MathMammoth_Grade1A.pdf
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Copyright 2007-2011 Taina Maria Miller. EDITION 1.8 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.
2
Contents Foreword .............................................................................. 5
Chapter 0: Kindergarten Math Review Introduction ..........................................................................
6
Equal Amounts; Same and Different .................................
7
Writing Numbers .................................................................
8
Counting ...............................................................................
10
Position Words, Colors, and Shapes ..................................
12
Patterns ................................................................................
14
Chapter 1: Addition Within 0-10 Introduction ............................................................................
15
Two Groups and a Total .......................................................
19
Learn Symbols “ + ” and “ = ” .............................................
22
Addition Practice 1 ...............................................................
25
Which is More? .....................................................................
27
Missing Items .........................................................................
29
Sums with 5 ............................................................................
34
Sums with 6 ............................................................................
36
Adding on a Number Line ....................................................
38
Sums with 7 ............................................................................
42
Sums with 8 ............................................................................
45
Addition Practice 2 ...............................................................
48
Sums with 9 ............................................................................
51
Sums with 10 ..........................................................................
55
Comparisons ..........................................................................
59
Review of Addition Facts .......................................................
62
3
Chapter 2: Subtraction Within 0-10 Introduction .............................................................................
66
Subtraction is “Taking Away” ..............................................
69
Count Down to Subtract ........................................................
72
Subtraction and Addition in the Same Picture ....................
76
When Can You Subtract? .....................................................
80
Two Subtractions from one Addition .................................
84
Two Parts — One Total ........................................................
87
Fact Families ...........................................................................
90
How Many More? ..................................................................
94
“How Many More” Problems and Difference ...................
97
“How Many More” Problems and Subtraction .................
101
Review ....................................................................................... 104
Chapter 3: Addition and Subtraction Facts Introduction ...........................................................................
105
Addition and Subtraction Facts with 4 and 5 ...................
107
Addition and Subtraction Facts with 6 ..............................
109
Addition and Subtraction Facts with 7 ..............................
112
Addition and Subtraction Facts with 8 ..............................
114
Addition and Subtraction Facts with 9 ..............................
118
Addition and Subtraction Facts with 10 ............................
121
Adding and Subtracting Many Numbers ...........................
125
Review — Facts with 6, 7, and 8 ............................................ 129 Review — Facts with 9 and 10 ............................................... 131
4
Foreword The Math Mammoth Grade 1-A and Grade 1-B worktexts comprise a complete math curriculum for the first grade mathematics studies. The main topics during first grade are the concepts of addition and subtraction, addition and subtraction facts, and place value till 100. Other topics studied are clock to the half hour, measuring length in inches and centimeters, shapes, and coins. When you use these books as your only or main mathematics curriculum, they can be like a “framework”, but you still have a lot of liberty in planning your child's studies. While addition and subtraction topics are best studied in the order they are presented, feel free to go through the geometry, clock, and money sections in a different order. This might even be advisable if your child is “stuck” on some concept, or is getting bored. Sometimes the brain “chews the cud” in the background, and the concept he/she was stuck on can become 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 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_grade1.htm that you can use to make additional worksheets for computation or for number charts. You can also always simply reprint some already studied pages. Also, the third chapter that practices addition and subtraction facts contains a lot of pages with problems, so you can choose to “save” some of them for later review. I wish you success in your math teaching! Maria Miller, the author
5
Chapter 0: Kindergarten Math Review Introduction This chapter is optional, and can be used to review the most important concepts of kindergarten math:
writing the numerals 0 to 9;
counting up to 20;
position words, color words, and some shapes (circle, triangle, square)
simple patterns
The Lessons in Chapter 0 page
span
Equal Amounts; Same and Different ..........
7
1 page
Writing Numbers ........................................
8
2 pages
Counting .....................................................
10
2 pages
Position Words, Colors, and Shapes ........
12
2 pages
Patterns .......................................................
14
1 page
6
Equal Amounts; Same and Different 1. Write an X for each thing in the other box.
a.
d.
b.
c.
e.
f.
2. Color the shapes that are the same as the first shape.
7
Writing Numbers 1. Write the number.
2. Count and write the number. a.
b.
c.
d.
e.
f.
8
3. Write the number.
4. Count and write the number.
a.
b.
c.
d.
e.
f.
9
Counting 1. Count. Write the number in the box.
a.
b.
c.
d.
e.
f.
g.
h.
2. Count. Write the number. Then circle the number that is MORE.
a.
b.
c.
d.
10
3. Write the missing number below the number line.
a.
b.
c.
4. Circle the group that has more things. Then count ALL (both groups). Write the number in the box below.
a.
d.
b.
c.
e.
f.
11
Position Words, Colors, and Shapes 1. a. Color
RED the top shape.
b. Color
BLUE the bottom shape.
2. a. Color
GREEN the shape on the right.
b. Color
BLUE the shape in the middle.
c. Color
YELLOW the shape on the left.
d. Color
ORANGE two shapes on the right.
e. Color
PURPLE two shapes on the left.
12
c. Color
YELLOW the middle shape.
3. a. Color
GREY two bottom shapes.
b. Color
BROWN two middle shapes.
4. a. Color
GREEN all the circles.
b. Color
ORANGE all the triangles.
c. Color
PURPLE all the squares.
13
c. Color
BLACK two top shapes.
Patterns 1. Continue the pattern for one more shape.
a.
b.
c.
d.
e.
f.
g.
2. Continue counting up or down.
1 2 3 4 5 ____ ____ ____ ____ ____ ____ 10 9 8 7 6 ____ ____ ____ ____ ____ ____ 14
Chapter 1: Addition Within 0-10 Introduction The first chapter of the Math Mammoth Grade 1-A Complete Worktext covers the concept of addition, and addition facts within 0-10. The chapter starts out with very easy addition problems within 0-5, using pictures. If the student does not yet know the symbols “ + ” and “ = ”, you can introduce them orally at first. Use blocks or rocks to make addition problems where you say: “Three blocks and four blocks makes seven blocks. Three blocks PLUS four blocks EQUALS seven blocks.” Play like that until the child can use the words PLUS and EQUALS in his/her own speech. This will make it easier for him/her to use the written symbols. Soon the lessons start including “missing addend” problems. This means problems such as 1 + ___ = 5 or ___ + 3 = 8, where a number to be added is missing. First, we use pictures, and then gradually use symbols only. I feel problems with the missing addends are very important, as they lead the students to learn the connection between addition and subtraction. Keep in mind that children may confuse this problem with 1 + 5 = ___ . To help the children see the difference, you can word these problems like this: “One and how many more makes five?” You can model them by drawing. First draw one ball. Tell the child that we need a total of five balls. He/she needs to draw more until there are five balls. In the missing addend problem (1 + ___ = 5), however many balls the child draws is the number that goes on the empty line. So, first there is one ball, then we need to add (draw) some more to make 5. How many more were drawn? After that, the chapter contains many lessons called Sums with... whose goal is to help the child memorize addition facts. My approach to memorization is many-fold: 1. Structured drill, such as you see in the lessons Sums with 5, Sums with 6, and so on. This is not random drills, because you will start by showing the pattern or the structure in the facts. This will help the student to tie the addition facts in with a context and help him/her understand the facts more on a conceptual level, instead of merely memorizing them at random. In Sums with 5, the child learns the number combinations that add up to 5: 0 and 5, 1 and 4, and 2 and 3. This understanding is the basis for the drills. 2. Using addition facts in games, in math problems, everyday life, or anywhere else. Games are especially useful because they help children like mathematics. 3. Random drilling may also be used as a tool among others. 4. Memory helps such as silly mnemonics or writing math facts on a poster and hanging it on the wall. These are not needed for all children. However, keep in mind that children will need LOTS of opportunities to add numbers to actually memorize the facts, so the memorization may not totally occur as your child works through this chapter. These same addition facts are further studied and used in the next chapters about subtraction, and in all later math work since they are constantly used. At the latest, your child should memorize addition facts during second grade, as recommended by the National Council of Teachers of Mathematics (NCTM). Please see the following page for a few games that I recommend using while studying this chapter. 15
Games 10 Out (or 5 Out or 6 Out etc.) You need: lots of number cards with numbers 1-10, such as regular playing cards without the picture cards, Uno cards without the special cards, etc. Rules: Deal seven cards to each player. Place the rest in a stack in the middle, face down. At his turn, each player may first take one card from the deck. Then, each player may ask for one card from the player on their right (like in 'Go Fish'), and the person has to give it if he has it. Then the player may discard any two cards in his hand that add up to 10, or the card 10 itself. The player who first discards all cards from his hand, wins. Adaptations: * Deal more cards instead of seven. * Deal fewer cards if there are very many players or the players are young. * Allow players to discard three cards that add up to 10. * Instead of ten, players discard cards that add up to 9, 8, 11, or some other number. Use the picture cards for 11, 12, and 13.
Some Went Hiding You need: As many small objects as is the sum you're studying. For example, to study the sums with 5, you need 5 marbles, or 5 blocks, etc. Rules: The first player shows the objects, and quickly hides SOME behind his/her back without showing how many. Then he/she shows the remaining objects to the next player, who has to tell how many went hiding. If the player gives the right answer, it is then his/her turn to hide some and ask the next player to answer. If he gives the wrong answer, he misses his turn. This game appeals best to young children. Adaptations: * Instead of getting a turn, the player may gain points or other rewards for the right answer.
Addition Battle You need: A standard deck of playing cards from which you remove the picture cards, and perhaps also some of the other higher number cards such as tens, nines, and eights. Alternatively, a set of dominoes works well for children who don't yet know their numbers beyond 12. Rules: In each round, each player is dealt two cards face up, and has to calculate the sum. The player with the highest sum gets all the cards from the other players. After enough rounds so that all of the cards are used, the player with the most cards wins. If there is a tie, such as two players have the sum of 11, those players get an additional two cards and “battle” with those to resolve the tie. Adaptations: * This game is easily adapted for subtraction, multiplication, and fractions. You can also use dominoes instead of two playing cards. Any board game where you move the piece by rolling two dice also works to practice addition. 16
The Lessons in Chapter 1 page
span
Two Groups and a Total .................................
19
3 pages
Learn Symbols “ + ” and “ = ” ........................
22
3 pages
Addition Practice 1 .......................................... 25
2 pages
Which is More? ..............................................
27
2 pages
Missing Items .................................................
29
5 pages
Sums with 5 ...................................................
35
2 pages
Sums with 6 ...................................................
36
2 pages
Adding on Number Line .................................
38
4 pages
Sums with 7 ...................................................
42
3 pages
Sums with 8 ...................................................
45
3 pages
Addition Practice 2 .........................................
48
3 pages
Sums with 9 ...................................................
51
4 pages
Sums with 10 .................................................
55
4 pages
Comparisons .................................................
59
3 pages
Review of Addition Facts ...............................
62
3 pages
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Addition Exercise from Dositey.com Write how many worms are on two leaves, and how many together. http://www.dositey.com/addsub/addex1.htm Children's Addition Quiz A set of five interactive addition problems that you answer online. http://www.thegreatmartinicompany.com/Math-Quick-Quiz/addition-kid-quiz.html Number Bond Machines Practice which two numbers add up to a given number. http://www.amblesideprimary.com/ambleweb/mentalmaths/numberbond.html Save the Whale Find how much the given “pipe” length is missing from 10 and save the whale. http://www.ictgames.com/save_the_whale_v4.html
17
Exuberant Eye Games Practice your basic facts with these kid-appealing simple games. http://www.games.exuberanteye.com/ Children' Compare Numbers from Mr. Martini's Classroom Compare two numbers. Press the number below to choose the biggest number that will appear. http://www.thegreatmartinicompany.com/Children-Math/compare-number.html Addition and Subtraction Game from The Little Animals Activity Centre Solve simple addition and subtraction problems by clicking on the ladybug with the right answer. http://www.bbc.co.uk/schools/laac/numbers/chi.shtml Number Line Arithmetic Use this virtual manipulative to illustrate addition on a number line http://nlvm.usu.edu/en/nav/frames_asid_156_g_1_t_1.html Line Jumper Addition questions on a number line. http://www.funbrain.com/funbrain/linejump/index.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 Fun 4 the Brain Practice basic addition with these games. http://www.fun4thebrain.com/addition.html
18
Two Groups and a Total 1. Make two groups. a.
4
1 and 3 d.
5
3 and 2
b.
4
2 and 2
5
e.
2 and 3
c.
4
3 and 1 f.
5
1 and 4
2. Make two groups. Write how many are in the second group. a.
4
1 and _____ d.
5
4 and _____ g.
5
1 and _____
b.
4
2 and _____ e.
5
3 and _____ h.
5
5 and _____
19
c.
4
3 and _____ f.
5
2 and _____ i.
5
0 and _____
3. Draw as many dots as the number shows. Then make two groups however you like. Write how many are in each group. a.
3
_____ and _____ d.
2
_____ and _____
b.
5
_____ and _____ e.
6
_____ and _____
c.
4
_____ and _____ f.
8
_____ and _____
4. The number at the top is the total. Draw the missing dots on the empty die face. Write on the lines how many dots are on each die face. a.
3
_____ and _____ d.
4
_____ and _____
b.
6
_____ and _____ e.
6
_____ and _____
20
c.
5
_____ and _____ f.
5
_____ and _____
2 and 2
4
1 and 4
“Two and two makes four.”
5
“One and four makes five.”
5. Write how many are in each group. Write the total in the box. a.
c.
b.
____ and ____
____ and ____
____ and ____ e.
d.
____ and ____ g.
f.
____ and ____
____ and ____
h.
____ and ____
i.
____ and ____
____ and ____
6. Draw circles for each number. Write the total in the box.
a.
2 and 2
b.
3 and 1
c.
3 and 3
d.
1 and 4
21
Learn Symbols + and =
3
+
2
=
5
1
THREE plus TWO equals FIVE
+
3
=
ONE plus THREE equals FOUR
1. Fill in the numbers. Add. Read the additions aloud using “plus” and “equals”.
a.
1
b.
+
3
=
______
c.
+
______
=
d.
______
+
______
=
______
+
______
=
f.
e.
______
+
______
=
______
g.
+
______
=
h.
______
+
______
=
______
i.
______
+
______
=
j.
+
______
4
=
______
22
+
______
=
2. Write the numbers. Add. Read the additions aloud using “plus” and “equals”. a.
b.
______
+
______
=
c.
______
+
______
______
=
d.
+
______
=
+
______
______
=
3. Add with zero. a.
2
b.
+ 0 = _____
_____ + _____ = _____
c.
d.
_____ + _____ = _____
_____ + _____ = _____
e.
f.
_____ + _____ = _____
_____ + _____ = _____
g.
h.
_____ + _____ = _____
_____ + _____ = _____
23
4. Write how many dots. Then add.
a.
b.
_____ + _____ = _____
_____ + _____ = _____
c.
d.
_____ + _____ = _____
_____ + _____ = _____
e.
f.
_____ + _____ = _____
_____ + _____ = _____
g.
h.
_____ + _____ = _____
_____ + _____ = _____
i.
j.
_____ + _____ = _____
_____ + _____ = _____
24
Addition Practice 1 1. In the second box, draw more to show the second number. Then add.
a.
b.
c.
2 + 1 = ______
3 + 2 = ______
1 + 2 = ______
d.
e.
f.
4 + 1 = ______
2 + 3 = ______
0 + 4 = ______
g.
h.
i.
2 + 2 = ______
1 + 0 = ______
3 + 1 = ______
2. Draw dots in each box for the numbers. Then add.
a.
2 + 2 = ______
d.
4 + 1 = ______
b.
c.
1 + 3 = ______
e.
0 + 5 = ______
f.
2 + 3 = ______
25
1 + 3 = ______
3. Add. If you want to, you can draw balls or sticks to help you.
a.
1 + 2 = ______
b.
3 + 0 = ______
c.
2 + 2 = ______
d.
2 + 3 = ______
e.
1 + 4 = ______
f.
0 + 5 = ______
g.
3 + 2 = ______
h.
2 + 1 = ______
i.
4 + 1 = ______
c.
3 + 1 = ______
4. Add both ways! You can draw marbles to help.
aa.
2 + 3 = 5
b.
3 + 2 = 5
d.
1 + 4 = ______
4 + 1 = ______
1 + 2 = ______
2 + 1 = ______
e.
0 + 2 = ______
2 + 0 = ______
26
1 + 3 = ______
f.
5 + 0 = ______
0 + 5 = ______
Which is More? The symbols < and > are like a “hungry alligator's mouth”. The mouth always opens towards the bigger number.
1 < 4
5 > 3
One is less than four.
Five is greater than three.
< means “LESS THAN”.
> means “GREATER THAN”.
1. Practice writing < and > .
2. Circle the bigger number. Read using “less than” and “greater than”.
a.
1 < 3
b. 2
“1 is less than 3.”
d. 6
< 5
c. 5
“2 is less than 5.”
> 2
e. 4
> 3
“5 is greater than 3.”
> 1
f. 2
< 4
3. Circle the bigger number. Read using “less than” and “greater than”. a.
6 > 0
b.
3 < 4
c.
4 < 5
d.
4 > 3
e.
1 < 2
f.
2 > 1
g.
3 < 5
h.
0 < 4
27
4. Write < or > in the box.
a.
1
4
b.
2
5
c.
6
3
d.
3
4
e.
5
1
f.
2
3
5. Write < or > between the numbers. You can draw circles to help you.
a.
1
4
b.
4
3
c.
2
5
d.
0
4
6. Write < or > between the two numbers. a.
1
4
b.
4
5
c.
2
4
d.
5
3
e.
1
2
f.
3
1
g.
5
4
h.
4
6
i.
3
5
j.
1
0
k.
2
5
l.
0
2
28
Missing Items 5
Something is missing from the addition. The TOTAL is not missing. The total is 5.
+
How many are in the second group? That's what is missing! There should be a total of 5 dots. Draw 4 in the second die face.
1 + ______ 4
There should be a total of 4 dots. The second die face has two. There are none in the first die face, so you need to draw them. Read: “2 plus what number makes 4?” or, “2 and how many more makes 4?” or, “What number and 2 makes 4?”
+ ______ + 2
1. Draw more dots for the addition. Write the missing number. The total is on top.
a.
d.
g.
1
3
5
3
3
5
+
+
+
+ _____
2
b.
+ _____
c.
_____ + 4
5
5
4
+
+
+
+ _____
e.
_____ + 2
f.
_____ + 3
5
4
4
+
+
+
+ _____
h.
_____ + 1 29
i.
_____ + 2
+
+
3 + _____ = 5
_____ +
The TOTAL is now written after the equal sign “ = ”. The answer is 3 + 2 = 5
3 = 4
See the TOTAL written after the equal sign “ = ”. The answer is 1 + 3 = 4
2. Draw more dots to show the missing number. Write the missing number.
+
a.
b.
2 + _____ = 4
+
d.
3 + _____ = 5
+
g.
5 + _____ = 5
j.
1
+
c.
1 + _____ = 1
e.
+
_____ + 1 = 5
f.
_____ + 1 = 4
h.
+
k.
+
+ _____ = 5
_____ + 2 = 2
30
+ 2 + _____ = 3
i.
_____ + 1 = 3
+
+
+ 2 + _____ = 5
l.
+ 3 + _____ = 4
3. Draw more dots in the empty box for the missing number. Read the problems aloud: “2 plus how many makes 4?”
+
a.
2 + ______ = 4
4 + ______ = 4
b.
+
d.
2 + ______ = 5
+
+
c.
______ + 3 = 4 +
+
e.
______ + 1 = 3
f.
______ + 4 = 5
There are no dots in either die face. The first die face is missing the dots. The second die face is supposed to have none, since there is a zero below it. Draw 4 dots in the first die face, because 4 + 0 = 4 .
+ ______ + 0 = 4
4. Draw dots in the boxes for the missing numbers. Notice that some groups are supposed to have zero dots.
a.
0 + ______ = 4
b.
+
d.
3 + ______ = 3
+
+
+
2 + ______ = 2
c.
+
+
e.
______ + 0 = 3
______ + 0 = 2
31
f.
0 + ______ = 1
5. Draw dots to illustrate each addition problem. Find what number is missing.
+
a.
4 + ______ = 5
+
b.
+
d.
3 + ______ = 4
1 + ______ = 5
1 + ______ = 2
c.
+
e.
+
g.
+
+
2 + ______ = 3
f.
+
h.
______ + 3 = 5
______ + 2 = 4 +
______ + 1 = 4
i.
3 + ______ = 3
6. Solve. You can draw dots to help you. Remember, the number after the “ = ” sign is the total.
a.
2 + ______ = 5
b.
______ + 2 = 4
c.
______ + 1 = 3
d.
______ + 3 = 3
e.
3 + ______ = 5
f.
0 + ______ = 2
g.
3 + ______ = 4
h.
______ + 2 = 4
i.
______ + 1 = 5
32
7. Practice “normal” addition.
a.
1 + 1 = ______
b.
2 + 1 = ______
d.
2 + 3 = ______ 1 + 4 = ______
4 + 0 = ______
c.
3 + 1 = ______
e.
0 + 5 = ______ 1 + 2 = ______
1 + 4 = ______ 2 + 2 = ______
f.
3 + 2 = ______ 4 + 1 = ______
8. Find the missing number. The marbles illustrate the total. Notice the patterns! a.
b.
c.
0 + ______ = 3
0 + ______ = 4
0 + ______ = 5
1 + ______ = 3
1 + ______ = 4
1 + ______ = 5
2 + ______ = 3
2 + ______ = 4
2 + ______ = 5
3 + ______ = 3
3 + ______ = 4
3 + ______ = 5
4 + ______ = 4
4 + ______ = 5 5 + ______ = 5
33
Sums with 5
|
1. Five elephants are grouped into two groups, in different ways. The “ ” symbol separates the two groups. Write the addition sentences.
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
2. Add.
a.
4 + 1 = ______
b. 2
+ 3 = ______
c.
1 + 1 = ______
2 + 2 = ______
1 + 3 = ______
0 + 5 = ______
3 + 2 = ______
1 + 4 = ______
1 + 4 = ______
1 + 2 = ______
2 + 1 = ______
3 + 2 = ______
3. Play “5 Out” and/or “Some Went Hiding” with 5 objects (see the introduction).
34
4. Drill. Don't write the answers in the boxes, but just think them in your head.
1+
=5
4+
=5
+2=5
+3=5
2+
=5
3+
=5
+0=5
+1=5
0+
=5
5+
=5
+4=5
+5=5
5. Draw more and compare the problems in each group.
a.
4 + 0 = ______
b. 6
+ 0 = ______
c. 3
+ 0 = ______
4 + 1 = ______
6 + 1 = ______
3 + 1 = ______
4 + 2 = ______
6 + 2 = ______
3 + 2 = ______
d. 7
+ 0 = ______
e. 5
+ 0 = ______
f. 8
+ 0 = ______
7 + 1 = ______
5 + 1 = ______
8 + 1 = ______
7 + 2 = ______
5 + 2 = ______
8 + 2 = ______
6. Draw more things to illustrate the missing number. Write the addition sentence. a.
b.
c.
______ + ______ = 3
______ + ______ = 4
d.
e.
f.
______ + ______ = 5
______ + ______ = 6
______ + ______ = 6
2
+ ______ = 5
35
Sums with 6 1. Six hippos are grouped into two groups, in different ways. Write the addition sentences.
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
| ______ + ______ = ______ 2. Play “6 Out” and/or “Some Went Hiding” with 6 objects (see the introduction). 3. Drill. Don't write the answers but just think them in your head.
1+
=6
4+
=6
+2=6
+3=6
2+
=6
3+
=6
+0=6
+1=6
6+
=6
5+
=6
+4=6
+5=6
4. Add the numbers and write the total on the line.
a.
1 + 5 = ______
b.
2 + 3 = ______
36
c.
4 + 2 = ______
5. Draw more boxes to illustrate the missing number and write it on the line. b.
a.
2 + ______ = 5
2 + ______ = 6 d.
c.
f.
e.
3 + ______ = 6 g.
5 + ______ = 6
1 + ______ = 6 i.
h.
1 + ______ = 5
4 + ______ = 6
0 + ______ = 6
3 + ______ = 5
6. Jack and Jill share 5 cucumbers and 6 lemons in different ways. Find how many Jill gets. For the number shown, you can cover the cucumbers or lemons with your hand to see how many Jill gets. a.
5
b.
6
7. Add.
2 + 3 = ______ Jack gets:
Left for Jill:
Jack gets:
Left for Jill:
4 + 1 = ______
2
1
3 + 3 = ______
1
4
4 + 2 = ______
5
5
1 + 3 = ______
3
0
1 + 5 = ______
0
2
2 + 2 = ______
4
3
2 + 4 = ______ 37
Adding on a Number Line 5 + 3 = 8
First jump 5...
Then jump 3 more.
You land on 8.
1. Draw the jumps to illustrate the addition and find the answer. You can use a different color for each number when you draw the jumps.
a.
5 + 2 = ______
b.
4 + 1 = ______
c.
6 + 3 = ______
d.
9 + 1 = ______
e.
7 + 3 = ______
f.
4 + 3 = ______
38
OR....
5+3=8
First draw an arrow that is 5 long. Then draw an arrow that is 3 long.
2. Write the addition sentence.
a.
______ + ______ = ______
b.
______ + ______ = ______
c.
______ + ______ = ______
d.
______ + ______ = ______
e.
______ + ______ = ______
f.
______ + ______ = ______
g.
______ + ______ = ______ 39
3. Draw arrows (or jumps) to show the addition.
a.
7 + 2 = ______
b.
2 + 3 = ______
c.
5 + 4 = ______
d.
7 + 1 = ______
e.
6 + 4 = ______
f.
4 + 2 = ______
g.
9 + 1 = ______
h.
1 + 5 = ______
40
4. Write the addition sentence for each picture. If the child is not familiar with numbers greater than 10, you can skip these.
a.
______ + ______ = ______
b.
______ + ______ = ______
c.
______ + ______ = ______
5. Add “1”, add “2” to the number. Use the number line to help.
a.
b.
c.
d.
7 + 1 = ______
5 + 1 = ______
6 + 1 = ______
8 + 1 = ______
7 + 2 = ______
5 + 2 = ______
6 + 2 = ______
8 + 2 = ______
e.
f.
g.
h.
10 + 1 = ______
12 + 1 = ______
13 + 1 = ______
11 + 1 = ______
10 + 2 = ______
12 + 2 = ______
13 + 2 = ______
11 + 2 = ______
41
Sums with 7 1. Seven marbles are grouped into two groups, in different ways. Write the addition sentences.
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
2. Drill. Don't write the answers here. Just think them in your head.
5+
=7
2+
=7
6+
=7
+3=7
+7=7
3+
=7
1+
=7
0+
=7
+2=7
+1=7
7+
=7
4+
=7
4+
=7
+6=7
+5=7
3. Add. a.
b.
c.
d.
3 + 3 =______
5 + 2 = ______
6 + 1 = ______
2 + 5 = ______
3 + 4 = ______
4 + 2 = ______
4 + 3 = ______
4 + 2 = ______
42
4. Play “7 Out” and/or “Some Went Hiding” with 7 objects (see the introduction). 5. Fill in the missing numbers. You may draw dots to help. Notice the patterns! a.
b.
c.
0 + ______ = 7
0 + ______ = 6
0 + ______ = 5
1 + ______ = 7
1 + ______ = 6
1 + ______ = 5
2 + ______ = 7
2 + ______ = 6
2 + ______ = 5
3 + ______ = 7
3 + ______ = 6
3 + ______ = 5
6. This is a new way to write addition! The answer goes under the line. a.
4 + 3
b.
1 + 5
c.
5 + 0
d.
4 + 1
e.
4 + 0
7 f.
2 + 5
g.
0 + 3
h.
1 + 3
i.
3 + 3
j.
2 + 2
k.
4 + 2
l.
2 + 0
m.
1 + 6
n.
3 + 4
o.
2 + 4
43
7. Solve the word problems. Draw pictures to help you! Think: Are you asked the TOTAL? Or do you already know the total? a. Lisa has three goldfish and Lauren
b. Paul has seven T-shirts. Two of
has six. How many goldfish do they have together?
them are red. How many are not red?
c. A fish bowl has four fish swimming
d. Paul has nine toy cars. Six of them
in it. Lisa added four more. How many fish are now in it?
are in the living room. The rest of them Paul cannot find. How many cars are missing?
e. Jill wants to have hats for all
f. Brenda ate two cookies, and later she
seven of her dolls. She has found three hats so far. How many does she still need?
ate four more. How many cookies did she eat in all?
+ What numbers can go into these puzzles?
= 6
+
+ +
+ +
= 5
= 5
= 6
44
= 7 +
+ = 7
= 6 = 6
Sums with 8 1. Eight marbles are grouped into two groups, in different ways. Write the additions.
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
| ______ + ______ = ______ 2. Drill. Don't write the answers here. Just think them in your head.
+5=8
+4=8
2+
=8
3+
=8
8+
=8
+0=8
+6=8
5+
=8
7+
=8
6+
=8
+2=8
+3=8
1+
=8
4+
=8
3. Play “8 Out” and/or “Some Went Hiding” with 8 objects (see the introduction).
45
+ 1=8
4. Fill in the missing numbers. You may draw dots to help. Notice the patterns! a.
b.
c.
1 + ______ = 8
1 + ______ = 7
1 + ______ = 6
2 + ______ = 8
2 + ______ = 7
2 + ______ = 6
3 + ______ = 8
3 + ______ = 7
3 + ______ = 6
4 + ______ = 8
4 + ______ = 7
4 + ______ = 6
5. Draw more marbles. Write the additions.
a. ______
+ ______ = 6
b. ______
+ ______ = 5
c. ______
+ ______ = 6
d. ______
+ ______ = 8
e. ______
+ ______ = 7
f. ______
+ ______ = 4
g. ______
+ ______ = 8
h. ______
+ ______ = 8
46
6. Find the missing numbers. a.
b.
c.
d.
3 + 4 =______
6 + 2 = ______
6 + 1 = ______
2 + 5 = ______
4 + 4 = ______
5 + 2 = ______
1 + 7 = ______
2 + 6 = ______
e.
f.
g.
h.
5 + ______ = 7
4 + ______ = 8
3 + ______ = 7
2 + ______ = 8
5 + ______ = 8
4 + ______ = 7
3 + ______ = 8
2 + ______ = 7
7. Add. a.
4 + 2
b.
6 + 2
c.
3 + 3
d.
7 + 1
e.
5 + 2
f.
1 + 2
g.
6 + 1
h.
4 + 3
i.
5 + 1
j.
3 + 2
8. Which number is greater? Or are they equal? Write < or > or = . (Write one of the alligator mouths or the equal sign). a.
7
e.
8
i.
4
=
7
b.
7
8
c.
6
4
4
f.
2
2
g.
0
0
4
j.
1
5
k.
6
8
47
10
10
h.
8
7
l.
2
0
d.
Addition Practice 2 1. Draw the number of triangles asked for. Write an addition sentence. a. Draw 3 more
b. Draw 2 more
_______ + _______ = _______
_______ + _______ = _______ d. Draw 3 more
c. Draw 5 more
_______ + _______ = _______
_______ + _______ = _______
e. Draw 3 more
f. Draw 4 more
_______ + _______ = _______
_______ + _______ = _______
2. Double means two times the same thing! Draw dots or sticks. Write the total in the box.
II
II
a. Double 2
b. Double 3
c. Double 4
d. Double 5
e. Double 6
f. Double 1
48
3. Add. a.
b.
c.
4 + 4 = ______
4 + 3 = ______
2 + 4 = ______
6 + 1 = ______
5 + 2 = ______
5 + 1 = ______
6 + 2 = ______
3 + 2 = ______
1 + 6 = ______
4. Draw jumps for each of the additions. Find the answer.
a.
4 + 2 = ______
b.
6 + 1 = ______
c.
7 + 3 = ______
d.
3 + 6 = ______
e.
2 + 5 = ______
f.
1 + 8 = ______
49
5. You can add either way! Which way is easier? a.
b.
c.
d.
7 + 2 = ______
2 + 5 = ______
6 + 2 = ______
1 + 4 = ______
2 + 7 = ______
5 + 2 = ______
2 + 6 = ______
4 + 1 = ______
6. Let's make charts! In the first chart, add one each time. Then, add two each time. Then, add three each time. a.
b.
c.
Add 1
Add 2
Add 3
2 + 2 = ______
2 + 3 = ______
6 + 1 = ______
3 + 2 = ______
3 + 3 = ______
7 + 1 = ______
4 + 2 = ______
4 + 3 = ______
8 + 1 = ______
5 + 2 = ______
5 + 3 = ______
9 + 1 = ______
6 + 2 = ______
6 + 3 = ______
5 +1=
6
7. Fill in the addition tables. Add the number above and the number to the left.
+ 4 5 6
50
1
2
3
Sums with 9 1. Nine marbles are grouped into two groups, in different ways. Write the addition sentences.
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
2. Drill. Don't write the answers here. Just think the answers in your head.
+8=9
+4=9
2+
=9
3+
=9
7+
+2=9
+6=9
9+
=9
6+
=9
+1=9
+7=9
+3=9
0+
=9
4+
=9
+5=9
3. Play “9 Out” and/or “Some Went Hiding” with 9 objects (see the introduction).
51
=9
4. What numbers make up nine? Fill in the missing numbers. a.
______ + 0 = 9
b.
6 + ______ = 9
c.
8 + ______ = 9
d.
______ + 4 = 9
e.
2 + ______ = 9
f.
3 + ______ = 9
5. Fill in the missing numbers. You may draw dots to help. Notice the patterns! a.
b.
c.
1 + ______ = 7
1 + ______ = 8
1 + ______ = 9
2 + ______ = 7
2 + ______ = 8
2 + ______ = 9
3 + ______ = 7
3 + ______ = 8
3 + ______ = 9
4 + ______ = 7
4 + ______ = 8
4 + ______ = 9
6. Add. a.
2 + 5
b.
1 + 6
c.
4 + 4
d.
7 + 1
e.
7 + 2
f.
3 + 5
g.
4 + 2
h.
3 + 4
i.
1 + 5
j.
4 + 5
52
7. Solve the word problems. Write an addition sentence or a missing addend sentence for each problem. Think: “ Is it asking the TOTAL? Or, do I already know the total, and something else is asked?” You can draw a picture to help! a. Mom has 2 eggs at home.
b. You see four crayons in the crayon
The cake recipe calls for five eggs. How many more eggs will she need?
box and the rest of them are lost. The full box has eight crayons. How many crayons are missing?
c. Jenny and Penny both have five
d. You have two dollars.
goldfish. How many do they have together?
Can you buy a doll for 11 dollars?
Daddy has ten dollars. How much money do you have together? Can you buy the doll together?
Betty has three goldfish. How many do the three girls have together?
e. There are two red chairs in the living
f. Joshua has five dollars. He wants to
room and six red chairs in the kitchen, and none in the other rooms. How many red chairs are in the house?
buy a truck for seven dollars. How many more dollars will he need?
g. If you have eight dollars, and a gift
h. Jack bought nails for five dollars and
for mom costs $10, how much more money do you need?
screws for four dollars. How much money did he spend in all?
53
First add 3 + 2. It is 5. Do not write 5 in the box!
3+2
4
↓
↓
5
4
Then compare 5 and 4. Five is greater. Draw > .
8. First add. Write the answer below (not in the box!). Then write < or > or = . a.
5+2
4
↓
↓
b.
4+4
7
↓
↓
4
c.
1+1
2
↓
↓
d.
3+6
7
↓
↓
7
9. First add. Think the answer in your mind. Then compare and write < or > . a.
1+4
3
b.
2+2
5
c.
0+0
2
d.
5+3
7
e.
4+4
9
f.
3+5
6
g.
6+2
7
h.
3+4
8
What numbers can go into the puzzles?
+ +
= 9 +
+ = 10
+ +
= 9
= 9 +
+
= 8
= 9
54
= 8 = 8
Sums with 10 1. Ten marbles are grouped into two groups, in different ways. Write the additions.
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
|
|
______ + ______ = ______
______ + ______ = ______
| ______ + ______ = ______ 2. Play “10 Out” and/or “Some Went Hiding” with 10 objects (see the introduction).
55
3. Drill. Don't write the answers here. Just think of the answers in your head.
+ 6 = 10
+ 4 = 10
1+
= 10
6+
= 10
3+
= 10
+ 3 = 10
+ 5 = 10
7+
= 10
9+
= 10
4+
= 10
+ 8 = 10
+ 9 = 10
2+
= 10
5+
= 10
8+
= 10
4. Fill in the missing numbers. You may draw dots to help. Notice the patterns! a.
b.
c.
2 + ______ = 10
2 + ______ = 9
2 + ______ = 8
3 + ______ = 10
3 + ______ = 9
3 + ______ = 8
4 + ______ = 10
4 + ______ = 9
4 + ______ = 8
5 + ______ = 10
5 + ______ = 9
5 + ______ = 8
5. Connect two numbers together if they make ten.
4
1
6
4
4
3
5
2
3
8
2
2
3
7
1
9
2
5
3
6
5
7
5
7
9
0
3
2
3
8
56
6. Which number is greater? Or are they equal? Write < or > or = . (Write one of the alligator mouths or the equal sign). a.
6
7
e.
8
6
b.
f.
10
8
5
5
c.
6
8
g.
9
8
d.
10
10
5
10
h.
7. First add. Think the answer in your mind. Then compare and write < or > or = . a.
1+9
9
b.
4+4
9
c.
5+2
6
d.
5+4
9
e.
5+5
10
f.
3+5
7
g.
6+3
10
h.
7+1
7
8. What numbers add up to ten? Fill in the missing numbers. a.
b.
c.
______ + 10 = 10
6 + ______ = 10
______ + 3 = 10
______ + 5 = 10
2 + ______ = 10
______ + 8 = 10
______ + 1 = 10
4 + ______ = 10
______ + 9 = 10
9. Draw a line to the correct answer.
7
7+1 2+6 3+4 5+2 4+4 1+6 5+3
8
9
57
7+3 3+6 4+6 1+8 5+4 3+7 2+8
10
10. Solve the word problems. a. There were three birds in
b. Tina has seven books from
the tree. Seven more flew in. How many birds are now in the tree?
the library. She has read three. How many books has she not read?
c. Jessica has ten dolls. She
d. Larry has three toy cars
sees four of them in her room. How many are elsewhere?
and his brother has three. How many do they have together?
e. Bill has ten toy cars but
f. Jack saw two birds on
he can only find six. How many are missing?
the lawn and five on the fence. How many birds did he see in all?
g. Together, Jessica and Jenny have
h. The store has ten dolls.
ten books. Jenny has five. How many does Jessica have?
Two of them are on the bottom shelf. The rest are on the top shelf. How many dolls are on the top shelf?
58
Comparisons =
=
= means “EQUAL”
6=2+4
7=7 Seven equals seven.
Six equals two plus four.
means
“LESS THAN”
78
3+45
means
Seven is less than eight.
Three plus four is greater than five.
“GREATER THAN”
1. First add. Think the answer in your mind. Then compare and write < or > or = . a.
4+1
5
b.
7
4+4
d.
2+5
7
e.
5
5+0
g.
2+2
3
h.
9
9
c.
f.
i.
6
2+3
10
5+5
2
2+2
2. Pick a number to write on the line so the comparison is true. a. 5 6 7
b. 4 5 6
c. 5 6 7
d. 2 3 4
_______ < 6
_______ < 5
______ > 6
______ > 3
e. 9 7 5
f. 3 6 9
g. 1 3 7
h. 2 4 6
______ > 7
_______ < 5
______ > 6
_______ < 3
59
3. Pick a number to write on the line so the comparison is true. a. 2 3 4
b. 4 5 6
c. 1 2 3
2 + _______ < 6
1 + _______ < 6
4 + _______ < 7
d. 4 5 6
e. 4 5 6
f. 7 8 9
2 + ______ > 6
1 + ______ = 6
1 + ______ > 9
g. 6 7 8
h. 2 4 6
i. 4 5 6
2 + ______ = 10
3 + _______ < 7
4 + ______ > 8
4. Compare. Write < , , or = .
a.
4+3
5
b. 7
+1
9
c.
4
4+2
d.
2+5
8
e.
3+4
6
f.
6
3+3
g.
8+2
10
h.
9+2
9
i.
2
2+1
5. Challenges! First add. Think the answers in your mind. Write < , > , or = .
7 +3
2+8
b.
1+1
1+4
d.
5+6
6+5
e.
2+5
2+2
g.
2+4
2+1
11 + 0
0 + 11
a.
h.
60
c.
4
1+4
f.
3
3+1
i.
0
0+0
6. What numbers add up to 10? Draw arrows to illustrate the addition sentences.
a.
______ + ______ = 10
b.
______ + ______ = 10
c.
______ + ______ = 10
d.
______ + ______ = 10
e.
______ + ______ = 10
7. Fill in as much of the addition table as you can, and don't worry about the rest. Color the square blue if the answer is 8.
+
1
2
3
4
0 1 2 3 4 5
61
5
6
7
Review of Addition Facts 1. Write different sums of 5 and sums of 6.
5 = ______ + ______
6 = ______ + ______
5 = ______ + ______
6 = ______ + ______
5 = ______ + ______
6 = ______ + ______
5 = ______ + ______
6 = ______ + ______
2. Draw a line to the correct answer.
4+1 2+3 3+3 5+0 4+2 5+1 0+6 1+4 2+4
5
3. Find the missing addends
6
______ + 2 = 6
______ + 0 = 6
2 + ______ = 5
0 + ______ = 5
1 + ______ = 5
3 + ______ = 6
6 + ______ = 6
4 + ______ = 6
______ + 1 = 6
______ + 4 = 5
4. Compare. Write < , > , or = .
2+2
5
4+4
5
2+4
6
2+3
5
5+5
5
2+5
6
2+4
5
5+0
5
2+6
6
62
5. Write different sums of 7 and sums of 8.
7 = ______ + ______
8 = ______ + ______
7 = ______ + ______
8 = ______ + ______
7 = ______ + ______
8 = ______ + ______
7 = ______ + ______
8 = ______ + ______
7 = ______ + ______
8 = ______ + ______
7 = ______ + ______
8 = ______ + ______
6. Draw a line to the correct answer.
4+3 2+6 3+5 4+4 5+2 1+6 5+3 7+1 6+2
7
7. Find the missing addends
8
______ + 2 = 7
______ + 4 = 8
______ + 4 = 7
3 + ______ = 7
2 + ______ = 8
3 + ______ = 8
5 + ______ = 8
7 + ______ = 8
6 + ______ = 7
5 + ______ = 7
8. Compare. Write < , > , or = .
3+3
7
6+1
7
6+4
8
4+3
7
6+6
7
4+4
8
5+3
7
6+4
7
5+4
8
63
9. Write different sums of 9 and sums of 10.
9 = ______ + ______
10 = ______ + ______
9 = ______ + ______
10 = ______ + ______
9 = ______ + ______
10 = ______ + ______
9 = ______ + ______
10 = ______ + ______
9 = ______ + ______
10 = ______ + ______
9 = ______ + ______
10 = ______ + ______
10. Draw a line to the correct answer.
9
2+7 3+6 4+6 5+5 9+1 1+8 5+4 3+7 2+8
11. Find the missing addends
10
______ + 2 = 10
______ + 6 = 9
______ + 4 = 9
7 + ______ = 10
2 + ______ = 9
3 + ______ = 9
5 + ______ = 10
7 + ______ = 9
6 + ______ = 10
4 + ______ = 10
12. Compare. Write < , > , or = .
2+6
9
6+6
10
10 + 4
10
4+6
9
5+5
10
10 + 0
10
3+6
9
4+4
10
10 + 7
10
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13. Add. a.
b.
c.
d.
8 + 1 = ______
4 + 1 = ______
0 + 0 = ______
5 + 3 = ______
6 + 2 = ______
10 + 0 = ______
9 + 1 = ______
0 + 4 = ______
1 + 7 = ______
3 + 6 = ______
7 + 1 = ______
4 + 4 = ______
3 + 4 = ______
6 + 4 = ______
6 + 3 = ______
4 + 5 = ______
14. Fill in the addition table as much as you can.
+
2
4
3
6
7
5
8
1 3 4 2
represents a number, and represents another number. Solve what they are in each case (a, b, and c). Hint: Make a guess! Then check if your guess is correct. If not, change your guess. a.
b.
c.
+
=6
+
= 7
+
=8
+
= 10
65
+
+ +
=7 =5
Chapter 2: Subtraction Within 0-10 Introduction The second chapter of the Math Mammoth Grade 1-A Complete Worktext covers the concept of subtraction, its various meanings, and addition/subtraction connection.
The concept of subtraction If your child does not yet know the word “minus”, it is a good idea to introduce it first orally. Simply use blocks, rocks, or other concrete objects. For example, show the child eight blocks, and take away three blocks. Then use both kinds of wordings: “Eight blocks, take away three blocks, leaves five blocks. Eight blocks minus three blocks equals five blocks.” Play with the blocks or other concrete objects until the child can use the words “minus” and “equals” in his/her own speech. This will make it much easier to introduce the actual written symbols. In the first lessons, the child can figure out the subtraction problems by simply counting how many objects are left.
Subtraction vs. addition So, how does the student learn how to subtract without actually counting concrete objects or pictures? As a transitional strategy, we will study counting down: the student solves 9 − 3, for example, by counting down three steps from nine: eight, seven, six. So the answer is six. However, the final goal is to learn to use the addition facts to find the answer to subtraction problems. For example, once the student knows that 5 + 5 = 10, then this fact is used to solve 10 − 5 = 5. For this purpose, the student must learn well the connection between addition and subtraction. This is why this book concentrates heavily on the connection between addition and subtraction with several lessons, ending up with the concept of fact families.
Other meanings of subtraction Besides “taking away”, subtraction is also used for these two situations:
Finding how much more one number is than another. Note that no one “takes away” anything in this situation. For example, if you have 3 dollars and you need 6 dollars, how many more dollars do you need? The student is instructed to write a “how many more” addition problem for this, which looks like this: 3 + ___ = 6. We also call these problems “missing addend” problems. It can be solved by remembering the addition fact 3 + 3 = 6, or by subtracting 6 − 3 = 3.
Two (or more) parts (of something) make up a whole. If you know the whole and one of its parts, you can figure out the other part. For example, if there are 10 white and red flowers, and seven of them are white, how many are red? We know the “parts” (the red and white flowers) add up to 10, so we write an addition 7 + __ = 10. Again, this can be solved by subtracting, or simply by knowing the addition fact 7 + 3 = 10.
These two situations are taught explicitly and can be found in the word problems throughout this chapter.
66
The Lessons in Chapter 2 page
span
Subtraction Is “Taking Away” .................................. 69
3 pages
Count Down to Subtract .........................................
72
4 pages
Subtraction and Addition in the Same Picture ........
76
4 pages
When Can You Subtract? .......................................
80
4 pages
Two Subtractions from One Addition ......................
84
3 pages
Two Parts — One Total ............................................
87
3 pages
Fact Families ..........................................................
90
4 pages
How Many More ...................................................
94
3 pages
“How Many More” Problems and Difference ..........
97
4 pages
“How Many More” Problems and Subtraction ........ 101
3 pages
Review ....................................................................
1 page
104
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Kids' Subtraction Quiz from Mr. Martini's Classroom Five problems to solve online. You can choose the highest number used from the list of numbers below the quiz. http://www.thegreatmartinicompany.com/Math-Quick-Quiz/subtraction-kid-quiz.html Subtraction Mystery Picture Find out the picture behind the tiles by solving subtraction questions within 0-10. http://www.dositey.com/addsub/Mystery4.htm Matching Pictures to Number Sentences Find the correct number sentence to go along with the picture. http://www.haelmedia.com/html/mc_m1_001.html Match Pictures to Number Sentences Match pictures to either addition or subtraction number sentences. http://www.haelmedia.com/html/mc_m1_001.html Addition and Subtraction Game from The Little Animals Activity Centre Solve simple addition and subtraction problems by clicking on the ladybug with the right answer. http://www.bbc.co.uk/schools/laac/numbers/chi.shtml Subtraction Game from Count Us In Subtract two numbers which bowls a ball down a bowling alley lane. http://www.abc.net.au/countusin/games/game8.htm
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Take It Away Subtract and click on the correct answer. http://www.primarygames.com/takeaway/start.htm Subtraction Pinball When the ball hits numbers, it defines a problem. Next you choose the correct answer. http://www.playkidsgames.com/games/pinball/subtraction/defaultk1.htm Simple Subtraction Help the duck fly faster by clicking on the cloud with the correct answer. http://www.toonuniversity.com/flash.asp?err=513&engine=12 Save the Apples! Click on the correct basket to get the monkey to carry the apple basket. A crocodile is waiting! http://www.playkidsgames.com/games/apples/savetheApples.htm Busy Bees Figure out how many of the 10 bees went inside the hive. http://www.hbschool.com/activity/busy_bees/index.html Soccer Subtraction Click to make the players disappear until the subtraction sentence is true. http://www.ictgames.com/soccer_subtraction.html Math Carts A downloadable racing game for young students to memorize addition and subtraction facts. Children choose various animal themed carts and unlock new carts and race tracks as they progress through the facts. There are three difficulty levels. Price: Free http://sandbox.yoyogames.com/games/163070-math-carts Tux Math A versatile arcade game for math facts with many options. Includes all operations. You need to shoot falling comets that can damage penguins' igloos. See also my review. Price: Free http://sourceforge.net/projects/tuxmath
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Subtraction is “Taking Away” From five bananas we take away three.
There are two left.
5 – 3
=
2
Five minus three
equals
two
From six carrots we take away one.
There are five left.
6 – 1
=
5
Six minus one
equals
five
1. Cross out the correct number. How many are left? Read each subtraction sentence aloud using the words “minus” and “equals”. 10 total. Cross out 4. How many are left?
a.
10 – 4 = ______
8 total, cross out 7.
d.
8 – 7 = ______
6 total. Cross out 6. How many are left?
b.
6 – 6 = ______
8 total, cross out 6.
e.
8 – 6 = ______
69
8 total. Cross out 2. How many are left?
c.
8 – 2 = ______
7 total, cross out 3.
f.
7 – 3 = ______
9 total, cross out 3.
g.
9 – 3 = ______
6 total, cross out 2.
h.
Cross out 5.
6 – 2 = ______
10 total, cross out 7.
i.
10 – 7 = ______ Cross out 5.
Cross out 4.
j.
9 – 5 = ______
k.
8 – 4 = ______
l.
m.
6 – 3 = ______
n.
6 – 5 = ______
o.
10 – 5 = ______
5 – 5 = ______
2. Subtract. Cover the crossed-out objects with your finger to see how many are left. Read each sentence using the words “minus” and “equals”.
a.
5 – 1 = ______
b.
6 – 3 = ______
c.
5 – 3 = ______
d.
4 – 1 = ______
e.
5 – 2 = ______
f.
6 – 2 = ______
g.
9 – 3 = ______
h.
7 – 1 = ______
i.
7 – 2 = ______
j.
8 – 2 = ______
k.
7 – 3 = ______
l.
8 – 4 = ______
70
3. Draw small circles to illustrate the numbers and cross out some of them to match the subtraction problem.
a.
8 – 3 = ______
b.
d.
7 – 2 = ______
e.
g.
6 – 3 = ______
h.
j.
9 – 5 = ______
k.
5 – 1 = ______
10 – 1 = ______
7 – 3 = ______
10 – 6 = ______
c.
f.
i.
l.
10 – 7 = ______
9 – 7 = ______
10 – 4 = ______
6 – 4 = ______
4. Write a subtraction sentence to match the picture.
a.
_____ – _____ = ______
b.
_____ – _____ = ______
c.
_____ – _____ = ______
d.
_____ – _____ = ______
e.
_____ – _____ = ______
f.
_____ – _____ = ______
71
Count Down to Subtract Count 4 steps backwards from 7. You end up at 3.
7
–
4
= 3
“Seven” “Six, five, four, three.” Start. Count down FOUR steps.
You can also use a single arrow:
1. Draw steps (or a single arrow) to illustrate the subtraction sentence.
a.
7 – 2 = _______
b.
8 – 4 = _______
c.
6 – 5 = _______
d.
9 – 3 = _______
e.
10 – 3 = _______
72
2. Write the subtraction sentence that the arrows illustrate.
a.
______ – ______ = 2
b.
______ – ______ = 3
c.
______ – ______ = 2
d.
______ – ______ = 5
3. Draw an arrow for the subtraction sentence and solve.
a.
10 – 5 = _______
b.
7 – 6 = _______
c.
4 – 4 = _______
d.
8 – 4 = _______
e.
10 – 1 = _______
f.
7 – 5 = _______
73
4. Write the previous and the next numbers. a.
______, 5 , ______
b.
______, 2 , ______
c.
______, 8 , ______
d.
______, 6 , ______
e.
______, 4 , ______
f.
______, 9 , ______
5. Write the two previous numbers. a.
______, ______, 7
b.
______, ______, 4
c. ______,
d.
______, ______, 6
e.
______, ______, 2
f. ______,
______, 10 ______, 8
To subtract without any pictures or objects, you can count down in your mind. Count down as many steps as what you need to take away or subtract.
8 “Eight” Start.
– 3
=5
10
“Seven, six, five.” Count down THREE steps.
“Ten” Start.
– 2
=8
“Nine, eight.” Count down TWO steps.
6. Subtract one. The answer is just the previous number! a.
b.
c.
d.
6 – 1 = ______
5 – 1 = ______
9 – 1 = ______
4 – 1 = _____
8 – 1 = ______
7 – 1 = ______
3 – 1 = ______
10 – 1 = _____
7. Subtract 2 or 3. You can count down. Compare the problems. a.
b.
c.
d.
6 – 2 = _____
9 – 2 = _____
7 – 2 = _____
10 – 2 = _____
6 – 3 = _____
9 – 3 = _____
7 – 3 = _____
10 – 3 = _____
74
8. Solve the word problems. Write a subtraction sentence for each. a. There were 7 birds in a tree.
b. Mom has 10 silver plates in
Three flew away. How many are left?
the cupboard. She took out four. How many are still in the cupboard?
c. All 9 girls in the class were jumping
d. Josh took five of his 10 toy cars to
rope. Then four of them left. How many kept on jumping?
a friend's house. How many cars did he leave at home?
e. Of her eight puzzles, Fanny put three
f. Tina had 6 bunches of flowers.
in the closet. How many were left to play with?
She sold six of them. How many were left?
9. Do these problems if you know the numbers past 10. The number line will help.
a.
14 – 2 = _______
b.
14 – 4 = _______ d.
17 – 2 = _______ 17 – 3 = _______
16 – 1 = _______
c.
16 – 3 = _______ e.
12 – 1 = _______ 12 – 2 = _______
75
11 – 3 = _______ 11 – 4 = _______
f.
13 – 2 = _______ 13 – 3 = _______
Subtraction and Addition in the Same Picture How many colored circles? How many white ones?
4
+ 6
= 10
3 + 4
Cover the colored circles.
Cover the colored circles. Write a subtraction sentence.
10 – 4 =
=7
7– 3 = 4
6
1. Make an addition sentence and a subtraction sentence from the same picture. a.
b.
______ + ______ = ______
______ + ______ = ______
7 – ______ = ______
6 – ______ = ______
c.
d.
______ + ______ = ______
______ + ______ = ______
5 – ______ = ______
6 – ______ = ______
e.
f.
______ + ______ = ______
______ + ______ = ______
8 – ______ = ______
6 – ______ = ______
76
2. Make an addition sentence and a subtraction sentence for the same picture. b.
a.
______ + ______ = ______
______ + ______ = ______
______ – ______ = ______
______ – ______ = ______
c.
d.
______ + ______ = ______
______ + ______ = ______
______ – ______ = ______
______ – ______ = ______
3. In each problem, draw circles and then color some circles to fit the addition sentence. Then cover the COLORED circles and make a subtraction sentence.
a.
7 + 1 = ______
b.
______ – ______ = ______
c.
______ – ______ = ______
2 + 3 = ______
d.
______ – ______ = ______
e.
6 + 3 = ______
2 + 5 = ______
______ – ______ = ______
7 + 4 = ______
f.
______ – ______ = ______
3 + 3 = ______
______ – ______ = ______
77
4. Cover the colored objects, and write a subtraction sentence to fit the picture.
a.
b.
______ – ______ = ______
______ – ______ = ______
c.
d.
______ – ______ = ______
______ – ______ = ______
e.
f.
______ – ______ = ______
______ – ______ = ______
g.
h.
______ – ______ = ______
______ – ______ = ______
5. In each problem, draw some circles and color some circles to fit the addition sentence. Then cover the COLORED circles and make a subtraction sentence.
9 + 1 = ______
a.
b.
______ – ______ = ______
c.
7 + 2 = ______
______ – ______ = ______
10 + 4 = ___
d.
______ – ______ = ______
10 + 2 = ___
______ – ______ = ______
78
6. Draw circles to fit the subtraction sentence. Write an addition sentence too.
a.
9 – 4 = ___
b.
______ + ______ = ______
c.
______ + ______ = ______
8 – 5 = ___
d.
______ + ______ = ______
e.
10 – 5 = ___
8 – 4 = ___
______ + ______ = ______
7 – 4 = ___
f.
______ + ______ = ______
9 – 8 = ___
______ + ______ = ______
First subtract and add. But do not write the answers! Just think them in your mind. Then compare, and write < or > or = .
3
3–1
6+5
6
10
10 – 1
9–7
8–7
6–4
2+3
8–5
5+3
5+2
8+2
10 – 1
10 – 3
7–4
8–5
10 – 2
8–2
10 + 0
10 – 0
8–1
8+1
79
When Can You Subtract? Sometimes we cannot really do the subtraction problem. For example:
3 – 0 = ______
3 – 4 = ??
3 – 1 = ______
3 – 5 = ??
3 – 2 = ______
3 – 6 = ??
3 – 3 = ______
We cannot take away four or five or six objects when there are only three!
These we can do!
1. Write the subtraction problems you can do when there are... ...four triangles
...six circles
...five sticks
IIIII 4 – 0 = ____
6 – 0 = ____
____ – ____ = ____
4 – 1 = ____
____ – ____ = ____
____ – ____ = ____
4 – 2 = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
You cannot do the subtraction problem when the second number is __________________ than the first number. (Or if you do, you go into debt!)
80
2. Count down to subtract.
a.
b.
c.
d.
7 – 1 = ______
9 – 1 = ______
10 – 1 = ______
12 – 1 = ______
7 – 2 = ______
9 – 2 = ______
10 – 2 = ______
12 – 2 = ______
7 – 3 = ______
9 – 3 = ______
10 – 3 = ______
12 – 3 = ______
3. Continue the patterns as long as you can! a.
b.
c.
7
–
0
= ____
10 – 5 = ____
8 – 2 = ____
7
–
1
= ____
9 – 5 = ____
7 – 2 = ____
7 – 2 = ____
8 – 5 = ____
6 – 2 = ____
7 – ____ = ____
____ – 5 = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
____ – ____ = ____
81
4. If you can't take away or subtract that many, cross out the problem.
4–0
2–4
3–2
3–6
9–5
4–2
3 – 10
3–4
5–6
7–7
5–6
4–3
4–5
8–5
5–8
4–5
4–3
7–9
10 – 1
5–3
5. For each problem, answer these questions: Can the child buy the item? If yes, how much money will she/he have left? If not, how much more money would she/he need to buy the item? You can draw pictures to help.
a. Jennie has three dollars. She wants to buy a doll that costs five dollars.
b. Jessie has $5. He wants a ball that costs $2.
c. Lola has seven dollars. She wants to buy a Lego set that costs four dollars.
d. Marvin has $5. He wants a book that costs $6.
e. Jack has eight dollars. He wants to buy a construction set that costs ten dollars.
f. Mary has seven dollars. She wants a car that costs two dollars.
g. Faye has $12. She wants to buy a game that costs $4.
h. Anthony has ten dollars. He wants a game that costs fifteen dollars.
82
6. Subtraction can be written this way too! Write the answer below the line. a.
10 – 3
b.
8 – 7
c.
6 – 5
d.
8 – 6
e.
8 – 0
f.
7 – 7
g.
7 – 6
h.
6 – 6
i.
6 – 1
j.
9 – 4
k.
10 – 8
l.
4 – 0
m.
6 – 4
n.
7 – 2
o.
9 – 3
7. If the answer is four, color the box red. If the answer is five, color the box orange. If the answer is ten, color the box yellow. And if you can't do the subtraction, color the box light blue.
10 – 6
6–7
5–6
5 – 10
7–3
1–6
10 – 5
9 – 10
8–3
1–3
7–9
1–2
10 – 0
3–5
6–9
4–8
6–1
0–9
9–4
7–8
8–4
0–4
2–6
6–9
9–5
83
Two Subtractions from One Addition From one addition fact, you can make TWO subtraction facts:
Sometimes the two subtraction facts are the same:
3+4=7
7–4=3
2+2=4
7–3=4
4–2=2
Take away the carrots in the top row.
Take away the carrots in the bottom row.
or
Take away the carrots in the bottom row.
or
4–2=2 Take away the carrots in the top row.
1. Write one addition and two subtraction sentences. Subtract either the things in the top row or in the bottom row.
a.
1 + 3 =
4
b.
4 – 3 = _____ or
c.
2 + 3 =
5
5 – _____ = _____
4 – 1 = _____
or
_____ + _____ = _____
d.
5 – _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
or _____ – _____ = _____
or _____ – _____ = _____
84
e.
_____ + _____ = _____
f.
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
or _____ – _____ = _____
or _____ – _____ = _____
g.
_____ + _____ = _____
h.
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
or _____ – _____ = _____
or _____ – _____ = _____
i.
_____ + _____ = _____
j.
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
or _____ – _____ = _____
or _____ – _____ = _____
k.
_____ + _____ = _____
l.
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
or _____ – _____ = _____
or _____ – _____ = _____
85
2. Write the addition fact and the subtraction facts. Draw X's in two groups.
XXXXXX X a.
c.
XXXX XXX
6 + 1 = 7
b.
4 + 3 = 7
7 – 1 = 6
7 – _____ = _____
7 – 6 = 1
7 – _____ = _____
7 + 1 = _____
d.
5 + 4 = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
e.
2 + 6 = _____
f.
3 + 5 = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
g.
1 + 8 = _____
h.
5 + 5 = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
86
Two Parts — One Total There are ten marbles. Some are blue and seven are green. How many are blue? You can write an addition sentence. You can ALSO write a subtraction sentence, even though nothing is taken away.
_____ + 7 = 10 10 – 7 = _____ Cover part of the total (the green marbles), and you will see the other part (the blue marbles).
There are five blue marbles and some green marbles in a bag. There is a total of nine marbles. How many are green?
_____ + _____ = _____
Draw the marbles. Write an addition sentence AND a subtraction sentence.
_____ – _____ = _____
1. Solve the word problems. Write an addition sentence AND a subtraction sentence. a. Mom put some blue and red flowers in a vase. Jen
counted five red flowers, and a total of ten flowers. How many of the flowers are blue?
b. There are nine children on a team, and four of them
_____ + _____ = _____ _____ – _____ = _____
_____ + _____ = _____
are boys. How many are girls?
_____ – _____ = _____
87
c. Jack has ten socks in his basket. Eight of them
are white, and the rest are black. How many are black?
_____ + _____ = _____ _____ – _____ = _____
d. Mary saw eight chairs on the lawn,
_____ + _____ = _____
and two had blown over. How many were still sitting upright?
_____ – _____ = _____
2. For each picture, make a word problem that is solved by subtraction. a.
b.
88
3. Write an addition sentence for the pictures.
a.
_____ + _____ + _____ = _____
b.
_____ + _____ + _____ = _____
c.
_____ + _____ + _____ = _____
d.
_____ + _____ + _____ = _____
4. Draw the missing marbles to match the addition sentence.
a.
3 + 2 + _____ = 8
b.
5. Draw a picture to solve these problems. a. Jane had some red, blue, and yellow roses
in a vase. Two roses were blue, and two were red. If she had a total of ten roses, how many of them were yellow?
b. Seven birds sat in a tree. One of
them was black, two were blue, and the rest were brown. How many were brown?
c. Mary has two long pencils, two medium-
size pencils, and the rest of her pencils are short. If she owns nine pencils, how many of her pencils are short?
89
1 + 5 + _____ = 10
Fact Families Two addition facts and two subtraction facts form a fact family if they use the same three numbers. For example, with 5, 3, and 2 we get a fact family on the right:
5
/ 2+3=5
5–3=2
3+2=5
5–2=3
1. Write the fact families to match the pictures. a.
6
b.
/
8
/
1 + 5 = 6
_____ + _____ = _____
5 + 1 = 6
_____ + _____ = _____
6 – _____ = _____
_____ – _____ = _____
6 – _____ = _____
_____ – _____ = _____
c.
9
d.
/
10
/
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____ 90
2. Write the fact families to match the pictures. a.
___
b.
___
/
/
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
3. Draw circles and write different fact families in which the sum is 7. a.
7
b.
7
/
/
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
c.
7
d.
7
/
/
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
91
4. Make the four facts for the given numbers. a. Numbers: 5, 3, 2
b. Numbers: 9, 4, 5
2 + 3 = 5
4 + 5 = 9
3 + 2 = 5
_____ + _____ = 9
5 – 3 = 2
9 – 4 = _____
5 – 2 = 3
9 – _____ = _____
c. Numbers: 4, 0, 4
d. Numbers: 10, 3, 7
4 + 0 = 4
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
4 – 0 = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
e. Numbers: 10, _______, 8
f. Numbers: 6, 0, _______
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
92
Sometimes two addition facts are the same, and the two subtraction facts are the same. For example, with 8, 4, and 4, we only get one addition fact and one subtraction fact.
4+4=8
8–4=4
(4 + 4 = 8)
(8 – 4 = 4)
5. Write the fact families. a.
c.
Numbers: 10, 5, 5
b.
Numbers: 9, 1, 8
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
Numbers: 6, 3, _____
d.
Numbers: 7, 1, _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
What numbers are
,
, and
representing?
–4=5
5–
=4
+4=5
–2=3
7–
=1
+2=3
–7=1
10 –
=5
+ 7 = 10
93
How Many More? Henry |
|
Henry
|
|
|
Cindy
Cindy
Cindy has more marbles. How many more?
Cindy has fewer marbles. How many fewer?
Match three marbles from each box.
Match two marbles from each box.
Two marbles did not get matched, so Cindy has 2 more marbles than Henry.
Four marbles did not get matched, so Cindy has 4 fewer marbles than Henry.
(Henry has 2 fewer marbles than Cindy.)
(Henry has 4 more marbles than Cindy.)
1. Fill in how many more or how many fewer marbles one child has than another.
Jane
Mark
Jim
Mary
a. Jane has ______ more than Jim.
b. Mark has ______ more than Mary.
Jim has ______ fewer than Jane.
Mary has ______ fewer than Mark.
Ann
Faye
Liz
Sam
c. Liz has ______ more than Ann.
d. Sam has ______ more than Faye.
Ann has ______ fewer than Liz.
Faye has ______ fewer than Sam.
Peter
Susan
Frank
Bill
e. Frank has ______ more than Peter.
f. Susan has ______ more than Bill.
Peter has ______ fewer than Frank.
Bill has ______ fewer than Susan.
94
2. Now it's your turn to draw. Draw marbles for the child that has none.
Jane
Mark
Jim
Mary
a. Jane has 3 more than Jim.
b. Mary has 4 more than Mark.
Eric
Jack
Bill
Jane
c. Eric has 2 fewer than Bill.
d. Jane has 5 fewer than Jack.
Bill
Lucy
Greg
Liz
e. Greg has 1 more than Bill.
f. Lucy has 5 more than Liz.
Ed
Ann
Sally
Mary
g. Sally has 2 fewer than Ed.
h. Ann has 4 fewer than Mary.
Sue
Jill
Ben
Mary
i. Ben has five more than Sue.
j. Jill has five fewer than Mary.
95
3. It is still your turn to draw. You can decide how many marbles the children have.
Jane
Mark
Jim
Mary
a. Jane has 5 more than Jim.
b. Mary has 2 more than Mark.
Eric
Jack
Bill
Jane
c. Eric has 6 fewer than Bill.
d. Jane has 7 more than Jack.
Bill
Lucy
Greg
Liz
e. Greg has 2 fewer than Bill.
f. Lucy has 8 more than Liz.
4. Solve these problems.
a. Ed has five cards, and Jack has seven. How many more cards than Ed does Jack have?
b. John is 8 years old and Jack is 5. How many years older is John?
c. Annie is 10 years old and Beth is 8. How many years younger is Beth?
d. Ruth had 9 dolls, and Tina had 4 dolls. How many fewer did Tina have?
96
“How Many More” Problems and Difference How many more emails does Jane have than John?
John
Jane
Draw more emails for John so that the children have the same amount. I drew _____ more emails.
You can write an addition for a “how many more” problem.
2 + _____ = 5 Read: “2 and how many more makes five?”
1. Draw more. Read the addition sentences.
a.
1 + _____ = 4
“1 and how many more makes 4?”
d.
4 + _____ = 10
b.
3 + _____ = 6
“3 and how many more makes 6?”
e.
c.
3 + _____ = 7
“3 and how many more makes 7?”
2 + _____ = 8
f.
1 + _____ = 5
The problem _____ + 2 = 5 is also read “2 and how many more makes five?” 2. Draw more. Solve.
a.
_____ + 5 = 7
5 and how many more makes 7?
d.
_____ + 2 = 7
b.
_____ + 2 = 6
2 and how many more makes 6?
e.
_____ + 4 = 7 97
c.
_____ + 1 = 8
1 and how many more makes 8?
f.
_____ + 3 = 6
How many more problems are DIFFERENCE problems. The difference of two numbers means how far the two numbers are from each other.
How far is 3 from 7?
How far is 8 from 13?
How much difference is there between 3 and 7?
How much difference is there between 8 and 13?
3 and how many more make 7?
8 and how many more make 13?
3 + ______ = 7
8 + ______ = 13
The answer to all these is 4.
The answer to all these is 5.
3. What is the difference between the numbers? Take steps on the number line.
a. from 6 to 10
b. from 5 to 8
______ steps
c. from 7 to 11
______ steps
d. from 5 to 5
______ steps
e. from 1 to 10
______ steps
______ steps
4. Find the difference between the numbers. “Travel” on the number line! From
8
4
1
3
6
10
8
9
To
10
10
9
1
5
5
12
15
Difference
5. Solve the difference between the numbers. Then write an addition. Be careful. a. from 3 to 5
b. from 1 to 5
c. from 2 to 7
______ steps
______ steps
______ steps
3 + 2 =5
1 + _____ = 5
2 + _____ = 7
98
6. Solve the difference between the numbers. Then write an addition. Be careful. a. from 6 to 9: ______ steps
b. from 4 to 8: ______ steps
6 + _____ = 9
_____ + _____ = _____
c. from 8 to 9: ______ steps
d. from 2 to 6: ______ steps
_____ + _____ = _____
_____ + _____ = _____
7. Who has more marbles? How many more? Write a “how many more” addition. You can also draw.
Jill
Ed
Sue
Al
a. Jill has 10 and Sue has 7.
b. Ed has 4 and Al has 7.
7 + _____ = 10
_____ + _____ = _____
Jill
has 3 more.
_______________ has _____ more.
c. Veronica has 4 and Ann has 6.
d. Hannah has 9 and Michelle has 2.
_____ + _____ = _____
_____ + _____ = _____
_______________ has _____ more.
_______________ has _____ more.
e. Britney has 11 and Jeanne has 10.
f. Ben has 5 and Don has 10.
_____ + _____ = _____
_____ + _____ = _____
_______________ has _____ more.
_______________ has _____ more.
99
8. Solve the problems. Think carefully: Is it asking for the total? OR is it asking, “How many more?” a. There are two cassette tapes on the table, and eight on the shelf.
How many tapes are there together?
How many more tapes are on the shelf?
b. There are five birds each in both the apple tree and the oak tree.
Four more flew into the oak tree. How many birds are now in the oak tree?
How many more birds are in the oak tree than in the apple tree?
c. Brenda has 2 toy cars, Jason has 9, and Joe has 10.
How many more than Jason does Joe have?
How many more than Brenda does Jason have?
100
“How Many More” Problems and Subtraction Nathalie needs ten safety-pins. She only has two. How many more does she need?
+
?
= 10 = 10
2 +
You can use subtraction to solve a problem that asks “how many more”, like the problem 2 + _____ = 10.
Use the Fact Family:
Simply subtract the numbers: 10 – 2 = ____.
2 + 8 = 10, 10 – 2 = 8
It gives you the answer to 2 + _____ = 10. Why? Because both problems are in the same fact family.
8 + 2 = 10, 10 – 8 = 2
1. Fill in. The “how many more” problem has the same answer as the subtraction problem!
+ a.
5
+ ____ = 7
+ b.
7 – 5 = _____
3
5
+ ____ = 10
3 + _____ = 10 10 – 3 = _____
c.
4
e.
4
+
+ ____ = 7
f.
2 + _____ = 9 9 – 2 = _____
101
5
+ ____ = 8
8 – 5 = _____
7 – 4 = _____ h.
+ ____ = 9
9 – 4 = _____
+
10 – 5 = _____ g.
+ ____ = 8
8 – 3 = _____
+ d.
+
i.
1 + _____ = 7 7 – 1 = _____
2. Solve the subtraction problem first. (It is probably easier.) Then copy the answer to the “how many more” problem. a.
2 + _____ = 8
8 – 2 = _____
b.
1 + _____ = 9
c.
9 – 1 = _____
3 + _____ = 10
10 – 3 = _____
d.
3 + _____ = 9
9 – 3 = _____
The “how many more” problem has the same answer as the subtraction problem! 3. Write a subtraction problem under each “how many more” problem, using the same numbers. Solve the subtraction problem first. a.
1 + _____ = 7
_____ – ____ = ____ d.
3 + _____ = 8
_____ – ____ = ____
b.
2 + _____ = 9
c.
_____ – ____ = ____ e.
2 + _____ = 10
_____ – ____ = ____
1 + _____ = 10
_____ – ____ = ____ f.
3 + _____ = 9 _____ – ____ = ____
4. Solve. THINK: Do you already know the total? Or is the problem asking for the total? You can also draw a picture to help! a. Mary ate two carrots. The rabbit ate
b. Baby put three blocks in a stack, and
six carrots. What was the total number of carrots eaten?
c. There were five lambs in the pen. Two
another four blocks in another stack. How many blocks did the baby use?
d. Lisa needs 8 dollars for a stuffed
hippo. She has saved 4 dollars. How many more dollars does she need?
more lambs went into the pen. How many lambs are now in the pen?
102
5. First write a “how many more” problem for each subtraction problem, using the same numbers. Then solve the easier problem. Copy the answer to the other problem. a.
8 – 6 = ____
b.
____ + ____ = ____ d.
10 – 8 = ____
10 – 9 = ____
c.
____ + ____ = ____ e.
____ + ____ = ____
9 – 8 = ____
9 – 7 = ____ ____ + ____ = ____
f.
____ + ____ = ____
7 – 6 = ____ ____ + ____ = ____
6. Solve. THINK: Do you already know the total? Or is the problem asking for the total? Write an addition or subtraction for each problem. You can also draw a picture to help! a. Mom needs six cucumbers. She
b. There were seven ducks on the pond.
already has three. How many more does she need?
Three flew away. How many were left?
c. Jane wants to buy a teddy bear for
d. A book has ten pages. Jerry has read
8 dollars. She has saved 6 dollars. How much more money does she need?
six pages. How many pages does he have left to read?
7. Solve. The number line helps. Skip (c) and (d) if you don't know numbers after 10. a.
b.
c.
d.
6 + _____ = 7
3 + _____ = 9
9 + _____ = 10
10 + _____ = 12
6 + _____ = 8
3 + _____ = 8
9 + _____ = 13
10 + _____ = 15
6 + _____ = 9
3 + _____ = 7
9 + _____ = 14
10 + _____ = 13
103
Review 1. Write a fact family to match the picture.
____ + ____ = ____
____ − ____ = ____
____ + ____ = ____
____ − ____ = ____
9
/
2. a. Write a subtraction that matches the addition 6 + 4 = 10. b. Write a subtraction that matches the addition 5 + ____ = 9.
Also solve the addition.
____ − ____ = ____ ____ − ____ = ____
3. a. There are 8 children playing in the yard. Two are girls. How many are boys?
b. Kay has four marbles. Susan has two more marbles than Kay.
Draw Kay's and Susan's marbles.
c. Five sparrows and two robins are feeding on seeds. One more robin flies in.
How many more sparrows than robins are there now? 4. Find the missing numbers. a.
b.
c.
d.
3 + _____ = 4
6 – _____ = 3
10 – 0 = _____
8 – 2 = _____
1 + _____ = 9
8 – _____ = 7
5 – 3 = _____
7 – 3 = _____
3 + _____ = 10
_____ – 1 = 6
6 – 6 = _____
10 – 1 = _____
2 + _____ = 7
_____ – 2 = 8
7 – 4 = _____
9 – 2 = _____
104
Chapter 3: Addition and Subtraction Facts Introduction The third chapter of the Math Mammoth Grade 1-A Complete Worktext provides lots of practice for learning and memorizing the basic addition and subtraction facts within 0-10.
Memorizing the facts The lessons named, Addition and Subtraction Facts With ..., aim at helping your child to memorize the basic facts within 0-10. We approach it from the concept of “fact families”, which makes the process to be logical and structured. These lessons have a lot of repetition and practice for both subtraction and addition facts. Some children may not need all of the practice. Use your judgment and skip some pages in this section if you feel it is necessary. You can also “save” some of the pages to be completed later, as a review. Alongside this book, you can also use math games or flashcards to reinforce these facts. You will find a list of some free online games at http://www.homeschoolmath.net/online/addition_subtraction.php 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”. This suggests that memorizing the addition and subtraction facts is not yet completely essential in first grade. It is advisable though to learn these facts fairly well at this point, because children will soon start learning to add those single-digit numbers where the sum is more than ten. Mathematics builds upon previously learned concepts and facts. Learning addition and subtraction facts is essential for later study. If your child does not memorize these facts yet, don't worry. Go on with your curriculum, but keep practicing the facts with games, worksheets, drill, etc. on the side until they get there.
The Lessons in Chapter 3 page
span
Addition and Subtraction Facts with 4 and 5 ..... 107
2 pages
Addition and Subtraction Facts with 6 .............. 109
3 pages
Addition and Subtraction Facts with 7 .............. 112
2 pages
Addition and Subtraction Facts with 8 .............. 114
3 pages
Addition and Subtraction Facts with 9 .............. 118
3 pages
Addition and Subtraction Facts with 10 ............ 121
3 pages
Adding and Subtracting Many Numbers ........... 125
4 pages
Review - Facts with 6, 7, and 8 .......................... 129
2 pages
Review - Facts with 9 and 10 ............................. 131
2 pages
105
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Exuberant Eye Games Practice your basic facts with these kid-appealing simple games. http://www.games.exuberanteye.com/ Mental Maths Practice Online practice of sets of 10 addition and subtraction questions; timed http://www.teachingtreasures.com.au/maths/mental-maths/yr1-maths-pg1.htm Math Facts Practice at playKidsgames.com Timed practice with various skill levels. http://www.playkidsgames.com/games/mathfact/default.htm Number Bond Machines Practice which two numbers add up to a given number. http://www.amblesideprimary.com/ambleweb/mentalmaths/numberbond.html Online Subtraction Flash Cards http://www.thegreatmartinicompany.com/WebMozilla/subtractionm.html and http://www.thegreatmartinicompany.com/WebMozilla/subtractionmfill.html Number Line Bounce Arrange the given bounce arrows on a number line using addition and subtraction until you reach the target number. Since it uses several operations, it is challenging for first graders, but give it a try. http://nlvm.usu.edu/en/nav/frames_asid_107_g_1_t_1.html
106
Addition and Subtraction Facts with 4 and 5
Facts with 4
Facts with 5
4 + 0 = 4
4 – 4 = 0
0 + 4 = 4
4 – 0 = 4
1 + 3 = 4
4 – 3 = 1
3 + 1 = 4
4 – 1 = 3
2 + 2 = 4
4 – 2 = 2
5 + 0 = 5
5 – 5 = 0
____ + ____ = 5
5 – ____ =____
4 + 1 = 5
5 – 4 = ____
1 + 4 = 5
5 – ____ =____
3 + 2 = 5 _____ + _____ = 5
5 – 3 = ____ 5 – ____ =____
1. Find the missing numbers. a.
b.
c.
d.
3 + _____ = 4
2 + _____ = 5
5 – 0 = _____
4 – 0 = _____
1 + _____ = 4
1 + _____ = 5
5 – 4 = _____
4 – 3 = _____
1 + _____ = 5
4 + _____ = 5
5 – 2 = _____
5 – 1 = _____
2 + _____ = 4
3 + _____ = 5
4 – 1 = _____
4 – 2 = _____
107
2. Color the square
yellow if the answer is 0. red if the answer is 1, blue if the answer is 2, green if the answer is 3, purple if the answer is 4, orange if the answer is 5.
5–4
2+3
4–4
1+2
4–2
1+3
2+2
3–2
5–0
0+0
5–2
1+1
0+2
5–1
0+1
1+4
0–0
4–1
3. Continue the patterns as long as you can!
17 – 0 = _____
10 + _____ = 10
5 – 2 = _____
17 – 1 = _____
10 + _____ = 11
6 – 2 = _____
17 – 2 = _____
10 + _____ = 12
7 – 2 = _____
17 – ____ = _____
10 + _____ = ____
____ – 2 = _____
17 – ____ = _____
____ + ____ = ____
_____ – ____ = _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
108
Addition and Subtraction Facts with 6 1. Write the fact families in which the sum is six. At the top, write the three numbers you are using for the fact families.
6, 0, 6
_____, _____, 6
_____, _____, 6
6 + 0 = 6
5 + 1 = 6
4 + 2 = 6
______ + ____ = 6
______ + ____ = 6
______ + ____ = 6
6 – 6 = 0
6 – 5 = ____
6 – 4 = ____
6 – 0 = 6
6 – ____ = ____
6 – ____ = ____
2. Write the numbers that add up to 6. Memorize these!
_____, _____, 6
0 + _____ = 6
or
______ + 0 = 6
1 + _____ = 6
or
______ + 1 = 6
3 + 3 = 6
2 + _____ = 6
or
______ + 2 = 6
6 – 3 = ____
3 + _____ = 6
3. Subtract. a.
6 –5
b.
6 –4
c.
d.
6 –6
6 –2
4. Play the “6 Out” card game (see the introduction in this book).
109
e.
6 –1
f.
6 –3
5. Find the missing numbers. a.
b.
c.
d.
4 + _____ = 6
5 + _____ = 6
_____ + 2 = 6
_____ + 1 = 6
6 + _____ = 6
0 + _____ = 6
_____ + 0 = 6
6 – _____ = 6
1 + _____ = 6
_____ + 4 = 6
_____ + 5 = 6
6 – _____ = 5
6. For each “how many more” problem, write a subtraction using the same numbers. Solve.
2 + _____ = 6
a.
6 d.
– 2 = _____ 0 + _____ = 6
_____ – _____ = ____
b.
2 + _____ = 4
_____ – _____ = ____ e.
3 + _____ = 6
_____ – _____ = ____
c.
4 + _____ = 5
_____ – _____ = ____ f.
2 + _____ = 5
_____ – _____ = ____
7. Write the fact families. a.
c.
1 + _____ = 6
b.
1 + _____ = 5
_____ + 1 = 6
_____ + _____ = _____
_____ – _____ = _____
5 – _____ = _____
_____ – _____ = _____
5 – _____ = _____
2 + 4 = 6
d.
0 + 4 = _____
_____ + _____ = _____
_____ + _____ = _____
_____ – _____ = _____
_____ – _____ = _____
_____ – _____ = _____
4 – 4 = 0
110
8. Solve the word problems. Think:
Are you asked for the total? OR Are you asked how many more? OR Are you asked how many are left?
a. The black cat has 4 kittens and the white cat has three.
How many kittens do they have altogether? How many more kittens does the white cat have than the black cat?
b. John had ten crayons but now he only has two.
How many crayons has he lost?
c. Mother found ten clothespins in one container and two in another.
How many clothespins were in the two containers?
How many more clothespins were in first container than in the second?
d. Jill has two eggs. She needs eight eggs to make some cakes.
Her neighbor has three eggs. How many more eggs does Jill need?
How many eggs do Jill and her neighbor have together? If the neighbor gives Jill the three eggs she has, how many more does Jill still need?
111
Addition and Subtraction Facts with 7 1. Write the fact families with 7. At the top, write the three numbers you are using.
7, 0, 7
_____, _____, 7
_____, _____, 7
7 + 0 = 7
6 + _____ = 7
5 + _____ = 7
_____ + ____ = 7
____ + ____ = _____
____ + ____ = _____
7 – ____ = _____
7 – _____ = _____
7 – _____ = _____
7 – ____ = _____
____ – ____ = _____
____ – ____ = _____
_____, _____, 7
2. Write down the numbers that add up to 7 and memorize the addition facts!
0 + ____ = 7
or
_____ + 0 = 7
4 + ____ = 7
1 + ____ = 7
or
_____ + 1 = 7
____ + ____ = _____
2 + ____ = 7
or
_____ + 2 = 7
7 – ____ = _____
3 + ____ = 7
or
_____ + 3 = 7
____ – ____ = _____
3. Play the “7 Out” card game.
112
4. Subtract. a.
b.
7 –5
c.
7 –4
d.
7 –6
e.
7 –2
f.
7 –1
7 –3
5. Fill in. Then draw a line between the facts that are from the same fact family.
5 + _____ = 7
7 – _____ = 4
7 – _____ = 6
7 – 0 = _____
6 + _____ = 7
_____ + 4 = 7
7 – 3 = _____
7 – 2 = _____
7 – _____ = 7
7 – _____ = 1
0 + _____ = 7
7 – _____ = 2
6. Add, subtract, and find the missing numbers. a.
b.
c.
7 – 3 = _____
5 + 2 = _____
_____ + 4 = 7
5 – 5 = _____
4 + 1 = _____
_____ + 2 = 6
6 – 2 = _____
2 + 4 = _____
_____ + 1 = 5
4 – 3 = _____
3 + 2 = _____
_____ + 2 = 7
7. Can you figure out how to fill in the rest of this subtraction chart?
–
12
1
11
2
11
10
9
8
7
6
5
4
3
6 9
4
113
1
Addition and Subtraction Facts with 8 1. Write the fact families in which the sum is eight.
8, ____, 8
_____, _____, 8
_____, _____, 8
8 + 0 = 8
7 + ____ = 8
____ + ____ = _____
____ + ____ = 8
____ + ____ = 8
____ + ____ = _____
8 – ____ = ____
8 – ____ = _____
____ – ____ = _____
____ – ____ = ____
____ – ____ = _____
____ – ____ = _____
_____, _____, 8
_____, _____, 8
____ + ____ = 8
____ + ____ = 8
____ + ____ = 8 ____ – ____ = ____
____ – ____ = ____
____ – ____ = ____ 2. Play the “8 Out” card game.
114
3. Write the addition facts with 8 and memorize them!
0 + _____ = 8
or
_____ + 0 = 8
1 + _____ = 8
or
_____ + 1 = 8
2 + _____ = 8
or
_____ + _____ = 8
3 + _____ = 8
or
_____ + _____ = 8
4 + _____ = 8
4. Find the missing numbers. a.
b.
c.
d.
8 – 3 = _____
5 + _____ = 8
4 + _____ = 8
8 – 7 = _____
8 – 1 = _____
1 + _____ = 8
6 + _____ = 8
8 – 0 = _____
8 – 2 = _____
2 + _____ = 8
7 + _____ = 8
8 – 4 = _____
First subtract 6 – 2. It is 4. 6 – 2 Do not write 4 in the box! Then compare 4 and 5. Five is greater. Draw < .
5
↓
↓
4
5
5. First Subtract. Write the answer below (not in the box!). Then write < or > or = . a.
5–2
4
↓
↓ 4
b.
7–4
5
↓
↓
c.
5
115
8–1
7
↓
↓
d.
6–3
2
↓
↓
First do 4 + 2 (on left side) and 8 – 3 (on the right side). Do not write the answers in the box! You can write the answers below. Then compare. Six is greater. Draw > .
4+2
8–3
↓
↓
6
5
6. First add and subtract. Write the answers below (not in the box!). Then compare, and write < or > or = . a.
e.
h.
k.
5–2
4–2
↓
↓
6+2
7+2
↓
↓
1–1
3–2
↓
↓
8–1
4–2
↓
↓
b.
f.
i.
l.
8–1
7–1
↓
↓
7–1
7–2
↓
↓
3 + 10
10
↓
↓
7–2
6–1
↓
↓
116
c.
g.
8–6
8–5
↓
↓
4+4
7–5
↓
↓
7
j.
m.
4+2
↓
↓
9–0
7+2
↓
↓
7. Fill in the missing numbers. Then draw a line between the facts that are from the same fact family.
6 + _____ = 8
8 – 4 = _____
_____ + 5 = 8
8 – 0 = _____
8 – _____ = 3
8 – _____ = 6
8 – 3 = _____
7 + _____ = 8
_____ + 4 = 8
_____ + 1 = 8
8 – 2 = _____
8 – _____ = 8
4 + _____ = 8
0 + _____ = 8
8 – 1 = _____
8. Solve the word problems. Drawing can help you solve these. a. Jack has 10 cars, Bill has 7, and Ed has 4.
How many more cars than Ed does Bill have? How many more cars than Ed does Jack have? How many more cars than Bill does Jack have?
b. Mary has saved 7 dollars. She'd like to buy a puzzle for 5 dollars and
a game for 3 dollars. Can she buy both things? If she can, how much money does she have left over?
If she can't, how much more money would she need to save?
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Addition and Subtraction Facts with 9 1. Write the fact families where the sum is 9.
9, 0 , 9
_____, _____, 9
_____, _____, 9
9 + ____ = 9
____ + ____ = ______
____ + ____ = ______
____ + ____ = 9
____ + ____ = ______
____ + ____ = ______
9 – ____ = ______
____ – ____ = ______
____ – ____ = ______
____ – ____ = ______
____ – ____ = ______
____ – ____ = ______
_____, _____, 9
_____, _____, 9
____ + ____ = ______
____ + ____ = ______
____ + ____ = ______
____ + ____ = ______
____ – ____ = ______
____ – ____ = ______
____ – ____ = ______
____ – ____ = ______
2. Play the “9 Out” card game.
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3. Write the addition facts with 9 and memorize them!
0 + _____ = 9
or
____ + 0 = 9
1 + _____ = 9
or
____ + 1 = 9
2 + _____ = 9
or
____ + ____ = 9
3 + _____ = 9
or
____ + ____ = 9
4 + _____ = 9
or
____ + ____ = 9
4. Find the missing numbers. a.
b.
c.
d.
9 – 5 = _____
2 + _____ = 9
_____ + 1 = 9
9 – _____ = 1
9 – 3 = _____
1 + _____ = 9
_____ + 3 = 9
9 – _____ = 0
9 – 6 = _____
7 + _____ = 9
_____ + 5 = 9
9 – _____ = 2
9 – 8 = _____
8 + _____ = 9
_____ + 7 = 9
9 – _____ = 4
5. Fill in the missing numbers. Then draw a line between the facts that are from the same fact family.
7 + _____ = 9
0 + _____ = 9
_____ + 8 = 9
9 – 3 = _____
9 – _____ = 3
9 – _____ = 6
9 – 1 = _____
5 + _____ = 9
_____ + 2 = 9
9 – _____ = 9
9 – 2 = _____
9 – _____ = 4
4 + _____ = 9
9 – _____ = 1
_____ + 0 = 9
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6. First add and subtract. Don't write answers in the box—just think them in your mind! Then compare and write < , > , or = in the box. a.
8
10 – 3
b.
9
d.
6+2
8+2
e.
10 – 1
g.
5–2
4–2
h.
8+0
9+3
c.
8–6
6+3
10
f.
8–4
8–5
8–0
i.
9–1
9+1
7. Subtract this way! a.
9 –5
b.
c.
9 –4
d.
9 –6
8 –2
e.
9 –2
f.
8. If the answer is 6 or 7, color the box blue. If the answer is 8 or 9, color the box red. And color the rest of the boxes yellow.
9–3
4+6
9–0
4+6
8–1
2+5
9–5
4+4
4–2
5+1
9–2
3+7
10 – 2
10 + 0
7–1
4+2
7–3
6+3
3–1
3+3
6–0
1+1
8–0
3+2
10 – 4
3+4
8–3
2+7
7–6
7+0
1+6
2+8
10 – 1
2+2
7–0
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8 –3
Addition and Subtraction Facts with 10 1. Write the fact families in which the sum is ten.
10, 0, 10
9, 1, 10
____, ____, 10
9 + _____ = 10
8 + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
10 – 10 = 0
10 – 9 = _____
10 – ____ = _____
10 – ____ = _____
10 – ____ = _____
10 – ____ = _____
____, ____, 10
____, ____, 10
____, ____, 10
____ + ____ = _____
____ + ____ = _____
10 + 0 = 10
7 + ____ = 10 ____ + ____ = _____
____ + ____ = _____
10 – _____ = ____
_____ – ____ = ____
_____ – ____ = ____
_____ – ____ = ____
2. Play the “10 Out” card game.
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_____ – ____ = ____
3. Write the addition facts with 10 and memorize them!
0 + _____ = 10
or
_____ + 0 = 10
1 + _____ = 10
or
_____ + 1 = 10
2 + _____ = 10
or
_____ + _____ = 10
3 + _____ = 10
or
_____ + _____ = 10
4 + _____ = 10
or
_____ + _____ = 10
5 + _____ = 10 4. Find the missing numbers. a.
b.
c.
10 – 3 = _____
0 + _____ = 10
10 – _____ = 7
10 – 6 = _____
7 + _____ = 10
10 – _____ = 2
10 – 2 = _____
9 + _____ = 10
10 – _____ = 4
5. Fill in. Then draw a line between the facts that are from the same fact family.
6 + _____ = 10
0 + _____ = 10
_____ + 5 = 10
10 – 5 = _____
8 + _____ = 10
10 – _____ = 6
10 – 1 = _____
10 – _____ = 3
_____ + 2 = 10
10 – 2 = _____
5 + _____ = 10
10 – _____ = 7
10 – _____ = 10
10 – 4 = _____
_____ + 10 = 10
7 + _____ = 10
9 + _____ = 10
10 – 9 = _____
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6. Write an addition sentence and a subtraction sentence for these word problems. Remember, you can always draw a picture of the situation to help you! a. Sarah has six coins in her piggy bank. Elisa has two coins in hers.
Today Elisa found three coins on the ground. Now who has more coins? How many more?
b. Dad had one box of nails at home, and then he bought six more boxes of nails.
The next day he gave one box to the neighbor. How many boxes of nails does Dad have now?
c. You have six dollars and I have three.
Can we together buy a meal that costs $8? If yes, is there any money left over, and how much?
If no, how much more money would we need?
d. You have three dollars and I have five.
Can we together buy a meal that costs $10? If yes, is there any money left over, and how much?
If no, how much more money would we need?
123
7. More missing numbers! a.
b.
c.
10 – 1 = _____
8 + _____ = 10
_____ + 7 = 10
10 – 8 = _____
6 + _____ = 10
_____ + 10 = 10
10 – 0 = _____
2 + _____ = 10
_____ + 6 = 10
10 – 4 = _____
5 + _____ = 10
_____ + 8 = 10
8. Let's not forget our 7's and 6's! a.
b.
c.
d.
7 – 3 = _____
7 – 2 = _____
6 – 1 = _____
6 – 2 = _____
7 – 5 = _____
7 – 4 = _____
6 – 3 = _____
6 – 4 = _____
7 – 7 = _____
7 – 6 = _____
6 – 5 = _____
6 – 6 = _____
represents a number, and represents another number. Solve what they are in each case (case a, case b, and case c). Guess and check! a.
b.
c.
+
= 10
+
= 10
+
= 10
–
=2
–
=6
–
=0
124
Adding and Subtracting Many Numbers When you add three numbers, you can add them in any order you wish. You can add the first two numbers first:
Or you can add the last two numbers first:
1 + 5 +2 \ / 6 + 2= 8
1 +5 + 2 \ / 1 + 7 = 8
Or you can add the first and the last number first:
It doesn't matter in which order you add multiple numbers. 1. Add. a.
1 + 2 + 3 = _____
b.
4 + 1 + 1 = _____
c.
2 + 5 + 3 = _____
1 + 7 + 2 = _____
3 + 0 + 2 = _____
1 + 6 + 2 = _____
6 + 1 + 3 = _____
3 + 3 + 2 = _____
3 + 1 + 4 = _____
2. Add. Again, you can add in any order. a.
5 1 + 4
b.
3 1 + 4
c.
2 2 + 4
d.
7 1 + 1
e.
4 0 + 3
f.
2 6 + 2
g.
1 1 + 8
h.
3 2 + 4
i.
7 2 + 1
j.
4 1 + 4
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Subtract two numbers this way:
7 –1– 2 \ / 6 – 2 = 4 First subtract 7 – 1. That's 6. Then subtract 6 – 2. 3. Do two subtractions. You can cover the circles in the pictures to help. b.
a.
c.
8 – 2 – 3 = _____
9 – 3 – 1 = _____
10 – 5 – 3 = _____
8 – 5 – 2 = _____
9 – 4 – 2 = _____
10 – 6 – 2 = _____
8 – 1 – 3 = _____
9 – 2 – 5 = _____
10 – 1 – 4 = _____
4. Solve. You can draw pictures to help. a. Mary had ten cookies. She gave two to her
brother, and two to her sister. How many does she have left? b. Seven birds were in the tree. Three flew away.
After a while, one more flew away. How many birds are left in the tree? c. Three cars were in the parking lot. Then, three
more cars drove in. After that, two more cars drove in. How many cars are there now? d. Jack had $5. His mom gave him $1,
and his dad gave him $2. How many dollars does Jack have now?
126
5. Do some more subtraction. a.
b.
c.
7 – 2 – 3 = _____
9 – 7 – 1 = _____
7 – 5 – 1 = _____
9 – 2 – 6 = _____
9 – 3 – 3 = _____
10 – 4 – 4 = _____
8 – 5 – 1 = _____
6 – 2 – 2 = _____
10 – 6 – 1 = _____
These (
) symbols are called parentheses. Solve what is inside the parentheses first. First add 1 + 5. Then subtract.
First subtract 5 – 2. Then add.
(1 + 5) – 2 \ / 6 – 2= 4
3 + (5 – 2) \ / 3 = 6 3 +
6. The parentheses show what numbers to add or subtract first. a.
(10 – 2) – 2 8
d.
b.
e.
10 – ____ = ____ g.
1 + (5 – 4) 1 + ____ = ____
c.
____ + 2 = ____
– 2 = ____
10 – (2 – 2)
(9 – 5) + 2
9 – (5 + 2)
____ – 2 = ____ f.
9 – ____ = ____ h.
9 – (0 + 8) 9 – ____ = ____
127
(3 + 5) – 2
3 + (5 – 2) 3 + ____ = ____
i.
9 – (9 – 2) 9 – ____ = ____
7. Solve the subtraction in the parentheses first. Compare the two problems and their results. a.
b.
c.
10 – (3 – 2) = _____
7 – (4 – 3) = _____
8 – (6 – 1) = _____
(10 – 3) – 2 = _____
(7 – 4) – 3 = _____
(8 – 6) – 1 = _____
8. Match the addition problems to the right pictures and solve them. a.
3 + 3 + 3 = ______
b.
2 + 2 + 2 + 2 = ______
c.
4 + 4 + 4 = ______
d.
2 + 2 + 2 = ______
e.
3 + 3 + 3 + 3 = ______
f.
1 + 1 + 1 + 1 + 1 = ______
9. Match the subtraction problems to the right pictures. a.
8–2–2–2–2=0
b.
8– 4 –4=0
c.
6–2–2–2=0
d.
6–3–3=0
Here are some difficult problems with four numbers!
4 + 3 + 1 + 2 = _____
10 – 1 – 2 – 1 = _____
8 – 4 – 1 – 2 = _____
5 + 1 + 1 + 3 = _____
9 – 3 – 2 – 1 = _____
4 + 4 + 1 + 1 = _____
128
Review — Facts with 6, 7, and 8 1. Write the addition facts with 6, 7, and 8.
0 + _____ = 6
0 + _____ = 7
0 + _____ = 8
1 + _____ = 6
1 + _____ = 7
1 + _____ = 8
_____ + _____ = 6
_____ + _____ = 7
_____ + _____ = 8
_____ + _____ = 6
_____ + _____ = 7
_____ + _____ = 8
_____ + _____ = 6
_____ + _____ = 7
_____ + _____ = 8
5 + _____ = 6
5 + _____ = 7
_____ + _____ = 8
6 + _____ = 6
6 + _____ = 7
_____ + _____ = 8
7 + _____ = 7
7 + _____ = 8 8 + _____ = 8
2. For each “how many more” problem, write a subtraction using the same numbers. Solve. a.
4 + _____ = 6
_____ – _____ = _____ d.
4 + _____ = 8
_____ – _____ = _____ g.
5 + _____ = 6
_____ – _____ = _____
b.
2 + _____ = 6
_____ – _____ = _____ e.
3 + _____ = 8
_____ – _____ = _____ h.
3 + _____ = 7
_____ – _____ = _____
129
c.
6 + _____ = 7
_____ – _____ = _____ f.
7 + _____ = 8
_____ – _____ = _____ i.
2 + _____ = 7
_____ – _____ = _____
3. Complete. Then draw a line to connect the facts from the same fact family.
_____ – 5 = 1
7 – 5 = _____
8 – 3 = ______
2 + _____ = 7
_____ + 2 = 6
5 + _____ = 7
8 – _____ = 3
6 – 1 = _____
1 + 5 = _____
_____ + 2 = 8
5 + _____ = 8
8 – 6 = ______
6 – 4 = _____
8 – _____ = 6
2 + 4 = ______
4. Complete. Then draw a line to connect the facts from the same fact family.
3 + _____ = 7
_____ + 6 = 7
8 – _____ = 7
6 – _____ = 3
_____ – 7 = 1
1 + 6 = _____
_____ + 1 = 8
3 + 3 = _____
3 + _____ = 6
_____ – 4 = 4
4 + _____ = 7
8 – 4 = _____
7 – 1 = _____
8 – _____ = 4
7 – _____ = 4
+ What numbers can go into the squares? All the numbers are less than 10.
–
= 8 –
+ = 0
+ +
= 6 = 2
130
= 7 –
– = 8
= 4 = 3
Review — Facts with 9 and 10 1. Write addition and subtraction facts with 9 and 10. a.
b.
c.
d.
0 + _____ = 9
1 + _____ = 10
10 – _____ = 9
9 – _____ = 9
1 + _____ = 9
2 + _____ = 10
10 – _____ = 8
9 – _____ = 8
2 + _____ = 9
3 + _____ = 10
10 – _____ = 7
9 – _____ = 7
3 + _____ = 9
4 + _____ = 10
10 – _____ = 6
9 – _____ = 6
4 + _____ = 9
5 + _____ = 10
10 – _____ = 5
9 – _____ = 5
2. Match the addition problems to the right pictures and solve them. a.
2 + 3 + 3 = ______
b.
3 + 2 + 2 = ______
c.
1 + 2 + 2 = ______
d.
3 + 4 + 2 = ______
e.
3 + 3 + 3 = ______
f.
2 + 2 + 2 = ______
3. Solve. The parentheses show what numbers to add or subtract first. a.
10 – (4 – 2) 10 – ____ = ____
b.
9 – (2 + 2) 9 – ____ = ____ 131
c.
5
+ (4 – 2)
____ + ____ = ____
4. Fill in the missing numbers. Draw a line to connect the facts that are from the same fact family.
9 – _____ = 7
_____ + 2 = 9
9 – _____ = 5
9 – _____ = 6
8 + _____ = 9
9 – 6 = _____
9 – 1 = _____
_____ + 5 = 9
9 – _____ = 2
9 – _____ = 4
3 + _____ = 9
_____ + 8 = 9
5. a. Draw a line to connect each pair of numbers that add up to 9. Which number is left by itself?
0
7 2
1
b. Draw a line to connect each pair of
numbers that add up to 10. Which number is left by itself?
2 8
3 5
2
6 9
7
1 4
3
4
8
9
6 9
5
4
0
2
5
1 7
10
3 6
8
1 9
7
3 6
8 5
6. Fill in the missing numbers. Draw a line to connect the facts that are from the same fact family.
10 – _____ = 8
_____ + 9 = 10
_____ + 1 = 10
10 – _____ = 5
4 + _____ = 10
10 – 5 = _____
10 – _____ = 1
5 + _____ = 10
10 – 4 = _____
10 – 3 = _____
2 + _____ = 10
_____ + 3 = 10
10 – 6 = _____
_____ + 7 = 10
10 – _____ = 8
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7. Solve. a. Millie has two boxes of crayons. Ken has seven boxes.
How many more boxes does he have than she has?
b. Mike has three yellow toy cars, four blue cars, and
three red cars. How many cars does he have in total?
c. There were four birds in a tree. Four more flew in.
How many birds are there now?
Later, five of them flew away. How many birds are there now?
d. Elisa knows she has ten crayons. She can only find four.
How many are missing?
e. A ten-piece puzzle has two pieces missing.
How many pieces are there now?
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