MathMammoth_Grade2B
Short Description
math practice...
Description
Copyright 2007-2009 Taina Maria Miller. EDITION 1.3 APRIL 2009 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, or by any information storage and retrieval system, without permission in writing from the author. Copying permission: Permission IS granted for the teacher to reproduce this material to be used with students, not commercial resale, by virtue of the purchase of this book. In other words, the teacher MAY make copies of the pages to be used with students. Permission is given to make electronic copies of the material for back-up purposes only.
Please visit www.MathMammoth.com for more information about Maria Miller's math books. Create free math worksheets at www.HomeschoolMath.net/worksheets/
2
Contents Chapter 6: Geometry and Fractions Introduction .......................................................................... 5 Shapes Review....................................................................... 7 Right Angles ......................................................................... 9 Parallel and Perpendicular Lines ....................................... 11 Forming Shapes ................................................................... 15 Solids ..................................................................................... 16 Fractions ............................................................................... 17 More on Fractions ............................................................... 19
Chapter 7: Place Value Till 1000 Introduction ......................................................................... 22 Hundreds Part 1 .................................................................. 24 Hundreds Part 2 .................................................................. 29 Skip-Counting Practice ...................................................... 31 Seven Hundred to Thousand ............................................. 34 Counting and Adding ......................................................... 36 Which Number is Greater? ...............................................
39
Comparing and Ordering .................................................. 43 Rounding to the Nearest Ten ............................................
47
Rounding to the Nearest Hundred ...................................
49
Review .................................................................................
50
Chapter 8: Mental Addition and Subtraction Introduction ........................................................................
51
Completing the Next Hundred .......................................... 52 Add and Subtract Whole Hundreds ................................. 56 Practice with Whole Hundreds .........................................
59
Addition/Subtraction Connection ....................................
61
Graphs ................................................................................
64
Adding Whole Tens ...........................................................
66
Subtracting Whole Tens ....................................................
69
Rounding and Estimating .................................................. 71
3
Adding Ones ...................................................................... 73 Subtracting Ones Mentally ............................................... 76 Review of Mental Math .................................................... 79
Chapter 9: Measuring Introduction ........................................................................ 80 Exploring Measuring ......................................................... 82 Inches and Half-Inches ...................................................... 83 Measuring to the Nearest Centimeter .............................. 85 Measuring to the Nearest Half-Inch ................................ 87 Feet and Miles.................................................................... 89 Metric System: Meters and Kilometers .......................... 91 Weight in Pounds .............................................................. 92 Weight in Kilograms ........................................................ 94 Estimate Weight ................................................................ 96 Volume ............................................................................... 97 Volume in Milliliters ........................................................ 101 Review ................................................................................. 103
Chapter 10: Adding and Subtracting in Columns Introduction ....................................................................... Adding 3-Digit Numbers in Columns .............................. Carrying to Hundreds ...................................................... Carrying to Tens and to Hundreds ................................. Subtracting in Columns ................................................... Borrowing Two Times ..................................................... Adding Money Amounts .................................................. Review ................................................................................
104 106 109 113 117 121 124 126
Chapter 11: Exploring Multiplication Introduction ...................................................................... Many Times the Same Group ......................................... Multiplication and Addition ........................................... Multiplying on a Number Line ....................................... Multiplication Practice ................................................... Review ..............................................................................
4
128 130 133 137 140 142
Chapter 6: Geometry and Fractions Introduction The sixth chapter of the Math Mammoth Grade 2-B Complete Worktext covers geometry topics and an introduction to fractions. In geometry, the emphasis is still on exploring shapes: Combining shapes to get new ones, and dividing shapes with lines to get other shapes. The student also learns the concepts of right angle and parallel lines. These two concepts get the child started on the road to classifying shapes by their angles and sides. For example, later the child will classify triangles into right triangles, acute triangles, and obtuse triangles. Quadrilaterals are classified into rectangles, parallelograms, kites, trapezoids, and so on. Finding a right angle or parallel sides in a shape is therefore important.
Introduction to fractions In the section on fractions, the student learns to write fractions from pictures or color parts to show a fraction. The student should also learn that when comparing unit fractions, the one with the largest denominator is actually the smallest part. The child does not need to know this language yet, of course. The basic idea is simple: One-half is a bigger part than one-fifth. The last lesson explores finding a fractional part of many objects. It is important that children do not “fixate” the idea of a fraction to just pies or other shapes divided into parts. They need to also understand that fractions can be used when the “whole” is a group of things.
The Lessons page
span
Shapes Review ...............................................
7
2 pages
Right Angles ..................................................
9
2 pages
Parallel and Perpendicular Lines ...................
11
2 pages
Forming Shapes ............................................
15
2 pages
Solids .............................................................
16
1 page
Fractions ........................................................
17
2 pages
More on Fractions .......................................... 19
3 pages
5
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Buzzing with Shapes Tic tac toe with shapes; drag the counter to the shape that has that amount of sides. http://www.harcourtschool.com/activity/buzz/buzz.html Patch Tool An online activity where the student designs a pattern using geometric shapes. http://illuminations.nctm.org/ActivityDetail.aspx?ID=27 Pattern Blocks This program is designed to help with fractions, but kids will enjoy just playing with the polygon shapes. http://www.arcytech.org/java/patterns/patterns_j.shtml Polygon Playground Drag various colorful polygons to the work area to make your own creations! http://mathcats.com/explore/polygons.html Interactive Tangram Puzzle Place the tangram pieces so they form the given shape. http://nlvm.usu.edu/en/nav/frames_asid_112_g_2_t_1.html Tangram set Cut out your Tangram set by folding paper http://tangrams.ca/inner/foldtan.htm Make Your Own Mandala A mandala is a circular symmetrical design based on eights. Make your own and experiment with symmetry. http://www.girlsgotech.org/world_around_us.html Fractions - Part of a Whole Divide the pie into pieces and color some. The computer shows the fraction. http://nlvm.usu.edu/en/nav/frames_asid_102_g_2_t_1.html Visualizing Fractions The other way around as in the previous activity: the computer shows a fraction, and you divide the pie and color the pieces. http://nlvm.usu.edu/en/nav/frames_asid_103_g_2_t_1.html Naming Fractions An interactive activity that asks the student to name the fraction shown. http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html Who Wants Pizza? Lessons and interactive exercises about fractions, based on the pizza model. http://math.rice.edu/~lanius/fractions/frac.html
6
Shapes Review 1. Draw examples. Note that the sides of the shapes can be of different lengths.
a. Triangles (tri means three)
b. Quadrilaterals (quadri means four)
___ vertices (corners)
___ vertices (corners)
___ sides
___ sides
c. Pentagons (penta means five)
d. Hexagons (hex means six)
___ vertices
___ vertices
___ sides
___ sides
2. How is a circle different from all of the shapes above?
3. Color all triangles yellow. Color all quadrilaterals green. Color all pentagons blue. Color all hexagons purple. Or choose your own colors for each kind of shape.
7
This rectangle's sides are four units and two units in length. How many little squares are inside of it? ______
4. Draw on the grid below these rectangles, and count how many little squares are inside of them. a. a rectangle with sides 2 and 5 units long. Squares inside: ______ b. a rectangle with sides 3 and 3 units long. Squares inside: ______ c. a rectangle with sides 7 and 1 units long. Squares inside: ______ d. a rectangle with sides 6 and 2. Squares inside: ______ e. a rectangle with sides 4 and 3. Squares inside: ______ f. a rectangle with sides ____ and ____. Squares inside: 16.
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Right Angles These look like corners, but in mathematics we call them angles. Imagine sitting inside of each angle, and the walls going up around you in the shape of the “corner”. In which angle would you have lots of space to sit? In which angle would you have only a little space to sit? Find two “square corners”. In math we call them right angles.
Sometimes we draw a round line (an arc) inside of the angle to mark it.
Right angles are marked this way.
Corners of books are examples of right angles.
1. Write how many angles each shape has. Write how many right angles each shape has.
a.
b.
c.
____ angles
____ angles
____ angles
____ right angles
____ right angles
____ right angles
d.
e.
f.
____ angles
____ angles
____ angles
____ right angles
____ right angles
____ right angles
9
2. Draw the shapes below. First draw dots for the corners. Then connect those with straight lines.
a. a rectangle
b. a square
c. a triangle with
one right angle
d. a triangle with
e. a quadrilateral with
f. a pentagon with
no right angles
one right angle
one right angle
3. Continue this pretty pattern. Look carefully. Where in the pattern (not in the grid) can you find right angles?
4. Which of these shapes have to ALWAYS have a right angle? a) triangle b) square c) pentagon d) hexagon e) rectangle 5. The shapes are divided into parts. Write how many right angles there are. a.
b.
Right angles in the big shape: _____
Right angles in the big shape: _____
Right angles in each part _____
Right angles in each part _____ c.
d.
Right angles in the big shape: _____
Right angles in the big shape: _____
Right angles in each part _____
Right angles in each part _____
10
Parallel and Perpendicular Lines
These lines are parallel. They travel the same direction and are evenly spaced beside each other.
These lines are parallel too. They do not cross each other, even if you continued them.
Would these lines cross each other if you continued them?
1. Draw a line from dot to dot, and from diamond to diamond so that you get two parallel lines. Use a ruler!
a.
b.
c.
2. What kind of lines are lines s and s'? What kind of lines are lines t and t'? The shape formed in the middle is a parallelogram.
3. Join the same kind of dots with lines so that you get parallelograms. Draw one of your own, too.
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4. This is a rectangle. Now a tough question: Is it also a parallelogram? Are the rectangle's top and bottom sides parallel? Are the rectangle's left and right sides parallel?
5. a. Which of these shapes are parallelograms?
b. Here are names for the shapes that
were not parallelograms: KITE
TRAPEZOID
Match them with the right shapes. 6. Make some shapes. In (e) and (f) you can make your own.
a. Color a parallelogram
using 8 triangles.
b. Color a triangle
using 9 triangles.
c. Color a hexagon using
6 triangles.
d. Color a parallelogram
e. Color a _____________
f. Color a _____________
using 12 triangles.
using _____ triangles.
using ____ triangles.
12
(This page intentionally left blank.)
13
14
Forming Shapes Cut out the shapes on the previous page. You can color their flip sides if you wish. 1. Take two big right triangles in the top row, marked RT (for “Right Triangle”). With them form ... a. Two triangles with different shapes b. a rectangle c. a parallelogram that is not a rectangle.
Remember you can flip the triangles, too! 2. What shapes can you form using two of the big triangles in the second row marked ET (for Equilateral Triangle)? Draw sketches here.
3. What shapes can you form using two of the big blue triangles marked OT (for Obtuse Triangle)? Draw sketches here.
4. What shapes can you form using the little triangles in the bottom row marked RT (for Right Triangle)? Draw sketches here.
5. a. Take the four little equilateral triangles (ET). Form a big equilateral triangle. b. Take the four little obtuse triangles (OT). Form a big obtuse triangle. c. Take the six big equilateral triangles (ET). Form a hexagon.
6. Take two DIFFERENT triangles. Place together their sides that are the same length. What shapes can you make?
7. Now use all of the shapes and make some fun things such as a sailboat, a bird, a dog, or a house. You can draw sketches of your shapes here.
15
Solids 1
A rectangular prism in everyday speech is called a “box”.
A cube is a box, too, but all of its sides are equally long.
A cylinder has the same-size circle on the bottom and at the top.
A pyramid's bottom shape can be any many-sided figure.
A cone has a circle at one end and a point at the other.
1. Label the pictures with box, cube, cylinder, pyramid, or cone.
f.
l.
c.
b.
a.
g.
h.
m.
e.
d.
i.
j.
k.
p.
n.
o.
16
Fractions The shapes below are divided into equal-size parts.
two equal parts (halves)
three equal parts (thirds)
five equal parts (fifths)
eight equal parts (eighths)
1. How many equal parts are in each drawing? What are the parts called?
c. a.
d.
b.
___ equal parts ______________
___ equal parts
___ equal parts
______________
______________
___ equal parts ______________
A fraction tells you two things: z z
how many equal parts a whole is divided into (the bottom number). how many of those parts you are taking or coloring (the top number).
One-half of the rectangle is colored.
→ how many equal parts →
how many parts colored
Two-fifths of the circle is colored.
→ how many equal parts →
1 2
how many parts colored
2 5
2. Color the parts to show the fraction.
a.
2 7
b.
2 2
c.
17
5 8
d.
3 4
3. Write the colored part as a fraction.
a.
b.
5
c.
d.
e.
4. Divide into equal parts and color. Write the fraction.
Divide into eight equal parts. Color three parts.
Divide into three equal parts. Color three parts.
a.
Divide into four equal parts. Color two parts.
b.
c.
5. a. A cake was divided into 8 equal parts. Jack ate 2 parts. Write as a fraction what part Jack ate. b. What part of the cake is left for others to eat?
Write it as a fraction. 6. Is the whole divided into equal parts? If yes, color ONE part of the whole, and write the fraction.
a.
b.
c.
d.
e.
7. Color one whole. Write one whole as a fraction, in many different ways.
a. 1 =
b. 1 =
c. 1 =
18
d. 1 =
e. 1 =
More on Fractions 1. In each picture, color one part of the whole, and write the fraction. Circle the largest piece. a.
b.
d. c.
2. Color the fractions in the fraction bars on the left.
1 5
1 10
1 2
1 4
Find the smallest fraction (the smallest piece). Find the greatest fraction (the largest piece).
3. Color the fractions in the fraction bars on the right.
1 6
1 3
1 9
Find the smallest fraction. Find the greatest fraction. Write a fraction that is smaller than any of these:
4. Color one part of each. Circle the fraction that is more: a.
1 3
or
1 2
b.
1 2
or
1 5
c.
1 5
or
1 4
d.
1 5
or
1 6
e.
1 8
or
1 6
f.
1 2
or
1 8
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A group of things can be “one whole”. You can find part of that, and use fractions.
1 apple of the 3 is light yellow. 1/3 of the apples are light yellow. 3/4 of the apples are light yellow. 1/4 of the apples are dark red.
2 apples of the 3 are dark red. 2/3 of the apples are dark red.
5. Color the given part.
a. Color
d. Color
2 of the pears. 3
b. Color
3 of the pears. 3
e. Color
3 of the lemons. 4
4 of the lemons. 5
6. a. Some children had 8 toy cars. Mark took 3 of them. What part of the cars did Mark take? Write a fraction. b. What part of the cars was left for the other children?
7. a. Jack ate 4/5 of the 5 bananas. How many bananas are left? b. Jack also ate half of the cake, which was cut into 12 slices.
How many slices did he eat? 8. Which is a bigger piece: 1/8 of a pizza, or 1/6 of a pizza?
20
c. Color
5 of the carrots. 6
f. Color
3 of the carrots. 7
A whole “group of things” is divided into parts. You can use fractions.
1/3 of the apples are light yellow. 2/3 of the apples are dark red.
1/4 of the apples are light yellow. 3/4 of the apples are dark red.
9. Find what part of many objects.
a. Divide the pears into
2 equal groups. 1 Color of the pears. 2
d. Color
3 of the pears. 4
b. Make 3 equal groups.
Color
e. Color
1 of the lemons. 3
1 of the lemons. 4
c. Make 3 equal groups.
Color
f. Color
1 of the carrots. 3
2 of the carrots. 3
10. Now YOU draw and color.
a. Draw 10 balls. Divide them into 5 equal groups. 2 Color of the balls. 5
b. Draw 12 balls. Divide them into 4 equal groups. 3 Color of the balls. 4
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c. Draw 12 balls. Divide them into 6 equal groups. 5 Color of the balls. 6
Chapter 7: Place Value Till 1000 Introduction The seventh chapter of the Math Mammoth Grade 2-B Complete Worktext deals with three-digit place value - ones, tens, and hundreds.
The first lessons present three-digit numbers with hundred-flats, ten-pillars, and one-cubes. The child practices separating three-digit numbers into the different “parts”: hundreds, tens, and ones. Number lines will help visualize the numbers and build number sense. These lessons provide the basis for understanding three-digit place value. The lesson Skip-Counting Practice shows how to add or subtract a ten: you look at the tens digit in the number, and add or subtract 1 from it. In counting practice, emphasize the similarity to numbers that are less than 100. For example, in counting by fives from 305, the sequence is essentially the same as if counting by fives from 5, but just with the “three hundred” added each time. The Counting and Adding lesson has further practice. The student forms three-digit numbers from their parts, compares, fills number charts, and adds. The lesson, Which Number is Greater, has very simple exercises about comparing numbers. Then, the Comparing and Ordering lesson has further practice, plus some more advanced exercises. For example, the student compares sums, and finds a number on the empty line so that the comparison sentence is true. This last lesson also has a fun domino game where students build three-digit numbers and try to get them as close as possible to a given whole hundred. We also briefly study rounding to the nearest ten and to the nearest hundred.
The Lessons page
span
Hundreds Part 1.............................................
24
5 pages
Hundreds Part 2 ...........................................
29
3 pages
Skip Counting ...............................................
31
3 pages
Seven Hundred to 1000 ................................
34
3 pages
Counting and Adding .................................... 36
3 pages
Which Number Is Greater? ...........................
39
4 pages
Comparing and Ordering ..............................
43
4 pages
Rounding to the Nearest Ten ........................
47
2 pages
Rounding to the Nearest Hundred ................
49
1 page
Review ..........................................................
50
1 page
22
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Base Blocks from the National Library of Virtual Manipulatives Place enough hundred-flats, ten-sticks, and one-blocks into the work area to show given numbers. Choose “Columns = 3” to restrict the program to three-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html Place Value to Thousands Multiple choice questions; help the duck swing his golf club. http://www.toonuniversity.com/flash.asp?err=496&engine=5 Arithmetic Workshop Place Values Tool Drag models of ones, tens, hundreds, or thousands to the work area, group them, break them up, or practice any of the four operations using the same visual models. http://www.iknowthat.com/com/L3?Area=EarlyMathWorkbench and choose “Place Value”. Cookie Dough Either spell the number in words or write the digits. http://www.funbrain.com/numwords/index.html Inequalities Arrange the digits to make two numbers so that the comparison is true. Use six digits for two 3-digit numbers. http://www.primarygames.co.uk/PG5/Inequal/sidequal.html Naming Numbers These pages teach number naming skills covered in K8 math courses. Each page has an explanation, interactive practice and challenge games about naming numbers. http://www.aaamath.com/B/nam.htm Mostly Postie Drag the parcel onto the scales, then enter the value shown to deliver your letter or parcel. Practices counting in 10s and 100s http://www.ictgames.com/mostlyPostie.html Helipad Hops Read the “number” of the SOS message, add/subtract to make it the nearest whole ten, and click on the whole ten helipad where the helicopter should land. http://www.ictgames.com/helipad%20hops7.html Place Value at AAAMath.com Read, practice, and play with 3-digit numbers. http://www.aaaknow.com/plc21ax2.htm Place value puzzler Place value or rounding game, click on the asked place value in a number or type in the asked rounding. http://www.funbrain.com/tens/index.html Line Dry Game Fill in a missing number on the clothes line based on different skip counting patterns. www.fuelthebrain.com/Game/play.php?ID=15
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Hundreds, Part 1 Ten ones make a ten-pillar:
Ten ten-pillars make ONE HUNDRED:
=
10 ones =
=
10
10 tens =
100
Just like tens and ones, so also whole hundreds are counted separately and are written down in their own column: hundtens ones reds
=
3
2
7
three hundred twenty-seven
1. Count the ones, tens, and hundreds and fill in the table. a. One hundred
b. One hundred
c. One hundred
d. One hundred
one
six
eleven
thirteen
1 hundred 0 tens 1 one
1 hundred 0 tens 6 ones
1 hundred 1 ten 1 one
1 hundred 1 tens 3 ones
100 + 0 + 1
100 + 0 + 6
100 + 10 + 1
100 + 10 + 3
hundreds tens ones
hundreds tens ones
hundreds tens ones
hundreds tens ones
1
0
1
1
24
1
1
f. ________________
g. ________________
twenty
__________________
_________________
1 hundred 2 tens 0 ones
1 hundred ___ tens ___ ones
1 hundred ___ tens ___ ones
e. One hundred
100 + _____ + _____
100 + _____ + _____
100 + _____ + _____ hundreds tens ones
hundreds tens ones hundreds tens ones
h. ________________
i. ________________
j. ________________
_________________
__________________
__________________
1 hundred ___ tens ___ ones
1 hundred ___ tens ___ ones
1 hundred ___ tens ___ ones
100 + _____ + _____
100 + _____ + _____
100 + _____ + _____
H T O
H T O
H T O
k. ____________________________
____ hundreds _____ tens _____ ones H T O
25
2. Fill the number chart from 101 to 200.
101
200
3. Fill in the numbers for these number lines.
4. Draw a number line from 160 to 180.
26
5. The dots are ones, the pillars are tens.Group together ten ten-pillars to make a hundred.
a. 2 hundreds 3 tens 5 ones = 235
b. ___ hundreds ___ tens ___ ones =
c. ___ hundreds ___ tens ___ ones =
d. ___ hundreds ___ tens ___ ones =
e. ___ hundreds ___ tens ___ ones =
f. ___ hundreds ___ tens ___ ones =
g. ___ hundreds ___ tens ___ ones =
h. ___ hundreds ___ tens ___ ones =
i. ___ hundreds ___ tens ___ ones =
j. ___ hundreds ___ tens ___ ones =
27
6. Break these numbers down into hundreds, tens, and ones. a. 134 = ___ hundred ___ tens ___ ones
b. 167 = ___ hundred ___ tens ___ ones
= 100 + 30 + 4
= 100 + ____ + ____
c. 158 = ___ hundred ___ tens ___ ones
d. 170 = ___ hundred ___ tens ___ ones
= 100 + ____ + ____
= 100 + ____ + ____
e. 108 = ___ hundred ___ tens ___ ones
f. 140 = ___ hundred ___ tens ___ ones
= _____ + ____ + ____
= _____ + ____ + ____
g. 106 = ___ hundred ___ tens ___ ones
h. 127 = ___ hundred ___ tens ___ ones
= _____ + ____ + ____
= _____ + ____ + ____
7. What number is... a. one more than 118
b. two more than 116
c. ten more than 108
one more than 134
two more than 102
ten more than 125
one less than 103
two less than 112
ten less than 140
one less than 130
two less than 139
ten less than 127
d. one more than 165
e. two more than 193
f. ten more than 164
one more than 199
two more than 178
ten more than 188
one less than 173
two less than 170
ten less than 200
one less than 167
two less than 190
ten less than 177
28
Hundreds, Part 2 1. Fill in the chart. a. Two hundred
b. Two hundred
c. _________________
four
thirteen
200 + 0 + 4
200 + 10 + 3
_____ + ____ + ____
hundreds tens ones 2 0 4
hundreds tens ones
hundreds tens ones
d. _________________
e. _________________
f. _________________
___________________
___________________
___________________
_____ + ____ + ____
_____ + ____ + ____
_____ + ____ + ____
H T O
H T O
H T O
___________________
2. Mark the numbers on the number line: 244, 256, 301, 308 299, 245, 255, 262, 223, 211.
29
3. a. Draw a number line from 400 to 500, similar to the one in 2.). Only write the numbers below the whole tens.
b. Mark on your number line these numbers: 413, 498, 460, 402, 455, 416, 436, 468, 486.
4. Break these numbers down into hundreds, tens, and ones. b. 867 = ____ hundreds ____ tens ____
a. 276 = ____ hundreds ____ tens ____ ones
ones
= 200 + 70 + 6
= 800 + ____ + ____
c. 350 = ____ hundreds ____ tens ____ ones
d. 770 = ____ hundreds ____ tens ____ ones
= _____ + ____ + ____
= _____ + ____ + ____
e.
409 = ____ hundreds ____ tens ____ ones
f. 940 = ____ hundreds ____ tens ____ ones
= _____ + ____ + ____
= _____ + ____ + ____
g. 700 = ____ hundreds ____ tens ____ ones
h. 542 = ____ hundreds ____ tens ____ ones
= _____ + ____ + ____
= _____ + ____ + ____
i. 601 = ____ hundreds ____ tens ____ ones
j. 383 = ____ hundreds ____ tens ____ ones
= _____ + ____ + ____
= _____ + ____ + ____
5. What are these broken down numbers?
a. 5 tens 1 hundred 3 ones = 153
f. 5 ones 5 hundreds = ____
b. 2 ones 1 hundred 4 tens = ____
g. 9 ones 2 hundreds = ____
c. 2 hundreds 2 ones 0 tens = ____
h. 9 hundreds 3 ones 7 tens = ____
d. 8 tens 0 ones 1 hundred = ____
i. 3 hundreds 3 tens = ____
e. 4 ones 4 hundreds 2 tens = ____
j. 9 ones 5 hundreds = ____
30
Skip-Counting Practice What number is ten more than 253? Imagine adding one ten-pillar. The tens digit “5” in 253 changes to“6”: 253 + 10 = 263. What number is ten less than 253? Imagine taking away one ten-pillar. The tens digit “5” changes to“4”.
253
253 − 10 = 243.
What number is ten more than 497? Imagine adding one ten-pillar. Then you will have 10 ten-pillars! Those make a hundred. So you will have one new hundred, and zero ten-pillars. 497 + 10 = 507. You can also look at the digit pair formed by the hundreds and tens digits. The digit-pair “49” in 497 changes to “50”:
497
497 + 10 = 507.
What number is ten less than 403? Imagine taking away one ten-pillar - but there aren't any! Then you will have to break one hundred in to 10 ten-pillars and take one of those away! So you will have one less hundred left, and nine ten-pillars. 403 − 10 = 393.
403
Look at the digit pair formed by the hundreds and tens digits: The digit-pair “40” in 403 changes to “39”: 403 − 10 = 393.
31
1. Write the number that is 10 less and 10 more than the given number. e. _____, 129, _____
i. _____, 698, _____
b. _____, 710, _____
f. _____, 841, _____
j. _____, 606, _____
c. _____, 450, _____
g. _____, 592, _____
k. _____, 209, _____
d. _____, 690, _____
h. _____, 478, _____
l. _____, 505, _____
a.
610 , 620, 630
2. Count by tens. a. 304, 314, ______, ______, ______, ______, ______, ______, ______, ______ b. 331, 341, ______, ______, ______, ______, ______, ______, ______, ______ c. 430, 440, ______, ______, ______, ______, ______, ______, ______, ______ d. 407, 417, ______, ______, ______, ______, ______, ______, ______, ______
3. Fill the number chart from 301 to 400.
301
400
32
4. What are the numbers that come before and after? a. _____, 700, _____
e. _____, 129, _____
i. _____, 998, _____
b. _____, 345, _____
f. _____, 801, _____
j. _____, 646, _____
c. _____, 450, _____
g. _____, 531, _____
k. _____, 209, _____
d. _____, 671, _____
h. _____, 478, _____
l. _____, 460, _____
5. Count by fives. The previous number chart can help. a. 305, 310, ______, ______, ______, ______, ______, ______, ______, ______, _____ b. 375, 380, ______, ______, ______, ______, ______, ______, ______, ______, _____ c. 435, 440, ______, ______, ______, ______, ______, ______, ______, ______, _____ d. _____, ______, ______, ______, ______, ______, ______, ______, ______, 400, 405
6. Count by twos. The number chart can help for some of these. a. 200, 202, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____ b. 468, 470, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____ c. 386, 388, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____ d. _____, _____, _____, _____, _____, _____, _____, _____, _____, _____, 502, 504 e. 479, 481, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____
7. What are these broken down numbers? a. 500 + 5 = ______
e. 20 + 9 + 400 = _____
i. 10 + 500 = ______
b. 60 + 6 + 500 = ______
f. 2 + 900 + 40 = _____
j. 5 + 100 = ______
c. 6 + 700 = _____
g. 8 + 300 = ______
k. 40 + 100 + 1 = ______
d. 600 + 70 = ______
h. 3 + 800 = ______
l. 1 + 400 + 10 = ______
33
Seven Hundred to a Thousand 1. Fill in the table. a. ____________________________
____ + ____ + ____
b. ____________________________
H T O
_____ + ____ + ____
c. Eight hundred five
____ + ____ + ____
H T O
d. ____________________________
H T O
____ + ____ + ____
H T O
2. Mark these numbers on the number line: 829, 805, 795, 748, 782, 835, 766, 743, 801
34
3. Draw a number line similar to the one in exercise 2. from 800 to 900.
4. Count by tens. a. 748, 758, _____, _____, _____, _____, _____, _____, _____, _____, _____ b. 274, 284, _____, _____, _____, _____, _____, _____, _____, _____, _____ c. _____, _____, _____, _____, 423, 433, _____, _____, _____, _____, _____
5. Count by fives. a. 500, 505, _____, _____, _____, _____, _____, _____, _____, _____, _____ b. 755, 760, _____, _____, _____, _____, _____, _____, _____, _____, _____ c. _____, _____, _____, _____, _____, _____, _____, _____, _____, 995, 1000
6. Count by twos. a. _____, _____, _____, _____, _____, _____, 506, 508, _____, _____, _____ b. 301, 303, _____, _____, _____, _____, _____, _____, _____, _____, _____ c. 695, 697, _____, _____, _____, _____, _____, _____, _____, _____, _____
7. Break these numbers down into hundreds, tens, and ones. a. 345 = 300 + 40 + 5
b. 401 = _____ + ____ + ___
605 = _____ + ____ + ___
320 = _____ + ____ + ___
c. 715 = _____ + ____ + ___
d. 987 = _____ + ____ + ___
909 = _____ + ____ + ___
210 = _____ + ____ + ___
35
Counting and Adding 1. What are these broken down numbers? a. 700 + 30 + 3 = 733
b. 200 + 40 + 5 = _____
500 + 40 + 5 = _____ d. 40 + 700 = ____
400 + 7 = _____
20 + 700 + 8 = _____
e. 50 + 600 = _____
900 + 2 + 50 = _____ g. 4 + 200 = _____
f. 60 + 200 = _____
30 + 3 + 900 = _____ h. 400 + 30 = _____
7 + 90 + 500 = _____
c. 100 + 50 = _____
1 + 800 = _____ i. 5 + 80 = _____
80 + 400 + 8 = _____
400 + 3 = _____
2. Underline or circle which is more. Write as numbers too. a.
b. 2 hundreds 4 tens
4 hundreds
7 hundreds 9 ones
d. 3 hundreds 9 ones
3 hundreds
3 hundreds
9 hundreds 3 tens
f.
1 hundred 6 tens
3 hundreds
h. 3 hundreds 5 tens
4 hundreds 8 tens
i. 2 hundreds 2 tens
2 hundreds
j. 3 hundreds 8 ones
8 hundreds 3 ones
6 hundreds
5 hundreds
600
500
c.
7 hundreds
e.
g.
36
8 hundreds
7 hundreds 9 ones
3. This number chart is supposed to be filled with whole TENS.
10
20
30
40
50
60
100
110
BEFORE you fill it in, here's a CHALLENGE: Can you find out the LAST number on the chart without filling it in?
_________
4. Use the chart above to help, and find how many whole tens are... a. in 50
c. in 130
e. in 250
g. in 780
b. in 90
d. in 200
f. in 550
h. in 1000
Now explain a quick “trick” to find the answers for the above problems: _________________ __________________________________________________________________________ 5. Fill in this number chart counting by FIVES.
5
10
15
BEFORE you fill it in, here's a CHALLENGE: Can you find out the LAST number on the chart without filling it in? _________ *Another challenge*: How many fives are in 50? in 250?
37
20
25
30
6. Ten, tens make a new hundred. Eleven tens is one ten more than that. Write the numbers the normal way. Manipulatives or drawing pictures may help. a. 10 tens = 100
d. 10 tens 2 ones =
b. 11 tens =
e. 10 tens 8 ones =
c. 12 tens =
f. 11 tens 5 ones =
g. 18 tens =
i. 15 tens 6 ones =
h. 20 tens =
j. 20 tens 7 ones =
k. 1 hundred 10 tens =
n. 2 hundreds 10 tens =
l. 1 hundred 13 tens =
o. 50 tens =
m. 1 hundred 16 tens =
p. 76 tens 3 ones =
7. Add the hundreds, tens, and ones. Then change each 10 tens into a hundred. The first one is done for you. a. 7 tens and 8 tens
= =
b. 6 tens 2 ones and 5 tens
15 tens
= _____ tens ____ ones = _____ hundreds _____ tens _____ ones
1 hundreds 5 tens
c. 7 tens 5 ones and 7 tens 4 ones
d. 1 hundred 3 tens and 9 tens
= _____ tens ____ ones
= _____ hundred _____ tens
= _____ hundreds _____ tens _____ ones
= _____ hundreds _____ tens
e. 1 hundred 6 tens and 8 tens
f. 1 hundred 8 tens 2 ones and 5 tens
= _____ hundreds _____ tens
= _____ hundreds _____ tens ____ ones
= _____ hundreds _____ tens _____ ones
= _____ hundreds _____ tens _____ ones
g. 8 tens 9 ones and 7 tens
h. 8 tens 9 ones and 7 ones
= _____ tens ____ ones
= _____ tens ____ ones
= _____ hundreds _____ tens _____ ones
= _____ hundreds _____ tens _____ ones
38
Which Number is Greater? 1. Circle the number that is more. a.
145
b.
154
234
c.
225
194 d.
240
189
302
When comparing three-digit numbers, 1. First look at ______________________. For example, 652 is less than 701, because 652 has less hundreds than 701. 2. If the numbers have the same amount of hundreds, then look at the _____________ For example, 652 > 639 because though it has the same amount of hundreds, it has more ________ than 639. 3. If the numbers have the same amount of hundreds AND the same amount of tens, then look at the _____________. For example, 652 < 655 because though it has the same amount of hundreds and the same amount of tens, it has more _________. Remember, the open end (or open mouth) of the symbols < and > ALWAYS points to the bigger number.
39
2. Draw squares for hundreds, sticks for tens, and dots for the ones. Then write either < or > in between the two numbers.
a. 160
170
b. 244
424
c. 305
503
d. 209
490
e. 478
500
f. 260
279
g. 404
244
h. 112
211
3. Write numbers that come before and after the given number. a. _____ < 179 < _____
c. _____ < 588 < _____
e. _____ < 800 < _____
b. _____ < 201 < _____
d. _____ < 640 < _____
f. _____ < 917 < _____
40
4. Mark the numbers on the number line. Then write them in order.
513, 530, 489, 468, 596, 606, 560, 466, 506, 516
_____ < _____ < _____ < _____ < _____ < _____ < _____ < _____ < _____ < _____ 5. Write either < or > in between the numbers. a. 159 < 300
b. 122
100
c. 320
328
d. 212
284
e. 200
190
f. 600
860
g. 456
465
h. 711
599
i. 780
500
j. 107
700
k. 566
850
l. 840
480
m. 320
300
n. 505
450
o. 860
289
p. 312
231
q. 400
499
r. 209
302
s. 391
919
t. 759
394
6. Choose the biggest number! a. 259, 592, 295
b. 470, 774, 747
c. 409, 944, 949
d. 506, 605, 505
e. 911, 119, 191
f. 482, 382, 284
g. 334, 433, 403
h. 208, 820, 802
41
7. Write a number that is in between the two given numbers. Note there are many possibilities! a. 140 < ____ < 149
d. 304 < ____ < 310
g. 568 < ____ < 654
b. 267 < ____ < 289
e. 160 < ____ < 170
h. 799 < ____ < 804
c. 279 < ____ < 290
f. 236 < ____ < 799
i. 156 < ____ < 158
8. Arrange the number triplets in order. a. 140, 156, 149
b. 357, 573, 750
c. 239, 286, 133
d. 670, 766, 676
e. 466, 344, 922
f. 190, 205, 291
g. 109, 901, 199
h. 233, 239, 228
i. 717, 175, 177
140 < 149 < 156
9. Find your way through the maze! The rules are: you can move either left, right, or down, provided that the number following is BIGGER than the number in the square you're in.
100 121 127 133 167 189 200 214 212 398 145 166 134 135 120 230 212 256 347 405 156 167 137 156 155 226 356 378 380 407 632 234 138 246 267 278 476 477 450 417 432 256 200 250 245 300 355 487 478 456 355 253 289 244 305 303 570 569 490 453 361 385 377 367 356 301 537 566 505 498 689 654 390 480 478 488 675 507 508 689 654 543 489 488 483 577 589 609 504 769 723 566 570 589 578 734 631 616 789 1000
42
Comparing and Ordering 1. Mark the numbers on the number line. Then write them in order.
810, 725, 799, 802, 843, 795, 810, 801, 766, 729
____ < _____ < _____ < _____ < _____ < _____ < _____ < _____ < _____ < ______
2. Write either < or > in between the numbers. a. 150 < 515
b. 22
120
c. 307
320
d. 412
284
e. 240
750
f. 860
680
g. 406
620
h. 558
540
i. 605
450
j. 107
705
k. 566
856
l. 890
870
m. 577
737
n. 405
440
o. 800
299
p. 153
315
q. 500
499
r. 705
557
s. 991
119
t. 232
302
43
3. Compare the expressions and write , or = . a. 300 + 60 + 5
365
b.
300 + 4
300 + 40
c.
200 + 60 + 4
60 + 4 + 200
d.
300 + 5
400 + 1
e.
4 + 900 + 8
500 + 90 + 8
f.
100 + 8
10 + 8
g.
800 + 70 + 2
700 + 80 + 7
h.
90 + 8
8 + 900
i.
8 + 600
60 + 800
j. 30 + 300 + 5
k.
5 + 50
60 + 500
l.
m. 40 + 4 + 600
20 + 800
n. 30 + 7 + 700
400 + 5
90 + 8 + 100 4 + 500 700 + 70 + 3
4. Write numbers on empty lines so that the comparisons are true. For some problems there are many possible answers. a.
750 + ____ > 757
b.
645 = 600 + 5 + ____
c.
200 + ____ > 200 + 60 + 4
d.
278 > ____ + 5
e.
____ + 4 = 304
f. ____ + 100 = 152
g.
____ + 4 < 900 + 8
h.
i. k. m.
788 = 80 +____ + 8
100 + 8 <
____ + 90
j. ____ + 500 = 530
300 + 20 + ___ < 322
l.
___ + 60 < 500 + 60
n.
44
900 + 30 > 900 + ____ 30 + ____ > 40 + ____
5. Arrange the numbers in order and write in boxes the corresponding letters. What is white and hiding in a bush? H Y S A S H E K M K L I A 770 455 105 77 757 350 957 803 503 707 517 515 777
____
<
____ < ____ < ____ <
____ < ____ < ____ < ____ < ____ < ____ < ____ < ____ < ____
MYSTERY NUMBERS (all numbers are less than 100)
a. It is the same whether you read it from
b. The digits of this number add up to 9. It is
left to right or from right to left. It is less than 100, but more than 92.
more than 50 but less than 60.
c. The digits of this number add up to 8. If
d. This number is between 30 and 40. If
you count by tens from it, you will eventually reach 73.
you count by tens from it, you will eventually get to 78.
e. It is less than 10. If you double it, you get
f. It is less than 15 but more than 9. If
a number that is more than 10, but you won't get 14, 18, or 12.
you count by fives from this number, you will eventually reach 36.
g. Its digits add up to 11. If you double it,
h. If you count by tens, three times, from it,
you'll get to 62.
you get a number between 50 and 60.
45
6. Learning game - make numbers with dominoes! You will need: paper, pencils and a standard set of dominoes (from 0-0 to 6-6), from which you take away 6-6, 5-5, and 5-6. Optionally for each player: you need 3 paper plates. Write on their top part the words: Hundreds, Tens, Ones. This game is for 2 to 6 people. Goal: In this game, you build a number with dominoes so that one (or two) dominoes make up the hundreds digit, one (or two) dominoes make up the tens digit, and one (or two) dominoes the ones digit. You just add up the dots in the domino(es) to get the digit. The goal is to build your number as close to a given target number as possible. The player who gets closest to the target number wins. Rules: The players determine who starts. The dominoes are upside down in front of the players. The game leader announces a target number, which is any whole hundred from 300 to 900. Then, each player takes 3 dominoes randomly, and makes his number out of them. Each player's dominoes are visible to the others. Then everyone will get a chance to take ONE more domino, if they wish (this is not compulsory). The player can add that domino to any of the digits (ones, tens, or hundreds). After that, the numbers are checked, and whoever gets the closest number to the target number, wins. For example, if you get the dominoes 4-3, 2-2, and 1-4, it means you can use the digits 7, 4, and 5. Let's say the target number is 600, so you build your number to be 547. Then, you choose to pick up one more domino, which ends up being 1-3. So you need to add 4 to one of your digits. You add it to your tens, getting 587. Another example. If you have built the number 789 and you pick a new domino 6-3, then you need to add 9 to one of your digits. But that will make them “spill over” to the next place value. So either you add 9 to your ones, resulting in 789 + 9 = 798, or you add 9 tens, resulting in 789 + 90 = 879, or you add 9 hundreds, resulting in 789 + 900 = 1689. Variation 1: In each round, you can choose to give the losers as many points as they were away from the target number, and continue playing till someone reaches a pre-determined “losing” number, such as 1,000. Variation 2: You can let each player either add or subtract the additional domino from any of the place values. For example, if you have built 328 and you pick 1-1, you could subtract 2 from your tens, leaving you 308.
46
Rounding to the Nearest Ten Rounding to the nearest ten This number line has the whole tens marked (720, 730, and so on). Let's think about all of the numbers between 740 and 750. Which of them are nearer to 740 than to 750? Which ones are nearer to 750?
Rounding a number to the nearest ten means finding which whole ten the number is closest to. We use the symbol ≈ when rounding. Read it as “is approximately” or “is about”. Read the examples below. They are also illustrated on the number line with arrows. 731 ≈ 730
767 ≈ 770
724 ≈ 720
(731 is approximately 730)
(767 is about 770)
(724 is approximately 720)
Numbers that end in 1, 2, 3, or 4 are rounded down to the previous whole ten. Numbers that end in 5, 6, 7, 8, and 9 are rounded up to the next whole ten. Notice that numbers ending in 5 are rounded up even though actually they are as far from the previous whole ten as they are from the next whole ten. For example, 855 is equally far away from 850 as it is from 860, but 855 ≈ 860 when rounding to the nearest ten. 1. Round the numbers to the nearest whole ten. Use the number line to help. a. 243 ≈ _______
b. 287 ≈ _______
c. 251 ≈ _______
d. 298 ≈ _______
e. 266 ≈ _______
f. 214 ≈ _______
g. 255 ≈ _______
h. 295 ≈ _______
i. 307 ≈ _______
j. 302 ≈ _______
k. 276 ≈ _______
l. 242 ≈ _______
47
2. Write the previous and the next whole ten, then round the number. a. _____, 472, _____
b. _____, 829, _____
c. _____, 514, _____
472 ≈ _______
829 ≈ _______
514 ≈ _______
d. _____, 317, _____
e. _____, 608, _____
f. _____, 455, _____
317 ≈ _______
608 ≈ _______
455 ≈ _______
g. _____, 943, _____
h. _____, 865, _____
i. _____, 364, _____
943 ≈ _______
865 ≈ _______
364 ≈ _______
Whole hundreds are whole tens, too Remember that 100, 200, 300 and all of the other whole hundreds are also whole tens. Why? Remember 100 is 10 tens. 200 would be 20 tens. So, when rounding 603 to the nearest whole ten, we get 603 ≈ 600. And 799 ≈ 800. 3. Round the numbers to the nearest ten. a. 402 ≈ _______
b. 396 ≈ _______
c. 804 ≈ _______
d. 97 ≈ _______
897 ≈ _______
393 ≈ _______
805 ≈ _______
997 ≈ _______
4. Round each number to the nearest whole ten. Place each answer in the cross-number puzzle. Across: Down: a. 633
a. 655
b. 796
b. 819
c. 447
c. 397
d. 54
d. 512
e. 306
e. 911
a. c. b.
c.
d.
e.
e.
48
Rounding to the Nearest Hundred We can also round numbers to the nearest hundred. The numbers “residing” in the red areas on the number line are rounded to 800. The numbers in the blue areas are rounded to 900.
Again, distance matters. Numbers from 801 to 849 are closer to 800 than to 900. Numbers from 851 to 899 are closer to 900 than to 800. And the “middle guy”, 850, is rounded up to 900: 850 ≈ 900. Where would you round these numbers when rounding to the nearest hundred?
531 ≈ ______
282 ≈ ______
839 ≈ ______
954 ≈ ______
You can imagine a number line in your mind like the one above, just change 800 and 900 to 500 and 600, or whatever the two whole hundreds are that your number is in between. Check that you understand this idea: z z z
Numbers ending in 01 till 49 will be rounded down, to the previous hundred. Numbers ending in 50 till 99 are rounded up, to the next whole hundred. Notice that numbers 1, 2, 3, ...., 49 get rounded to 0!
1. Round the numbers to the nearest hundred. a. 243 ≈ ______
b. 287 ≈ ______
c. 751 ≈ ______
d. 98 ≈ ______
e. 566 ≈ ______
f. 414 ≈ ______
g. 355 ≈ ______
h. 795 ≈ ______
i. 907 ≈ ______
j. 512 ≈ ______
k. 976 ≈ ______
l. 42 ≈ ______
2. Fill in. In (a) and (b), round to the nearest hundred. In (c), first add and then round to the nearest ten. a. Normally Mary receives about ______ spam emails
daily, but on 5/9 she got about _______ spams. b. During the work week from 5/7 till 5/11
she received about _______ spams. c. During the workweek from 5/7 till 5/11
she received about _______ real emails.
49
Spam Emails Mary Received
Real Emails Mary Received
Date
Spams
Date
Emails
Mo 5/7
125
Mo 5/7
13
Tu 5/8
97
Tu 5/8
17
Wd 5/9
316
Wd 5/9
21
Th 5/10
118
Th 5/10
12
Fr 5/11
106
Fr 5/11
18
Review 1. a. Write the number illustrated by the image: _________ b. Write the number that is 1 more
than the number you wrote in (a): ________ c. Write the number that is 10 more
than the number you wrote in (a): ________ d. Write the number that is 100 more
than the number you wrote in (a): ________ 2. Write the numbers that come before and after the given number. a. _____, 910, _____
b. _____, 239, _____
c. ____, 400, _____
3. Write the numbers that are 10 less and 10 more than the given number. a. _____, 560, _____
b. _____, 482, _____
c. _____, 292, _____
4. Write either < or > in between the numbers. a. 238
265
b. 391
193
c. 405
450
d. 981
819
5. Write with numbers. a. 2 tens 7 hundreds 3 ones = _______
c. 2 ones 6 hundreds = _______
b. 8 hundreds 9 tens = _______
d. 7 tens 3 hundreds 1 one = _______
6. What are these broken down numbers? a. 700 + 9 = _______
b. 70 + 600 + 4 = _______
c. 80 + 500 = _______
7. Round the numbers to the nearest ten. a. 639 ≈ _______
b. 505 ≈ _______
c. 282 ≈ _______
8. Count by fives: _____, _____, _____, _____, _____, 715, 720, _____, _____, _____
50
Chapter 8: Mental Addition and Subtraction Introduction The eighth chapter of the Math Mammoth Grade 2-B Complete Worktext covers mental adding and subtracting topics with 3-digit numbers.
The goal of this whole chapter is to solidify children's understanding of 3-digit place value, since being able to add and subtract whole hundreds, whole tens, and ones is based on understanding well the 3-digit place value. These problems build number sense and also build children's understanding of addition and subtraction. In most lessons, the addition or subtraction is first illustrated with pictures so the student can learn the concepts relating to the different place values. You can obviously also use base ten blocks or other similar manipulatives to this end. The lesson on graphs uses three-digit numbers in context with the problems.
The Lessons page
span
Completing the Next Hundred ........................ 52
4 pages
Add and Subtract Whole Hundreds ................
56
3 pages
Practice with Whole Hundreds .......................
59
2 pages
Addition/Subtraction Connection ...................
61
3 pages
Graphs ............................................................
64
2 pages
Adding Whole Tens ........................................ 66
3 pages
Subtracting Whole Tens .................................
69
2 pages
Rounding and Estimating ...............................
71
2 pages
Adding Ones ...................................................
73
3 pages
Subtracting Ones Mentally .............................
76
3 pages
Review of Mental Math .................................. 79
1 page
Helpful Resources on the Internet Random Stop 1000 Place digits strategically into the addition problem so that the sum is as close as 1000 as possible. http://www.primarygames.co.uk/pg4/SpeedStop/randomstop.html
51
Completing the Next Hundred
60
+
=
+
+ ___
= 100
260
=
+ ___ =
300
We need 10 ten-pillars to make a hundred. Draw the missing ones.
1. Compare and complete the next hundred. a. 80 + ____ = 100
b. 30 + ____ = 100
c. 40 + ____ = _____
280 + ____ = 300
330 + ____ = _____
940 + ____ = 1000
680 + ____ = ____
530 + ___ = _____
740 + ____ = _____
2. Complete the next hundred and write a corresponding problem where you complete just 100. a. 540 + ____ = 600
b.
120 + ____ = ____ ____ + ____ = 100
c.
____ + ____ = 100
40 + 60 = 100 d.
250 + ____ = 300
e.
440 + ____ = ____
630 + ____ = 700 ____ + ____ = 100
f.
780 + ____ = _____
____ + ____ = 100
____ + ____ = 100
a. 590 + 10 = 600
e. 710 + ____ = ____
i. 940 + ____ = 1000
b. 550 + ____ = 600
f. 720 + ____ = _____
j. 880 + ____ = _____
c. 110 + ____ = ____
g. 370 + ____ = _____
k. 290 + ____ = _____
d. 440 + ____ = ____
h. 250 + ____ = ____
l. 970 + ____ = _____
3. Complete to the next hundred.
52
How to subtract tens from whole hundreds? Break down one hundred into 10 ten-pillars.
200 – 40 = ?
200 – 40 = ____
Cross out four ten-pillars. How much is left?
4. Break down a hundred, then subtract. Draw a picture. a. Break down a hundred. Cross out 5 tens.
b. Break down a hundred. Cross out 7 tens.
200 – 50 = ____
300 – 70 = ____
c. Break down a hundred. Cross out 8 tens.
d. Break down a hundred. Cross out 1 ten.
300 – 80 = ____
200 – 10 = ____
e. Break down a hundred. Cross out 70.
f. Break down a hundred. Cross out 60.
400 – 70 = ____
200 – 60 = ____
5. Subtract and compare the problems! a. 100 – 10 =
b. 100 – 50 =
c. 100 – 40 =
d. 100 – 90 =
600 – 10 =
300 – 50 =
600 – 40 =
800 – 90 =
400 – 10 =
700 – 50 =
200 – 40 =
900 – 90 =
900 – 10 =
500 – 50 =
800 – 40 =
1000 – 90 =
53
6. Write a number sentence for each word problem, and solve. a. Roy and Rhonda collect pennies. Roy has 640 pennies now. Rhonda has 500.
How many more pennies does Roy have than Rhonda? How many more pennies does Roy need to have 700 pennies?
b. An uncle gave both of them 50 pennies.
How many pennies does Roy have now? How many pennies does Rhonda have now?
c. How many more does Roy need now to have 700 pennies?
How many more does Rhonda need now to have 600 pennies?
d. Jane collects pretty rocks. She has 120.
How many more will she need to have 200? How many more will she need to have 300?
e. Janet works after school on Tuesdays and Thursdays, and also on Saturdays.
On the weekdays she gets paid $15 and on Saturdays $30. How much does she earn in one week? In two weeks? In three weeks? In four weeks (a month)? How many weeks will she need to work and earn money to buy a bicycle for $250? She earned the money and bought the bike. How many dollars does she have left?
54
7. Count by 20s, 40s and 50s, and fill in the grids. a.
420
b.
440
520
40
80
240
280
720 900
c.
600
650
920
700
1000
1000
610 620 630 640
740
a. How many different number sentences can you make
by placing + or – signs into the squares?
500
40
50 =
200
20
70 =
500
40
50 =
200
20
70 =
500
40
50 =
200
20
70 =
500
40
50 =
200
20
70 =
b. Use the numbers 90, 70, and 40, addition and subtraction, and make number sentences.
What is the smallest possible answer? What is the greatest possible answer?
55
Add and Subtract Whole Hundreds Ten ones make a ten-pillar:
Ten ten-pillars make ONE HUNDRED:
=
ten ones =
=
10
ten tens =
100
1. A dot is one, a stick is a ten, and a square is a hundred. Write the addition sentences. Add in columns. Put the hundreds in their own column.
+
H
T
O
2 + 1
0 0
0 0
+
a. 200 + 100 = 300 T
O
H
T
O
H
T
O
+
O +
+
c. ____+ _____ = _____
+
d. 307 + _____ = _____ H
+
T
b. 260 + _____ = _____ H
+
H
T
O +
+
e. ____+ _____ = _____
f. ____+ _____ = _____
Only the ________________ digit changes in the answer.
56
+
2. Cross out as many hundreds as the problem indicates. Do the problems in columns as well. H
T
O
4 – 1
0 0
0 0
H
O
T
O
–
a. 400 – 100 = _______
H
T
b. 350 – 100 = _______
T
O
H
–
–
c. 140 – 100 = _______
H
d. _______ – 200 = _______
T
O
H
–
T
O
–
e. _______ – 100 = _______
f. _______ – 200 = _______
H H
T
T
O –
–
g. _______ – 500 = _______
h. _______ – 400 = _______
Only the ________________ digit changes in the answer.
57
O
3. Draw pictures like in the previous exercises for these problems.
a. 279 + 300 =
b. 478 + 200 =
c. 356 + 300 =
d. 188 + 500 =
4. Draw illustrations. Cross out some. Write a subtraction sentence. a. Draw 607. Cross out 200.
b. Draw 890. Cross out 500.
c. Draw 594. Cross out 300.
d. Draw 716. Cross out 400.
58
Practice with Whole Hundreds 204 + 300 = 504
465 – 200 = 265
I'm adding three whole hundreds (300). ONLY the hundreds' digit will change.
I'm subtracting two whole hundreds (200). ONLY the hundreds' digit will change.
1. Add whole hundreds. Think back to the pictures in the previous lesson. a. 500 + 200 =
b. 502 + 100 =
c. 140 + 200 =
d. 100 + 900 =
300 + 500 =
330 + 100 =
409 + 200 =
410 + 400 =
600 + 200 =
107 + 100 =
270 + 200 =
800 + 200 =
a. 600 – 300 =
b. 170 – 100 =
c. 550 – 200 =
d. 609 – 100 =
800 – 200 =
550 – 100 =
920 – 200 =
609 – 200 =
400 – 300 =
107 – 100 =
706 – 200 =
690 – 200 =
2. Subtract whole hundreds.
3. Continue the patterns! a.
b.
c.
310 + 100 = _____
182 + 100 = _____
245 + 100 = _____
310 + 200 = _____
182 + 200 = _____
245 + 200 = _____
310 + 300 = _____
182 + 300 = _____
245 + _____ = _____
310 + _____ = _____
182 + _____ = _____
245 + _____ = _____
310 + _____ = _____
182 + _____= _____
245 + _____ = _____
310 + _____ = _____
182 + _____= _____
245 + _____ = _____
59
4. Subtract and add many times. a. 600 – 200 – 200 =
b. 1000 – 200 – 200 – 200 =
500 – 300 – 200 =
700 – 200 – 100 – 400 =
c. 200 + 300 + 100 + 200 =
d. 650 – 300 – 100 – 100 =
211 + 200 + 100 + 300 =
107 + 200 + 500 + 100 =
5. Subtract and add whole hundreds. – 100
a. 700
____
– 100
b. 460
– 200
– 200
____
c. 205
____
+ 600
____
– 100
+ 200
____
– 300
____
+ 200
____
– 400
+ 500
____
____
– 200
____
– 200
____
– 100
____
– 300
____
+ 300
+ 400
____
– 200
____
300
– 300
____
260
+ 600
____
905
6. Find the missing addends. a.
b.
c.
500 + ____ = 700
____ + 300 = 1000
200 + ____ + 200 = 700
200 + ____ = 700
____ + 100 = 1000
700 + ____ + 100 = 1000
670 + ____ = 770
____ + 450 = 850
400 + ____ + 200 = 800
301 + ____ = 701
____ + 230 = 330
200 + ____ + 400 = 1000
60
Addition / Subtraction Connection Two parts make a total. You can z z
add the parts to get the total; or subtract a part from the total - and get the second part
|----------- total 31 ----------| 20
11
20 + 11 = 31
32 + 21 = 53
31 – 11 = ___
53 – 21 = ___
31 – 20 = ___
53 – 32 = ___
1. For each addition sentence, write two subtraction sentences. Fill in the missing parts. |-------- total _____ ---------| 700 a. 700 + 100 = ____
|-------- total _____ ---------|
|-------- total _____ ---------|
b. 69 + 24 = ____
c. 450 + 400 = ____
e. ____ + ____ = ____
f. ____ + ____ = ____
100
____ – 100 = ____ ____ – 700 = ____ d. ____ + ____ = ____
86 – 40 = ___
____ – ____ = ___
98 – 50 = ____
____ – ____ = ____
604 – 400 = ____
____ – ____ = ____
2. a. A store sells blue chairs and green chairs. Out of the 605 chairs, 200 are green. How many are blue? b. Another store has 500 red chairs and 304 white chairs.
What is the total number of chairs the store has?
61
|----------- total 96 -----------|
Sometimes you know the total and you don't know one part.
16
?
16 + ? = 96
You can write a missing addend sentence, and a subtraction sentence.
96 – 16 = ___
3. Write a missing addend problem and a subtraction problem with the same numbers. |-------- total _____ ---------|
|-------- total _____ ---------|
|-------- total _____ ---------|
a. 560 + 100 = 660
b. 200 + ____ = 900
c. ____+____= ____
660 – 560 = 100
____–____= ____
560
100
|-------- total _____ ---------|
|-------- total _____ ---------| 29
d. 32 + ___= 76
____–____= ____
80
750 – 150 = ___ |--------- total 260 ----------| 120
e. ___ + ____ = ___
f. ____+____= ____
____–____= ____
____–____= ____
4. Solve. a. A basket contains 26 vegetables: 6 carrots, 10 radishes, and _____ tomatoes. b. Mom took 8 potatoes from a bowl, and now there are 16 left.
How many potatoes were in the bowl? c. In a bouquet of 36 roses, 15 are white and 10 are red. The rest are yellow.
How many are yellow? 5. Find the difference. a. 10 and 49
b. 400 and 705
62
c. 200 and 650
6. Solve the word problems. You can draw pictures to illustrate them! a. Ryan bought three carpets for $200 each, and one small carpet for $9.
What was Ryan's total bill? The store owner then gave him a $100 discount. How much was the bill after the discount?
b. A piece of wood is 510 centimeters long.
Brian cut off two 200 cm pieces. How long is the rest of the original piece? . c. A manufacturing plant produces 300 car tires in a day.
Each day, they add 100 tires to their stock and sell the rest. How many tires do they sell in one day? How many tires do they sell in two days? How many tires do they sell in three days? How many days does it take to sell one thousand tires?
d. Anita had 566 stamps. Her aunt gave her 300 new ones for her birthday.
After that she decided to give 100 of her stamps to her brother. How many stamps does Anita have now?
e. A table-chairs set costs $100. James bought one of those,
and also a kiddy swimming pool for $50. What was James' total bill? He paid with $200. How much money does he have left now?
63
Graphs 1. Below, you see page counts of 16 different second grade math books. 217 388 403 424 365 290 304 315 243 352 289 392 346 308 329 323 Fill in the chart with tally marks and numbers. Then draw a bar graph. Page count tally marks number 200-249 250-299 300-349 350-399 400-449 a. How many books had their page count between 350 and 399 pages? b. How many books had more than 400 pages? c. What was the lowest page count?
2. The number of households in the different parts of town are in scrambled order below: 275, 658, 256, 308, 286. Find which number goes with which bar on the graph. Write the right number after each bar on the graph.
64
3. The pictograph shows how many people visited the fairgrounds on different days. Each
symbol means 100 people. Draw a bar graph.
Day Thursday Friday Saturday Sunday Monday
a. What was the most popular day of the fair?
How many people visited on that day? b. How many more people visited on Sunday than on Friday? c. How many more people visited on Thursday than on Monday? d. What was the total number of visitors on Thursday and Friday? e. Which day or days would you have gone, if you wanted to avoid the crowds?
Which day or days would you have gone, if you liked to be in a crowd?
4. Joe practiced basketball in the yard. Make a pictograph showing how many baskets he made each day. First choose a picture. Then choose how many baskets that picture represents. Day Baskets
Day
Mon
80
Mon
Tue
60
Tue
Wed
100
Wed
Thu
120
Thu
Sat
40
Sat
Sun
50
Sun
Baskets
65
Adding Whole Tens 1. Add whole tens. and
and a. 160 + 30 = ____
b. 350 + 20 =____
and
and
c. ____ + ____ = ____
d. ____ + ____ = ____
Now you draw the illustrations for the problems.
e. 352 + 30 =
f. 412 + 70 =
g. 529 + 60 =
h. 204 + 40 =
With these problems, the hundreds' digit and the ones' digit do not change in the answer. (Later you will see problems where the hundreds digit will change.)
2. Count by tens - up and down! a. 700, 710, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____ b. ____, ____, ____, ____, ____, ____, 270, 280, ____, ____, ____, ____ c. ____, ____, ____, ____, 390, 380, ____, ____, ____, ____, ____, ____
66
3. Count by tens either forward or backward: a.
b.
c.
d.
e.
f.
g.
450 460
451 461
542 532
944 954
736 746
655 645
829 839
4. Add. Compare the problems. On the last lines, make more similar problems of your own.
30 + 50 =
a.
b.
71 + 20 =
c.
45 + 40 =
d. 10 + 90 =
230 + 50 =
571 + 20 =
245 + 40 =
410 + 90 =
630 + 50 =
871 + 20 =
745 + 40 =
810 + 90 =
____+___ =
____+___ =
____+___ =
____+___ =
____+___ =
____+___ =
____+___ =
____+___ =
5. Add whole tens again, but this time circle ten 10-sticks to make a new hundred.
a.
b.
+
____ + ____ = ____
175 + 40 = 215 c.
+
d.
+
____ + ____ = ____
+
____ + ____ = ____
67
e.
f.
+
____ + ____ =____
____ + ____ = ____
h.
+
g.
+
+
____ + ____ = ____ ____ + ____ =____
+
i.
j.
____ + ____ =____
+
____ + ____ = ____
With these problems, you get a new hundred so the hundreds digit does change.
6. Continue the patterns! a.
b.
c.
510 + 60 = ____
770 + 10 = ____
420 + 70 = ____
510 + 70 = ____
770 + 20 = ____
420 + 80 = ____
510 + 80 = ____
770 + 30 = ____
420 + 90 = ____
510 + 90 = ____
770 + 40 = ____
420 + ___ = ____
510 + 100 = ____
770 + 50 = ____
420 + ___ = ____
510 + 110 = ____
770 + 60 = ____
420 + ___ = ____
68
Subtracting Whole Tens 1. Cross out as many ten-pillars as the problem indicates and see what is left.
a. 160 – 30 = ____
b. 270 – 40 = ____
c. ____ – 30 = ____
d. ____ – 30 = ____
e. 283 – 60 = ____
f. ____ – 50 = ____
g. ____ – 30 = ____
h. ____ – 60 = ____
i. ____ – 50 = ____
In these problems, only the __________ digit changes.
2. Subtract. Compare the problems. a.
b.
c.
d.
50 – 20 =
70 – 30 =
54 – 40 =
82 – 50 =
150 – 20 =
570 – 30 =
154 – 40 =
182 – 50 =
250 – 20 =
370 – 30 =
254 – 40 =
482 – 50 =
650 – 20 =
870 – 30 =
754 – 40 =
882 – 50 =
69
3. Continue the patterns! a.
b.
590 – 60 =
677 – 20 =
492 – 70 =
c.
855 – 30 =
d.
590 – 70 =
677 – 30 =
492 – 80 =
865 – 30 =
590 – 80 =
677 – ___ =
492 – 90 =
875 – 30 =
4. Subtract and add whole tens. – 20
750 – 10
466
– 20
___
– 20
___
+ 80
___
+ 40
___
– 50
___
– 30
___
___
– 40
___
– 50
– 10
___
– 30
___
680
+ 40
___
– 10
___
406
Place either + or – signs into the squares so the number sentences are true.
30
40
50 = 20
670
50
20 = 640
100
40
50 = 10
930
30
50 = 950
240
40
50 = 230
430
40
50 = 520
140
80
50
200
40
50
20 = 130
70
30 = 260
Rounding and Estimating Remember? When you are rounding to the nearest ten, the rules are: If a number ends in 1, 2, 3, or 4, then round down. If a number ends in 5, 6, 7, 8, or 9, then round up. Think: Between which two whole tens is the number? Then round. z z
Examples:
348 ≈ 350
197 ≈ 200
544 ≈ 540
423 ≈ 420
1. Round the numbers to the nearest whole ten. The number line can help. a. 554 ≈ ____
b. 585 ≈ ____
c. 595 ≈ ____
d. 567 ≈ ____
e. 692 ≈ ____
c. 654 ≈ ____
d. 347 ≈ ____
e. 288 ≈ ____
283 ≈ ____
816 ≈ ____
497 ≈ ____
2. Round these numbers to the nearest ten. a. 78 ≈ ____
b. 98 ≈ ____
64 ≈ ____
105 ≈ ____
We can use rounding to estimate sums and differences. Estimation gives us an approximate answer, or “about so much”. To estimate, first round the numbers. Then add or subtract.
78 + 54 ≈ 80 + 50 = 130
423 + 69
377 – 45
≈ 420 + 70 = 490
≈ 380 – 50 = 330
3. Estimate these sums and differences. a.
148 + 43
≈ 150 + ____ = ____ d.
≈
237 + 52
b.
678 + 45
≈ ____ + ____ = ____ e.
66 + 42
≈
c.
≈ ____ + ____ = ____ f.
≈
71
89 + 56
23 + 98
4. Estimate these sums and differences. a.
178 – 43
≈ d.
b.
278 – 56
c.
≈
≈
17 + 43 + 21 + 56
e.
≈ f.
241 + 58 + 23
301 – 32 – 29
≈ 58 + 89 – 53 – 27
g.
≈
67 – 31 + 59
≈
5. Solve the word problems using estimation (rounded numbers). a. In September Mom used the internet for 53 hours, in October for 28 hours, in November
for 19 hours, and in December for 35 hours. Approximately how many hours did she use it during those four months?
b. Susan bought 4 pens. Two of the pens cost 29¢ each, one cost 32¢, and one
cost 44¢. Estimate the total cost of the pens.
c. Jack, Ben, and Rick have been helping Grandpa to do yard work during the summer. Jack
has earned 39 dollars, Ben has earned 27 dollars, and Rick has earned 122 dollars. Approximately how much more has Rick earned than Ben? Approximately how much have they earned altogether?
d. You have $180. Estimate: do you have enough to buy a sofa for $118 and a table for $45?
How about if you buy a lamp for $29, four chairs at $19 each, and a table for $65?
72
Adding Ones 1. Add and compare the problems. Most of the time the hundreds' digit doesn't change. a. 33 + 4 =
133 + 4 = e. 65 + 2 =
265 + 2 =
b. 77 + 9 =
c. 83 + 9 =
677 + 9 =
683 + 9 =
f. 94 + 6 =
g. 27 + 9 =
494 + 6 =
315 + 8 = h. 44 + 9 =
327 + 9 =
2. Write... a. ...every second number.
521
d. 15 + 8 =
744 + 9 =
b. ...every fourth number.
523
714
718
531
3. Add. a.
b.
c.
d.
235 + 4 = ____
671 + 9 = ____
983 + 8 = ____
714 + 8 = ____
167 + 2 = ____
527 + 5 = ____
294 + 6 = ____
327 + 6 = ____
477+ 7 = ____
898 + 8 = ____
691 + 5 = ____
546 + 9 = ____
4. Find two numbers that could go on the empty lines - but don't use zero. a. 131 + ____ + ____ = 139
d. 552 + ____ + ____ = 557
b. 765 + ____ + ____ = 770
e. 552 + ____ + ____ = 562
c. 765 + ____ + ____ = 772
f. 474 + ____ + ____ = 482
73
5. There is a time when the hundreds' digit does change, though. Continue the patterns: a.
b.
c.
d.
95 + 5 =
293 + 6 =
694 + 5 =
995 + 4 =
95 + 6 =
293 + 7 =
694 + 6 =
995 + 5 =
95 + __ =
293 + 8 =
694 + 7 =
995 + 6 =
95 + __ =
293 + __ =
694 + __ =
995 + 7 =
95 + __ =
293 + __ =
694 + __ =
995 + 8 =
95 + __ =
293 + __ =
694 + __ =
995 + 9 =
95 + __ =
293 + __ =
694 + __ =
995 + 10 =
When you add to a number that has “a 90”, the sum may go over to the next hundred.
6. Add. Watch to see if the sum goes over to the next hundred. a.
b.
c.
d.
393 + 8 = 401
797 + 6 =
294 + 6 =
592 + 9 =
498 + 5 =
892 + 6 =
497 + 7 =
895 + 3 =
793 + 4 =
993 + 7 =
291 + 6 =
999 + 2 =
292 + 6 =
595 + 8 =
198 + 8 =
697 + 9 =
7. What is the missing addend? a.
b.
c.
d.
125 + ___ = 128
175 + ___ = 182
695 + ___ = 701
229 + ___ = 234
295 + ___ = 304
824 + ___ = 833
599 + ___ = 604
354 + ___ = 360
661 + ___ = 671
99 + ___ = 106
517 + ___ = 522
822 + ___ = 831
356 + ___ = 359
468 + ___ = 488
306 + ___ = 313
892 + ___ = 901
74
8. What numbers do the animals represent in the problems? Write the answers in the table below, and then use the key to unveil the message.
763 +
= 770
348 +
= 352
569 +
225 +
= 233
384 +
359 +
Key: 2 3 4 5 6 7 8 9 DEYWI UOL
= 361
637 +
= 642
= 571
498 +
= 501
= 390
194 +
= 203
Animal Number Letter
Place numbers between 1 and 10 in the empty lines so the number sentence is true. a.
b.
465 + ____ + ____ = 478
294 + ____ + ____ = 308
465 + ____ + ____ = 478
294 + ____ + ____ = 308
465 + ____ + ____ = 478
294 + ____ + ____ = 308
465 + ____ + ____ = 478
294 + ____ + ____ = 308
465 + ____ + ____ = 478
294 + ____ + ____ = 308
How many solutions are there to the problem in a.?
75
In b.?
Subtracting Ones Mentally Strategy: Subtract in two parts First subtract to the previous whole ten, then the rest.
82 – 7 82 – 2 –5 = 80 –5 = 75
273 – 9 273 – 3 – 6 = 270 – 6 = 264
Strategy: Use known facts Compare to the addition and subtraction facts with single-digit numbers.
187 – 2 = ? You can subtract 7 – 2. The 180 will not change. The answer is 185.
454 – 8 = ? You can't do 4 – 8, so use the fact 14 – 8 = 6. The answer will be in the 440s, and end in 6.
1. Subtract and compare the problems. a. 37 – 4 =
137 – 4 = e. 44 – 8 =
644 – 8 =
b. 77 – 9 =
c. 83 – 8 =
277 – 9 =
683 – 8 =
f. 46 – 3 =
g. 91 – 5 =
346 – 3 =
691 – 5 =
d. 14 – 8 =
114 – 8 = h. 46 – 5 =
246 – 5 =
2. First, subtract to a whole ten, then some more. Do it mentally if you can. a. 152 –
b. 244 – 9
c. 823 – 8
d. 775 – 7
e. 233 – 7
f. 191 – 5
g. 842 – 7
h. 684 – 7
6 152 – 2 – 4 =
3. Subtract MANY, MANY, MANY times! a. 77 – 2 – 2 – 2 – 2 – 2 – 2 – 2 =
b. 520 – 5 – 5 – 5 – 5 – 5 – 5 =
c. 944 – 3 – 3 – 3 – 3 – 3 – 3 – 3 =
d. 1000 – 7 – 7 – 7 – 7 – 7 =
e. 355 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 =
76
4. Subtract. CHECK by adding. Is the sum you get the same number you subtracted from? a. 105 – 5 =
____ + 5 = d. 105 – 7 =
____ + 7 = g. 902 – 9 =
b. 797 – 5 =
c. 634 – 4 =
____ + 5 =
____ + 4 =
e. 780 – 6 =
f. 437 – 9 =
____ + 6 =
____ + 9 =
h. 640 – 2 =
i. 156 – 3 – 7 =
____ + 9 = j. 405 – 6 – 2 =
____ + 7 + 3 = k. 239 – 6 – 6 =
l. 210 – 2 – 7 =
5. Solve the word problems. Write a number sentence for each question. a. Emily was 129 cm tall the last time
b. Anna is 133 cm tall.
she was measured, and now she has grown 7 cm more. How tall is she now?
Who is taller, Anna or Emily? How much taller?
c. The rent used to be $238, but this month
d. 185 people were called to a meeting.
it was raised by $9 and the next month there will be another $10 raise. What will the new rent be?
Eight couldn't come and seven others didn't show up. How many did come for the meeting?
e. Ernie rode 125 km in a bus, and then
f. A computer cost $510 but Dad got
walked 6 km to Grandma's house. How many kilometers did he travel?
an $11 discount. What was the final price?
77
6. What numbers do the animals represent in the problems? Write the answers into the table below, and then use the key to unveil the message.
Key:
0 1 2 3 4 5 6 7 8 9 10 o e i u d h n p r s t
b.
a.
c.
362 –
= 358
389 –
= 384
203 –
= 193
120 –
= 113
361 –
= 353
541 –
= 539
501 –
= 501
603 –
= 594
203 –
= 197
700 –
= 699
642 –
= 639
How can you get a
into a refrigerator?
Animal Number Letter
,
Animal Number Letter
,
Animal Number Letter
78
Review of Mental Math 1. Test yourself! – 30
700
– 40
+ 7
___
___
___
–
+
–
–
430
– 5
429
422
482
+ 200
___
– 9
___
+
400
– 20
___
+
___
–
425
+ 70
725
873
–
715
700
2. Add and subtract. a. 335 + 4 = ___
b. 547 – 4 = ___
c. 828 + 4 – 8 = ___
335 + 40 = ___
547 – 40 = ___
828 – 20 + 40 = ___
335 + 400 = ___
547 – 400 = ___
828 – 500 + 200 = ___
3. Solve the word problems. Write a number sentence for each problem. a. Grandpa had 150
. During one week, wolves killed six of them, plus, nine new little lambs were born. How many sheep were in the flock at the end of the week?
b. Jake's aquarium has 70 fish. Thirty of them are goldfish, and the rest are rainbow fish.
How many are rainbow fish? Jake bought 5 more goldfish and 7 more rainbow fish. How many fish does he have now?
c. If you travel 400 km in a car, 11 km on a bike, and walk 2 km, and
then return the same way, how many kilometers did you travel?
79
Chapter 9: Measuring Introduction The ninth chapter of the Math Mammoth Grade 2-B Complete Worktext covers measuring length, weight, and volume. The lesson “Exploring Measuring”, conveys the idea of measuring as repeatedly applying the measuring unit. In the rest of the lessons, the student learns many of the commonly used measuring units. The student measures length in inches and half-inches, and learns to measure to the nearest half-inch or to the nearest centimeter. The bigger units - feet, miles, meters, and kilometers are also introduced but this grade does not yet include conversions between the units. The lessons on measuring weight have several activities to do at home using a bathroom scales. The goal is to let students become familiar with pounds and kilograms, and have an idea of how many pounds or kilograms some common things weigh. In order to estimate weight, a child has to know the approximate weights of some objects, and then compare the weight of the unknown object to some known weight. This knowledge is gained through experience. Similarly, in studying volume, the lessons include many hands-on activities so that the student gets firsthand experience in measuring, and has a basic knowledge of how “big” the units cup, pint, quart, gallon, milliliter, and liter are. When it comes to measuring, experience is the best teacher. So, encourage your child to use measuring devices (such as a measuring tape, scales, and measuring cups), and to “play” with them. In this way the various measuring units start to become a normal part of his/her life, and are never forgotten. In third grade, the study of measuring turns toward conversions between the different units. So these activities are laying an important foundation on the concrete level.
The Lessons page
span
Exploring Measuring ......................................... 82
1 page
Inches and Half-Inches .....................................
83
2 pages
Measuring to the Nearest Centimeter ................ 85
2 pages
Measuring to the Nearest Half-Inch .................
87
2 pages
Feet and Miles...................................................
89
2 pages
Metric System: Meters and Kilometers ...........
91
1 page
Weight in Pounds .............................................
92
2 pages
Weight in Kilograms .........................................
94
2 pages
Estimate Weight ...............................................
96
1 page
Volume ............................................................
97
4 pages
Volume in Milliliters ........................................ 101
2 pages
Review ....................... ....................................
1 page
103
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Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Measuring Scales An interactive scales model. You can put weights on it and read the scales. http://www.standards.dfes.gov.uk/primary/teachingresources/mathematics/nns_itps/measuring_scales/num Scales Reader Practice reading the scales in grams and/or kilograms. http://www.ictgames.com/weight.html Measure It! Click on the ruler to measure a red bar. http://www.funbrain.com/measure/index.html Reading Scales Helps teachers to illustrate a variety of measuring devices and how to read them. http://www.teacherled.com/2009/02/18/reading-scales-2/ Measurements Online lessons with interactive exercises on metric prefixes, symbols, number values, metric mass, length, volume, US length and volume, and temperature conversions. http://www.aaamath.com/B/mea.htm Reading a tape measure worksheets Worksheet generator - you can choose to hat accuracy to measure - inches, or inches & feet. http://themathworksheetsite.com/read_tape.html
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Exploring Measuring We measure things to find z z z z z
how much a thing weighs as compared to other things how long or wide a thing is as compared to other things how much space a thing takes as compared to other things how much liquid a thing holds as compared to other things. ... and much much more.
For all measuring, you need a measuring unit. You repeat the measuring unit many times, and compare to the thing you are measuring.
1. Measure how wide a table is, using a small shoe and then a big shoe as a measuring unit. It is enough to have the left and the right shoe. Place the left shoe at the edge of the table, and the right shoe right after the left. Then move the left shoe in front of the right, and so on. Keep count. The table is ______ small shoes wide. The table is ______big shoes wide. 2. Fill a small pot or bucket with water. Measure the amount of water using a coffee cup, or a pint jar. The pot holds ______ coffee cups of water. The pot holds ______ pint jars of water. 3. Billy measured how wide his book was. First he used paper clips, and then small crayons. His book was 10 paper clips wide. How many small crayons wide was the book? Look carefully at Billy's paper clips and crayons. 4. Why don't people use Daddy size shoes or paper clips as measuring units? 5. Ryan measured that his room was 27 Daddy-size shoes wide. He also measured it using baby shoes. Ryan's room was 80 / 10 baby shoes wide (circle the right number).
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Inches and Half-Inches This line is 1 inch long.
Two half-inches make an inch!
This line is 1/2 inch long.
3 inches and a 1/2-inch = 3 1/2 inches (three and a half inches)
three half-inches = 1 1/2 inches (one and a half inches)
1. How long of a train of inches and half-inches are end-to-end? a. b.
_____ inches _____ inches _____ inches
c.
_____ inches
d.
2. How long are these things in inches?
|
|
a. _________ inches
b. _________ inches
c. _______ inches
You can cut out the ruler above and tape it on an existing ruler or cardboard! 83
3. Measure how long these lines are in inches. a.
________ inches
b.
________ inches
c.
________ inches
d. ________ inches 4. Write the names of the shapes. Find the side lengths of these shapes. Remember that two half-inches make a whole inch. a.
Rectangle
b. _________________________ ABCD
ABCD
Side AB ______ inches
Side AB ______ inches
Side BC ______ inches
Side BC ______ inches
Side CD ______ inches
Side CD ______ inches
Side DA ______ inches
Side DA ______ inches
All the way around ________ inches
All the way around ________ inches
c. _____________________________ ABCD
Side AB ______ in Side BC ______ in Side CD ______ in Side DA ______ in All the way around ________ inches
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Measuring to the Nearest Centimeter Most objects are NOT exactly a certain number of whole centimeters. You can measure them to the nearest centimeter. The pencil below is a little over 10 cm long. It is about 10 cm long.
|
| This pencil is about 9 cm long. The end of the pencil is closer to 9 cm than to 8 cm.
1. Circle the number that is nearest to each arrow.
2. Measure the lines to the nearest centimeter. a. about _________ cm
b. about _________ cm
c. about _________ cm
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3. Join these dots with lines to form a shape. What shape is it? _____________________ Measure its sides to the nearest centimeter. Write “about __ cm” next to each side. How many centimeters is the perimeter (all the way around the shape)? ______ cm
4. This line is 1 cm long: . Your finger is probably about that wide; put it on top of the 1-cm line and check! Guess how long these lines are. Then measure. My guess:
Measurement:
a.
about ___ cm
about ___ cm
b.
about ___ cm
about ___ cm
c.
about ___ cm
about ___ cm
d.
about ___ cm
about ___ cm
5. Draw some lines here. a. 6 cm long
b. 3 cm long
c. 12 cm long d. 17 cm long
6. Find some small objects and measure how long or how tall they are in centimeters. If the item is not exactly so-many centimeters long, then measure it to the nearest centimeter and write “about” before your cm-number. For example: about 8 cm. Item
How long
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Measuring to the Nearest Half-Inch 1. Circle the whole-inch or half-inch number that is nearest to each arrow.
Most objects are NOT exactly a certain number of whole inches, or even whole and half inches. You can measure them to the nearest inch, or to the nearest half-inch. The pencil below is a little over 4 inches long. It is about 4 inches long.
|
| The pencil above is about 3 1/2 inches long. The red line showing the end of the pencil is closer to 3 1/2 than to 3. 2. Measure the pencils to the nearest half-inch. a. about _________ inches
b. about _________ inches
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c. about _________ in.
d. about _________ in.
3. Find some small objects and measure how long or how tall they are. Write your results in the table. If the item is not exactly so-many inches or half-inches long, then measure it to the nearest whole or half-inch, and write “about” before your inch-number. For example: about 8 inches. Item
How long
4. Measure all of the sides of this triangle to the nearest half-inch. Find also the perimeter (all of the way around).
Side AB ________ in.
Side BC ________ in. Side CA ________ in.
Perimeter ________ in.
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Feet and Miles This is a tape measure. The numbers 1, 2, 3, and so on, are inches. Number 12 is on a black background, and above it you see “1F”. That means 1 foot. 12 inches equals 1 foot. Unroll the tape measure some more, until you find “2 F” or “2 ft” (which means two feet), and “3 ft” (three feet), and so on. Stretch out the tape measure as far as you can. What is the most number of feet it has? You use feet as your measuring unit when you measure the width of a room or of a table, the length of a house, or of a swimming pool. People often use both feet and inches. For example, a table can be 5 feet, 10 inches long. A boy can be 4 feet, 7 inches tall.
This tape measure has both inches and centimeters. The numbers on the top part are inches, and the numbers on the bottom part are centimeters. The number 60 means 60 cm, and the “1” after it means 61 cm.
Tape measures often have centimeters on one side and inches on the other side.
Distances between towns or between countries are measured in miles. 1 mile is 5,280 feet (five-thousand two-hundred eighty)! That is a lot of feet - many, many more than your tape measure has.
1. Find a pair of big shoes such that each shoe is 1 foot long (12 inches), or use two 1-foot long rulers. Using the shoes or rulers, measure the width of... a. the room you are in ____ feet b. a table ____ feet c. __________________ ____ feet
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2. How tall are these people? Ask your mom, dad, or others. You: ____ feet ___ inches
________________: ____ feet ___ inches
Your mom: ____ feet ___ inches
________________: ____ feet ___ inches
3. Use the tape measure to find the distances in feet and inches. Let an adult help you. Item
How long
4. Which unit would you use to find the following items - inches, feet, miles, or feet and inches? Distance
Measuring unit
from New York to Los Angeles from a house to a neighbor's the width of a notebook the distance around the earth Distance
how tall a refrigerator is the width of a porch
the length of a playground
the length of a board
from a train station to the next
the length of a train
the width of a computer screen
5. a. Susan unrolled the tape measure. On top of the 12-inch mark she saw some other measuring unit. What did she see? b. What did Susan see on top of the 24-inch mark?
On top of the 36-inch mark?
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Measuring unit
Metric System: Meters and Kilometers Many people in the USA use feet and miles to measure long distances. Most people in the world use meters and kilometers instead. Find a tape measure that has centimeters. Find the 100th centimeter on it. That is the 1-meter point. 100 centimeters equals 1 meter. Distances between towns or between countries are measured in kilometers. 1 kilometer is 1,000 meters (thousand meters)!
1. a. Out-of-doors, draw a line that is one meter long. Can you take such a big step? Can the teacher? b. On the 1-meter line, practice taking two or three steps that together are 1 meter long.
Then take similar steps to measure the length of a house or some other similar distance. Count your steps. If you take 2 steps for each meter, find half of your count to get the length in meters. If you take 3 steps for each meter, find one-third of your count (or let an adult do it). 2. Which unit would you use to find these below: centimeters, meters, or kilometers? Distance
Unit
Distance
Unit
the length of a park
the distance around your wrist
from Miami to the North Pole
the height of a room
the length of a cell phone
the length of an airplane trip
the length of a bus
the length of a grasshopper
3. Here is a little reference chart for you! Write on the empty lines the words: small, medium-size, long U.S.Customary System
Metric System
______________ distances →
inches
centimeters
______________ distances →
feet
meters
______________ distances →
miles
kilometers
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Weight in Pounds Weight means how heavy something is. You can measure weight using scales. Bathroom scales measure weight in pounds or in kilograms. In this lesson you will need: z z z z z
a bathroom scales that measures in pounds a bucket and water encyclopedias or some other fairly heavy books a plastic bag or some other bag a backpack
The numbers on your scales may go up by twenties, and not by tens. In the picture here, the longer line halfway in-between the two numbers is ten more than the smaller of the two numbers. Each little line means a 2-pound increment. The scales are stopped at the second little line after 140 pounds, which means 140 + 2 + 2 pounds, or 144 pounds. We use “lb” to abbreviate the word pounds. 15 pounds = 15 lb. The “lb” comes from the Latin word libra, which also means a pound.
1. How many pounds are the scales showing? You can mark the in-between ten-numbers on the scale to help.
a.
b.
c.
d.
e.
f.
2. Step onto the scales. I weigh ___ pounds. 92
3. Find out how many pounds your family members weigh. Write a list below. ________________________ ___ pounds
________________________ ___ pounds
________________________ ___ pounds
________________________ ___ pounds
________________________ ___ pounds
________________________ ___ pounds
Weigh also some of your family members together. ________________ and ____________________ weigh together ____ pounds. ________________ and ____________________ weigh together ____ pounds.
4. Weigh some other items. Note that on bathroom scales, you cannot weigh very light items, nor very big and bulky ones because you can't place them on the scales. a bucket full of water
___ pounds
mom's skillet
___ pounds
a bucket half full of water
___ pounds
________________________
___ pounds
a stack of heavy books
___ pounds
________________________
___ pounds
5. Find out how many pounds of water you can carry. Can you carry a big bucket when it is full? If not, pour out some of the water until you can carry the bucket. I can carry a bucket full of water that weighs ____ pounds. 6. a. Fill a bag with books. Can you carry it? If not, take out some books
until you are able to carry the bag. I can carry a bag of books that weighs ____ pounds. b. Do the same as above, but use a backpack.
I can carry a backpack that weighs ____ pounds. c. Weigh yourself with and without the heavy bag of books.
I weigh ____ pounds. I weigh ____ pounds with the heavy bag. The difference is ____ pounds. The heavy bag therefore weighs ____ pounds. Use this method to weigh items you can hold but that cannot be placed on the scales. d. Weigh yourself with and without a heavy book.
I weigh ____ pounds. I weigh ____ pounds with the heavy book. The difference is ____ pounds. Som the book weighs ____ pounds.
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Weight in Kilograms Weight means how heavy something is. You can measure weight using a scales. Bathroom scales measure weight in pounds or in kilograms. Kilogram is abbreviated kg. The scales that use kilograms, usually have shorter lines for each kilogram increment. The whole ten numbers are marked. In the picture below, the in-between numbers ending in “5” are marked with the number 5. In this lesson you need to use bathroom scales that measure weight in kilograms. You will also need z z z z
a bucket and water encyclopedias or some other fairly heavy books a plastic bag or some other bag a backpack
The scales are showing 22 kg.
1. How many kilograms are the scales showing?
a.
c.
b.
2. Step onto the scales. How much do you weigh? ___ kg 3. Find out how many kilograms your family members weigh. Write a list below. ________________________ ___ kg
________________________ ___ kg
________________________ ___ kg
________________________ ___ kg
________________________ ___ kg
________________________ ___ kg
4. Weigh also some of your family members together. ________________ and ____________________ together weigh ____ kg. ________________ and ____________________ together weigh ____ kg.
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5. Now weigh some other items in your home with the bathroom scales. Note that you cannot weigh very light items on it. You also cannot weigh very big and bulky items (such as tables) on it because you can't place them fully on the scales. Try to find objects that are not very big. a bucket full of water
___ kg
mom's skillet
___ kg
a bucket half full of water
___ kg
________________________
___ kg
a stack of heavy books
___ kg
________________________
___ kg
6. Find out how many kilograms of water you can carry. Can you carry the bucket when it is full? If not, pour out some water until you can carry the bucket. I can carry a bucket of water that weighs ____ kg . 7. a. Find out how many kilograms of books you can carry in a bag. Fill the bag with books and weigh it. Can you carry it? If not, take out some books until you are able to carry the bag. I can carry a bagful of books that weighs ____ kg. b. The same as above, but use a backpack.
I can carry a backpack that weighs ____ kg. c. Weigh yourself with and without the heavy bag of books.
I weigh ____ kg. I weigh ____ kg with the heavy bag. What is the difference? ____ kg. You can use this method to weigh items that cannot easily be placed on the scales, but that you can hold. d. Weigh yourself with and without a heavy book.
I weigh ____ kg. I weigh ____ kg with the heavy book. What is the difference? ____ kg. So, how much does the book weigh? ____ kg.
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Estimate Weight Use known weights of things to estimate the weight of other things. 2-3 bananas
about 1 pound.
about 1/2 kg
about 2 pounds.
about 1 kg 1 qt / 1 L
8-12 pounds
about 4-5 kg
I weigh ____ pounds.
I weigh ____ kg.
An adult female about 120-160 pounds.
about 50-70 kg
1. Circle the right weight.
a.
70 lb
b.
170 lb
e.
15 kg
c.
2 lb 20 lb
7 lb 2 lb
g.
f.
5 kg
200 lb 50 lb
h.
20 kg 5 kg
2 kg 10 kg
d.
80 kg 500 kg
2. Circle the sentences that make sense. a. I met a 10-year old boy
e. The neighbor's cat is
who weighed 6 pounds! b. Sherry weighed 8 pounds
overweight and weighs 8 kg. f. Mr. Garrison, the teacher, weighs 30 kg.
when she was born. c. I can't carry this big fridge;
g. Larry is in 8th grade
it weighs over 200 pounds. d. Hannah's math book
and weighs 50 kg. h. Amy's backpack full of
weighs 25 pounds.
school books weighs 3 kg. 96
Volume Volume means how much space something takes. A sandcastle takes a certain amount of space. A bottle of water takes space. A book takes space. But how much? In this lesson you will learn how we measure the volume of water (or other liquids). You will need z z z z
z
a quart jar a pint jar
z
a 1-cup measuring cup
z
water in a bucket or other big container a few food containers a coffee cup a drinking glass
1. Fill the pint jar with water. Pour it all into the quart jar. Then fill the pint jar again and pour it into the quart jar. Is it now full (or close to full)? It should be. It takes ___ pints of water to fill 1 quart jar. 2. Pour out water from your full quart jar back into the pint jar until the pint jar is full. Is your quart jar now half full? (It should be.) How much water is left in the quart jar? ____ pint. 3. Find out how many times you need to fill the 1-cup measuring cup with water and pour it into the pint jar until the pint jar is full. ___ times. 1 pint is ___ cups. 4. Find out how many times you need to fill the 1-cup measuring cup with water and pour it into the quart jar until the quart jar is full. ___ times. 1 quart is ___ cups. 5. Find out if your coffee cup measures MORE or LESS than the a 1-cup measuring cup - or exactly 1 cup. Do the same with the drinking glass.
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6. You need three different empty food containers. Find out how many cups of water you can fit into them. Write an “X” in the “and a little more” column if you cannot fit another 1-cup of water into your container, but you could fit a little more. how many cups
and a little more?
Container 1 Container 2 Container 3 7. At the next supper or breakfast time, do a little experiment. Before eating, measure exactly one cup of the food you're going to eat and then put it on your plate. Will it fill you up? Is it too much or too little food? For example, you can find out these things: z z z
Will 1 cup of yogurt fill you up? Is it too much, too little, or just right? Will 1 cup of oatmeal fill you up? Is it too much, too little, or just right? Will 1 cup of pasta fill you up? Is it too much, too little, or just right? z z z
A quart is abbreviated with “qt”. A pint is abbreviated with “pt”. A cup is abbreviated with “C”.
5 qt means 5 quarts. 3 pt means 3 pints. 2 C means 2 cups.
8. Now that you have learned about cups, pints, and quarts, fill in numbers on the blank lines.
a.
= ___
b.
= ___
c.
= ___
e. d.
= ___
= ___
= ___
f.
g.
= ___
9. Do the same but without pictures. a. 1 qt = ___ pt
1/2 qt = ___ pt
b. 1 pt = ___ C
c. 1 qt = ___ pt
d. 4 C = ___ qt
2 pt = ___ C
2 qt = ___ pt
2 C = ___ qt
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10. Circle the amount that holds more liquid volume. Circle both if they hold the same amount.
a.
OR
b.
c.
OR
d.
e.
OR
OR
f.
OR
OR
h. g.
OR
OR
11. Solve the word problems. Give you answer in a reasonable unit either “so many” cups, pints, or quarts. a. Mom bought 1 quart of ice cream and divided it equally among four children.
How much ice cream did each child get? b. During one day, Dad drank 1 pint of coffee, 1 pint of juice, and 1 quart of water.
What is the total amount of liquid did he drink during the day? c. A 1-quart juice box is half full. How many cups of juice
could you pour out of it? 12. Fill in with the words: cup, pint, or quart. a. Mary drank 2 ______s of tea at the party. b. Mom bought 1 ______ of yogurt for the four children. c. Ron was quite thirsty and so he drank a whole ________ of water. d. The large pitcher can hold 2 _________s of juice. e. After pouring out 2 ________s of juice, the one quart container was left only half full.
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Gallons One gallon is a larger measure of volume than even one quart. You use gallons when the liquid or other thing takes a lot of space, even more than a few quarts. You might have heard about these items. Fill in some more items that you have heard the word “gallon” used with. z z z z z z z z z
a 5-gallon bucket a 1-gallon milk bottle a 1/2-gallon milk bottle a car's gas tank is so many gallons a water heater can hold so many gallons a bathtub can hold so many gallons A very large pot can hold 1 gallon of soup or stew. _____________________________________ _____________________________________
One gallon of water is so much that you can fill FOUR quarts out of it.
=
It would be a lot to drink!
13. Test yourself! Put one gallon of water into a bucket, preferably a 5-gallon bucket. (Four quarts make one gallon.) Can you carry it? Put another gallon of water into the same bucket. Can you still carry it? How many gallons of water can you carry in the bucket? Now put that many gallons into another bucket as well, and try to carry one such bucket in each hand. How many gallons of water can you carry using two buckets? Water can get pretty heavy! 14. a. How many quart jars of water would it take to fill a 5-gallon bucket? b. Mom bought 1 gallon of bleach, and used 1 cup of it in the washer.
How many times can she use that amount before she runs out of bleach?
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Volume in Milliliters You can also measure volume in units called liters and milliliters. A liter is very close to a quart, but just a little bit more. In other words, a quart jar is just a little bit less than a liter, but they are very close. Milliliters are tiny units. It takes 1,000 milliliters to make one liter. Milliliter is abbreviated ml. Liter is abbreviated l, or sometimes with a capital L. For this lesson, you will need z z
z z
water small cups and glasses of various sizes a 1-cup measuring cup and a pint jar a measuring cup that measures in milliliters.
1. How many milliliters of liquid is in the measuring cup?
b.
a.
___ ml
. c. ___ ml
___ ml
2. Write what amount in milliliters the level of liquid is closest to.
a.
c.
b.
about ____ml
about ___ ml 101
about ___ ml
3. a. Fill a glass with water, and pour it into the measuring cup. How many milliliters is it? _____ ml. If the water in the measuring cup isn't exactly at the marked lines, look at the line it is closest to. b. In a similar manner, measure the volume of a few other cups, glasses, jars,
or other small containers. Write down your results below. Item
Volume in milliliters
4. How much is 100 ml? Pour what you think is 100 ml of water into a glass. In other words, guess how much water 100 ml is! Then check by pouring it into your measuring cup. Do this many times until you can estimate 100 ml fairly well. 5. a. Fill your 1-cup measuring cup with water. Guess how many milliliters is 1 cup. My guess: 1 cup is ____ ml. Then measure this with your milliliter-measuring cup. It is _____ ml. b. Fill a pint jar with water. Guess how many milliliters it is. My guess: 1 pint is ____ ml.
Then measure this with your milliliter-measuring cup. It is _____ ml. Since 1 pint is about ____ ml, then 1 quart is about _____ ml. 6. a. Measure 1,000 ml, which is 1 liter, into a pitcher. Could a person drink that much water if he was really thirsty? b. How many pint-jars could you fill with 1 liter of water?
7. Some milliliter additions! Remember that 1 liter is 1,000 ml. a. 800 ml + ____ ml = 1,000 ml
b. 400 ml + ____ ml = 900 ml
c. 300 ml + ____ ml = 1 liter
d. 100 ml + ____ ml = 1 liter
e. 400 ml + ____ ml = 700 ml
f. 950 ml + ____ ml = 1 liter
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Review 1. Underline the measuring device you would use to find out these measurements: a. how heavy a computer is
b. how far it is from the house
to the edge of the road measuring tape / measuring cup / scales
measuring tape / measuring cup / scales
c. how much juice a bottle will hold
d. the width of a chair
measuring tape / measuring cup / scales
measuring tape / measuring cup / scales
2. Cross out the sentences that don't make sense. a. The neighbor lady weighs only 120 kg!
b. My math book is 20 meters wide.
c. Jake drank a pint of juice.
d. From Gary's house to town is 25 miles.
3. Measure this line to the nearest centimeter. about _________ cm 4. Measure this line to the nearest half-inch. about _________ in. 5. a. Draw a line that is 3 1/2 inches long. b. Draw a line that is
9 cm long. 6. The teacher needs to arrange these tasks beforehand, and check the students' results. a. Your teacher gives you water in a container.
Measure how many milliliters of water it is. __________ ml b. Your teacher gives you an item. Find out how heavy it is. _______________
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Chapter 10: Adding and Subtracting in Columns Introduction The tenth chapter of the Math Mammoth Grade 2-B Complete Worktext deals with addition and subtraction in columns using three-digit numbers. In the first lesson, the student adds three-digit numbers, carrying to tens when it is necessary. The next lesson is about the situation when there are more than ten tens, so carrying to hundreds is necessary. This is first illustrated with pictures, and then practice problems follow. In the third lesson, the student carries two times - both to tens and to hundreds. The pictures in the beginning of the lesson show ten ones grouped to form a new ten, and 10 tens grouped to form a new hundred. Please spend some time studying with these pictures. There are two processes happening in the same situation. Next comes subtracting in columns. In the first lesson, Subtracting in Columns, the student borrows one time per problem - either from the tens or from the hundreds. The pictures show how a ten is broken into ten ones or how a hundred is broken into 10 tens. The concept of borrowing two times can be a bit tricky. This is studied more in third grade. Lastly, the chapter includes a lesson in adding money amounts, which is probably easy after the previous addition practice.
The Lessons page
span
Adding 3-Digit Numbers in Columns .............. 106
4 pages
Carrying to Hundreds ...................................... 109
3 pages
Carrying to Tens and to Hundreds ..................
113
4 pages
Subtracting in Columns ..................................
117
4 pages
Borrowing Two Times .................................... 121
3 pages
Adding Money Amounts ................................
124
2 pages
Review ............................................................
126
2 pages
104
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Base Blocks Addition A virtual manipulative that shows regrouping in addition. Choose “Columns = 3” to restrict the work to three-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html?from=category_g_1_t_1.html Base Blocks Subtraction The number to be subtracted (the subtrahend) is illustrated as red blocks whereas the minuend is with blue blocks. Drag a red block on top of a blue to “subtract” - they cancel each other. Drag bigger place values to the column on their right to “break them up” - in other words regroup or borrow. Choose “Columns = 3” to restrict the work to three-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_155_g_1_t_1.html?from=category_g_1_t_1.html Regrouping in vertical addition Shows hundreds, tens, ones as pictures, and asks you to regroup if needed. http://www.harcourtschool.com/justforkids/math/elab/samplepages/g3a02.htm Arithmetic Workshop at iKnowThat.com Build numbers with blocks and model carrying and borrowing. http://www.iknowthat.com/com/L3?Area=EarlyMathWorkbench
105
Adding 3-Digit Numbers in Columns Add hundreds in their own column: hundreds tens ones
2 4 1 3 3 5
+ 241
+
335
=
.
Trading or carrying to tens happens the same way with numbers that have hundreds as with numbers that don't. Look at the examples. Ten ones form a ten-pillar. The hundreds are added separately. 1
17 + 25 42 17
+
25
=
30 and 12
=
42
1
117 + 125 117
+
125
=
230 and 12
=
242
242
1
149 + 134 149
+
134
=
270 and 13
106
=
283
283
1. Fill in the numbers and add. Note that sometimes there are no tens or no ones.
+
a.
+
____ + ____ = ____ +
b.
+
____ + ____ = ____ +
c.
+
____ + ____ = ____
d.
+
+
____ + ____ = ____
+
e.
+
____ + ____ = ____
f.
+
+ +
____ + ____ = ____
107
2. Add. Carry to the tens if necessary. Add the hundreds in their own column. a.
301 + 510
b.
213 + 716
c.
402 + 370
d.
881 + 111
e.
381 + 411
f.
638 + 139
g.
227 + 536
h.
129 + 454
i.
218 + 675
j.
458 + 137
k.
207 223 + 438
l.
437 116 + 437
m.
224 301 + 408
n.
238 308 + 425
o.
556 127 + 104
3. a. There were 547 factory workers. Then the factory
hired 128 more workers, and at the same time 20 people retired. How many workers are there now?
b. One bag contains 100 balloons. If you buy three
bags of balloons, and then blow up 20 balloons, how many balloons are left in the bags?
What numbers are missing from the additions?
+ 1
1 1 6 + 5
2
3 5
7 7 6
+
5 5
5
5 8 0
108
3
4 7 + 7
9 9 2
Carrying to Hundreds +
4 0 6 0 10 ten-pillars make a hundred. + 1 0 0
=
40 + 60
= 100
+
=
40 + 80
Now we have two ten-pillars more.
=
4 0 + 8 0 1 2 0
What if we already have some hundreds? Look at the pictures: 1
+ 170
=
+
50
=
220
1 7 0 + 5 0 2 2 0
All of the ten-pillars (70 and 50) make a hundred and twenty, so the sum goes over 200. 1
+ 190
+
= 40
1 9 0 + 4 0
=
All of the ten-pillars (90 and 40) make over a hundred so the sum goes over 200. 1
+ 186
+
= 143
=
Similarly, all of the ten-pillars make over a hundred. If there are more than ten tens, they make a new hundred.
109
1 8 6 + 1 4 3
1. Circle ten ten-pillars to form a hundred and make an answer picture where you use the “new” hundred you formed.
+
a.
=
140 + 90 = 100 and 13 tens =
+
b.
+
c.
d.
e.
f.
=
+
=
=
+
=
+
=
110
2. Add mentally. Compare the problems. a.
b.
c.
d.
70 + 40 =
50 + 60 =
90 + 50 =
30 + 90 =
170 + 40 =
150 + 60 =
290 + 50 =
330 + 90 =
270 + 40 =
250 + 60 =
490 + 50 =
530 + 90 =
3. Add mentally. a.
b.
c.
d.
70 + 40 =
160 + 60 =
290 + 50 =
80 + 90 =
130 + 40 =
80 + 60 =
170 + 50 =
130 + 90 =
160 + 50 =
270 + 60 =
220 + 50 =
270 + 90 =
280 + 50 =
130 + 50 =
190 + 20 =
250 + 50 =
4. Add. If the sum of the tens goes over hundred, carry the new hundred into the hundreds' column. a.
80 + 30
b.
220 + 90
c.
64 + 53
d.
370 + 74
e.
533 +282
f.
67 + 72
g.
224 +193
h.
464 +392
i.
355 + 374
j.
787 + 82
5. What number was added? a.
167 + 1_2 359
b.
240 + 1_2 422
c.
391 + 4_2 813
111
d.
653 + 1_3 846
e.
375 + 1_4 559
6. Add and match the answers with the letters in the key. Then use the key to unravel the message. W
L
233 + 758
553 + 346
E
A
772 + 132
G
R
231 240 + 432
S
191 + 751
282 + 647
E
474 + 343
N
216 116 + 529
T
597 + 330
O
111 + 729
Key:
P
I
217 + 639
470 + 399
F
85 205 + 643
H
136 134 + 589
105 301 + 459
817 840 856 859 861 865 869 899 903 904 927 933 929 942 991
When the 942 865 840
and the
ran a race, who won?
856 899 856 927 865 817 903 942 , because
942 865 856
942 865 856
861 869 933 817 859 859 840
991 817 929
869 903
933 840 859 933 869 861 856 933 817 942 904 933
112
Carrying to Tens and to Hundreds 10 little ones form a new ten. 10 tens form a new hundred. The total is 224. Can you see that in the picture?
145 + 79 hundreds tens ones 1 1
+
1 4 5 7 9 2 2 4
Add in the ones column: 5 + 9 = 14. There are more than 10 ones, so carry to the tens column. Add in the tens column: 1 + 4 + 6 = 12. There are more than 10 tens, so carry to the hundreds column.
10 little ones form a new ten. 10 tens form a new hundred. The total is 304. Can you see that in the picture?
166 + 138 hundreds tens ones 1 1
+
1 6 6 1 3 8 3 0 4
Add in the ones column: 6 + 8 = 14. There are more than 10 ones, so carry to the tens column. Add in the tens column: 1 + 6 + 3 = 10. There are more than 10 tens, so carry to the hundreds column.
You have to carry to the tens and to the hundreds. You have to carry two times.
113
1. Circle ten ones to form a ten. Then circle 10 tens to form a new hundred. Add in columns - carry to tens and to hundreds. a.
b.
+
c.
+
+
1 5 7 + 2 6 8
1 7 5 + 1 2 8
2 3 8 + 2 7 4
d.
e.
f.
+
+
+
+
+
+
2. Add. Carry two times if necessary. a.
306 + 461
b.
299 + 225
c.
488 + 322
d.
115 + 536
e.
586 + 336
f.
704 + 156
g.
260 + 341
h.
248 + 376
i.
173 + 646
j.
493 + 348
114
3. Add in parts. Follow the example. Add and break down the tens and hundreds as needed. a. Two numbers to add.
300 200 60 + 70 = 6 8 b. 700
c.
d.
e.
f.
100
Add the hundreds. Add the tens. Add the ones.
Break down into hundreds, tens, and ones
Count the hundreds. Count the tens. Count the ones.
500 130 14
500 = 100 + 30 = 10 + 4
600 40 4
____
____
____
20 +
90 = ____ = ___ + ___ = ____
8
8
____
___ + ___
____
500
100
____
____
____
30 +
80 = ____ = ___ + ___ = ____
2
9
____
___ + ___
____
400
200
____
____
____
50 +
40 = ____ = ___ + ___ = ____
7
6
____
___ + ___
____
100
300
____
____
____
40 +
70 = ____ = ___ + ___ = ____
9
9
____
___ + ___
____
600
100
____
____
____
60 +
60 = ____ = ___ + ___ = ____
8
4
____
___ + ___
____
115
4. Add. Carry two times if necessary. a.
b.
404 199 + 156
c.
701 129 + 101
d.
335 219 + 278
e.
103 380 + 647
245 189 + 348
5. Solve the word problems. Write number sentence(s) for each. You can add or subtract in columns. a. From Flowertown to Princetown
b. The school bought pencils for $128,
is 142 miles. How many miles is a round trip from Flowertown to Princetown back to Flowertown?
pens for $219, and notebooks for $549. Find the total bill.
c. One side of a rectangle is 156 feet and
d. If a car goes 50 miles on 1 gallon
another side is 277 feet. Draw a picture and mark the lengths on the sides.
of gasoline, how far will it go on 2 gallons of gasoline? How about with 3 gallons? With 4 gallons? How many gallons will it take to travel 400 miles?
What is the distance if you walk all of the way around it?
What numbers are missing from the addition problems?
+ 1 3
9 9
1
2
3
1
+ 5
3
6
1
7
+ 7
116
6 5
9
8
8
0
0
+ 7 4
9
Subtracting in Columns Remember? If you can't subtract the ones, you break down one ten-pillar into ten ones, or you borrow a ten. If you don't have enough tens, the process is similar. Look at the pictures. h
365 – 229 = ? We can't cross out nine ones because there are only five ones.
Break down one ten into 10 ones. Now we can subtract! Cross out → two hundreds, two tens and nine ones. What is left? _______
→
3 hundreds + 5 tens + 15 ones
Break down one hundred into 10 tens. Now we can subtract! Cross out one hundred and seven tens. What is left? _______ →
320
→
2 hundreds + 12 tens
346 – 152 = ? We can't cross out five ten-sticks because there are only four tens.
Break down one hundred into 10 tens. Now we can subtract! Cross out one hundred five tens and two ones. What is left? ______
→
3 2 0 – 1 7 0 1 5 0 Break one hundred into 10 tens. You BORROW one hundred.
2 14
3 4 6 – 1 5 2 Break one hundred into 10 tens.
→
346
You BORROW one ten.
2 12
320 – 170 = ? We can't cross out seven ten-sticks because there are only two tens.
3 6 5 – 2 2 9 1 3 6 Break one ten into 10 ones.
→
365
t o 5 15
2 hundreds + 14 tens + 6
117
You BORROW one hundred.
1. Fill in. Draw squares, sticks and dots. Break down the minuend (the number you subtract from) as needed. Cross out what is subtracted. a. Cross out 90 First break one hundred down into 10 tens.
4 1 0 – 9 0
→ →
410
3 hundreds 11 tens
b. Cross out 170
First break one hundred down into 10 tens.
→
__ hundreds ___ tens BORROW one hundred.
c. Cross out 280
3 5 0 – 2 8 0
→ →
350
BORROW one hundred.
3 4 0 – 1 7 0
→ 340
BORROW one hundred.
__ hundreds ___ tens
d. Cross out 286
4 5 7 – 2 8 6
→ →
457
__ hundreds ___ tens ___ ones
e. Cross out 164
3 2 6 – 1 6 4
→ 326
→
__ hundreds ___ tens ___ ones
118
2. Subtract a.
906 – 46
b.
599 – 225
c.
414 – 322
d.
773 – 536
e.
670 – 226
f.
708 – 156
g.
560 – 341
h.
748 – 376
i.
973 – 646
j.
907 – 576
k.
511 – 250
l.
757 – 384
m.
955 – 493
n.
403 – 121
o.
911 – 506
3. Solve the problems. Write a number sentence for each problem. a. There are 365 days in one year. How
b. Max read two books in a week.
many days are there in two years?
The first book had 237 pages and the second book had 156 pages. How many pages did Max read total that week?
In three years?
c. There are 207 school days in one year.
d. Mike is on page 235 of his book. The
How many school days are there in two years?
book has 518 pages. How many pages does he still have to read?
119
e. Middletown is in between Easttown and Westtown.
The distance from Easttown to Westtown is 425 km. The distance from Easttown to Middletown is 173 km. Draw a picture first.
What is the distance from Middletown to Westtown? (Middletown is between Easttown and Westtown.)
f. Jack's family is driving from Easttown to Middletown.
The car's odometer shows they have driven 69 kilometers. How far do they still have to go?
4. What numbers go on empty lines? Follow the pattern. a.
b.
c.
d.
120 + 120 = 240
230 + 230 = 460
300 + 300 = 600
1 + 119 = 120
121 + ___ = 240
235 + ___ = 460
290 + ___ = 600
2 + ___ = 120
122 + ___ = 240
240 + ___ = 460
280 + ___ = 600
3 + ___ = 120
___ + ___ = 240
___ + ___ = 460
___ + ___ = 600
___ + ___ = 120
___ + ___ = 240
___ + ___ = 460
___ + ___ = 600
___ + ___ = 120
___ + ___ = 240
___ + ___ = 460
___ + ___ = 600
___ + ___ = 120
___ + ___ = 240
___ + ___ = 460
___ + ___ = 600
___ + ___ = 120
___ + ___ = 240
___ + ___ = 460
___ + ___ = 600
___ + ___ = 120
___ + ___ = 460
___ + ___ = 600
___ + ___ = 120
How long can you continue this pattern?
How long can you continue this pattern?
How long can you continue this pattern?
How long can you continue this pattern?
120
Borrowing Two Times First break one ten down into 10 ones. Now you can cross out 9 ones but can't subtract two tens.
There are not enough ones to subtract.
→
325 – 29
→
→ 3 hundreds + 1 ten + 15 ones 1
3 2 5 – 2 9
Then break one hundred into 10 tens. Now you can cross out 2 tens. What is left? _______
→
2 hundreds + 11 tens + 15 ones
15
2
11 1 15
3 2 5 – 2 9
3 2 5 – 2 9
6
2 9 6
Subtraction in columns uses the same process. First borrow a ten so you have a total of 15 ones, then borrow one hundred to have a total of 11 tens. 334 – 178 = ? First break one ten down into 10 ones. Now you can cross out 8 ones but can't subtract 7 tens.
There are not enough ones to subtract 8.
→
334 – 178
→
→ 3 hundreds + 2 tens + 14 ones 2
3 3 4 – 1 7 8
Then break one hundred into 10 tens. Now you can cross out 7 tens, 8 ones, and one hundred. What is left? _______
→
2 hundreds + 12 tens + 14 ones
14
2
12 2 14
3 3 4 – 1 7 8
3 3 4 – 1 7 8
6
6
Subtraction in columns uses the same process.
121
1. Draw squares, ten-sticks and ones and break down the minuend (the number you subtract from). Cross out what is needed. First, break one ten down into 10 ones. Then break one hundred down into 10 tens. When subtracting in columns, first, BORROW one ten and then one hundred. a. Cross out 97
→
221
→
2 2 1 – 9 7
→ 2 hundreds 1 ten 11 ones
→
1 hundred 11 tens 11 ones
b. Cross out 175
3 4 1 – 1 7 5 341 c. Cross out 287
3 5 0 – 2 8 7
→ 350
→ d. Cross out 246
3 3 4 – 2 4 6
→ 334
→ e. Cross out 169
3 2 6 – 1 6 9
→ 326
→
122
2. Subtract. a.
924 – 467
b.
593 – 225
c.
412 – 322
d.
713 – 536
e.
618 – 119
f.
712 – 156
g.
520 – 341
h.
743 – 376
i.
923 – 646
j.
524 – 266
k.
523 – 357
l.
630 – 251
m.
465 – 266
n.
911 – 226
o.
775 – 286
p.
902 – 543
What numbers are missing from the subtraction problems?
8
3 – 1
3
3 1 5
–
6 3 6
–
5 1 7
9 5
2 6 4
123
8 4 –
4 2 0 7
Adding Money Amounts Align the decimal points!
You can add money amounts in columns. Make sure the decimal points are aligned. Add the point to the answer in the same place.
Align the decimal points!
↓ $ 1.7 8 + 2.2 0 $ 3.9 8
1
$ 0.5 8 + 2.2 6 $ 2.8 4
↑
Carrying happens the same way as if there was no decimal point.
↑
Add a decimal point to the answer
Add a decimal point to the answer
1 1 1 1
34 ¢
$ 0.3 4 + 0.6 9 $ 1.0 3
47 ¢
69 ¢
$ 0.4 7 0.4 7 + 0.3 4 $ 1.2 8
47 ¢
34 ¢
Total cost $1.03.
Total cost $1.28.
1. Add in columns. a. $0.29 + $0.56
$ + $
. . .
b. $1.41 + $0.09
$ + $
. . .
c. $0.77 + $2.24 + $1.80
$ + $
. . . .
2. Find the total cost of buying the things listed. 65 ¢
a. scissors and a pen
34 ¢
52 ¢
124
b. two erasers and a pen
Cafeteria Menu
$0.88
$1.52
$2.75
$2.20
$1.05
$0.62
3. Find the total cost in each case. a. Mark bought a sandwich,
b. Judy bought coffee
an apple, and a bottle of water.
and a slice of pizza.
c. Edward bought soup, a sandwich,
d. Elaina bought three apples
and coffee.
and a bottle of water.
4. First find the total cost, and then the change. You can use real money or draw coins to help. a. Mom bought soup and pizza.
She paid with $5.
b. Jack bought two cups of coffee
and paid with $3.
125
Review 1. Add. a. 205 + 100 =
b. 540 + 200 =
c. 337 + 300 =
d. 528 + 400 =
205 + 10 =
540 + 20 =
337 + 30 =
528 + 40 =
205 + 1 =
540 + 2 =
337 + 3 =
528 + 4 =
b. 578 – 400 =
c. 205 – 100 =
d. 540 – 200 =
2. Subtract. a. 337 – 300 =
337 – 30 =
578 – 40 =
205 – 10 =
540 – 20 =
337 – 3 =
578 – 4 =
205 – 1 =
540 – 2 =
3. Test yourself! +
110
+
150
+
200
+
233
+
240
+
+
310
510
+
600
999
4. Add, and find what numbers are missing. a.
346 211 + 477
b.
299 199 + 225
c.
303 198 + 287
d.
409 219 + 136
e.
588 170 + 192
f.
2 4 + 477
g.
5 9 + 25
h.
20 + 6 6
i.
5 + 236
j.
68 + 19
731
914
892
126
820
900
5. Subtract. a.
812 – 159
b.
556 – 391
c.
773 – 278
d.
929 – 605
e.
500 – 276
f.
902 – 176
g.
540 – 241
h.
700 – 516
i.
903 – 564
j.
424 – 66
6. Find the missing numbers. a. ___ + 100 = 706
b. 470 – ___ = 400
c. ____ – 500 = 150
d. 256 + ___ = 756
e. ___ – 140 = 600
f. ____ – 99 = 400
g. 220 + ___ = 1000
h. 1000 – ___ = 850
i. 739 – ____ = 239
Can you place numbers from 1 through 12 into the circles so that the sum of each connecting line is 26? Hint: The numbers going to the top corners are 7, 6, and the numbers going to the bottom corners are 5, 8.
127
Chapter 11: Exploring Multiplication Introduction The eleventh and last chapter of the Math Mammoth Grade 2-B worktext covers the concept of multiplication, its connection with repeated addition and some easy multiplication practice. The lessons here are self-explanatory. The student first learns the meaning of multiplication as “many times the same size group”. Then there is practice writing multiplication as repeated addition and vice versa. Number line jumps are another way to illustrate multiplication. The actual study and memorization of the multiplication tables is in the third grade. However, you can certainly help your child to notice the patterns in the easy tables of 2, 5, and 10, and encourage their memorization. If the time allows and the child is receptive, you can study multiplication tables even further at this time.
The Lessons page
span
Many Times the Same Group .......................... 130
3 pages
Multiplication and Addition ............................ 133
4 pages
Multiplying on a Number Line ........................ 137
3 pages
Multiplication Practice .................................... 140
2 pages
Review ............................................................. 142
2 pages
128
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Math Dice Game for Addition and Multiplication Instructions for three simple games with dice; one to learn the concept of multiplication, another to practice the times tables, and one more for addition facts. http://www.teachingwithtlc.blogspot.com/2007/09/math-dice-games-for-addition-and.html Explore the Multiplication Table This applet visualizes multiplication as a rectangle. http://www.mathcats.com/explore/multiplicationtable.html Multiple Counting Practice Click on the numbers on the grid to skip count. http://www.hsuppappserv.com/multiplecounting/multiplecounting/ Multiplication Memory Game Click on corresponding pairs (problem-answer). http://www.dositey.com/addsub/memorymult.html Multiplication Mystery Drag the answer tiles to the right places in the grid as they are given, and a picture is revealed http://www.harcourtschool.com/activity/mult/mult.html Multiplication.com Interactive Games A bunch of online games just for the times tables. http://www.multiplication.com/interactive_games.htm
129
Many Times the Same Group 1. Write.
a. 2 times the word
b. 3 times the word "ME"
c. 5 times the word
"CAT"
d. 0 times the word
e. 4 times the word
f. 1 time the word
"FROG"
"SCHOOL"
"HERE"
a. 2 times a group of 3 balls
b. 3 times a group of 5 balls
c. 1 time a group of 7 balls
d. 4 times a group of 1 balls
e. 0 times a group of 2 balls
f. 3 times a group of 3 balls
g. 0 times a group of 8 balls
h. 4 times a group of 0 balls
i. 5 time a group of 2 balls
"YOU"
2. Draw groups of balls.
130
3. Fill in the missing parts.
a. 2 times 5
b. ___ times ___
c. ___ times ___
d. ___ times ___
e. ___ times ___
f. ___ times ___
5 × 3
2 × 7
This means “5 times a group of 3.”
This means “2 times a group of 7.”
It is called multiplication.
You multiply 2 times 7.
4. Now it’s your turn to draw! Notice also the symbol × which is read “times.”
a. 2 times 4
b. 3 times 6
c. 1 times 7
2×4
3×6
1×7
d. 6 times 1
e. 4 times 0
f. 2 times 2
6×1
4×0
2×2
131
5. Write the multiplication sentence. Write the total after the " = " sign.
a. 2 × 6 = 12
b. ___×___ = ___
c. ___×___ = ___
d. ___×___ = ___
e. ___×___ = ___
f. ___×___ = ___
a. 8 × 1 = ___
b. 1 × 10 = ___
c. 2 × 2 = ___
d. 5 × 2 = ___
e. 2 × 8 = ___
f. 3 × 3 = ___
6. Draw the groups. Write the total.
132
Multiplication and Addition 2 2 + 2
When the same group is repeated many times, you can write an addition sentence, and a multiplication sentence.
5 + 5 + 5 = 15
6
You add the same number many times. Multiplication is repeated addition.
3 × 5 = 15
3×2=6
1. Write addition and multiplication.
a. ___+___+___ = ___
b. ___+___+___ = ___
___×___ = ___
___×___ = ___
c. ___+___ = ___
___×___ = ___
d. f. e.
+ ___×___ = ___
+ ___×___ = ___
+ ___×___ = ___
2. Draw groups to match the multiplication sentence. Write an addition sentence, too.
a. 2 × 7
b. 4 × 1
7 + 7 = 14
133
c. 4 × 5
3. Write a multiplication sentence and an addition sentence.
a.
b.
___ groups, ___ scissors in each.
___ groups, ___ rams in each.
___ + ___ + ___ + ___ scissors, or
___ + ___ + ___ + ___ rams, or
___ × ___ scissors = ___
___ × ___ rams = ___
c.
d.
___ groups, ___ bears in each.
___ groups, ___ carrots in each.
___ + ___ + ___ bears, or
___ + ___ carrots, or
___ × ___ bears = ___
___ × ___ carrots = ___
e.
f.
___ groups, ___ books in each.
___ groups, ___ bulbs in each.
___ + ___ + ___ books, or
___ + ___ + ___ + ___ bulbs, or
___ × ___ books = ___
___ × ___ bulbs = ___
g.
h.
___ groups, ___ rams in each.
___ groups, ___ scissors in each. ___ + ___ + ___ + ___ + ___ scissors, or
___ + ___ rams, or ___ × ___ rams = ___
___ × ___ scissors = ___
134
4. Write an addition and a multiplication sentence for each picture. a.
b.
___ + ___ + ___ = ___
___ + ___ + ___ + ___ + ___ = ___
___ × ___ = ___
___ × ___ = ___
c.
d.
___ + ___ + ___ = ___
___ + ___ = ___
___ × ___ = ___
___ × ___ = ___
e.
f.
g.
h.
135
5. Now it is your turn to draw. Draw balls or sticks. Then write the multiplication sentence. b. Draw 2 groups of eight balls.
a. Draw 3 groups of seven sticks.
___ + ___ + ___ = ___ ___ × ___ = ___ c. Draw 4 groups of four balls.
d. Draw 5 groups of two balls.
e. Draw 4 groups of two sticks.
f. Draw 10 groups of one stick.
g. Draw 5 groups of three sticks.
h. Draw 7 groups of two sticks.
136
Multiplying on a Number Line Five jumps, each is two steps.
5 × 2 = 10.
Four jumps, each is three steps.
4 × 3 = 12.
1. Write the multiplication sentence that the jumps on the number line illustrate.
` a.
b.
c.
d.
137
2. Draw more “skips” of three.
3. Multiply times 3. Use the skips above to help. a. 5 × 3 =
b. 8 × 3 =
c. 6 × 3 =
d. 2 × 3 =
4×3=
7×3=
3×3=
9×3=
4. How many skips of three are needed? Use the number line above to help. a. ___ × 3 = 24
___ × 3 = 9
b. ___ × 3 = 18
c. ___ × 3 = 21
d. ___ × 3 = 6
___ × 3 = 15
___ × 3 = 12
___ × 3 = 3
5. Draw more “skips” of four.
6. Multiply times 4. Use the skips above to help. a. 2 × 4 =
b. 6 × 4 =
c. 8 × 4 =
d. 5 × 4 =
4×4=
7×4=
3×4=
1×4=
7. How many skips of four are needed? Use the number line above to help. a. ___ × 4 = 24
___ × 4 = 8
b. ___ × 4 = 0
___ × 4 = 12
138
c. ___ × 4 = 16
d. ___ × 4 = 20
___ × 4 = 8
___ × 4 = 4
8. Continue and draw jumps to fit the multiplication problem.
a. 6 × 4 =
b. 5 × 5 =
c. 6 × 1 =
d. 9 × 3 =
e. 3 × 10 =
9. Add repeatedly (or skip-count) to multiply. You can use the number line to help.
a. 3 × 2 =
b. 5 × 2 =
c. 5 × 6 =
d. 3 × 10 =
6×3=
7×4=
3×9=
2 × 11 =
4×5=
3×8=
4 × 10 =
3×7=
139
Multiplication Practice 1. Multiply. Think of repeated addition! a. 2 × 3 = ___
b. 3 × 2 = ___
c. 3 × 10 = ___
2 × 4 = ___
3 × 3 = ___
5 × 10 = ___
2 × 5 = ___
3 × 4 = ___
6 × 10 = ___
2. Write a multiplication sentence from the addition sentence. Solve. a. 11 + 11
b. 0 + 0 + 0 + 0
c. 10 + 10 + 10 + 10 + 10
___ × ___ = ___
___ × ___ = ___
___ × ___ = ___
d. 1 + 1 + 1 + 1 + 1
e. 4 + 4 + 4
f. 20 + 20 + 20
___ × ___ = ___
___ × ___ = ___
___ × ___ = ___
g. 300 + 300 + 300
h. 10 + 10 + 10 + 10 + 10 + 10 + 10
___ × ___ = ___
___ × ___ = ___
3. If the answer is... 0, color the petal yellow. 1, color the petal orange. 2, color the petal red. 3, color the petal green. 6, color the petal blue. 7, color the petal purple. 10, color the petal brown.
140
4. Count by twos. Then fill in the multiplication table of 2.
0, 2, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___
1 × 2 = __
4 × 2 = __
7 × 2 = __
10 × 2 = __
2 × 2 = __
5 × 2 = __
8 × 2 = __
11 × 2 = __
3 × 2 = __
6 × 2 = __
9 × 2 = __
12 × 2 = __
5. Count by fives. Then fill in the multiplication table of 5.
0, 5, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___
1 × 5 = __
4 × 5 = __
7 × 5 = __
10 × 5 = __
2 × 5 = __
5 × 5 = __
8 × 5 = __
11 × 5 = __
3 × 5 = __
6 × 5 = __
9 × 5 = __
12 × 5 = __
6. Count by tens. Then fill in the multiplication table of 10.
0, 10, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___
1 × 10 = __
4 × 10 = __
7 × 10 = __
10 × 10 = __
2 × 10 = __
5 × 10 = __
8 × 10 = __
11 × 10 = __
3 × 10 = __
6 × 10 = __
9 × 10 = __
12 × 10 = __
141
Review 1. Draw groups to illustrate the multiplication sentences. Write an a addition sentence.
a. 5 × 1 = ___
b. 2 × 10 = ___
c. 3 × 2 = ___
2. Draw number-line jumps to illustrate these multiplication sentences.
a. 3 × 6 = ___
b. 4 × 3 = ___
3. Multiply. a. 2 × 3 = ___
b. 3 × 3 = ___
c. 6 × 10 = ___
2 × 10 = ___
3 × 20 = ___
2 × 40 = ___
2 × 20 = ___
7 × 1 = ___
2 × 200 = ___
d. 1 × 3 = ___
e. 4 × 5 = ___
f. 10 × 10 = ___
2 × 0 = ___
5 × 5 = ___
2 × 30 = ___
3 × 4 = ___
6 × 5 = ___
1 × 500 = ___
142
4. Hannah made many math problems from the same picture. Solve the problems. a. 4 + 4 + 4 = ___
d. 12 − 4 − 4 = ___
b. 3 × 4 = ___
e.
1 of 12 is ___ 3 2 of 12 is ___ f. 3
c. 12 − 4 = ___
5. Make as many math problems as you can from this picture:
6. Draw a line from the problems to 10 or 50 if they are equal to 10 or 50.
5+6
29 − 9
15 − 5 1 of 10 2
10
25 + 25
16 − 3 − 3
90 − 50
0 × 10
1 of 100 2
1 of 20 2
5×2 3+3+3
2×5
1×5
61 − 11
45 + 3 + 5
50
20 + 20 + 10
2 × 20
7. Solve the problems. a. Annie had 80 flowers and Katie had 40. Annie gave Katie 20 flowers.
Who has more now? b. John had 60 toy cars and Jim had 10. John gave half of his to Jim.
Who has more now? c. Mary gave 10 marbles to Annie. Now, Annie has 35 and Mary has 22.
How many did they each have initially?
143
1 × 50 1 of 80 2
10 × 10
6+4
5 × 10
70 − 20
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