................................................
19
2 pages
(hours)
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Number Cracker Help Mr. Cracker obtain the secret code before the insidious Prof. Soup catches him by guessing what number comes next in a series of numbers. http://www.funbrain.com/cracker/index.html Squigly Squigly is hiding in one of the apples. Click on the ordinal number that tells the order of Squigly's apple. http://www.primarygames.com/squigly/start.htm MathBlox Click on two falling blocks that add up to the given number and they disappear. With various levels and number ranges. http://www.iknowthat.com/com/L3?Area=Mathblox
6
Number Jump Move the ball along the number line to smash the flies. http://www.carstensstudios.com/mathdoodles/numberjump.htm Connect Sums Click on the neighboring die-faces/numbers/coins so that the points add up to the given target sum. http://www.carstensstudios.com/mathdoodles/connectsums.html Sum Stacker Drag dies from stack to stack until the sums of each stack equal the sums given. http://www.carstensstudios.com/mathdoodles/sumsstacker.html
7
Some Review 1. The box with a “T” means a ten. Write the addition sentences.
a.
32
+
7
=
+
+
+
39
b. ____ + ____ = ____
c. ____ + ____ = ____
2. Add whole tens. You draw a ten-box, or some more ten-boxes to the picture.
+
+
+
a. 25 + 10 = _____
b. 14 + 10 = _____
c. 32 + 10 = _____
25 + 20 = _____
14 + 20 = _____
32 + 20 = _____
25 + 30 = _____
14 + 30 = _____
32 + 30 = _____
3. Subtract from whole tens. One of the tens is shown with 10 dots, instead of a ten-box. Cover some of the dots to subtract.
60 – 3 = _____
a.
b.
30 – 4 = _____
60 – 8 = _____
30 – 6 = _____
60 – 7 = _____
30 – 5 = _____
4. Add in columns. The two numbers to be added are shown with dots and ten-boxes. b.
a.
+
+
8
5. Cross out to subtract in (a) and (b). In (c) and (d), subtract in columns.
4
5
− 2
3
c.
a. 49 – 6 = _____
9
8
− 6
5
d.
b. 47 – 16 = _____
6. Add and subtract. a.
b.
c.
d.
70 + 6 = _____
30 + 4 + 4 = _____
90 + ____ = 94
60 + ____ = 90
50 + 9 = _____
50 + 7 + 2 = _____
40 + ____ = 47
40 + ____ = 80
e.
f.
g.
h.
70 − 1 = _____
5 − 5 = ____
88 − 8 = _____
50 + ____ = 56
100 − 5 = _____
24 − 4 = _____
57 − 7 = _____
30 + ____ = 39
7. Solve the word problems. a. Luis bought two boxes of crayon for $6 each, and a stack of paper for $3. What was his total cost?
b. Ernie has 7 marbles, and Jackie has 5. Jackie gives Ernie two of his. How many more marbles does Ernie have now than Jackie?
c. Jack has twenty shirts, and ten of them are white. How many are not white?
d. A book costs $45. Can you buy it if you already have $22 and your grandma gives you another $20?
9
Adding and Subtracting Within 0-100 1. Skip-count by fives, starting at 5. Color these numbers light blue.
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
2. Color yellow all the even numbers from 32 to 70.
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
3. What can the last digit of an even number be? Even numbers end in ____, ____, ____, ____, or ____.
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
1
4. Skip-count by tens starting at 17. Color these numbers pink. What is similar about these numbers?
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
They all end in ____.
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
5. Skip-count by tens backwards starting at 93. Color these numbers green. What is similar about these numbers?
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
They all end in ____.
91 92 93 94 95 96 97 98 99 100
1
6. Color purple all the odd numbers from 89 to 51.
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
7. What can the last digit of an odd number be?
41 42 43 44 45 46 47 48 49 50
Odd numbers end in ____, ____, ____, ____, or ____.
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
8. Skip-count by fours starting at 4. Color these numbers yellow.
71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
10
9. Skip-count. First find by which number to skip-count - by 2s, by 5s, or by 10s. a. 40,
42, 44, _____, _____, 50, _____, _____, _____, _____, _____
b. _____,
_____, _____, _____, 48, 58, 68, _____, 88, _____
c. _____,
_____, _____, _____, 65, 63, 61, _____, _____, _____
d. _____,
_____, _____, 70, 65, 60, _____, _____, _____, _____
10. Write the addition sentences. The box with a “T” is a ten. Under each problem, there is another, similar, addition problem for you to solve. Can you see how it is similar?
+
+
+
a.
____ + ____ = ____
c.
____ + ____ = ____
e.
____ + ____ = ____
b.
34 + 3 = ____
d.
53 + 6 = ____
f.
32 + 5 = ____
11. Subtract by crossing some out. Under each problem, there is another, similar, problem.
a.
59 – 6 = _____
c.
47 – 5 = _____
e.
60 – 3 = _____
b.
39 – 6 = _____
d.
67 – 5 = _____
f.
50 – 3 = _____
12. Add and subtract. The problems in each box are similar. a.
b.
c.
d.
2 + 6 = _____
4 + 4 = _____
3 + 6 = _____
8 + 2 = _____
42 + 6 = _____
74 + 4 = _____
53 + 6 = _____
48 + 2 = _____
72 + 6 = _____
94 + 4 = _____
23 + 3 = _____
98 + 2 = _____
e.
f.
g.
h.
7 – 5 = _____
9 – 4 = _____
10 – 4 = _____
8 – 5 = _____
37 – 5 = _____
29 – 4 = _____
50 – 4 = _____
38 – 5 = _____
67 – 5 = _____
99 – 4 = _____
80 – 4 = _____
88 – 5 = _____
11
13. Draw more dots so you complete the next whole ten. Write an addition sentence.
+ a.
+
13 + ___ = 20
b.
+
____ + ___ = ____
c.
____ + ___ = ____
14. Complete the next whole ten. The problems in the bottom row are challenging! a.
32 + ___ = ____
b.
74 + ___ = ____
c.
48 + ___ = ____
d.
42 + 3 + ____ = 50
e.
37 + ____ + 1 = 40
f.
84 + ____ + 4 = 90
15. Subtract the same number each time.
a.
– 10
b.
– 20
c.
50
____
100
____
45
____
52
____
20
____
95
____
64
____
40
____
96
____
23
____
21
____
11
____
Find numbers for the boxes so that the sum of each row and of each column is a. 50 b. 80. a.
42
+
+ +
+ +
+ +
b.
+ +
+
–5
40
75
+
+
41
+ +
+
+
+
+
+ +
+
12
+
74
72 +
+
Ordinal Numbers The numbers 1, 2, 3, 4, and so on are called cardinal numbers. The fourth tree from the left is circled. It is also the second tree from the right.
But we also often use ordinal numbers. Ordinal numbers are used when talking about the order of things. List of some ordinal numbers:
The seventh letter of the word is S. Ordinal Number Name 1st first 2nd second 3rd third 4th fourth 5th fifth 6th sixth 7th seventh 8th eighth
Ordinal Number Name 9th ninth 10th tenth 11th eleventh 12th twelfth 13th thirteenth 14th fourteenth 15th fifteenth 16th sixteenth
1. Circle. a. The second car from the left. b. The fifth car from the right. c. The seventh snowflake
from the left. d. The fourth snowflake
from the right. e. The ninth letter from the left. f. The twelfth letter from
EXTRAORDINARY
the right.
13
2. Color.
a. The third flower from the left
b. The first three flowers on the left
c. The fifth flower from the right.
d. The first five flowers on the right.
3. Find the letters, and find out what Greg's surprise gift was. The second row from the top, the first letter from the left.
___
The fourth row from the top, the third letter from the left.
___
The first row from the top, the fifth letter from the right.
___
The fifth row from the bottom, the second letter from the right.
___
The 1st row from the bottom, the 1st letter from the left.
___
The sixth row from the top, the third letter from the right.
___
The 3rd row from the top, the 2nd letter from the left.
___
The 1st row from the top, the 2nd letter from the left.
___
E B W J Y U O
4. a. Choose the letters of the given word to make a new word.
___
10th 5th
___
L E K A Z T H
A N P U N S A
B I T D Y O V
G V L W I Q E
P S F M C R L
b. Put the letters in the given order
to make a new word. N D Y R T C I A I O 7th 1st 10th 9th 4th 3rd 2nd 8th 5th 6th
S U R P R I S I N G ___
S H N D K D T
___ ___
6th 9th 1st
14
Fact Families When you have two addition and two subtraction facts that use the same numbers, it is called a “fact family”. Sometimes in a subtraction problem, the total is asked:
4+5= 9
4 + 5 =9
5+4= 9
5 + 4 =9
− 8 = 20 You know 20 and 8 are the “parts”, and the total is missing. To find the total, just add the “parts”: 20 + 8 = 28
9 −5=4
9− 5 = 4
9 −4=5
9− 4 = 5
Notice the TOTAL. The subtraction sentences start with the total.
Notice the PARTS. The two parts make up the total.
1. Write two addition and two subtraction sentences - a fact family! a.
b.
c.
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ − ____ = ____
____ − ____ = ____
____ − ____ = ____
____ − ____ = ____
____ − ____ = ____
____ − ____ = ____
2. Fill in the missing numbers. The four problems form a fact family. a.
b.
=8
c.
____ + ____ = 10
____ + ____ = ____
+2=8
____ + ____ = 10
____ + ____ = ____
2+
10 − 7 =
8−2= 8−
=2
10 −
9 − =7
15
= 6
____ − ____ = ____
3. Write a matching addition sentence for the subtraction sentence. There are two possibilities. a.
____ + ____ = ____
b.
8 − 2 = 6
____ + ____ = ____
c.
20 − 7 = 13
____ + ____ = ____ 60 − 20 = 40
– 6 =2
When the first number is missing in a subtraction, it is the TOTAL that is missing.
The total is missing. 6 and 2 are the “parts”. So we add them. 2 + 6 = 8. The missing number is 8!
You can find the TOTAL by adding the two numbers (those are the “parts”).
It's like “adding backwards”:
4. The total is missing from the subtraction sentence. Solve. a.
– 5 = 4
b.
– 7 = 2
c.
b.
– 7 = 80
c.
– 7 = 10
5. Find the missing numbers. a.
–2=4 – 50 = 50
60 + 4 =
– 8 = 20
16 +
9–
=5
77 + = 20
= 78 – 9 = 60
Find the missing numbers. This time adding backwards will NOT work! a. 50 −
= 10
b. 100 −
= 91
c. 10 −
−2=1
33 −
= 31
76 −
= 72
9−
−5=2
16
Dividing into Two Parts — Halves If you divide something into two of the same size parts, or two equal parts, then either part is one-HALF of the whole. We write one-half this way:
1 2
You can also write one-half this way: 1/2 You can also find half of so-many objects. For example, you can find half of ten apples. It is five apples. You can also find half of a number. For example, half of 6 is 3.
1. a. Color one half of each shape.
b. Color two halves of each shape.
2. Draw a line through these shapes and divide them into two halves. Color one half.
b.
a.
e.
c.
d.
3. Divide the items into two EQUAL groups. Write an addition sentence. Find half of the total.
10 balls
40
24
a. ____ + ____ = _____
b. ____ + ____ = _____
c. ____ + ____ = _____
1 of 10 is ____. 2
1 of 40 is ____. 2
1 of 24 is ____. 2
17
4. Remember your doubles? Fill in the chart.
1 + 1 = ____
1 2
of 2 is 1 .
6 + 6 = ____
1 2
of ___ is ____.
2 + 2 = ____
1 2
of 4 is 2 .
7 + 7 = ____
1 2
of ___ is ____.
3 + 3 = ____
1 2
of ___ is ____.
8 + 8 = ____
1 2
of ___ is ____.
4 + 4 = ____
1 2
of ___ is ____.
9 + 9 = ____
1 2
of ___ is ____.
5 + 5 = ____
1 2
of ___ is ____.
10 + 10 = ____
1 2
of ___ is ____.
5. Divide the items into two EQUAL groups. Write an addition sentence. Find half of the total.
a. ____ + ____ = _____
b. ____ + ____ = _____
c. ____ + ____ = _____
1 of ___ is ____. 2
1 of ___ is ____. 2
1 of ___ is ____. 2
6. Solve the word problems, and fill in another chart of doubles and halves to help you. a. Jack and Joe split $60 between them.
10 + 10 = _____
1 2
of ___ is ____.
b. What is half of 60 minutes?
20 + 20 = _____
1 2
of ___ is ____.
c. Half of 100 students were sick.
30 + 30 = _____
1 2
of ___ is ____.
40 + 40 = _____
1 2
of ___ is ____.
50 + 50 = _____
1 2
of ___ is ____.
How many dollars did each get?
How many were not sick? d. Aunt Katie gave Missie half of $40.
Missie spent $10 on a toy. How many dollars does Missie have now?
e. The recipe called for 10 apples. That was exactly half of Mom's apples.
How many apples had mom bought originally?
18
Fourths and Other Parts 1 4 A square is divided into four equal parts. One part is colored. The colored part is one-fourth:
1 of the circle 4
1 of the stars 4
1 of the rectangle 4
1 of the hearts 4
1 4
We also write one-fourth as 1/4. If you need to find 1/4 of any thing, first divide it into four equal groups.
1 4 one-fourth
2 4
3 4
4 4
two-fourths
three-fourths
four-fourths
1. Color the part indicated.
a.
1 2
b.
1 4
c.
3 4
d.
2 2
e.
2 4
f.
1 2
g.
3 4
h.
4 4
i.
1 4
j.
1 2
19
2. Divide these items into four EQUAL groups. Find one-fourth of the total. 12 balls
8 balls
a.
1 of 8 is ____. 4
b.
40
1 of 12 is ____. 4
c.
16
1 of 40 is ____. 4
d.
1 of 16 is ____. 4
1 of 100 is _____. 4
3. a. Here you see 100 little squares. Color 1/4 of them.
1 of 60 is _____. 4
b. Here you see 60 little squares.
Color 1/4 of them.
3 of 80 is _____. 4
c. Here you see 80 little squares.
Color 3/4 of them.
1 dollar = 100 pennies
4 quarters = 1 dollar 4. Remember the quarter coin? The word “quarter” means one-fourth.
=
Four quarters makes one dollar, or 100 cents. 1 of 100 cents is _____ cents = 1 quarter. 4 1 of 100 cents is _____ cents = 2 quarters. 2 3 of 100 cents is _____ cents = 3 quarters. 4
20
Chapter 2: Clock Introduction The second chapter of the Math Mammoth Grade 2-A Complete Worktext deals with reading the clock to the five-minute intervals, and finding simple time intervals. It is helpful to have a practice clock, such as an alarm clock, where the child can turn the clock hands. First we practice telling time in the hours:minutes form (such as 10:20), and then using the colloquial phrases “ten after”, “quarter till”, and so on. Also studied are simple time intervals, or how much time passes. When practicing these, tell the child to imagine moving the minute (or hour) hand on a clock. He/she can initially use a practice clock for this. The section also has one lesson about the calendar. Of course the calendar and the months are best learned just in the context of everyday life, as the months pass. Hang a wall calendar on the wall and instruct your child to look at it every day, and to cross out days as they pass.
The Lessons in Chapter 2 page
span
Review - Whole and Half Hours ..................
23
1 page
The Minutes ..................................................
24
3 pages
Five Minute Intervals ..................................... 27
4 pages
How Much Time Passes? ..............................
31
2 pages
Half and Quarter Hours .................................
33
2 pages
The Calendar ................................................
35
2 pages
Review .........................................................
37
1 page
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Analog and Digital Clocks These clocks show you the current time, side by side. Useful for illustration. http://nlvm.usu.edu/en/nav/frames_asid_316_g_2_t_4.html What Time Will it Be? Move the hands on the clock to show what time it will be after a certain amount of minutes. http://nlvm.usu.edu/en/nav/frames_asid_318_g_2_t_4.html Match Clocks Make the digital clock to show the time given with the analog clock. http://nlvm.usu.edu/en/nav/frames_asid_317_g_2_t_4.html
21
Time Flies Practice telling time with two types of watches. In the second part, practice what you have learned by selecting the digital time that matches the time displayed. http://www.alfy.com/Games/playgame.aspx?gameID=354&gameName=Time+Flies Flashcard Clock Read the analog and type in the time in digital form. Very clear clock and good fast response! http://www.teachingtreasures.com.au/maths/FlashcardClock/flashcard_clock.htm Telling Time Practice Interactive online practice: you drag the hands of the clock to show the correct time. http://www.worsleyschool.net/socialarts/telling/time.html Teaching Time Analogue/digital clock games and worksheets. Also an interactive “class clock” to demonstrate time. http://www.teachingtime.co.uk/ Time-for-time Resource site to learn about time: worksheets, games, quizzes, time zones. http://www.time-for-time.com/default.htm A Matter of Time Lesson plans for telling time, interactive activities, and some materials to print. http://www.fi.edu/time/Journey/JustInTime/contents.html Elapsed Time Line This interactive tool shows 2 clocks that have draggable fingers to set a "from" and "to" time, and a number line. You can demonstrate how to use a number line to calculate elapsed time. www.teacherled.com/2008/10/05/elapsed-time-line/ Clockwise Plug in a time, and the clock runs till it, or clock runs to a time and you type it in. http://www.shodor.org/interactivate/activities/clock2/index.html Clock (evaluation version words across the screen) Use the buttons to advance the clock in 5, 10, 15, 30 minute increments or drag the hands. Shows digital time also. For illustrations only, does not have any quiz or questions. http://www.interactive-resources.co.uk/mathspack1/clock/clock.html The Right Time A couple of interactive exercises about reading the clock. http://www.pitara.com/activities/math/time/time.asp?QNum=3 What Time Is It? Look at the analog clock and pick the digital clock that shows the same time. http://www.primarygames.com/time/start.htm
22
Review - Whole and Half Hours 1. Write or say the time using the expressions o'clock or half past.
a.
b.
c.
d.
2. Write the time in two ways: using the expressions o'clock or half past, and with numbers.
a. _____ o'clock _____ : _____
b. half past _____
c. half past _____
_____ : _____
_____ : _____
d. _____ o'clock _____ : _____
3. Write the time an hour later. Use numbers. Now it is:
a. 6:00
b. 11:30
c. 3:00
d. 2:30
e. 9:30
c. 12:30
d. 10:00
e. 1:30
An hour later, it is: 4. Write the time a half-hour later. Use numbers. Now it is:
a. 5:00
b. 7:30
A half-hour later, it is:
23
The Minutes When the hour hand moves from one number to the next (from 1 to 2, or from 6 to 7, etc.), it takes one hour to do that. In that same one hour of time, the minute hand travels from 0 to 60 minutes. So one hour is 60 minutes. A half-hour is 30 minutes. When you read the minute hand, you use the green numbers. They go by fives, and are not normally marked on clocks. You need to know them. (Just skip-count by fives!)
The hour hand is past 8. The minute hand is at 15. The time is 8:15.
The hour hand is past 3. The minute hand is at 25. The time is 3:25.
1 hour = 60 minutes. 1/2 hour = 30 minutes.
The hour hand is past 11. The minute hand is at 10. The time is 11:10.
1. The arrow shows how much the minute hand travels. How many minutes of time passes?
a. _____ minutes
b. _____ minutes
c. _____ minutes
24
d. _____ minutes
2. Write the time.
a. ____ : _____
b. ____ : _____
c. ____ : _____
d. ____ : _____
e. ____ : _____
f. ____ : _____
g. ____ : _____
h. ____ : _____
3. Find the clock that shows 11:25 and the clock that shows 11:05.
a.
b.
c.
d.
4. Write the time that the clock shows, and the time 5 minutes later.
5 min. later →
a. ____ : _____
b. ____ : _____
c. ____ : _____
d. ____ : _____
____ : _____
____ : _____
____ : _____
____ : _____
25
Notice! The hour hand looks like it is pointing to 10. But the minute hand has not yet reached 60 minutes, so it is not yet 10 o'clock. We still say it is 9 hours (and some minutes). The minute hand is at 55. The time is 9:55.
5. Write the time. Note: the hour hand is close to some number, but it has not reached that yet.
a. ____ : _____
b. ____ : _____
c. ____ : _____
d. ____ : _____
e. ____ : _____
f. ____ : _____
g. ____ : _____
h. ____ : _____
6. Write the time that the clock shows, and the time 5 minutes later.
5 min. later →
a. ____ : _____
b. ____ : _____
c. ____ : _____
d. ____ : _____
____ : _____
____ : _____
____ : _____
____ : _____
26
Five-Minute Intervals When the MINUTE hand travels from one number to the next on the clock face, 5 minutes of time passes. Each interval is five minutes. That is why you skip-count by fives, when figuring out the minutes.
1. Continue writing the times at each five-minute interval. You can use your practice clock.
a.
b.
c.
d.
8 : 20
_____ : _____
_____ : _____
_____ : _____
8 : 25
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____
_____ : _____ _____ : _____ _____ : _____
_____ : _____ _____ : _____ _____ : _____
27
We can also tell the time by saying how many minutes it is past the whole hour, or how many minutes it is till the next whole hour. Use the expression “so-many minutes past” only if the minutes are less than 30. After that, use “so-many minutes till” the next whole hour.
20 past 1
10 till 7
“20 minutes past 1 o'clock”. “10 minutes till 7 o'clock.”
2. How many minutes is it past the whole hour, or till the next whole hour?
a. It is ____ minutes past 2 o'clock.
b. It is ____ minutes past 3 o'clock.
c. It is ____ minutes past ____ o'clock.
d. It is ____ minutes past _____ o'clock.
e. It is ____ minutes till 7 o'clock.
f. It is ____ minutes till ____ o'clock.
g. It is ____ minutes till ____ o'clock.
h. It is ____ minutes till ____ o'clock.
i. ____ past ___
j. ____ past ___
k. ____ past ___
l. ____ past ___
m. ____ till ___
n. ____ till ___
o. ____ till ___
p. ____ till ___
28
3. Write the time using the wordings “past”, “till”, “half past” or “o'clock”, and the time 5 minutes later.
a. ____ till ___
b. ____ till ___
c. ____ past ___
d. ____ past ___
____ till ___
____ till ___
____ past ___
____ past ___
5 min. later →
e.
f.
g.
h.
i.
j.
k.
l.
5 min. later →
5 min. later → 4. Write the time using the hours:minutes way. Use your practice clock to help. a. 10 past 8 ______:______ e. 9 o'clock ______:______
b. 15 till 7
c. 25 past 12
______:______
______:______
f. 20 till 6
g. 5 till 11
______:______
______:______
29
d. half-past 7 ______:______ h. 25 till 4 ______:______
5. Write the time using the expressions “past”, “till”, or “half past”. a. 6:45
b. 9:30
c. 12:10
d. 4:55
e. 8:35
f. 1:40
g. 2:15
h. 11:50
6. How many minutes does the minute hand “cover”, or “pass through”, on the clock?
a. From 10:00 till 10:15
b. From 1:20 till 1:35
c. From 5:50 till 6:10
d. From 2:05 till 2:40
______ minutes
______ minutes
______ minutes
______ minutes
7. Write the later times.
a.
c.
e.
z
15 min. later ____:_____
z
15 min. later ____:_____
z
20 min. later ____:_____
z
20 min. later ____:_____
z
30 min. later ____:_____
z
30 min. later ____:_____
z
15 min. later ____:_____
z
15 min. later ____:_____
z
20 min. later ____:_____
z
20 min. later ____:_____
z
30 min. later ____:_____
z
30 min. later ____:_____
z
15 min. later ____:_____
z
15 min. later ____:_____
z
20 min. later ____:_____
z
20 min. later ____:_____
z
30 min. later ____:_____
z
30 min. later ____:_____
b.
d.
f.
30
How Much Time Passes? 1. How many minutes till 2:30? Till 8:05? a.
b.
It is 2:00. → ______ minutes till
It is 7:30. → ______ minutes till
It is 2:10. → ______ minutes till
It is 7:35. → ______ minutes till
It is 2:20. → ______ minutes till
It is 7:45. → ______ minutes till 2:30
It is 2:25. → ______ minutes till
It is 7:50. → ______ minutes till
8:05
2. The class ends at 1:00. How many minutes of class is left at these times?
a.
b.
c.
d.
_______ minutes
_______ minutes
_______ minutes
_______ minutes
3. How many minutes pass? Imagine turning the minute hand on a clock. from
1:45
1:55
1:40
1:45
1:55
to
1:55
2:05
2:05
2:15
2:10
minutes
10 minutes
from
2:00
7:05
8:45
6:40
11:15
to
2:35
7:15
9:05
7:10
11:30
minutes 4. a. The bus trip started at 10 past 4, and ended at half past 4. How many minutes did it take? b. Joshua started math homework at 20 till 5, and ended at 5 past 5.
How much time did he spend? c. Music class starts at 10:15, and ends at 10:45. How long is it?
31
5. How many hours is it? from to
8 AM
7 AM
9 AM
11 AM
10 AM
12 noon
1 PM
4 PM
11 PM
7 PM
4 PM
7 PM
12 AM
9 AM
7 AM
12 midnight
12 midnight
12 midnight
12 midnight
12 midnight
hours 6. How many hours till midnight? from to hours 7. a. Dad's workday starts at 8:00 in the morning, and ends at 5 PM. How many hours is Dad at work? b. Mary's school day starts at 9 AM and ends at 2 PM. How long is her school day? c. The airplane took off at 10 AM and landed at 1 PM. Then it again took off again
at 2 PM and landed at 6 PM. How many hours was the airplane in the air? d. How many hours are there in 1 day-night period?
8. a. The turkey needs to cook 3 hours in the oven to be ready at 7 PM. When should it be put into the oven? b. It takes 2 hours to mow the lawn. Jim wants to be done at 1 PM.
When should he start mowing? c. Mom needs 7 hours of sleep tonight. She wants to wake up at 6 AM.
When should she go to bed? 9. Imagine the minute hand going all the way around on the clock - or full hours. Fill in how many whole hours pass. from
10:30
10:30
1:40
5:45
3:20 AM
to
11:30
12:30
4:40
11:45
12:20 PM
full rounds or hours
32
Half and Quarter Hours The clock face is divided into four equal parts. Each part is one-fourth. We can see that one-fourth of 60 minutes is 15 minutes. The word “quarter” means one-fourth. When we say, “A quarter past 6”, we mean one-fourth of an hour past 6 o'clock, or 15 minutes past 6. When we say, “A quarter till 6”, we mean one-fourth of an hour till 6 o'clock, or 15 minutes till 6. When we say, “Half-past 6”, we mean a half-hour past 6 o'clock, or 30 minutes past 6.
15 past 4, OR a quarter past 4
1 hour = 60 minutes. 1/2 hour = 30 minutes. 1/4 hour = 15 minutes.
15 till 8, OR a quarter till 8
half past 10
1. Write the time using “a quarter past”, “a quarter till”, “half past”, or “o'clock”.
a.
b.
c.
d.
e.
f.
g.
h.
33
2. Write the times using hours:minutes. a. a quarter till 5
b. a quarter past 12
c. a quarter till 9
d. a quarter past 3
_____ : ______
_____ : ______
_____ : ______
_____ : ______
e. half past 11
f. a quarter till 12
g. a quarter past 8
h. a quarter till 1
_____ : ______
_____ : ______
_____ : ______
_____ : ______
3. Write the time using “a quarter past”, “a quarter till”, “half past”, or “o'clock”. a. 7:30
b. 5:15
c. 5:45
d. 9:45
e. 12:15
f. 12:30
g. 11:45
h. 7:45
4. Which clock shows the time a half-hour later than the given time? a. a quarter past 5 b. half past 4 c. 3 o'clock
1.
2.
3.
4.
5.
6.
d. a quarter till 6 e. a quarter till 7 f. a quarter past 4
5. a. Mom started cooking rice at a quarter past 5. It needs to cook for 30 minutes. When will it be ready? b. A rain storm lasted half an hour, starting at a quarter till 2. When did it end? c. The class ends at 2 o'clock. Now there are still 15 minutes left of class time.
What time is it now?
34
The Calendar January Su Mo Tu 1 6 7 8 13 14 15 20 21 22 27 28 29
We 2 9 16 23 30
Th 3 10 17 24 31
Fr 4 11 18 25
Sa 5 12 19 26
February
March
Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
May
June
April Su Mo Tu 1 6 7 8 13 14 15 20 21 22 27 28 29
We 2 9 16 23 30
Th 3 10 17 24
Fr 4 11 18 25
Sa 5 12 19 26
Su Mo Tu We Th 1 4 5 6 7 8 11 12 13 14 15 18 19 20 21 22 25 26 27 28 29
July Su Mo Tu 1 6 7 8 13 14 15 20 21 22 27 28 29
We 2 9 16 23 30
Th 3 10 17 24 31
Th 2 9 16 23 30
Sa 3 10 17 24 31
Su 1 8 15 22 29
Mo 2 9 16 23 30
August Fr 4 11 18 25
Sa 5 12 19 26
Su Mo Tu We Th Fr 1 3 4 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 24 25 26 27 28 29 31
October Su Mo Tu We 1 5 6 7 8 12 13 14 15 19 20 21 22 26 27 28 29
Fr 2 9 16 23 30
Sa 4 11 18 25
We 4 11 18 25
Th 5 12 19 26
Fr 6 13 20 27
Sa 7 14 21 28
Fr 5 12 19 26
Sa 6 13 20 27
Fr 5 12 19 26
Sa 6 13 20 27
September Sa 2 9 16 23 30
Su Mo 1 7 8 14 15 21 22 28 29
November Fr 3 10 17 24 31
Tu 3 10 17 24
Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Tu 2 9 16 23 30
We 3 10 17 24
Th 4 11 18 25
December Su Mo 1 7 8 14 15 21 22 28 29
Tu 2 9 16 23 30
We 3 10 17 24 31
Th 4 11 18 25
Discuss with your teacher: 1. What do the letters “Su Mo Tu We Th Fr Sa“ mean? 2. (Use the calendar above.) What day of the week is... a. April 4th
b. October 13th
c. December 3rd
d. May 28th
e. September 1st
f. February 19th
g. your birthday
h. today
i. your mom's birthday
35
3. a. List here all the months that have 31 days.
b. List here all the months that have 30 days.
c. Which month is the shortest month? ________________________
How many days does it have? ____ 4. Write the dates, using the form (month) (day), like in problem (2). The day number is an ordinal number! a. today's date
b. tomorrow's date
c. your birthday
d. your mom's birthday
e. Monday next week
f. the first Monday of June
5. Write the date exactly one week (7 days) later than these dates: a. January 3rd
b. February 11th
c. May 22nd
d. June 5th
e. August 30th
f. November 26th
g. March 13th
h. September 28th
6. a. Let's say it is now April first. How many months is it till June? Till August? Till December? Till October? b. Let's say it is now January first. How many months is it till February? Till April?
Till July? Till September? 7. If you have already had your birthday for this year, how many months ago was it? If you haven't had it yet, how many months is it from today until your birthday? 8. Mary goes to a swimming club every Thursday. List here the May dates when Mary goes swimming. 9. Jack ordered a passport on July 3rd. He is supposed to pick it up two weeks later. What date is that?
36
Review - Clock to the Nearest Five Minutes 1. Write the time with hours:minutes, and using “past”, “till”, “half past” or “o'clock”.
a. ____ : ______
b. ____ : ______
c. ____ : ______
d. ____ : ______
________________
________________
f. ____ : ______
g. ____ : ______
h. ____ : ______
________________
________________
________________
_____ till ____
_____ past ____
e. ____ : ______
_____ till ____
2. Write the later time. Time now 15 min. later
2:30
6:55
____ : _____
____ : _____
Time now 20 min. later
9:05
5:40
____ : _____
____ : _____
3. How many minutes pass? Imagine turning the minute hand on a clock. from
1:45
1:55
1:40
1:45
1:55
to
1:55
2:05
2:05
2:15
2:10
8 AM
7 AM
9 AM
11 AM
10 AM
12 noon
1 PM
4 PM
11 PM
7 PM
minutes
10 minutes
4. How many hours is it? from to hours
37
Chapter 3: Addition and Subtraction Facts Within 0-18 Introduction The third chapter of the Math Mammoth Grade 2-A Complete Worktext provides lots of practice for learning and memorizing the basic addition facts of single-digit numbers where the answer is between 10 and 18, and learning to use them with subtraction.
Completing the ten - concept This concept is important to learn. The child learns what number is needed to complete the next whole ten. For example, what number do you add to 23 to get 30, or 23 + __ = 30. The next step is to study what happens when the sum goes over the next ten. In the lesson “Going Over Ten”, the child learns to add 8 + 5 by first adding 8 + 2 (which completes the ten) and then the “leftover” 3. These prepare the child for addition facts where the sum is more than 10.
Memorizing the facts The National Council of Teachers of Mathematics (NCTM) recommends in their Grade 2 Curriculum Focal Points that children “...develop quick recall of basic addition facts and related subtraction facts”. Mathematics builds upon previously learned concepts and facts. Learning addition and subtraction facts is essential for later study. For example, the child will soon study double-digit addition and subtraction, and needs to be able to add and subtract small numbers efficiently. The next lessons in the book provide lots of practice for learning and memorizing the addition facts. There are 20 such facts: 9 + 2 till 9 + 9: 8 + 3 till 8 + 8: 7 + 4 till 7 + 7: 6 + 5 till 6 + 6:
8 facts 6 facts 4 facts 2 facts
After those lessons, we reverse the process and practice subtracting. First, the child subtracts TO ten with problems such as 16 − __ = 10. Then come subtraction problems which “cross” the ten the other direction, such as 16 − 7. Again the student first practices these by subtracting in two parts: First subtracting to ten, then the rest. For example, 16 − 7 becomes 16 − 6 − 1. The various lessons about the fact families give lots of practice and further reinforce memorizing the facts. These lessons also include many word problems. You can choose to skip some of these lessons or problems, or use them later for review. They do not contain any new concepts. Alongside this book, you can also use math games or flashcards to reinforce the addition and subtraction facts. You can find a list of some free online games at www.homeschoolmath.net/math_resources_2.php
38
The Lessons in Chapter 3 page
span
Review: Completing the Next Whole Ten ......
41
2 pages
Review: Going Over Ten ................................
43
2 pages
Adding with 9 .................................................
45
2 pages
Adding with 8 .................................................
47
2 pages
Adding with 7 .................................................
49
2 pages
Adding with 6 .................................................
51
1 page
Review - Facts with 6, 7, and 8 ......................
52
2 pages
Subtract to Ten ...............................................
54
4 pages
Subtraction and the Difference ......................... 56
2 pages
Number Rainbows- 11 and 2 .........................
58
2 pages
Fact Families - 11 and 12 ..............................
60
2 pages
Number Rainbows - 13 and 14 ......................
62
1 page
Fact Families - 13 and 14 ...............................
63
3 pages
Fact Families - 15 ...........................................
66
2 pages
Fact Families - 16 ...........................................
68
2 pages
Fact Families - 17 and 18 ................................
70
3 pages
Review .............................................................
73
2 pages
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Space Jumps Adding two single-digit numbers, first jump to ten, then the rest to the spaceship. Practices addition that goes over ten. http://www.ictgames.com/spacejumps.html Bridging Shuttle Bridging Through Ten means the same as adding to ten first, then the rest. Get a “flight plan”, then first add to ten by typing the number needed into the oval, and press the red button. Then type the rest that the shuttle needs to go, into the other oval, and press the red button. http://www.ictgames.com/bridging.html Speedy Sums Click on numbers that add to the target sum. The more numbers you use, the higher your score will be. http://www.mathplayground.com/speedy_sums.html
39
Math Magician Games Flashcard problems in all 4 operations, including subtraction. Answer 20 questions in 1 minute. http://www.oswego.org/ocsd-web/games/Mathmagician/mathssub.html AplusMath Games Matho (math and bingo combined), concentration, hidden picture, and Planet Blaster games for the basic operations. http://www.aplusmath.com/games/ Addition Surprise Draw the answer square in the addition table. http://www.hbschool.com/activity/add/add.html Exuberant Eye Games Practice your basic facts with these kid-appealing simple games. http://www.games.exuberanteye.com/ Power Lines Puzzle Arrange the numbers into the pattern so that the numbers on the “lines” add up to the given sum. http://www.primarygames.co.uk/pg2/powerlines/powerlines1.html Online Addition Flashcards http://www.thegreatmartinicompany.com/additionfill.html Number Bond Machines Practice which two numbers add up to a given number. Set the number to be 11, 12, ... 18 to practice basic facts as in this chapter. http://www.amblesideprimary.com/ambleweb/mentalmaths/numberbond.html
40
Review: Completing the Next Whole Ten 1. Write the previous and next whole ten. Circle the ten that is nearer the number. a. ____,
56, ____
b. ____,
____, 37, ____
72, ____
c. ____,
____, 25, ____
94, ____
____, 31, ____
2. Write the previous and next whole tens. Below, write the two differences: the difference between the previous whole ten and the number, and the difference between the number and the next whole ten. See the example. a.
b.
c.
60 , 63 , 570
_____ , 46 , _____
_____ , 95 , _____
7
3
Differences:
____
____
____
____
d.
e.
f.
_____ , 72 , _____
_____ , 41 , _____
_____ , 44 , _____
Differences:
____
____
____
____
____
____
3. Complete the next ten. Below, write the same kind of problem within numbers 0-10. a.
17 + ____ = 20
b.
62 + ____ = ____
7 + ____ = 10
c.
2 + ____ = ____
94 + ____ = ____ 4 + ____ = ____
4. Complete the next ten. Think of the corresponding problem within the range of 0-10. a.
42 + ____ = 50
b.
22 + ____ = ____
c.
66 + ____ = ____
55 + ____ = ____
97 + ____ = ____
32 + ____ = ____
61 + ____ = ____
34 + ____ = ____
83 + ____ = ____
41
5. Fill in the missing numbers. Compare the top and bottom problems! a.
73 + ____ = 80
b.
73 + ____ = 81
35 + ____ = 40
c.
35 + ____ = 41
14 + ____ = 20 14 + ____ = 21
6. Find your way through the maze! Start at the top. You can only go on a square where the sum is a whole ten.
13 + 6
54 + 6
73 + 8
45 + 7
99 + 4
15 + 9
14 + 8
15 + 5
13 + 6
32 + 7
45 + 7
73 + 7
64 + 5
82 + 9
16 + 7
30 + 12
39 + 1
74 + 6
73 + 9
52 + 7
46 + 7
32 + 7
31 + 9
86 + 4
65 + 4
92 + 4
21 + 8
24 + 7
22 + 8
32 + 6
83 + 6
11 + 7
98 + 2
57 + 3
17 + 9
44 + 9
12 + 8
95 + 6
38 + 5
53 + 9
71 + 9
34 + 4
36 + 7
19 + 4
28 + 11
53 + 7
29 + 2
26 + 6
78 + 6
32 + 5
7. Complete the next whole ten. a.
17 + ____ + 1 = 20
b.
35 + ____ + 2 = 40
c.
41 + ____ + 6 = 50
12 + ____ + 4 = 20
32 + ____ + 3 = 40
44 + ____ + 3 = 50
13 + ____ + 4 = 20
36 + ____ + 3 = 40
42 + ____ + 5 = 50
8. Find as many different sums as you can to make one hundred!
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
90 + ____ + ____ = 100
42
Review: Going Over Ten Sums that go over 10 Let's add 8 + 6 so that we first make a ten.
Let's add 9 + 7 so that we first make a ten.
8+ 6 | \ 8+2+4
9+ 7 | \ 9+1+6
10 + 4 = 14
10 + 6 = 16
The 6 is broken into two parts: 2 and 4. That is because 8 and 2 make a ten. Then, we have 10 and 4. We get 14.
The 7 is broken into two parts: 1 and 6. That is because 9 and 1 make a ten. Then, we have 10 and 6. We get 16.
1. Circle all the blue balls and some of the red ones so that you get a ten. Then add the rest of the red balls. a.
c.
8
8
+
4
10
+ 2
+
b.
9
7
+
5
10 + ____ = ____
= ____
6
d.
9
10 + ____ = ____ e.
+
+
3
10 + ____ = ____
5
f.
10 + ____ = ____
9
+
8
10
+ ____ =
____
2. Write a number on the empty line that completes ten. Then add the last number. a. ( 7 + 3 ) + 2 =
b. ( 5 + ___ ) + 3 =
c. ( 8 + ___ ) + 4 =
d. ( 6 + ___ ) + 4 =
e. ( 9 + ___ ) + 7 =
f. ( 7 + ___ ) + 5 =
43
3. Complete. Break the second number into two parts so that you get a ten. a.
8 + 7 / \ 8 + 2 + ____
b.
8 + 9 / \ 8 + 2 + ____
10 + ____ = ____ d.
c.
8 + 5 / \ 8 + 2 + ____
10 + ____ = ____
9 + 4 / \ 9 + 1 + ____
e.
10 + ____ = ____
9 + 6 / \ 9 + ___ + ____
10 + ____ = ____
9 + 9 / \ 9 + ___ + ____
f.
10 + ____ = ____
10 + ____ = ____
4. Add up to 10, 11, 12 and notice the patterns! a.
b.
c.
d.
8 + ___ = 10
7 + ___ = 10
9 + ___ = 10
6 + ___ = 10
8 + ___ = 11
7 + ___ = 11
9 + ___ = 11
6 + ___ = 11
8 + ___ = 12
7 + ___ = 12
9 + ___ = 12
6 + ___ = 12
15
24
58
89
99
5. Circle the even numbers.
40
51
6. Solve the word problems. a. You have $8 and you buy a toy for $5 and candy for $2.
How much money do you have now? b. Cassie had $8. Then she found $5 in her piggy
bank, and her mom gave her $2. How much money does she have now? c. Matthew had $8. He spend $3 on a bottle of juice.
Later he found $2 on the street. How much money does he have now?
44
67
100
2
Adding with 9 9 wants to be a 10! So, it takes one from the other number (from 3). So, 9 becomes 10, and 2 are left over.
Imagine that 9 really wants to be a 10! It takes one from the other number (from 5). So, 9 becomes 10, and 4 are left over.
+ 9
+
= 5
=
= 10 + 4
=
+ 14
9
+
= 3
=
= 10 + 2 =
Use the list on the right to practice. Don't write the answers there. Just point to different problems and say the answer aloud.
12
9+1=
1. Add. First encircle the ten.
9+2= 9+3= 9+4=
a. 9 + 5
b. 9 + 4
c. 9 + 7
10 + 4 = ____
10 + ____ = ____
10 + ____ = ____
9+5= 9+6= 9+7=
d. 9 + ___
e. 9 + ___
f. 9 + ___
9+8=
10 + ____ = ____
10 + ____ = ____
10 + ____ = ____
9+9=
2. It is good to memorize the doubles, also. Fill in. 2 + 2 = ____
5 + 5 = ____
8 + 8 = ____
3 + 3 = ____
6 + 6 = ____
9 + 9 = ____
4 + 4 = ____
7 + 7 = ____
10 + 10 = ____
45
3. Add to nine. Think how 9 wants to be a ten, and takes 1 from the other number. a. 9 + 6
b. 9 + 8
10 + 5 = ____
c. 9 + 5
10 + ____ = ____
e. 9 + 7
10 + ____ = ____
f. 9 + 9
10 + 6 = ____
d. 9 + 2
g. 9 + 8
10 + ____ = ____ h. 9 + 3
10 + ____ = ____
10 + ____ = ____
10 + ____ = ____
4. Here are addition facts with nine. Do not write the answers down, but just practice the sums.
9+0=
9+5=
9+9= 9+4=
9+3=
9+6=
9+1= 9 + 10 =
9+7=
9+8=
9+2=
5. Add. Remember, you can add both ways. For example, 7 + 9 = 9 + 7. a. 9 + 4 = ____
b. 9 + 7 = ____
c. 3 + 9 = ____
d. 5 + 9 = ____
8 + 9 = ____
4 + 9 = ____
9 + 2 = ____
8 + 9 = ____
9 + 5 = ____
9 + 4 = ____
9 + 9 = ____
9 + 6 = ____
a. 9 + ____ = 13
b. 9 + ____ = 16
c. 9 + ____ = 17
d. 9 + ____ = 12
9 + ____ = 15
9 + ____ = 14
9 + ____ = 11
9 + ____ = 18
6. What is missing?
You can use this same "trick" with 19, 29, 39, 49, and so on. Imagine that 49 really wants to be 50, and so it "steals" 1 from the other number. Solve. a. 49 + 7 = _____
b. 59 + 5 = _____
c. 69 + 3 = _____
19 + 6 = _____
89 + 9 = _____
29 + 6 = _____
46
Adding with 8 Imagine that 8 wants to be a 10! It takes two from the other number (from 3). So, 8 becomes 10, and only 1 is left over.
+ 8
+
= 3
=
8 wants to be a 10! So, it takes two from the other number (from 5). So, 8 becomes 10, and 3 are left over.
= 10 + 1
=
+ 11
=
=
8 + 5 = 10 + 3 =
Use the list on the right to practice. Don't write the answers there. Just point to different problems and say the answer aloud.
13
8+1=
1. Add. First, circle the ten.
8+2= 8+3= 8+4=
a. 8 + 5
b. 8 + 4
c. 8 + ____
10 + 3 = ____
10 + ____ = ____
10 + ____ = ____
8+5= 8+6= 8+7=
d. 8 + ____ =
e. 8 + ____ =
f. 8 + ____ =
8+8=
10 + ____ = ____
10 + ____ = ____
10 + ____ = ____
8+9=
2. It is good to memorize the doubles, also. Fill in. 2 + 2 = ____
5 + 5 = ____
8 + 8 = ____
3 + 3 = ____
6 + 6 = ____
9 + 9 = ____
4 + 4 = ____
7 + 7 = ____
10 + 10 = ____
47
Here are addition facts with eight. Do not write the answers down, but just practice the sums.
8+0=
8+5=
8+8=
8+9=
8+3=
8+7=
8+1=
8+4=
8 + 10 =
8+1=
8+6=
8+2=
3. Add and fill in what is missing. a. 8 + 4 = ____
b. 8 + 8 = ____
c. 8 + ____ = 14
8 + 6 = ____
8 + 5 = ____
8 + ____ = 16
8 + 2 = ____
8 + 7 = ____
8 + ____ = 17
d. 8 + ____ = 13
e. 5 + 8 = ____
f. 6 + 8 = ____
8 + ____ = 12
8 + 7 = ____
8 + 9 = ____
8 + ____ = 11
3 + 8 = ____
8 + 8 = ____
4. Find the pattern and continue it. a.
b.
8 + 2 = ____
18 + 2 = ____
1 2
of 0 is ____.
8 + 4 = ____
18 + 4 = ____
1 2
of 2 is ____.
8 + 6 = ____
18 + 6 = ____
1 2
of 4 is ____.
1 2
of ____ is ____.
1 2
of ____ is ____.
1 2
of ____ is ____.
1 2
of ____ is ____.
8 + ____ = ____
18 + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____ ____ + ____ = ____
____ + ____ = ____ ____ + ____ = ____
48
c.
Adding with 7 We have already studied these addition facts with 7:
These are the new facts with 7:
7 + 4 = ____ 7 + 8 = ____
8 + 7 = ____ 7 + 5 = ____
7 + 9 = ____
9 + 7 = ____
7 + 10 = ____
10 + 7 = ____
7 + 6 = ____ 7 + 7 = ____
1. First circle ten balls. Then add.
7+1= a. 7 + 7
b. 7 + 5
10 + ___ = ____
10 + ___ = ____
c. 7 + 6
7+2= 10 + ___ = ____ 7+3= 7+4=
Use the list on the right to practice. Don't write the answers there. Just point to different problems and say the answer aloud.
7+5= 7+6=
2. Let's practice doubles - and doubles plus one more.
7+7= a. 6 + 6 = ____
b. 7 + 7 = ____
c. 8 + 8 = ____
6 + 7 = ____
7 + 8 = ____
8 + 9 = ____
7+8= 7+9=
d. 9 + 9 = ____
d. 5 + 5 = ____
d. 4 + 4 = ____
9 + 10 = ____
6 + 5 = ____
4 + 5 = ____
49
Here are some addition facts where we add to seven. Do not write the answers down but just go over them until you remember them easily.
7+0=
7+5=
7+6=
7+9=
7+3=
7+9=
7+7=
7+4=
7 + 10 =
7+8=
7+1=
7+2=
3. Fill in the missing numbers. a. 7 + 4 = ____
b. 8 + 7 = ____
c. 7 + ____ = 14
d. 7 + ____ = 12
6 + 7 = ____
7 + 10 = ____
7 + ____ = 13
7 + ____ = 16
7 + 5 = ____
3 + 7 = ____
7 + ____ = 15
7 + ____ = 11
e. 7 + 7 = ____
f. 4 + 7 = ____
g. 8 + ____ = 13
h. ____ + 7 = 17
9 + 7 = ____
7 + 9 = ____
8 + ____ = 16
____ + 7 = 10
7 + 8 = ____
3 + 7 = ____
8 + ____ = 17
____ + 7 = 12
+7 4. Try these boxes! Add 7 each time. Add 8 each time. Add 9 each time.
+8
+9
4
11
3
11
2
____
7
____
6
____
4
____
8
____
5
____
7
____
10
____
7
____
8
____
5
____
9
____
3
____
3
____
2
____
6
____
9
____
4
____
5
____
50
Adding with 6
6
+
=
+ 5
= ____
6
+
=
+ 6
= ____
Here are addition facts where we add to six. Do not write the answers down. Just go over the problems until you remember them easily.
6+0=
6+5=
6+9= 6+6=
6+3=
6+7=
6+4= 6+8=
6 + 10 =
6+1=
6+2=
1. Fill in the missing numbers. a.
b.
c.
d.
6 + 4 = _____
6 + 8 = _____
6 + ____ = 14
6 + ____ = 13
6 + 6 = _____
6 + 9 = _____
6 + ____ = 16
6 + ____ = 15
6 + 5 = _____
6 + 7 = _____
6 + ____ = 12
6 + ____ = 11
e.
f.
g.
h.
5 + 6 = _____
9 + 6 = _____
7 + ____ = 14
___ + 6 = 13
6 + 7 = _____
8 + 6 = _____
8 + ____ = 14
___ + 6 = 14
4 + 6 = _____
6 + 6 = _____
9 + ____ = 14
___ + 6 = 15
2. Do not forget adding many numbers, either. a. 6 + 6 + 2 = _____
10 + 4 + 5 = _____
b. 8 + 6 + 3 = _____
20 + 2 + 5 = _____
51
c. 6 + 9 + 3 = _____
50 + 6 + 4 = _____
Review - Facts with 6, 7, and 8 1. Here are the 20 addition facts with single-digit numbers where the sum is between 10 and 20. Connect the problems to the right answer.
6+6
8+6 11
5+8
5+7
9+9
15
7+9 9+5
9+2
12
5+6
16
8+7
17
9+8
4+7 13
3+9
9+4
8+8 7+7
6+7
14
8+3
18
6+9
4+8
2. Figure out the pattern and continue it. a.
b.
c.
9 + ____ = 19
____ + 16 = 17
6 + ____ = 6
8 + ____ = 18
____ + 14 = 17
6 + ____ = 8
7 + ____ = 17
____ + 12 = 17
6 + ____ = 10
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
52
3. Fill in the addition table.
+
6
2
8
4
5
1
7
3
9
3 5 7 9 4. Try your skills! a. 6 + 9 = _____
b. 8 + 9 = _____
c. 5 + 9 = _____
d. 6 + 6 = _____
9 + 8 = _____
9 + 2 = _____
9 + 3 = _____
9 + 4 = _____
4 + 9 = _____
7 + 6 = _____
4 + 8 = _____
3 + 9 = _____
6 + 5 = _____
7 + 5 = _____
9 + 7 = _____
8 + 7 = _____
When you add lots of numbers, first add the numbers that form a ten. It makes adding easier!
8+6+4
5+6+2+5
= 8 + 10 = 18
= 10 + 8 = 18
5. Add in the easiest order. First find numbers that make 10! a. 1 + 6 + 9 = _____
b. 3 + 6 + 6 = _____
c. 4 + 7 + 3 + 5 = _____
5 + 4 + 7 = _____
3 + 5 + 7 = _____
6 + 5 + 1 + 4 = _____
8 + 6 + 4 = _____
7 + 8 + 2 = _____
8 + 3 + 6 + 2 = _____
5 + 6 + 5 = _____
3 + 6 + 4 = _____
9 + 6 + 1 + 4 = _____
53
Subtract to Ten 1. Subtract the "ones" that are not in the whole ten-groups. You should only have tens left!
a.
b.
c.
d.
13 − 3 = 10
15 − ____ = 10
26 − ____ = ____
38 − ____ = ____
e. 17 − ____ = 10
f. 21 − ____ = 20
g. 19 − ____ = 10
h. 64 − ____ = 60
Subtracting in parts Let's subtract 13 − 5. First we subtract so many balls that we have only 10 left. So, we take away 3 balls. 13 − 3 = 10. Then, we subtract the rest, which means we subtract 2 more. 10 − 2 = 8.
13 − 5 /
\
13 − 3 − 2 10 − 2 = 8
2. First subtract so many that you have only 10 left. Then subtract the rest. b. 13 − 8
a. 15 − 7 /
\
15 − 5 − 2 10 − 3 = ____ d. 14 − 9 /
/
c. 13 − 4 \
13 − ___ − ____ 10 − ____ = ____ e. 12 − 5
\
14 − ___ − ____ 10 − ___ = ____
/
/
\
13 − ___ − ____ 10 − ____ = ____ f. 16 − 8
\
/
12 − ___ − ____ 10 − ___ = ____
\
16 − ___ − ____ 10 − ___ = ____
3. First subtract to 10. Then subtract some more. a. 13 − 6
b. 14 − 9
c. 15 − 8
/ \ 13 − 3 − 3 = ____
/ \ 14 − ____ − ____ = ____
/ \ 15 − ____ − ____ = ____
54
4. First subtract to 10. Then subtract some more. a. 16 − 7 /
b. 12 − 4 \
/
d. 13 − 6 \
/
\
16 − ____ − ____ = ____
12 −____ − ____ = ____
13 − ____ − ____ = ____
d. 11 − 3
e. 12 − 7
f. 15 − 8
/
\
/
11 − ____ − ____ = ____
\
/
12 − ____ − ____ = ____
\
15 − ____ − ____ = ____
5. First subtract those that are not in the ten-group. Compare the top and bottom problems.
a.
15 − 7 = ____
b.
13 − 6 = ____
c.
16 − 9 = ____
d.
25 − 7 = ____
e.
23 − 6 = ____
f.
26 − 9 = ____
6. Subtract. a.
12 − 4 =
b.
15 − 6 =
14 − 5 =
c.
12 − 5 =
15 − 9 =
14 − 8 =
12 − 3 =
15 − 7 =
14 − 7 =
12 − 6 =
15 − 8 =
14 − 6 =
7. Subtract a number so that the answer is 10 or 9. Do you notice a shortcut? a. 13 − ____ = 10
13 − ____ = 9
b. 11 − ____ = 10
c. 15 − ____ = 10
d. 12 − ____ = 10
11 − ____ = 9
15 − ____ = 9
12 − ____ = 9
8. Subtract in two steps. First subtract to the previous whole ten. Then, subtract some more. How much did you subtract (take away) all totaled? a. 29 − ____ = 20
b. 34 − ____ = 30
c. 72 − ____ = 70
20 − 5 = ____
30 − 3 = ____
70 − 6 = ____
I subtracted a total of ____.
I subtracted a total of ____.
I subtracted a total of ____.
55
Subtraction and The Difference The difference of two numbers on the number line means how far apart they are from each other. The difference of 7 and 3 is 4, because 7 and 3 are four steps apart.
We can solve the difference of two numbers in two ways:
Let's find the difference of 12 and 8 in two ways. 1. Subtract:
1. Subtract the numbers. 2. Write a “how many more” addition (missing addend).
12 – 8 = ____.
2. Think: “8 and how many more makes 12?” You can write an addition 8 + ____ = 12 Either way, the answer is 4 .
1. Find the difference of the numbers by subtracting.
Numbers
Subtraction
Difference
7
2
7–2=5
5
10 9
Numbers
6
3
4
10
5
5
9
6
Subtraction
Difference
2. Think of adding more to find the difference of two numbers. a. The difference of 10 and 6
b. The difference of 7 and 12
c. The difference of 9 and 4
6 + ____ = 10
7 + ____ = 12
4 + ____ = 9
d. The difference of 15 and 8
e. The difference of 5 and 12
f. The difference of 9 and 17
8 + ____ = 15
5 + ____ = 12
9 + ____ = 17
3. Subtract. Think of the differences or “how many more”.
+3
+__
+__
a. 15 – 12 = ____
b. 11 – 9 = ____
c. 16 – 11 = ____
12 and how many more makes 15?
9 and how many more makes 11?
11 and how many more makes 16?
56
4. Solve these subtraction problems by thinking of the differences or “how many more”.
+__ a. 14 – 11 = ____
+__ e. 20 – 15 = ____
+__
+__ b. 20 – 19 = ____
+__
c. 17 – 15 = ____
+__
+__
+__
f. 15 – 11 = ____
d. 13 – 10 = ____
g. 12 – 8 = ____
h. 18 – 14 = ____
5. Subtract by thinking how far apart the two numbers are (the difference). a. 20 – 16 =
b. 40 – 38 =
c. 65 – 61 =
d. 33 – 31 =
e. 100 – 99 =
f. 87 – 84 =
g. 53 – 50 =
h. 79 – 78 =
6. Find what is missing. a. 6 + ____ + 4 = 14
b. 2 + ____ + 2 = 8
c. 10 + ____ + 4 = 17
8 + ____ + 3 = 13
3 + ____ + 3 = 9
10 + ____ + 2 = 15
7. Solve the word problems. Write number sentences for them. a. Jen is on page 20 and Mark is on page 17 of the same book.
How many more pages has Jen read?
b. Mom had one dozen eggs plus five in another carton.
She used 6 eggs. How many does she have now?
c. Ingrid is reading a 50-page book. She's on page 42.
How many more pages does she have left to read?
d. In family A, the kids are 13 and 9 years old. In family B, the kids are 15 and 12.
In which family is there a bigger difference in the kids' ages?
57
Number Rainbows - 11 and 12 This is a number rainbow for 11. If two numbers are connected with an arc, they add up to 11. Use the number rainbow to help you with addition and subtraction facts! 1. Practice subtraction from 11. Don't write the answers below; just think them in your head.
11 – 6 =
11 – 7 =
11 – 8 =
11 – 2 =
11 – 3 =
11 – 9 =
11 – 4 =
11 – 5 =
2. Similarly, practice subtraction from 12.
12 – 5 =
12 – 7 =
12 – 10 =
12 – 6 =
12 – 9 =
12 – 4 =
12 – 3 =
12 – 8 =
58
3. Fill in and color the number rainbows. Don't look at the previous page! Then practice the subtraction problems.
11 – 4 =
11 – 2 =
11 – 3 =
11 – 9 =
11 – 8 =
11 – 5 =
11 – 6 =
11 – 7 =
12 – 8 =
12 – 3 =
12 – 4 =
12 – 9 =
12 – 6 =
12 – 10 =
12 – 7 =
12 – 5 =
For more practice, make your own number rainbows and subtraction problems on empty paper!
59
Fact Families - 11 and 12 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 11
10, 1, 11
___, ___, 11
10 + 1 = ___
11 – 10 = ___
7 + ___ = 11
___ – ___ = ___
1 + 10 = ___
11 – 1 = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 11
___, ___, 11
9 + ___ = 11
___ – ___ = ___
6 + ___ = 11
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
___, ___, 11
8 + ___ = 11
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
2. Find the pattern and continue it. a.
b.
c.
11 – 0 = ____
0 + 11 = ____
11 – 1 = ____
11 – 2 = ____
2 + 9 = ____
11 – 3 = ____
11 – 4 = ____
4 + 7 = ____
11 – 5 = ____
___ – ___ = ____
____ + ____ = ____
___ – ___ = ____
___ – ___ = ____
____ + ____ = ____
___ – ___ = ____
___ – ___ = ____
____ + ____ = ____
___ – ___ = ____
60
3. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 12
10, 2, 12
___, ___, 12
10 + 2 = ___
12 – 10 = ___
7 + ___ = 12
___ – ___ = ___
2 + 10 = ___
12 – 2 = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 12 9 + ___ = 12
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
___, ___, 12 6 + ___ = 12
12 – ___ = ___
___, ___, 12 8 + ___ = 12
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
4. Subtract from 11 and 12. a.
12 – 10 = ____
b.
11 – 8 = ____
c.
12 – 6 = ____
d.
12 – 3 = ____
11 – 9 = ____
12 – 7 = ____
11 – 4 = ____
12 – 10 = ____
12 – 8 = ____
11 – 3 = ____
12 – 9 = ____
11 – 5 = ____
11 – 6 = ____
12 – 5 = ____
12 – 4 = ____
11 – 7 = ____
5. Let's practice missing addends as well! a.
6 + ____= 11
b.
7 + ____= 12
c.
9 + ____= 11
d.
6 + ____= 12
8 + ____ = 11
8 + ____ = 12
7 + ____ = 11
9 + ____ = 12
5 + ____ = 11
5 + ____ = 12
4 + ____ = 11
4 + ____ = 12
61
Number Rainbows - 13 and 14 1. Fill in and color the number rainbows. Then practice the subtraction problems.
13 – 7 =
13 – 4 =
13 – 9 =
13 – 10 =
13 – 5 =
13 – 6 =
13 – 11 =
13 – 8 =
14 – 8 =
14 – 3 =
14 – 7 =
14 – 6 =
14 – 5 =
14 – 9 =
14 – 11 =
14 – 4 =
For more practice, make your own number rainbows and subtraction problems on empty paper! 62
Fact Families - 13 and 14 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 13
10, 3, 13
___, ___, 13
10 + 3 = ___
13 – 10 = ___
8 + ___ = 13
___ – ___ = ___
3 + 10 = ___
13 – 3 = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 13
___, ___, 13
9 + ___ = 13
___ – ___ = ___
7 + ___ = 13
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
2. Subtract. a. 13 – 8 = ____
b. 13 – 5 = ____
c. 12 – 7 = ____
d. 12 – 9 = ____
13 – 6 = ____
13 – 4 = ____
13 – 7 = ____
13 – 9 = ____
3. Connect with a line the problems that are from same fact family. You don't need to write the answers.
13 – 7 = 5+
= 12
11 – 3 = 8+
= 13
12 – 3 = 7+
= 11
' ' ' ' ' ' ' '
11 – 4 =
12 – 7 =
11 – 8 =
13 – 6 =
5+
3+
= 13
= 12
12 – 5 =
13 – 5 =
6+
= 13
3+
= 11
9+
= 12
4+
= 11
63
4. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 14
___, ___, 14
10, 4, 14 10 + ___ = ___
___ – 10 = ___
8 + ___ = 14
___ – ___ = ___
___ + 10 = ___
___ – 4 = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 14
___, ___, 14
9 + ___ = 14
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
7 + ___ = 14
14 – ___ = ___
5. For each addition problem, write a subtraction problem using the same numbers so that the numbers in the boxes end up being the same. a. 9 +
= 14
14 – 9 = d. 9 +
= 13
= 11
____ – ____ = j. 5 +
= 14
14 – 6 =
____ – ____ = g. 5 +
b. 6 +
= 14
____ – ____ =
e. 7 +
____ – ____ = = 12
____ – ____ = k. 8 +
= 13
____ – ____ =
64
= 12
12 – 6 = = 14
h. 7 +
c. 6 +
f. 6 +
= 15
____ – ____ = i. 4 +
= 14
____ – ____ = l. 6 +
= 11
____ – ____ =
6. Solve the word problems. a. Jack arranged his toy cars in rows. The first row had seven cars, the second had
7, and the third row had 4. How many cars does Jack have?
b. If you have 14 strawberries and I have 8, how many more do you have?
c. Dad has six cherries and Mom has five more than him. How many cherries
does Mom have?
d. At first Mom had 20 apples to make an pie, but she gave each of the four kids
one apple before she made the pie. How many apples did she have for the pie?
7. Figure out the patterns and continue them!
a.
+
40
b.
+
48
+
17
+
56
+
21
+
64
+
25
+
+
+
+
____
____
____
+
+
+
+
____
____
____
____
72
+
29
65
____
____
Fact Families - 15 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 15
___, ___, 15
10, 5, 15 10 + ___ = ___
15 – 10 = ___
8 + ___ = 15
___ – ___ = ___
___ + 10 = ___
15 – ___ = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 15
9 + ___ = 15
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
2. Subtract. For each problem write a corresponding addition fact. a.
b.
c.
d.
15 – 5 = ___
15 – 8 = ___
15 – 4 = ___
15 – 3 = ___
___ + ___ = ___
___ + ___ = ___
___ + ___ = ___
___ + ___ = ___
e.
f.
g.
h.
15 – 2 = ___
15 – 6 = ___
15 – 7 = ___
15 – 9 = ___
___ + ___ = ___
___ + ___ = ___
___ + ___ = ___
___ + ___ = ___
3. Count by threes. + 3
9
+ 3
____
+ 3
____
+ 3
____
+ 3
____ 66
+ 3
____
+ 3
____
+ 3
____
33
4. Solve the word problems. a. At first Mom had 17 peaches to make an pie, but she gave each of the three kids
one peach before she made the pie. How many peaches did she have for the pie?
b. Jill, Tom, and Nancy made a stack of school books. Jill had three books, Nancy
had seven, and Tom had five. How many books were in the stack?
c. Now Jill took her books out of the stack.
How many are left in the stack?
d. Five kids came to play ball. Then, six more kids came. Then, one child had to
go home. How many kids are playing ball now?
5. For each addition problem, write a subtraction problem using the same numbers so that the numbers in the boxes end up being the same. a.
9+
= 15
15 – 9 = d.
5+
8+
6+
= 14
____ – ____ = = 11
____ – ____ = g.
b.
= 15
____ – ____ =
e.
7+
= 15
____ – ____ = h.
8+
= 12
____ – ____ =
67
c.
6+
= 15
____ – ____ = f.
7+
= 13
____ – ____ = i.
7+
= 11
____ – ____ =
Fact Families - 16 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 16
10, 6, 16
8, ___, 16
10 + ___ = ___
16 – 10 = ___
8 + ___ = 16
___ – ___ = ___
___ + 10 = ___
16 – ___ = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 16 9 + ___ = 16
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
2. Subtract. a.
15 – 10 = ___
b.
13 – 9 = ___
c.
14 – 8 = ___
d.
15 – 7 = ___
13 – 10 = ___
16 – 9 = ___
13 – 8 = ___
16 – 7 = ___
16 – 10 = ___
14 – 9 = ___
16 – 8 = ___
13 – 7 = ___
3. Connect with a line the problems to the answer.
15 – 9 15 – 10
3 4
14 – 9 14 – 10 13 – 9
17 – 9 16 – 9
7 8
16 – 10 5 6
18 – 9 17 – 10
68
17 – 9 16 – 9 18 – 9
9 10
19 – 10 19 – 9
4. Figure out the patterns and continue them! +
a.
6
b.
+
9
+
12
+
+
12
+
16
15
+
+
+
+
+
____
____
____
____
+
+
+
+
____
____
____
____
+
20
24
____
____
5. Solve the word problems. a. A class has 24 kids. Two of them
b. If you have $10, and mom gives
were sick one day and two had to leave to go to the dentist. How many kids were in class that day?
you $4 more, can you buy a book for $13?
d. Jenny has saved $12. She wants to
c. You had $20 and you bought shoes for
buy a gift that costs $16. How much more money does she need?
$17. How many dollars do you have left?
6. Compare the expressions and write , or = . a.
35
20 + 5
b.
23 + 5
23 + 6
c.
16 – 8
15 – 8
d.
15
6+7
e.
31 + 4
31 + 3
f.
15 – 9
16 – 9
g.
36
30 + 7
h.
20 + 8
30 + 5
i.
15 – 6
14 – 6
69
Fact Families - 17 and 18 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 17
Fact families with 18
10, ___, 17
10, ___, 18
10 + ___ = ___
17 – 10 = ___
10 + ___ = 18
___ – ___ = ___
___ + 10 = ___
17 – ___ = ___
___ + ___ = ___
___ – ___ = ___
9, ___, 17
9, ___, 18
9 + ____ = 17
___ – ___ = ___
9 + ___ = 18
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
___ + ___ = ___
___ – ___ = ___
b. 15 – 9 = ____
c. 14 – 6 = ____
d. 12 – 9 = ____
17 – 9 = ____
15 – 8 = ____
14 – 7 = ____
12 – 8 = ____
18 – 10 = ____
16 – 9 = ____
13 – 6 = ____
11 – 9 = ____
18 – 9 = ____
16 – 8 = ____
13 – 7 = ____
11 – 8 = ____
2. Subtract and add. a. 17 – 10 = ____
e. 6 + 6 = ____
f. 9 + ____ = 19
g. 8 + 9 = ____
h. 7 + ____ = 14
7 + 7 = ____
9 + ____ = 15
8 + 7 = ____
7 + ____ = 16
8 + 8 = ____
9 + ____ = 18
8 + 5 = ____
7 + ____ = 18
9 + 9 = ____
9 + ____ = 17
8 + 3 = ____
7 + ____ = 13
70
3. Write , or = . You can often compare the expressions without calculating! a. 8 + 9
d. 45 + 8
g.
1 2
of 16
j.
1 2
of 40
8+8
b. 20 – 9
20 – 8
45 + 7
e. 50 – 6
50 – 8
1 2
m. 31 + 7
of 14
h. 14 – 2
1 2
20 + 20
k.
31 + 9
n. 25 – 8
of 50
1 2
of 14
1 2
of 60
c.
25 – 9
1 2
of 12
12
f. 15 – 8
17 – 8
i. 10 + 5
20 – 5
l.
1 2
of 80
20 + 20
o.
1 2
of 20
10
4. Continue the patterns. a.
b.
c.
17 – 10 = ____
20 – 10 = ____
1 2
of 20 + 10 = 20
16 – 9 = ____
30 – 20 = ____
1 2
of 18 + 9 = ____
15 – 8 = ____
40 – 30 = ____
1 2
of 16 + 8 = ____
____ – ____ = ____
____ – ____ = ____
1 2
of ____ + ____ = ____
____ – ____ = ____
____ – ____ = ____
1 2
of ____ + ____ = ____
____ – ____ = ____
____ – ____ = ____
1 2
of ____ + ____ = ____
____ – ____ = ____
____ – ____ = ____
1 2
of ____ + ____ = ____
____ – ____ = ____
____ – ____ = ____
1 2
of ____ + ____ = ____
____ – ____ = ____
____ – ____ = ____
1 2
of ____ + ____ = ____
71
5. Solve the word problems. a. A baby slept 4 hours and woke up to nurse. Then she slept
another 2 hours and woke up to nurse. Then she slept 3 hours more and nursed again. Then she slept 3 hours till the morning. How many hours did the baby sleep?
b. A new jacket costs 18 dollars. John
c. The temperature outside is 50 degrees
has saved 9 dollars. How much more does he need?
Fahrenheit, and inside it is 70 degrees. What is the difference in temperature?
d. Mom needs 16 eggs. Eggs are sold in cartons of 12.
How many cartons does she need to buy? How many eggs will she have left over?
6. Fill in the addition table.
+
1
3
5
7
2
4
6
10
9
8
11
31
6 8 5
7. Find the missing numbers. Try to work backwards, starting from 60! –10
100
–1
___
–5
___
–4
___
–2
___
72
–8
___
–5
___
–5
___
60
Review 1. Complete the next ten. a.
b.
c.
d.
13 + ____ = 20
42 + ____ = 50
29 + ____ = ____
65 + ____ = ____
88 + ____ = 90
28 + ____ = 30
15 + ____ = ____
82 + ____ = ____
74 + ____ = 80
26 + ____ = ____
73 + ____ = ____
49 + ____ = ____
2. UNDERLINE the problems where the answer is ten. CIRCLE the ones where the answer is more than ten. a.
b.
c.
d.
e.
5 + 1 = ___
6 + 1 = ___
7 + 1 = ___
8 + 1 = ___
9 + 1 = ___
5 + 2 = ___
6 + 2 = ___
7 + 2 = ___
8 + 2 = ___
9 + 2 = ___
5 + 3 = ___
6 + 3 = ___
7 + 3 = ___
8 + 3 = ___
9 + 3 = ___
5 + 4 = ___
6 + 4 = ___
7 + 4 = ___
8 + 4 = ___
9 + 4 = ___
5 + 5 = ___
6 + 5 = ___
7 + 5 = ___
8 + 5 = ___
9 + 5 = ___
5 + 6 = ___
6 + 6 = ___
7 + 6 = ___
8 + 6 = ___
9 + 6 = ___
5 + 7 = ___
6 + 7 = ___
7 + 7 = ___
8 + 7 = ___
9 + 7 = ___
5 + 8 = ___
6 + 8 = ___
7 + 8 = ___
8 + 8 = ___
9 + 8 = ___
5 + 9 = ___
6 + 9 = ___
7 + 9 = ___
8 + 9 = ___
9 + 9 = ___
Compare the columns! What do you notice? 3. Find the missing steps. –5
75
–5
__
–2
__
–3
__
–6
__ 73
–3
__
–1
__
–10
__
40
4. Solve the puzzle. What happened to the teddy bear in the desert?
Key:
5+9 7+8
13 – 8 2 + 9 10 + 5
9+7
4+7
9+6
____ ____
____
____
____
____
7 + 7 13 – 6
19 – 4 11 + 5 13 – 7
3 + 13 11 – 5 13 – 4
6+9
____ ____
____
____
____
A 9
____
____
____
____
____
____
E I O G H T W N 6 14 11 5 16 15 8 7
5. Solve the word problems. a. Jack has 13 tennis balls and Robert has 20. How many do they have together? How many more does Robert have than Jack?
b. You have saved 20 dollars to buy a big Lego set that costs $28. How much will you still need to save? A neighbor pays you 2 dollars to mow the lawn. So you do. Do you now have enough money to buy the Lego set? How much do you still need? How about if you mow the lawn a second time? A third time?
c. In a board game, you need to move 18 more squares to get to the end of the game. You roll 6 and 5 on two dice. How many more squares do you need to go to get to the end? What kind of numbers on the two dice would get you to the end?
74
Chapter 4: Adding and Subtracting with Two-Digit Numbers Introduction The fourth chapter of the Math Mammoth Grade 2-A Complete Worktext deals with addition and subtraction within 0-100, both mentally and in columns, especially concentrating on how to carry when adding in columns (trading) and how to borrow when subtracting in columns (regrouping).
Mental math Mental math is important because it builds number sense. Chapter 4 includes many lessons that practice mental math. For example, the child practices adding and subtracting 2-digit numbers when one of the numbers is a whole ten (problems such as 30 + 14, or 66 - 20). Also studied are problems such as 36 + 8 or 45 + 9. These problems connect with the idea of going over ten as in problems 6 + 8 and 5 + 9. So, just as the child knows that 6 + 8 fills the first ten and is 14, he/she will learn that 36 + 8 fills the next whole ten (40) and is 44.
Carrying to tens Simultaneously with this, the child learns adding two-digit numbers in columns, and “carrying” to tens, which is illustrated and explained in detail with the help of pictures. Some people call it trading, as in trading 10 ones into 1 ten. As a “stepping stone” into the usual way of adding in columns with a carry, you can show the child the method below. This can be used if the child does not readily understand why the little “1” that is carried corresponds to a ten. In the process below, the ones are added, and the answer is written using both columns. Then, the tens are added and the answer is written under the sum from ones. Lastly, both sums are added. tens ones 3 6 1
8
add ones first → 1
4
+
tens ones 6 3 1
8
1 add tens here → 4
4
+
tens ones 3 6 +
0
total →
1
8
1 4
4
5
4
0
The lesson Add in Columns Practice contains problems where the sum is more than 100.
Borrowing or regrouping The next lessons teach subtracting in columns. First we only deal with the easy problems where you don't need to regroup (borrow). Then the following lessons practice in detail the process of regrouping (borrowing). You can use either term with your child, or even choose not to use either if you feel it is confusing. You can alternatively use the phrase “breaking a ten into ten ones”. First, the lesson Regrouping practices breaking down a ten into ten ones because we cannot subtract from the ones. It is crucial that the child understands what happens here. Otherwise,
75
he/she might end up learning the procedure of borrowing as a memorized algorithm only, and will probably at some point misremember how it was done. That is why this lesson deals with the regrouping process in detail with plenty of visual exercises. If you notice that the child does not understand the concept of borrowing, he/she may need more practice with concrete manipulatives or visual exercises before proceeding.
More mental math After learning regrouping, we practice mental subtraction in three separate lessons. One of them expounds on several methods for mental subtracting. Another is about Euclid's game - a fun game that also practices subtraction of two-digit numbers.
The Lessons page
span
78
3 pages
Subtracting Whole Tens ..................................... 81
2 pages
Carrying to Tens ..............................................
83
3 pages
Going Over to the Next Ten ...........................
86
3 pages
Two-Digit Numbers Ending in 9 ....................
89
2 pages
Add in Columns Practice ................................
91
2 pages
Two-Digit Numbers Ending in 8 or 7...............
93
2 pages
Addition Practice .............................................
95
2 pages
Many Addends .................................................
97
3 pages
Subtracting in Columns ...................................... 100
1 page
Regrouping, Part 1 ...........................................
101
3 pages
Regrouping, Part 2 ...........................................
104
3 pages
Regrouping, Part 3 ...........................................
107
2 pages
Graphs and Problems ......................................
109
3 pages
Mental Subtraction Methods .............................. 112
3 pages
Euclid's Game....................................................
115
3 pages
Mixed Review ..................................................
118
2 pages
Adding with Whole Tens ..................................
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit.
Base Blocks Addition A virtual manipulative that shows regrouping in addition. Choose “Columns = 2” to restrict the work to two-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html?from=category_g_1_t_1.html
76
Base Blocks Subtraction The number to be subtracted (the subtrahend) is illustrated as red blocks whereas the minuend is with blue blocks. Drag a red block on top of a blue to “subtract” - they cancel each other. Drag bigger place values to the column on their right to “break them up” - in other words regroup or borrow. Choose “Columns = 2” to restrict the work to two-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_155_g_1_t_1.html?from=category_g_1_t_1.html Callum's Addition Pyramid Add the pairs of numbers to get a number on the next level and finally the top number. Three difficulty levels. http://www.amblesideprimary.com/ambleweb/mentalmaths/pyramid.html Techno Tortoise Practice adding 2 two-digit numbers into parts on a number line. http://www.ictgames.com/technowithflock.html Mr. Martini's Classroom: Addition and Subtraction Inequalities Compare expressions that involve addition and subtraction of one and two-digit numbers. http://www.thegreatmartinicompany.com/inequalities/number-comparison.html and http://www.thegreatmartinicompany.com/inequalities/add-subtract-comparison.html Mr. Martini's Classroom: Long Addition Practice adding two-digit numbers in columns online. http://www.thegreatmartinicompany.com/longarithmetic/longaddition.html Simple Kids Math Online practice of math problems. http://www.simplekidsmath.com/Default.aspx?level=2 - addition http://www.simplekidsmath.com/Default.aspx?level=3 - subtraction Mathionare Addition Quiz Answer increasingly more difficult addition questions (one and two-digit numbers), and win a million! http://www.mathsisfun.com/games/mathionaire-addition-quiz.html Button Beach Challenge Figure out what number the various colored buttons represent. http://www.amblesideprimary.com/ambleweb/mentalmaths/buttons.html Teaching Treasures - Year 2 Maths Worksheets Simple online addition and subtraction worksheets where the student types in the answer and can check it. http://www.teachingtreasures.com.au/maths/maths_level2.html Count on Convict Practice “adding up” strategy for mental subtraction. First type the amount to move on to the next whole ten, then count on tens, then the rest. http://www.ictgames.com/countonconvict.html
77
Adding with Whole Tens 1. One of the numbers is a whole ten. Add.
+ a.
+
32 + 10 = 42
b.
+
+
54 + 10 = ____
c.
____ + 20 = ____
+
d. ____ + ____ = ____
+
+
e. ____ + ____ = ____
f. ____ + ____ = ____
+
g. ____ + ____ = ____
+
h. ____ + ____ = ____
Adding whole tens and another 2-digit number Break down the other number into tens and ones. Add the tens. Then, add the ones.
i. ____ +
50 + 26 / \ 50 + 20 + 6 70 + 6 = 76
____ = ____
39 + 40 / \ 30 + 9 + 40 70 + 9 = 79
2. Add. You can break the second number into tens and ones first. a. 10 + 34 = ____
b. 10 + 28 = ____
c. 20 + 24 = ____
d. 30 + 21 = ____
(10 + 30 + 4)
(10 + ____ + ____ )
(20 + ____ + ____ )
(30 + ____ + ____ )
e. 50 + 17 = ____
f. 40 + 33 = ____
g. 60 + 23 = ____
h. 30 + 37 = ____
(50 + ____ + ____ )
78
3. Add. You can break the first number into tens and ones first. a. 45 + 20 = ____
b. 27 + 20 = ____
(40 + 5 + 20)
( ____ + ___ + ____ )
e. 46 + 30 = ____
f. 16 + 50 = ____
c. 45 + 40 = ____
d. 62 + 30 = ____
g. 38 + 60 = ____
h. 78 + 10 = ____
4. Add. a. 77 + 10 = ____
b. 20 + 45 = ____
c. 16 + 10 = ____
d. 30 + 37 = ____
77 + 20 = ____
30 + 45 = ____
16 + 30 = ____
20 + 37 = ____
Remember rounding to the nearest ten? Numbers ending in 1, 2, 3, or 4 are are closer to the previous ten than the next, so they are rounded down.
Numbers ending in 6, 7, 8, or 9 are closer to the next ten so they are rounded up.
72 ≈ 70
46 ≈ 50
(72 is approximately 70)
(46 is approximately 50)
The middle numbers ending in 5 are rounded up.
5 ≈ 10
5. Round these numbers to the nearest ten. a. 23 ≈ ____
b. 54 ≈ ____
c. 78 ≈ ____
d. 96 ≈ ____
e. 65 ≈ ____
f. 95 ≈ ____
g. 8 ≈ ____
h. 3 ≈ ____
6. Amy bought shoes for $39, a top for $8, and a skirt for $23. Round these prices to the nearest ten, and then add them to find her total bill.
7. Jacob has $61. Then he buys a toy airplane for $29. Use rounded numbers to estimate how much money he has left.
79
8. Fill in the missing numbers and find how many tens were added. a. 10 + ____ = 60
b. 12 + ____ = 22
c. 45 + ____ = 65
d. 23 + ____ = 63
30 + ____ = 50
12 + ____ = 52
45 + ____ = 55
23 + ____ = 53
10 + ____ = 90
12 + ____ = 42
45 + ____ = 75
23 + ____ = 93
9. Add 10, 20, 30, or 40. In the box below the number, write “E” if the number is even, and “O”, if the number is odd. What can you notice?
+ 20
+ 10
12
22
E
E
19
+ 40
23
+ 30
____
32
58
____
37
+ 20
+ 30
____
+ 40
7
____
____
+ 10
____
85
____
How many different solutions can you find for this puzzle? Find at least two. All numbers are whole tens.
+ +
+ +
+ +
+
+ = 100
+ +
+
+ +
= 100
+
+ +
+ = 80
= 70
+ = 70 = 80
80
+ +
+ +
= 60
= 70
= 100 +
+ = 100
= 70 = 60
Subtracting Whole Tens 1. Look at the pictures. Cross out as many ten-pillars as the problem indicates. What is left?
a. 30 – 10 = 20
b. 40 – 20 = ____
c. 50 – 30 = ____
d. 70 – 40 = ____
e. 33 – 10 = 23
f. 47 – 20 = ____
g. 26 – 10 = ____
h. 55 – 30 = ____
The ____________ digit does not change.
2. Count by tens backwards. a. 76, 66, ______ , ______ , ______ , ______ , ______, ______ b. _____ , ______ , 52, 42, ______ , ______ , ______ , ______ c. _____ , ______ , ______ , ______ , ______ , ______ , 17, ______
3. Subtract. a. 23 – 10 = ____
b. 48 – 20 = ____
c. 56 – 10 = ____
d. 87 – 20 = ____
23 – 20 = ____
48 – 30 = ____
56 – 30 = ____
87 – 40 = ____
e. 75 – 10 = ____
f. 31 – 10 = ____
g. 81 – 40 = ____
h. 74 – 40 = ____
75 – 20 = ____
31 – 20 = ____
81 – 50 = ____
74 – 20 = ____
81
4. Find the pattern and continue it. a. 88 – 10 = ____
b. 100 – 60 = ____
c. 34 – 10 = ____
88 – 20 = ____
90 – 50 = ____
44 – 20 = ____
88 – 30 = ____
80 – 40 = ____
54 – 30 = ____
88 – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
5. Use rounded numbers to solve these problems. a. Three suitcases weigh 29 kg, 18 kg, and 31 kg. About how much do they weigh in total? b. Garden chairs cost $29 apiece. Can Charlene buy three of them with $80? c. Michael received $50 for his birthday. If he buys three books that cost $9 each, about how much will he have left?
Find numbers for the puzzles.
+ –
= 90 –
+ = 30
– +
= 30
= 40 +
–
= 30
= 80
82
= 30 = 10
Carrying to Tens tens ones
When adding 3 + 9, we can circle ten cubes to form a ten. We write “1” in the tens column. There are two little cubes left over, so we write “2” in the ones column.
+ 1
When adding 35 + 8, we can circle ten little cubes to form a ten. There already are three tens, so in total we now have four tens. These are written as “4” in the tens column.
3 9 2
tens ones
3 +
There are three little cubes left over, so we write “3” in the ones column.
4
5 8 3
1. Circle ten cubes to make a whole ten. Count the whole tens, including the one you made by circling the cubes. Count the ones. Write the tens and ones in their own columns. tens ones
a.
3 3 + 9
tens ones
2 b.
tens ones
tens ones
3 c.
+
8 9
d.
tens ones
e.
3 + 1
6 8
2 7 + 7
tens ones
f.
83
+
5 8
2 + 2
5 7
tens ones
When we form a new ten from the ones (little cubes), we are trading or exchanging the ten ones into 1 ten.
1
This is also called carrying to tens. Imagine someone “gathering” ten little cubes in his lap and “carrying” them over into the tens column as 1 ten.
3 + 2 6
5 7 2
To show this new ten, write a little “1” in the tens column above the other numbers. Then add in the tens-column as usual, adding the little “1” also.
2. Circle ten ones to make 1 new ten. Add the tens and ones in columns. tens ones 1
tens ones 1
1 3 + 2 9 2
a.
2 4 + 3 8
b.
tens ones 1
3 5 + 1 9 4
c.
e.
g.
tens ones 1
2 4 + 4 7 1
d.
f.
+
h.
+
84
+
+
3. Add. If the ones go over ten, carry one whole ten to the tens column. a.
42 + 15
b.
27 + 45
c.
65 + 26
d.
83 + 15
e.
34 + 19
f.
52 + 41
g.
13 + 44
h.
63 + 27
i.
36 + 51
j.
66 + 29
k.
18 +40
l.
39 +36
m.
59 + 35
n.
72 + 22
o.
17 + 23
2
Sometimes we can get two tens from all the ones (little cubes). On the right, when you add the ones, you get 6 + 7 + 8 = 21. So, we carry two tens to the tens column and write a little “2” above the tens column.
3 2 + 1
6 7 8 1
4. Add. Carry to the tens column. a.
34 19 + 26
b.
15 27 + 45
c.
18 27 + 26
d.
26 48 + 19
e.
34 20 + 19
5. Count by fours. a. 0, 4, _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ b. 100, 96, 92, _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____
85
Going Over to the Next Ten Sums that go over to the next ten Let's add 59 + 5 so that we first complete 60. 59 + 5 |
\
59 + 1 + 4 60 + 4 = 64 The 5 is broken into two parts: 1 and 4. That is because 59 and 1 makes sixty. Then, we have 60 and 4. We get 64.
9 and 1 make a ten. We get 6 tens. 59 + 5 = 64
1. Circle ten little cubes to make a ten. Count the tens and ones. Write the answer.
a. 13 + 9 = ______
b. 15 + 8 = ______
c. 17 + 7 = ______
d. 24 + 7 = ______
e. 25 + 6 = ______
f. 37 + 9 = ______
g. 36 + 6 = ______
h. 48 + 4 = ______
i. 58 + 5 = ______
86
2. Complete. Break the second number into two parts so that you complete the next ten. a.
28 + 8 /
b. \
/
28 + 2 + ____
39 + 3 /
c.
/
e.
27 + 5 /
39 + 1 + ____
80 + ____ = ____ f.
38 + 7
\
/
27 + ____ + ____
____ + ____ = ____
\
79 + 1 + ____
50 + ____ = ____
\
79 + 9
\
47 + 3 + ____
30 + ____ = ____ d.
47 + 5
\
38 + ____ + ____
____ + ____ = ____
____ + ____ = ____
3. Continue the patterns. COMPARE the columns. a.
b.
8 + 1 = ____
28 + 1 = ____
5 + 4 = ____
15 + 4 = ____
8 + 2 = ____
28 + 2 = ____
5 + 5 = ____
15 + 5 = ____
8 + 3 = ____
28 + 3 = ____
5 + 6 = ____
15 + 6 = ____
8 + 4 = ____
28 + 4 = ____
5 + ___ = ____
15 + ___ = ____
8 + ___ = ____
28 + ___ = ____
5 + ___ = ____
15 + ___ = ____
8 + ___ = ____
28 + ___ = ____
___ + ___ = ___
___ + ___ = ____
What do you notice?
4. Fill the missing addends. a. 8 + ____ = 10
b. 13 + ____ = 20
c. 67 + ____ = 70
8 + ____ = 11
13 + ____ = 21
67 + ____ = 71
d. 7 + ____ = 10
e. 18 + ____ = 20
f. 86 + ____ = 90
7 + ____ = 12
18 + ____ = 22
86 + ____ = 92
87
5. Solve the word problems. Write a number sentence for each problem, not just the answer. a. Ben wants to buy a bicycle that costs $30.
He has saved $22. How much more money will he need?
b. Jill had already saved $20. She earned five dollars for
raking the yard, and another five dollars for weeding. How much money does she have now?
c. Mom bought 28 rosebushes and has planted eight of them.
How many still need planted?
d. Thirty-seven people attended Uncle Jim's 50th birthday
party. Thirty-two of them came before noon. How many came after?
e. Dad bought a bunch of 40 grapes and ate half of them. Then,
little sister ate 7 grapes. How many are left now?
6. Add and compare. Notice the patterns. a.
b.
6 + 2 = ____
36 + 2 = ____
9 + 1 = ____
29 + 1 = ____
6 + 3 = ____
36 + 3 = ____
9 + 2 = ____
29 + 2 = ____
6 + 4 = ____
36 + 4 = ____
9 + 3 = ____
29 + 3 = ____
6 + ___ = ___
36 + ___ = ____
9 + 4 = ____
29 + 4 = ____
6 + ___ = ___
36 + ___ = ___
9 + ___ = ___
29 + ___ = ___
6 + ___ = ___
36 + ___ = ____
9 + ___ = ___
29 + ___ = ___
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
88
Two-Digit Numbers Ending in 9 1. Circle the dots to form a complete ten. Compare to the problem with the ones' digits.
a. 19 + 5 = ____
b. 29 + 7 = ____
c. 49 + 5 = ____
9 + 5 = ____
9 + 7 = ____
9 + 5 = ____
The answer goes to the next ten!
2. Add. For each problem, write down the corresponding problem with just the ones' digits. a. 19 + 7 = ____
b. 49 + 9 = ____
c. 59 + 5 = ____
d. 39 + 4 = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
e. 59 + 8 = ____
f. 19 + 2 = ____
g. 49 + 3 = ____
h. 79 + 5 = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
3. Add. Compare the problems.
9 + 3 = ____
b. 9 + 6 = ____
c. 9 + 4 = ____
d. 9 + 7 = ____
19 + 3 = ____
39 + 6 = ____
49 + 4 = ____
29 + 7 = ____
29 + 3 = ____
59 + 6 = ____
79 + 4 = ____
89 + 7 = ____
e. 9 + 2 = ____
f. 9 + 9 = ____
g. 9 + 5 = ____
h. 9 + 8 = ____
39 + 2 = ____
69 + 9 = ____
19 + 5 = ____
29 + 8 = ____
29 + 2 = ____
79 + 9 = ____
59 + 5 = ____
89 + 8 = ____
a.
89
4. The following problems review the basic facts with 9 and 8. By this time you should have already memorized these addition facts. Try to remember what number will fit - not count.
a.
b.
c.
d.
9 + ____ = 14
4 + 9 = ____
8 + ____ = 11
7 + 8 = ____
9 + ____ = 15
8 + 9 = ____
8 + ____ = 15
2 + 8 = ____
9 + ____ = 13
2 + 9 = ____
8 + ____ = 17
8 + 8 = ____
9 + ____ = 18
5 + 9 = ____
8 + ____ = 12
5 + 8 = ____
9 + ____ = 12
6 + 9 = ____
8 + ____ = 14
6 + 8 = ____
9 + ____ = 17
3 + 9 = ____
8 + ____ = 13
3 + 8 = ____
9 + ____ = 11
1 + 9 = ____
8 + ____ = 18
1 + 8 = ____
9 + ____ = 16
9 + 9 = ____
8 + ____ = 16
9 + 8 = ____
9 + ____ = 10
7 + 9 = ____
8 + ____ = 10
4 + 8 = ____
5. Find the pattern and continue it!
a.
+
40
b.
+
48
+
16
53 +
21 +
____
____
+
61 +
27
+
c.
+
66 +
34 +
____
+
+
____
____
+
42 +
____
+
+
+
____
____
+
____
90
+
67
+
____ +
____
+
71
____
____
+
74
76
Add in Columns Practice 1. Add in columns. a.
9 + 71
b.
24 + 67
c.
55 + 36
d.
45 + 25
e.
38 + 14
f.
58 + 25
g.
29 + 38
h.
79 + 15
i.
62 + 28
j.
37 + 35
k.
34 9 + 35
l.
25 42 + 49
m.
58 30 + 6
n.
29 44 + 12
o.
16 14 + 19
2. Write the numbers under each other so that the ones and tens are in their own columns. Add. a. 45 + 27
b. 8 + 56
tens ones
tens ones
+
f. 6 + 31 + 25
+
+
g. 40 + 7 + 9
+
c. 40 + 32
d. 25 + 45
e. 47 + 9
+
+
+
h. 46 + 8 + 20
+
i. 5 + 8 + 13
+
91
j. 5 + 4 + 57
+
In the tens column, you add 1 + 5 + 6 = 12. The “1” of 12 is in the hundreds' column, and the “2” of 12 is in the tens column.
+
Ten tens makes a hundred. 12 tens makes more than a hundred - a hundred and 2 tens. In the tens column, you add 8 + 7 = 15. The “1” of 15 is in the hundreds' column, and the “5” of 15 is in the tens column.
+
Ten tens makes a hundred. 15 tens makes more than a hundred - a hundred and 5 tens. 3. Add. You will have more than 10 tens. a. 27 + 80
b. 95 + 47
+
c. 29 + 75
+
+
d. 62 + 84
+
4. Add. a.
67 + 61
b.
90 + 65
c.
39 + 81
d.
85 + 62
e.
29 + 94
f.
57 + 72
g.
70 + 68
h.
85 + 78
i.
86 + 15
j.
96 + 90
k.
65 18 + 26
l.
74 7 + 45
m.
68 47 + 32
n.
12 88 + 49
o.
8 50 + 79
92
Two-Digit Numbers Ending in 8 or 7 1. Circle dots to complete a ten. Compare it to the problem below with the ones' digits.
+
+
____ + __ = ____ 8
+
18 + 5 = ____
____ + ___ = ____
8 + 5 = 13
8 + 9 = 17
+ 6 = 14
The answer goes to the next ten!
2. Add. For each problem, write the corresponding problem with just the ones' digits. a. 68 + 7 = ____
b. 58 + 2 = ____
c. 38 + 6 = ____
d. 48 + 4 = ____
8 + 7 = 15
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
e. 14 + 8 = ____
f. 72 + 9 = ____
g. 65 + 8 = ____
h. 55 + 9 = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
3. Add. Compare the problems. a. 8 + 3 = _____
b. 8 + 6 = _____
c. 8 + 4 = _____
d. 8 + 7 = _____
18 + 3 = _____
38 + 6 = _____
48 + 4 = _____
28 + 7 = _____
28 + 3 = _____
58 + 6 = _____
78 + 4 = _____
88 + 7 = _____
e. 8 + 2 = _____
f. 8 + 9 = _____
g. 8 + 5 = _____
h. 8 + 8 = _____
38 + 2 = _____
68 + 9 = _____
18 + 5 = _____
28 + 8 = _____
28 + 2 = _____
78 + 9 = _____
58 + 5 = _____
88 + 8 = _____
93
4. Add. Circle dots to form a ten. Note the answer goes over to the next ten.
a. 27 + 4 = ____
b. 47 + 5 = ____
c. 37 + 7 = ____
5. Add. For each problem, write the corresponding problem with just the ones' digits. a. 75 + 7 = ____
5 + 7 = 12
b. 47 + 7 = ____
c. 57 + 6 = ____
d. 37 + 4 = ____
___ + ___ = ____
___ + ___ = ____
___ + ___ = ____
6. Add. Compare the problems. a. 7 + 6 = ____
b. 7 + 5 = ____
c. 7 + 4 = ____
d. 7 + 7 = ____
17 + 6 = ____
47 + 5 = ____
17 + 4 = ____
67 + 7 = ____
27 + 6 = ____
77 + 5 = ____
47 + 4 = ____
87 + 7 = ____
e. 7 + 9 = ____
f. 7 + 3 = ____
g. 7 + 8 = ____
h. 7 + 10 = ____
67 + 9 = ____
37 + 3 = ____
57 + 8 = ____
17 + 10 = ____
87 + 9 = ____
77 + 3 = ____
27 + 8 = ____
47 + 10 = ____
7. Solve the word problems. a. Jeanine needed 24 eggs to make an omelet for her family.
She already had 15 eggs. How many more does she need?
b. Her large family eats lots of potatoes. Dad bought a 50-pound
bag of potatoes. There are only 12 pounds remaining. How many pounds of potatoes have they eaten?
94
Addition Practice 1. Break the second number into tens and ones, and then add mentally. a.
b.
20 + 34 /
\
/
20 + ____ + ____ =
c.
70 + 18
50 + 27
\
/
70 + ____ + ____ =
\
50 + ____ + ____ =
2. Add mentally. a. 17 + 10 = _____
b. 16 + 20 = _____
c. 50 + 14 = _____
26 + 10 = _____
34 + 30 = _____
60 + 23 = _____
42 + 10 = _____
67 + 20 = _____
30 + 45 = _____
3. Find the pattern and continue it. This pattern “grows” at each step. +
1
+
+
3
7
+
+
13
21
+
31
+
____
+
____
____
4. Add. a.
44 + 48
b.
32 + 59
c.
16 + 47
d.
23 + 67
e.
55 + 29
5. Compare the expressions and write < , > , or = . a. 8 + 3
40 + 5
b. 8 + 54
9 + 53
c. 5 + 6 + 56
61 + 6
d. 2 + 36
29 + 7
e. 46 + 8
48 + 5
f. 85 + 9
6 + 88
95
6. Explain why these are wrong:
33 + 48
55 + 39
711
814
7. Add. Compare the problems! a.
b.
c.
d.
7 + 8 = ____
4 + 9 = ____
8 + 4 = ____
7 + 9 = ____
17 + 8 = ____
14 + 9 = ____
48 + 4 = ____
57 + 9 = ____
37 + 8 = ____
44 + 9 = ____
78 + 4 = ____
37 + 9 = ____
8. Count by threes. a. 42, 45, _____, _____, _____, _____, _____, _____, _____, _____, ____ b. 1, 4, _____, _____, _____, _____, _____, _____, _____, _____, ____
9. Add. a.
b.
c.
d.
29 + 4 = ____
45 + 8 = ____
22 + 8 = ____
78 + 6 = ____
38 + 9 = ____
24 + 9 = ____
46 + 8 = ____
69 + 5 = ____
48 + 6 = ____
36 + 8 = ____
91 + 8 = ____
62 + 9 = ____
Figure out the missing numbers for these addition problems. a.
b.
+ 1 4 4 1
c.
+
d.
e.
3
+ 2 5
+ 7 8
+ 2 6
7 1
5 1
9 1
6 1
96
Many Addends When adding the ones, you may get two or even three tens. Carry them to the tens' column.
Adding the ones we get 8 + 7 + 8 = 23. Carry 2 tens to the tens column.
2
48 27 + 18 93
Adding the ones we get 9 + 9 + 7 + 6 = 31. Carry 3 tens to the tens column.
3
19 19 27 + 26 91
1. Add mentally. First add the numbers that make 10 (if there are any). a. 8 + 4 + 5 =
b. 5 + 8 + 7 =
c. 8 + 5 + 6 + 4 =
9+9+9=
9+2+6=
4+9+5+6=
2. Add. The answers are “hidden” in the list of numbers below the problems. a.
52 30 + 11
b.
13 25 + 54
c.
33 38 + 27
d.
36 27 + 19
e.
36 27 18 + 16
f.
40 18 16 + 22
g.
15 17 18 + 39
h.
12 29 25 + 14
i.
19 79 + 19
j.
56 32 + 29
k.
45 65 + 19
l.
51 15 + 79
129
145
74
80
82
89
91
92
93
96
97
97
98
117
117
122
3. Solve the problems. Write an addition or subtraction sentence or a missing addend sentence for each one. You can add in columns if you need to. a. A bus can seat 30 people. There were
b. The first bus had 22 people on it, and
already 23 people. Is there room for nine more people?
the second bus had 25. What is the total number of people on the buses?
Yes/No, because
c. How many buses do you need if you
d. A bus was full, but then six people
have 57 people?
got off. How many people were on it now?
How many buses do you need if you have 88 people?
e. A bus was full. First it dropped off
f. A bus had some people in it, and then
13 people. Then it dropped off 7 more people. How many people were left on the bus?
13 more got on. Now there are 29 people on the bus. How many were on the bus originally?
g. A bus had some people on it. Then 9
h. A bus had some people on it. It picked
people got on. Then 15 people got off. Now there are 17 people on the bus. How many were on it originally?
up 12 people, and then 7 people more. Then it was full. How many people were on the bus originally?
98
4. Add mentally. Try to find the easiest order. a. 30 + 2 + 40 + 8 = _____
c. 9 + 40 + 1 + 4 = _____
b. 50 + 4 + 10 + 7 = _____
d. 20 + 10 + 8 + 9 = _____
5. Add. Below the numbers, write “E” if the number is even, and “O”, if the number is odd. a. 19 + 5 + 7 = 31
O
O
O
b. 25 + 7 + 3 = ____
c. 7 + 11 + 23 = ____
O
d. 57 + 21 = ____
g. 17 + 27 + 5 = ____
e. 5 + 1 + 11 + 9 = ____
h. 25 + 13 + 3 + 1 = ____
f. 25 + 9 = ____
i. 57 + 21 = ____
Underline the correct choice in the sentences below. Can you think why it is that way? If I add two odd numbers, the answer is (even/odd). If I add three odd numbers, the answer is (even/odd). If I add four odd numbers, the answer is (even/odd).
47 + 29 60 + 16
Can you figure out how Mary is adding and why it works?
76
52 17 + 14 70 + 13 83
Use Mary's method with these problems:
13 15 + 48
27 28 + 31
16 25 + 47
99
46 25 + 12
36 27 + 34
Subtracting in Columns tens ones
1. a.
– 3
tens ones
b.
2
Cross out 3 tens and 2 ones. What is left? __ tens and __ ones
–
Cross out 6 tens and 1 one. What is left? __ tens and __ ones
You can simply subtract the tens in the tens-column and the ones in the ones-column.
2. Subtract. a.
57 – 10
b.
66 – 24
c.
78 – 44
d.
87 – 20
e.
55 – 11
f.
95 – 35
g.
28 – 25
h.
67 – 33
i.
76 – 32
j.
88 – 66
c.
96
d.
27
e.
76
3. Figure out what was subtracted.
57
a.
48
b.
–
– 37
– 25
– 33
– 12
33
4. Subtract and add. Compare the problems. a.
72 + 20 = ____
b.
29 + 10 = ____
c.
55 – 20 = ____
d.
63 + 30 = ____
72 + 10 = ____
29 + 50 = ____
55 + 20 = ____
63 – 40 = ____
72 – 10 = ____
29 – 10 = ____
55 + 40 = ____
63 – 20 = ____
72 – 30 = ____
29 + 30 = ____
55 – 30 = ____
63 – 60 = ____
100
Borrowing/Regrouping, Part 1 Break a ten.
We will now study “borrowing” in subtraction. As a first step, we study breaking a ten-pillar into ten little cubes. 4 tens 5 ones This is also called “regrouping”, because one ten “changes groups” First we have 45. We from the tens group into the ones. “break” one ten-pillar into little cubes.
3 tens 15 ones Now we have 3 tens and 15 ones. It is still 45, but written in a different way.
Break a ten.
Here is another example. First we have 5 tens 3 ones. We “break” one ten-pillar into 10 little cubes. We end up with 4 tens 13 ones. 5 tens 3 ones
4 tens 13 ones
1. Break a ten into 10 ones. What do you get? You can draw ten-pillars and cubes to help. Break a ten. a. 3 tens 0 ones
Break a ten. b. __tens __ones
2 tens ___ ones Break a ten.
c. __tens __ones
Break a ten.
__tens __ones
d. __tens __ones
Break a ten. e. __tens __ones
__tens __ones
__tens __ones Break a ten.
__tens __ones
f. __tens __ones
101
__tens __ones
Let's study subtraction. The pictures on the right illustrate 45 – 17.
Break a ten.
First, a ten is broken into 10 ones. So, 4 tens 5 ones becomes 3 tens 15 ones.
4 tens 5 ones
After that, cross out (subtract) 1 ten 7 ones.
Cross out 1 ten 7 ones from the second picture. What is left? ___ tens ___ ones
The pictures on the right illustrate 52 – 39.
3 tens 15 ones
Break a ten.
First, a ten is broken into 10 ones. So, 5 tens 2 ones becomes 4 tens 12 ones.
5 tens 2 ones
After that, cross out (subtract) 3 tens 9 ones.
Cross out 3 tens 9 ones from the second picture. What is left? ___ tens ___ ones
4 tens 12 ones
2. Fill in.
Break a ten.
3 tens 6 ones
Break a ten.
2 tens 16 ones
___ tens ___ ones
a. Cross out 8 ones from the second picture. What is left? ___ tens ___ ones
b. Cross out 2 tens 7 ones from the second
picture. What is left? ___ tens ___ ones
Break a ten.
___ tens ___ ones
___ tens ___ ones
Break a ten.
___ tens ___ ones
___ tens ___ ones
___ tens ___ ones
c. Cross out 2 tens 5 ones from the second
d. Cross out 4 tens 4 ones from the second
picture. What is left? ___ tens ___ ones
picture. What is left? ___ tens ___ ones
102
3. First, break a ten. Then subtract ones and tens separately. Look at the example.
a. 5 tens 5 ones
4 tens 15 ones – 1 ten 7 ones
– 1 ten 7 ones
b. 7 tens 2 ones
– 3 tens 5 ones
–
3 tens 8 ones
c. 6 tens 0 ones
– 2 tens 7 ones
–
__ tens __ ones
__ tens __ ones 2 tens 7 ones
d. 6 tens 4 ones
– 3 tens 8 ones
–
__ tens __ ones
e. 7 tens 6 ones
– 4 tens 7 ones
–
– 6 tens 5 ones
–
__ tens __ ones 3 tens 8 ones __ tens __ ones
__ tens __ ones 4 tens 7 ones
f. 5 tens 0 ones
– 2 tens 2 ones
–
__ tens __ ones
g. 8 tens 1 one
__ tens __ ones 3 tens 5 ones
__ tens __ ones 2 tens 2 ones __ tens __ ones
__ tens __ ones 6 tens 5 ones
h. 6 tens 3 ones
– 2 tens 8 ones
__ tens __ ones
–
__ tens __ ones 2 tens 8 ones __ tens __ ones
4. Jessica had 37 colored pencils. Then she took a set of 12 different colored pencils and gave those to her brother, and another set of 6 pencils and gave those to her sister. a. How many pencils does Jessica have now? b. How many more pencils does Jessica have than her brother? c. How many more pencils does Jessica have than her sister?
103
Borrowing/Regrouping, Part 2 The picture illustrates subtracting 16 from 53. First, we break a ten into ten ones. Then we cross out 1 ten 6 ones. When the subtraction is written down in columns, we cross the “5” in the tens-column and write 4 above it. We also cross the “3” in the ones column and write 13 above it.
5 tens, 3 ones
This shows the same thing as the pictures: one of the tens is "broken down" into ten ones, so there is one less ten in the tens column, and 10 more ones in the ones column.
4 tens, 13 ones
Cross out 1 ten 6 ones from the second picture. What is left? ___ tens ___ ones
Then we can subtract tens and ones separately.
4
13
5 – 1 3
3 6 7
Here is another example. The picture illustrates subtracting 28 from 40. First, we break a ten into ten ones. Then we cross out 2 tens 8 ones. When the subtraction is written down in columns, we cross the “4” in the tens-column and write 3 above it, because one of the tens was "moved" or "borrowed" into the ones column.
4 tens
3 tens, 10 ones
Cross out 2 tens 8 ones from the second picture. What is left? ___ tens ___ ones
We also cross the “0” in the ones column and write 10 above it, because there are now 10 new ones that came from the ten that was "borrowed".
3
10
4 – 2 1
0 8 2
1. Borrow from the tens, then subtract. a. 6 tens 3 ones → 5 tens 13 ones
Take away 1 ten, 7 ones.
b. 5 tens 2 ones → ___ tens ___ ones
5
13
6 – 1
3 7
Take away 2 tens, 7 ones.
104
5 – 2
2 7
c. 6 tens 0 ones → ___ tens ___ ones
6 – 3
Take away 3 tens, 9 ones.
d. 7 tens 1 one → ___ tens ___ ones
0 9
e. 3 tens, 5 ones → ___ tens ___ ones
3 – 1
Take away 1 ten, 7 ones.
7 – 4
1 6
f. 8 tens → ___ tens ___ ones
5 7
8 – 3
Take away 3 tens, 4 ones.
g. 7 tens, 6 ones → ___ tens ___ ones
Take away 4 tens, 8 ones.
7 – 1
Take away 1 ten, 6 ones.
0 4
h. 9 tens → ___ tens ___ ones
Take away 5 tens, 1 one.
6 8
9 – 5
i. 5 tens, 4 ones → ___ tens ___ ones
j. 8 tens → ___ tens ___ ones
Take away 2 tens, 5 ones.
Take away 4 tens, 7 ones.
–
0 1
–
k. 7 tens, 4 ones → ___ tens ___ ones
l. 4 tens 7 ones → ___ tens ___ ones
Take away 3 tens, 8 ones.
Take away 2 tens, 9 ones.
–
105
–
2. Subtract. Check by adding the result and what was subtracted. The sum should be the number you subtracted from. a.
4 16
Check:
56 – 27
1
29 + 27
29
56
b.
90 – 28
d.
c.
Check:
42 – 15
+ 28
e.
40 – 35
65 – 39
h.
52 – 14
i.
65 – 26
j.
70 – 48
k.
55 – 17
+ 15
f.
82 – 25
g.
Check:
l.
31 – 18
66 – 28
Figure out the missing numbers in these subtraction problems! You might need to borrow from the tens.
3 – 1
8 –
7 5
– 2 3 4 7
0 7
6 2 – 1 4
– 3
1 6
4 2
6 8
7 0
5
1
–
– 3 4 5
2 7
106
– 1 3 7
– 5 3 8 –
9 4 4
Regrouping/Borrowing, Part 3 You can subtract
How do we know when to break down a ten into 10 ones, and when not to?
6–0 6–1 6–2
From six cubes, we can cross out 0, 1, 2, 3, 4, 5, or 6 cubes. We cannot cross out 7, 8, 9, etc. because there are not that many cubes to begin with.
You would go into debt
6–3 6–4 6–5 6–6
6 – 7 6 – 11 6 – 8 6 – 12 6 – 9 6 – 13 6 – 10 etc.
1. Cross out the subtractions that would “make you go into debt”. Do you notice any patterns? (You can also write how much you would go into debt; for example –4 is a negative 4.)
3–0 3–1 3–2 3–3 3–4 3–5 3–6 3–7 3–8 3–9
4–0 4–1 4–2 4–3 4–4 4–5 4–6 4–7 4–8 4–9
5–0 5–1 5–2 5–3 5–4 5–5 5–6 5–7 5–8 5–9
6–0 6–1 6–2 6–3 6–4 6–5 6–6 6–7 6–8 6–9
7–0 7–1 7–2 7–3 7–4 7–5 7–6 7–7 7–8 7–9
8–0 8–1 8–2 8–3 8–4 8–5 8–6 8–7 8–8 8–9
2. Look at the ones' digits. Do you need to move a ten to ones' column (regroup)? a. Do you need to regroup?
–
61 26
Y/N
d. Do you need to regroup? Y/N
b. Do you need to regroup?
–
74 23
Y/N
–
54 32
c. Do you need to regroup?
–
50 25
–
90 27
Y/N
e. Do you need to regroup? Y/N
–
82 56
f. Do you need to regroup? Y/N
107
If you subtract in columns and you don't have enough ones, you have to BREAK a ten and add ten ones to the ones' column. 3. Do you need to move a ten to the ones column? Find the answers in the line of numbers below. a. Do you need to regroup?
–
60 16
b. Do you need to regroup?
Y/N
–
57 32
c. Do you need to regroup?
Y/N
d. Do you need to regroup?
–
80 28
–
97 25
f. Do you need to regroup?
Y/N
g. Do you need to regroup?
–
50 10
–
60 41
Y/N
h. Do you need to regroup?
Y/N
–
88 77
Y/N
e. Do you need to regroup?
Y/N
–
43 17
–
37 27
i. Do you need to regroup?
Y/N
Y/N
35 44 26 19 25 11 63 22 72 49 10 26 51 52 78 30 25 40 4. Subtract. Borrow from the tens when needed. Check by adding!
a.
54 – 37
b.
94 – 34
c.
82 – 25
d.
62 – 29
e.
99 – 57
f.
40 – 23
g.
76 – 48
h.
83 – 63
i.
89 – 17
108
Graphs and Problems
1. The graph shows how many newspapers Jack sold at his newspaper stand from Monday through Sunday.
a. For each day, find about how many newspapers Jack sold. Look how tall each column is, and find the nearest whole-ten number. Newspapers
about ____
about ____
about ____
about ____
about ____
about ____
about ____
Day
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
b. About how many newspapers did Jack sell on Saturday and Sunday together? c. About how many more newspapers did Jack sell on Sunday than on Monday? 2. Break the number you're subtracting into tens and ones, and subtract in parts. a. 45 – 23
b. 76 – 15
/ \ 45 – 20 – 3 = ____
/ \ 76 – 10 – 5 = ____
d. 60 – 35
e. 88 – 38
f. 70 – 16
g. 90 – 28
h. 73 – 32
i. 64 – 33
c. 47 – 15
109
3. Solve the word problems. Write an addition or subtraction sentence for each question. You can add or subtract in columns if you need to. a. Jim has 62 marbles, Peter has 28, and Ed has 33 marbles.
How many more marbles does Jim have than Peter? How many more marbles does Jim have than Ed? If Peter and Ed combined their marbles, will they have more than Jim?
b. Mom had $72. She bought a gadget for $44.
How many dollars does she have left?
c. You're on page 48 in your book that has a total of 95
pages. You read ten more pages. Now how many pages do you have left to read?
4. a. How many Arctic animals does the zoo have? How many rain forest birds? b. How many European and Arctic animals does the zoo have together? c. How many more African animals does the zoo have than Australian animals?
110
5. The teacher made a chart that shows how many books the children read each month. Books read
Jan
Feb
Mar
Apr
Annie
13
21
18
14
Freddie
8
5
11
9
Lisa
8
13
16
18
Jonathan
10
8
14
15
Total
a. How many books did Jonathan read in March? b. Who read the most books in February?
In April?
c. How many more books did Annie read in February than in January? d. How many more books did Lisa read in April than Freddie? e. Find how many books each child read in all. Put the number in the “total” column. Annie
+
Freddie
Lisa
+
+
f. How many more books in all did Annie read than Freddie?
111
Jonathan
+
Mental Subtraction Methods Method 1: Subtract in two parts
53 – 8 = 53 – 3 – 5 = 50 – 5 = 45
6 72 – = 72 – 2 – 4 = 70 – 4 = 66
Subtract 8 in two parts: first 3, then 5. In other words, first subtract to the previous whole ten, then the rest.
Subtract 6 in two parts: first 2, then 4. In other words, first subtract to the previous whole ten, then the rest.
1. Subtract the elevated number in parts: first subtract to the previous whole ten; then the rest.
−5 /
−7
\
/
a. ( 51 − 1 ) − 4 =
/
−7 \
/
e. ( 75 − ___ ) −___ =
−7 g. ( 35 − ___ ) −___ =
/
\
f. ( 63 − ___ ) −___ =
−6 \
\
c. ( 33 − ___ ) −___ =
−6 \
d. ( 92 − ___ ) −___ =
/
/
b. ( 62 − ___ ) −___ =
−5 /
−4 \
−5 \
/
h. ( 74 − ___ ) −___ =
\
i. ( 52 − ___ ) −___ =
2. First subtract the balls that are not in the ten-groups. a.
c.
51 − 7 = ____
b.
42 − 4 = ____
51 − 5 = ____
42 − 5 = ____
51 − 3 = ____
42 − 3 = ____
51 − 6 = ____
42 − 6 = ____
34 − 8 = ____
d.
65 − 6 = ____
34 − 5 = ____
65 − 9 = ____
34 − 7 = ____
65 − 7 = ____
34 − 9 = ____
65 − 8 = ____
112
Method 2: Use known subtraction facts Since 14 – 6 = 8, we know that the answer to 74 – 6 will end in 8, but it will be in the sixties (sixty-something). So it is 68. Since 15 – 8 = 7, we know that the answer to 55 – 8 will end in 7, but it will be in the forties (forty-something). So it is 47. 3. Subtract. Compare the problems. a. 18 – 4 = ____
b. 14 – 9 = ____
c. 17 – 8 = ____
d. 12 – 9 = ____
48 – 4 = ____
24 – 9 = ____
27 – 8 = ____
52 – 9 = ____
78 – 4 = ____
44 – 9 = ____
37 – 8 = ____
32 – 9 = ____
e. 11 – 6 = ____
f. 15 – 9 = ____
g. 13 – 8 = ____
h. 16 – 8 = ____
51 – 6 = ____
65 – 9 = ____
33 – 8 = ____
86 – 8 = ____
71 – 6 = ____
45 – 9 = ____
93 – 8 = ____
36 – 8 = ____
4. Now you think of the “helping problem” yourself. a. 34 – 5 = ____
b. 65 – 9 = ____
c. 51 – 8 = ____
d. 62 – 7 = ____
73 – 7 = ____
36 – 8 = ____
93 – 6 = ____
83 – 8 = ____
5. a. Terry is on page 56 of her book. The book has a total of 92 pages. How many pages does she have left to read? b. Terry reads 9 pages more. Now how many pages does she have left to read?
6. Find what was subtracted. –
78
–
77
–
72
–
70
–
65
113
–
60
–
57
–
53
46
Method 3:
Add.
You can “add backwards”. This works well if the two numbers are close to each other. Instead of subtracting, think how much you need to add to the number being subtracted (the subtrahend) in order to get the number you're subtracting from (the minuend). Think: 84 + ___ = 92 (84 and how many more makes 92?)
Think: 25 + ___ = 75
+___
+___
(25 and how many more makes 75?)
92 – 84 =
75 – 25 =
7. To find these differences, think of adding more.
+8
+__
+__
a. 92 – 84 =
b. 51 – 49 =
c. 76 – 69 =
Think: 84 + ___ = 92
Think: 49 + ___ = 51
Think: 69 + ___ = 76
+__
+__
+__
d. 43 – 35 =
e. 70 – 61 =
f. 84 – 78 =
g. 32 – 28 =
j. 90 – 83 =
m. 100 – 95 =
h. 22 – 14 =
k. 64 – 56 =
n. 64 – 55 =
i. 53 – 46 =
l. 72 – 65 =
o. 44 – 37 =
The triangle and square represent “mystery numbers”. Find what the mystery numbers are in each case. a.
+
+ 10 = 34
= ______
b.
+
= 22
–
=4
= ____,
114
= ____
c.
+ +
= ____,
= 22 = 36 = ____
Euclid's Game Euclid's game is simple, fun, and lets you practice finding the difference of two numbers! Rules: 1. The first player chooses any number on the 100-chart and circles or colors it. 2. The next player chooses any other number on the 100-chart and circles or colors it. After this, the numbers get marked by crossing them out. At his turn, each player has to find the difference of any two numbers already marked, and mark that number. The player can choose any two numbers for this; they just have to be already marked numbers. The player who cannot find any more numbers to mark is the loser.
Use the 100-chart on the next page as a game board. You can print it anew for every new game. Alternatively you may write the 100-chart on paper, of course. Example. Initially Jane chooses 28 and Joe chooses 9. After that:
9
10
11 12 13 14 15 16 17 18 19
20
21 22 23 24 25 26 27 28 29
30
31 32 33 34 35 36 37 38 39
40
41 42 43 44 45 46 47 48 49
50
You can continue Jane's and Joe's play if you'd like.
51 52 53 54 55 56 57 58 59
60
Eventually you should see all of the numbers from 1 to 28 marked, with Jane as the loser.
61 62 63 64 65 66 67 68 69
70
71 72 73 74 75 76 77 78 79
80
81 82 83 84 85 86 87 88 89
90
Jane: I mark 19 since it's the difference of 28 and 9. Joe: I mark 10 since it's the difference of 19 and 9. Jane: I mark 18 since it's the difference of 28 and 10. Joe: I mark 1 since it's the difference of 19 and 18. ... and so on.
1
2
3
4
5
6
7
8
91 92 93 94 95 96 97 98 99 100
Questions to ponder after you have played a few games: 1. Let's say that 28 and 9 are chosen as the initial numbers, like in Jane's and Joe's game. Can Jane and Joe ever mark a number that is more than 28? 2. Let's say that the two initial numbers are both even. What can you say about the numbers that get marked in the game? 3. Let's say that the two initial numbers are both multiples of 5, such as 55 and 30. What can you say about the numbers that get marked in the game? 4. Can you mark off all of the the numbers on the 100-chart during the game, if the initial numbers are (you can try these out): a. 90 and 7? b. 100 and 1? c. 100 and 10? d. 100 and 13?
115
100-Charts for Euclid's game or other uses 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
116
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
91 92 93 94 95 96 97 98 99 100
1
1
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
91 92 93 94 95 96 97 98 99 100
117
Mixed Review 1. Complete the next ten. a.
b.
c.
d.
16 + ____ = 20
47 + ____ = ____
39 + ____ = ____
75 + ____ = ____
64 + ____ = 70
38 + ____ = ____
27 + ____ = ____
92 + ____ = ____
2. Add. a.
43 + 28
b.
33 + 39
c.
24 + 47
d.
23 + 37
e.
55 + 17
f.
38 13 + 42
g.
39 10 + 46
h.
41 14 + 36
i.
38 29 + 23
j.
18 19 + 55
3. Add. a.
b.
c.
d.
25 + 8 = ____
76 + 5 = ____
88 + 3 = ____
82 + 8 = ____
24 + 9 = ____
50 + 6 = ____
34 + 7 = ____
10 + 9 = ____
4. For each problem, write one where you subtract from 11, 12, 13, 14, 15, 16, 17, or 18. a.
55 – 7 = ____
b.
15 – 7 = 8 d.
72 – 7 = ____ ____ – ___ = ____
74 – 8 = ____
c.
____ – ___ = ____ e.
51 – 3 = ____ ____ – ___ = ____ 118
93 – 5 = ____ ____ – ___ = ____
f.
33 – 4 = ____ ____ – ___ = ____
5. Subtract. – 6
88
– 9
____
– 10
____
– 7
____
– 8
____
– 5
____
– 7
____
– 3
____
33
6. Subtract. Check by adding. a.
d.
Check:
88 – 54
66 – 17
b.
+ 54
e.
Check:
63 – 48
c.
+ 48
71 – 22
f.
Check:
69 – 27
84 – 49
7. Solve the problems. a. There are some people on the bus. At the bus stop, 13 people come in.
Now there are 52 people in the bus. How many were there originally?
b. Molly has 23 stuffed toys that she likes to play with, and
16 stuffed toys that she does not care for. Her little sister Annie has 17 stuffed toys. Molly gives the 16 toys to her little sister. How many does Annie have now? Who has more stuffed toys now? How many more?
c. Andy has $47 in his wallet. He earns $15 by selling lemonade.
Can he now buy a remote-controlled toy car for $65? If yes, how much money would have have left after buying it? If not, how much more money would he need?
119
+ 27
Chapter 5: Counting Money Introduction The fifth chapter of the Math Mammoth Grade 2-A Complete Worktext covers counting quarters, dimes, nickels, and pennies. Also, the one-dollar bill and the five-dollar bill are introduced.
Counting Coins The main goal of this chapter is to be able to count coins and find the amount of money in cents or dollars. Also practiced is finding change by counting up. Only small money amounts are used. In one lesson, the one-dollar bill and the five-dollar bill are introduced, and the student learns to write money amounts using dollars and cents, with the decimal point in between. The latter part of second grade also includes a lesson about adding money amounts.
The Lessons page
span
Counting Coins Review ................................. 122
3 pages
Change............................................................ 125
3 pages
Dollars ........................................................... 128
3 pages
Counting Change ........................................... 131
2 pages
120
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Change Maker Determine how many of each denomination you need to make the exact change. Good and clear pictures! Playable in US, Canadian, Mexican, UK, or Australian money. http://www.funbrain.com/cashreg/index.html Using Money Drag the right amount of coins and bills (US) to the answer space to match the given amount. The pictures look a little fuzzy. http://www.mathcats.com/microworlds/usingmoney.html Counting Money Activity from Harcourt Count the coin value and type it into the box and click “Check”. http://www.hbschool.com/activity/counting_money/ Cash Out Give the correct change by clicking on the bills and coins. http://www.mrnussbaum.com/cashd.htm Piggy bank When the coins fall from the top of the screen, choose those that add up to the given amount, and the piggy bank fills. http://fen.com/studentactivities/Piggybank/piggybank.html Money Instructor Checkbook math exercises and worksheets. Includes a checkbook to print, writing dollars and cents worksheet, checking account deposit, checkbook transactions, and word problems. http://www.moneyinstructor.com/checks.asp
121
Counting Coins Review
A quarter 25 cents
Count up →
A dime 10 cents
20 ¢
A nickel 5 cents
A penny 1 cent
25 ¢ 26 ¢ 27 ¢
10 ¢
25 ¢ 35 ¢ 45 ¢ 50 ¢ 51¢
75 ¢
1. How much money? Write down the amount in cents. a. b.
c.
e.
2 quarters 50 cents
d.
f.
g. h.
122
3quarters 75 cents
20 ¢
21 ¢
80 ¢ 85 ¢
You may count each two nickels as ten.
2. How much is the total if you have: a. a quarter and three dimes
b. three quarters and a dime
c. four nickels and four dimes
d. a quarter, a dime, six pennies
e. nine pennies and eight dimes
f. three quarters, two dimes, a penny
3. Cross out the coins you need to buy the item. Write how many cents you have left.
a.
b.
17 ¢
92 ¢ c.
Left ____¢
Left ____¢
d.
58 ¢
e.
Left ____¢
Left ____¢
123
Left ____¢
f.
64 ¢
33 ¢
95 ¢
Left ____¢
Often you have several ways to make a given amount. For example, to make 54 cents, you can use two quarters and four pennies. Or, you may use five dimes and four pennies. Are there any other ways to do it? 4. Find two ways to make these amounts. Use either real money, or draw. a. 26¢
b. 37¢
c. 43¢
d. 53¢
e. 61¢
f. 88¢
5. Remember $1 means 1 dollar, which is 100 cents. How much more is needed to make $1? a.
b.
c.
92¢ + ____¢ = 100¢
70¢ + ____¢ = $1
40¢ + ____¢ = $1
80¢ + ____¢ = $1
74¢ + ____¢ = $1
33¢ + ____¢ = $1
79¢ + ____¢ = $1
64¢ + ____¢ = $1
45¢ + ____¢ = $1
50¢ + ____¢ = $1
58¢ + ____¢ = $1
31¢ + ____¢= $1
124
Change When you buy something in a store, you often do not have the exact amount of money to pay for it. Instead, you give the clerk more money than what the item costs. The clerk then gives you some money back. This is called your change. A pen costs 40¢. You don't have the coins to make exactly 40¢, so you give the clerk 50¢. That is 10¢ too much! But then the clerk gives you back 10¢ — your change. You give:
Your change:
50¢
10¢
Price: 40¢
The clerk gives you back the difference between the price and what you paid. In each problem below, find the change you get back. Think of the DIFFERENCE between the price and what you pay. Or, think how many cents you paid “too much”. That will be your change. You can set up a “play store” to do these problems, using real money, one person as a clerk, and one person as a customer. 1. Write how many cents you give, and how many cents is your change. a.
You give: Your change:
b.
You give:
Your change:
Price: 20¢
______¢
Price: 30¢
______¢
______¢
______¢
c.
You give: Your change:
Price: 35¢
______¢
______¢
125
d.
You give: Your change:
Price: 17¢
______¢
______¢
e.
You give: Your change:
Price: 22¢ ______¢
______¢
g.
You give:
Your change:
Price: 60¢
______¢
______¢
f.
You give: Your change:
Price: 11¢
______¢
______¢
h.
You give:
Your change:
Price: 80¢
______¢
______¢
2. Circle the coins you use to pay. Write how many cents your change is. You have: a. You buy a drink for 55¢.
Change: ______ ¢
You have: b. You buy raisins for 33¢.
Change: ______ ¢
You have: c. You buy a toy for 46¢.
Change: ______ ¢
You have: d. You buy a book for 88¢.
Change: ______ ¢
You have: e. You buy a basket for 75¢.
Change: ______ ¢
You have: f. You buy crayons for 63¢.
Change: ______ ¢
126
3. Practice some more! Figure out the change. a. Paper costs 70¢.
b. A banana costs 41¢.
c. A book costs 94¢.
You give $1.
You give 50¢.
You give $1.
Change: _____¢
Change: _____¢
Change: _____¢
d. A toy costs 20¢.
e. A drink costs 70¢.
f. A towel costs 62¢.
You give 50¢.
You give $1.
You give 75¢.
Change: _____¢
Change: _____¢
Change: _____¢
4. Now you buy many items. First add their prices to find the total. Then find the change. Draw the coins that could be your change. a. A magazine costs 20¢. You buy three of them. You give $1.
Total cost: 60¢ Change: 40¢ b. A toy costs 15¢ and another toy 20¢. You give 50¢.
Total cost: _____ ¢ Change: _____ ¢ c. A lollipop costs 8¢. You buy two of them. You give 20¢.
Total cost: _____ ¢ Change: _____ ¢ d. A pencil costs 5¢. You buy four of them. You give 25¢.
Total cost: _____ ¢ Change: _____ ¢ e. An eraser costs 35¢ and a pencil 10¢. You give 50¢.
Total cost: _____ ¢ Change: _____ ¢
127
Dollars = $1.20 This is one dollar. It is worth 100 cents. $1 or $1.00
= $5.26 This is a five-dollar bill. It is worth 500 cents. $5 or $5.00
Write first the dollars, then a point, then the cents. Use the “$” symbol in front of dollar amounts. Do not use the ¢ symbol.
1. How much money? Write the amount.
a. $________
b. $________
c. $________
d. $________
e. $________
f. $________
g. $________
h. $________
128
2. Write the dollar amount.
$2.15
b. $________
c. $________
d. $________
a.
e. $________
f. $________
If you don't have any dollars, put a zero in the dollars place.
1¢ or $0.01
35¢ or $0.35
6¢ or $0.06
3. Write the amount using the dollar symbol and a decimal point. a.
b.
c.
$________
$________
$________
d.
e.
f.
$________
$________
$________
129
Sometimes you have more than 100 cents. That means you have more than 1 dollar, because 1 dollar is 100 cents.
100¢ or $1.00
105¢ or $1.05
121¢ or $1.21
4. Write the amount in dollars.
a.
b.
$________
$________
c.
d.
$________
$________
5. Draw bills and coins for these amounts. a. $1.32
b. $2.06
c. $2.54
d. $3.80
130
Counting Change When you buy an item, you might not have the exact coins and bills for the amount it costs. You can then pay with a bigger bill, and get back some change. To give change, or to check the change you are given, count up from the price of the item until you reach the amount the customer gives.
Customer gives $1
Count up from the price →
69¢ Customer gives $1
Count up from the price →
34¢
35 ¢ 40 ¢ 50 ¢
75 ¢
70 ¢ 80 ¢ 90 ¢ 100 ¢
100 ¢
The change is these coins. The change is 66 cents.
The change is these coins. The change is 31 cents.
1. Draw the coins for the change.
a.
78¢
Change: _______
Customer gives $1
b.
65¢
Change: _______
Customer gives $1
c.
47¢ Change: _______
Customer gives $1
d.
52¢ Change: _______
Customer gives $1
131
2. Draw the coins for the change.
a.
$1.15
Customer gives $2
b.
Change: _______
$2.30
Customer gives $2.50
c.
Change: _______
$1.78
Customer gives $2
d.
Change: _______
$2.32 Customer gives $3
Change: _______
3. Find the change. You can draw coins or use real money to help. a. A toy: $1.44
b. A drink: $0.88
Customer gives $1.50
Customer gives $1
Change $________
Change $________
c. Coffee: $0.97
d. A pencil set: $1.55
Customer gives $1.00
Customer gives $1.75
Change $________
Change $________
e. A book: $3.25
f. A postcard: $0.35
Customer gives $4
Customer gives $0.50
Change $________
Change $________
132
View more...
Comments
