Copyright 2006 - 2012 Taina Maria Miller. EDITION 1.5 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 to reproduce this material to be used with one (1)
teacher's students by virtue of the purchase of this book. In other words, one (1) teacher MAY make copies of these worksheets to be used with his/her students. Permission is not given to reproduce the material for resale. If you have other needs, such as school-wide licensing, contact the author at www.MathMammoth.com/contact.php.
Please visit www.MathMammoth.com for more information about ebooks and books by Maria Miller. Create free math worksheets at www.HomeschoolMath.net/worksheets/
2
Contents Introduction ...........................................................................
4
Adding with Whole Tens ...................................................... 7 Subtracting Whole Tens ....................................................... 10 Adding in Columns ............. .................................................. 12 Doubling ............................................................................... One-Half .............................................................................
14 16
Regrouping with Tens ........................................................ Going Over to The Next Ten ..............................................
18 21
Add with Two-Digit Numbers Ending in 9 ........................ 24 Add in Columns Practice ..................................................... 26 Add with Two-Digit Numbers Ending in 8 or 7 ................ 28 Addition Practice ................................................................. 30 Many Addends .................................................. ..................
32
Subtracting in Col umns ....................................................... 35 Regrouping (Bo rrowing), Part 1 .... ................................... 38 Regrouping (Bo rrowing), Part 2 .... ................................... 41 Regrouping (Borrowing), Part 3 .......................................
44
Graphs and Problems .......................................................... 46 Adding 2-Di git Numbers Ment ally ...... ................................ 49 Mental Subtraction Methods .............................................. More Mental Subtraction ....... ............................................. Euclid's Game ...................................................................... Review ....... ............................................................................
52 55 58 61
Answers ................................................................................. 64 More from Math Mammoth ................................................ 78
3
Introduction Math Mammoth Add & Subtract 2-B is a continuation to the book Math Mammoth Add & Subtract 2-A. The goal of this book is to study addition and subtraction within 0-100, both mentally and in
columns, especially concentrating on regrouping in addition (carrying) and in subtraction (borrowing).
Mental math Mental math is important because it builds number sense. This book includes many lessons that practice mental math. For example, the child practices adding and subtracting two-digit numbers when one of the −
numbers is a whole ten (problems such as 30 + 14, or 66 20). Also studied are problems such as 36 + 8 or 45 + 9. These problems use the idea of going over ten as in problems 6 + 8 and 5 + 9. The child knows that 6 + 8 fills the first ten and is four more than the ten. He/she will learn to use that fact when adding 36 + 8. The sum 36 + 8 fills the next whole ten (40), and is four more than that, or 44.
Regrouping in tens Simultaneously with this, the child learns adding two-digit numbers in columns, and regrouping with tens, or “carrying,” which is illustrated and explained in detail with the help of visual models. These visual models take the place of base-ten blocks or other manipulatives. You are welcome to use manipulatives to get the idea across, if you prefer. The main concept to understand is that 10 ones are regrouped to form a new ten, and this new ten is written using a little “1” in the tens column. As a “stepping stone” into the standard way to add, you can show the child the method below. This can be used if the child does not readily understand why the little “1” above the tens column corresponds to a ten. Below, the ones are added first, and the answer is written using both columns. Then, the tens are added and the answer is written under the sum of ones. Lastly, both sums are added. tens ones 3 6 1
8
add ones first → 1
+
4
tens ones 6 3 +
add tens here →
1
8
1 4
4
tens ones 3 6 +
0
total →
1
8
1 4
4
5
4
0
Regrouping in subtraction The next lessons teach subtracting in columns. First we only deal with the easy problems where you don't need to regroup (borrow). Then the following lessons practice in detail the process of regrouping or borrowing. You can use either term with your child, or even choose not to use either if you feel it is confusing. You can alternatively use the phrase “breaking a ten into ten ones.” First, the lesson Regrouping practices breaking down a ten into ten ones because we cannot subtract from the ones. It is crucial that the child understands what happens here. Otherwise, he/she might end up only memorizing the procedure, and will probably at some point misremember how it was done. That is why this lesson deals with the regrouping process in detail with plenty of visual exercises.
4
If you notice that the child does not understand the concept of regrouping, he/she may need more practice with concrete manipulatives or visual exercises before proceeding.
More mental math After learning regrouping, we practice mental subtraction in three separate lessons. One of them expounds on several methods for mental subtracting. Another is about Euclid's game—a fun game that also practices subtraction of two-digit numbers. I wish you success with math teaching! Maria Miller, the author
Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. You can access an up-to-date online version of this list at www.mathmammoth.com/weblinks/add-subtract-2B.htm Base Blocks Addition
A virtual manipulative that shows regrouping in addition. You can either solve addition problems that are provided, or create your own. “Lasso” with a mouse ten units, ten tens, or ten hundreds to regroup them. Choose “Columns = 2” to restrict the work to two-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html?from=category_g_1_t_1.html Base Blocks Subtraction
A virtual manipulative that helps teach borrowing in subtraction. Choose "Create Problem", then click on the blue whereas blocks tothe create a problem. TheBLUE number to be Click subtracted (theproblem subtrahend) is illustrated the red REDand blocks minuend is by the blocks. BEGIN to start solving. by 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. http://nlvm.usu.edu/en/nav/frames_asid_155_g_1_t_1.html?from=category_g_1_t_1.html Callum's Addition Pyramid
Add the pairs of numbers to get a number on the next level and finally the top number. Three difficulty levels. http://www.amblesideprimary.com/ambleweb/mentalmaths/pyramid.html Techno Tortoise
Practice adding two two-digit numbers in parts on a number line. http://www.ictgames.com/technowithflock.html Mr. Martini's Classroom: Addition and Subtraction Inequalities
Compare expressions that involve addition and subtraction of one and two-digit numbers. http://www.thegreatmartinicompany.com/inequalities/number-comparison.html
and http://www.thegreatmartinicompany.com/inequalities/add-subtract-comparison.html
5
Mr. Martini's Classroom: Long Addition
Practice adding two-digit numbers in columns online. http://www.thegreatmartinicompany.com/longarithmetic/longaddition.html Mathionare Addition Quiz
Answer increasingly more difficult addition questions (one and two-digit numbers), and win a million! http://www.mathsisfun.com/games/mathionaire-addition-quiz.html Button Beach Challenge
Figure out what number the various colored buttons represent. http://www.amblesideprimary.com/ambleweb/mentalmaths/buttons.html Teaching Treasures - Year 2 Maths Worksheets
Simple online addition and subtraction worksheets where the student types in the answer and can check it. http://www.teachingtreasures.com.au/maths/maths_level2.html Euclid's Game
An online version of Euclid's game (a Java applet). http://www.cut-the-knot.org/blue/EuclidAlg.shtml Count on Convict
Practice “adding up” strategy for mental subtraction. First type the amount to move on to the next whole ten, then count on tens, then the rest. http://www.ictgames.com/countonconvict.html Double Digit Addition
Match the addition problem with the correct sum. Enjoy! http://www.quia.com/mc/818288.html Addition Level 2
A matching game where you add a one-digit number and a two-digit number. http://www.quia.com/mc/65798.html Speed Grid Addition
Find numbers on the grid that add up to the given number. This uses both single-digit and two-digit numbers. http://www.oswego.org/ocsd-web/games/SpeedGrid/Addition/urikares.html
6
Adding with Whole Tens 1. The numbers are shown with ten-sticks and one-dots. Write the sums.
+
+
a.
b.
54 + 10 = ______
______ + 20 = ______
+ c.
+ d.
______ + ______ = ______
______ + ______ = ______
+ e.
+ f.
______ + ______ = ______
______ + ______ = ______
Adding whole tens and another 2-digit number
Break down the other number into tens and ones. Add the tens. Then, add the ones. 2. Add. Break the second number into tens and ones first. Then add the tens. a.
10 + 34 = _______
b. 10
(10 + 30 + 4)
+ 28 = _______
c.
(10 + _____ + _____ )
20 + 24 = _______ (20 + _____ + _____ )
d.
30 + 21 = _______
e.
50 + 17 = _______
f.
40 + 33 = _______
g.
60 + 23 = _______
h.
30 + 37 = _______
i.
70 + 25 = _______
7
Math MammothAdd & Subtract 2-B (Blue Series)
3. Add. Break the first number into tens and ones first. Then add the tens. a.
45 + 20 = _______
b.
(40 + 5 + 20) d.
27 + 20 = _______
( _____ + _____ + 20 )
46 + 30 = _______
45 + 40 = _______
c.
( _____ + _____ + 40)
e.
16 + 50 = _______
f.
38 + 60 = _______
4. Add. a. 77
+ 10 = ______
b.
20 + 45 = ______
c.
16 + 10 = ______
d. 77
+ 20 = ______
e.
30 + 45 = ______
f.
16 + 30 = ______
50 + 48 = ______
h.
60 + 21 = ______
i.
19 + 20 = ______
g.
Remember rounding to the nearest ten?
Numbers ending in 1, 2, 3, or 4 are closer to the previous ten than the next, so they are rounded down.
Numbers ending in 6, 7, 8, or 9 are closer to the next ten so they are rounded up.
≈
≈
72 70 (72 is approximately 70)
46 50 (46 is approximately 50)
Middle numbers ending in 5 are rounded up. ≈
5
10
5. Round these numbers to the nearest ten. a.
23 ≈ ______
b.
54 ≈ ______
c.
78 ≈ ______
d.
96 ≈ ______
e.
65 ≈ ______
f.
95 ≈ ______
g.
8 ≈ ______
h.
3 ≈ ______
6. Gwen bought shoes for $39, a top for $8, and a skirt for $23. Round these prices to the nearest ten, and then add them to find the total cost. 7. Jacob had $61. Then he bought a toy for $29. Use rounded numbers to estimate how much money he has left.
8
Math MammothAdd & Subtract 2-B (Blue Series)
Subtracting Whole Tens 1. Cross out as many ten-pillars as the problem indicates. What is left?
a.
b.
30 – 10 = ______
d.
47 – 20 = ______
50 – 30 = ______
e.
26 – 10 = ______
c.
70 – 40 = ______
f.
55 – 30 = ______
What can you notice? 2. Count by tens backwards. a.
76, 66, ________ , ________ , ________ , ________ , ________
b.
_______ , ________ , 52, 42, ________ , ________ , ________
c.
________ , ________ , ________ , ________ , 27 , 17, ________
3. Subtract. a.
b.
c.
23 – 10 = ________
48 – 20 = ________
56 – 10 = ________
23 – 20 = ________
48 – 30 = ________
56 – 30 = ________
d.
e.
f.
75 – 10 = ________
31 – 10 = ________
81 – 40 = ________
75 – 20 = ________
31 – 20 = ________
81 – 50 = ________
10
Math MammothAdd & Subtract 2-B (Blue Series)
4. Find the pattern and continue it. a.
88 – 10 = ______
b. 100
– 60 = ______
c.
34 – 10 = ______
88 – 20 = ______
90 – 50 = ______
44 – 20 = ______
88 – 30 = ______
80 – 40 = ______
54 – 30 = ______
88 – ______ = ______
_____ – _____ = _____
_____ – _____ = _____
88 – ______ = ______
_____ – _____ = _____
_____ – _____ = _____
88 – ______ = ______
_____ – _____ = _____
_____ – _____ = _____
88 – ______ = ______
_____ – _____ = _____
_____ – _____ = _____
5. Use rounded numbers to solve these problems. a. Three suitcases weigh 29 kg, 18 kg, and 31 kg. About how much is their total weight?
b. Dale Chairs cost $29ofapiece. Can $80? buy three them with
c. Henry received $50 for his birthday.
If he buys three books that cost $9 each, about how much will he have left?
Find numbers for the – puzzles.
+
= 90
–
–
+ +
= 30
= 30 = 30
11
= 40 + – =
30
= 80
= 10
Math MammothAdd & Subtract 2-B (Blue Series)
2. Fill in the numbers and add. tens
a.
+
+
+
d.
+
f.
tens
ones
tens
ones
+
ones
+
ones
+
ones
+
+
+
b.
tens
e.
tens
+
tens
c.
ones
+
3. Add. a.
2 0 + 5 7
b.
6 2 + 3 6
f.
4 6 + 4 0
g.
7 1 + 2 4
k.
2 5 1 3 + 4 0
l.
4 1 3 2 + 2 4
c.
4 5 + 1 3
d.
3 7 + 3 2
e.
1 4 + 7 2
h.
3 2 + 5 5
i.
3 3 + 4 3
j.
6 4 + 2 5
m.
3 2 5 0 + 1 5
n.
3 3 1 2 + 4 3
o.
5 4 1 1 + 2 4
13
Math MammothAdd & Subtract 2-B (Blue Series)
Doubling Doubling a number means adding it to itself. It is finding two times the number. Examples:
Double 7 is 7 + 7 is 14.
Double 20 is 20 + 20 is 40.
1. Find the double of these numbers. a.
Double 5
b.
_____ + _____ = _____
Double 30
c.
_____ + _____ = _____
Double 50
_____ + _____ = _____
2. Find the double of these numbers by adding in the boxes. a.
+
22 + 22
b.
Double 34
c.
+
13 + 13
d.
+
Double 41
+
3. Make a doubles chart. Notice it has a pattern!
Double 6 is 6 + 6 = _____. Double 13 is 13 + 13 = _____. Double 7 is 7 + 7 = _____. Double 14 is 14 + 14 = _____. Double 8 is 8 + 8 = _____. Double 15 is 15 + 15 = _____. Double 9 is 9 + 9 = 18.
Double 16 is 16 + 16 = 32.
Double 10 is 10 + 10 = 20.
Double 17 is 17 + 17 = 34.
Double 11 is 11 + 11 = 22.
Double 18 is 18 + 18 = 36.
Double 12 is 12 + 12 = 24.
Double 19 is 19 + 19 = 38.
14
Math MammothAdd & Subtract 2-B (Blue Series)
We can use doubles chart to solve problems about equal sharing. Example. Two children need to clean 18 chairs. They divide the job equally.
How many chairs does each child clean? We can use the doubles chart. Since 9 + 9 = 18, each child will clean 9 chairs.
Solve the problems. You can use the doubles chart. 4. Mother tells two children to make 16 sandwiches. The children share the job How many sandwiches willequally. each child make? 5. You and your brother share equally 32 pieces of candy. How many pieces of candy will you get?
6. A batch of brownies makes 16 brownies. Mom makes a double batch. How many brownies will she make?
7. Two teachers divide 28 worksheets evenly. How many worksheets will each one get?
8. In a board game, you throw two dice and move that many spaces. Mary got double four. Andrea got double six. How many spaces did Mary move? How many spaces did Andrea move?
9. Mother and her friend need to make 20 dolls to sell. They share the job evenly. How many dolls will each woman make?
15
Math MammothAdd & Subtract 2-B (Blue Series)
One-Half When you divide something into two equal parts, you have divided it into two halves. Each part is half of the whole. We write one-half this way:
1
,
2
or this way: 1/2 .
6 + 6 = 12
To find half of 10 apples, divide the ten into two equal parts. 5 + 5 = 10. Half of ten apples is five apples.
1. a. Color one half of each shape.
1 2 of 12 is 6.
b. Color two halves of each shape.
2. Draw a line through these shapes and divide them into two halves. Color one half.
b.
a.
e.
c.
d.
3. Divide the things into two EQUAL groups. Write an addition sentence. Find half of the total. a.
10
b.
40
____ + ____ = _____
____ + ____ = _____
1 2 of 10 is ____.
1 2 of 40 is _____.
16
c.
24
____ + ____ = _____ 1 of 24 is _____. 2
Math MammothAdd & Subtract 2-B (Blue Series)
4. Fill in the doubles chart. Then use it to find one-half of the given numbers.
6 + 6 = _____
11 + 11 = _____
1 2
of 16 is _____.
7 + 7 = _____
12 + 12 = _____
1 2
of 28 is _____.
8 + 8 = _____
13 + 13 = _____
1 2
of 26 is _____.
1
9 + 9 = _____
14 + 14 = _____
10 + 10 = _____
15 + 15 = _____
2 1 2
of 30 is _____. of 22 is _____.
5. Divide the dots into two EQUAL groups. Find half of the total. a.
1 of 26 is ____. 2
c.
b.
1 of 30 is ____. 2
d.
1 of ____ is _____. 2
1 of ____ is _____. 2
6. Solve the word problems, and fill in another chart of doubles to help you. a. Jack and Joe split $60 between them. How many dollars did each one get? b. What is half of 60 minutes?
10 + 10 = ______ 20 + 20 = ______
c. Half of 100 students were sick.
30 + 30 = ______
How many were not sick?
40 + 40 = ______
d. Aunt Katie gave Missie half of $40.
Missie spent $10 on a toy. How many dollars does Missie have now?
50 + 50 = ______
e. The recipe called for 10
apples. That was exactly half of Mom's apples. How many apples had Mom bought srcinally?
17
Math MammothAdd & Subtract 2-B (Blue Series)
When we make a new ten from the ones (cubes), we are regrouping. The ten little ones get grouped and become a ten.
tens ones
1
This is also called carrying to tens. Imagine someone “gathering” ten little cubes in his lap and “carrying” them over into the tens column as 1 ten.
3 + 2 6
5 7 2
To show this new ten, write a little “1” in the tens column above the other numbers. Then add in the tens-column as usual, adding the little “1” also. 2. Circle ten ones to make a new ten. Add the tens and ones in columns.
a.
tens 1
ones
1
3
+ 2
b.
9
tens 1
ones
2
4
+ 3
8
2 tens 1
ones
3
5
c.
tens 1
ones
2
4
+ 4
7
d.
+ 1
9
e.
f.
g.
h.
19
Math MammothAdd & Subtract 2-B (Blue Series)
3. Add. If you can make a new ten from the ones, regroup the new ten with the other tens. a.
4 2 + 1 5
b.
2 7 + 4 5
c.
6 5 + 2 6
d.
8 3 + 1 5
e.
3 4 + 1 9
f.
5 2 + 4 1
g.
1 3 + 4 4
h.
6 3 + 2 7
i.
3 6 + 5 1
j.
6 6 + 2 9
k.
1 8 +4 0
l.
3 9 +3 6
m.
5 9 + 3 5
n.
7 2 + 2 2
o.
1 7 + 2 3
tens ones 2
Sometimes we can get or regroup two tens from all the ones (cubes). On the right, when you add the ones, you get 6 + 7 + 8 = 21. This makes two
3 6
new tens
. We need to add them with the other tens in the tens column. So, we write a little “2” above the tens column.
2 7 + 1 8 1
4. Add. Regroup the ones to make new tens. Add the new tens in the tens column. a.
3 4 1 9 + 2 6
b.
1 5 2 7 + 4 5
c.
1 8 2 7 + 2 6
d.
2 6 4 8 + 1 9
e.
3 4 2 0 + 1 9
5. Count by fours. a. 0,
4, _____ , _______ , _______ , _______, _______ , _______ , _______
b. 100,
96, 92, _______ , _______ , _______ , _______ , _______ , _______ 20
Math MammothAdd & Subtract 2-B (Blue Series)
Going Over to the Next Ten Sums that go over to the next ten
Let's add 59 + 5 so that we first complete 60. 59 + 5 | \
59 + 1 + 4 60 + 4 = 64 The 5 is broken into two parts: 1 and 4. That is because 59 and 1 makes sixty. Then, we have 60 and 4. We get 64.
9 and 1 make a ten. We get 6 tens. 59 + 5 = 64
1. Circle ten little cubes to make a ten. Count the tens and ones. Write the answer.
a. 13
+ 9 = ______
b. 15
+ 8 = ______
c. 17
+ 7 = ______
d. 24
+ 7 = ______
e. 25
+ 6 = ______
f. 37
+ 9 = ______
g. 36
+ 6 = ______
h. 48
+ 4 = ______
i. 58
+ 5 = ______
21
Math MammothAdd & Subtract 2-B (Blue Series)
2. Complete. Break the second number into two parts so that you complete the next ten.
28 + 8
a.
/
47 + 5
b. \
28 + 2 + ____
/
39 + 3 /
79 + 9 /
47 + 3 + ____
30 + ____ = ______ d.
c. \
79 + ____ + ____
50 + ____ = ______ 27 + 5
e. \
/
\
80 + ____ = ______ f.
38 + 7
\
/
\
39 + ____ + ____
27 + ____ + ____
40 + ____ = ______
______ + ____ = _____ ______ + ____ = _____
38 + ____ + ____
3. Continue the patterns. COMPARE the columns, and NOTICE what is the same.
8 + 1 = _______
a.
28 + 1 = _______
b.
78 + 1 = _______
c.
8 + 2 = _______
28 + 2 = _______
78 + 2 = _______
8 + 3 = _______
28 + 3 = _______
78 + 3 = _______
8 + 4 = _______
28 + 4 = _______
78 + 4 = _______
8 + ____ = _______
28 + ____ = _______
78 + ____ = _______
8 + ____ = _______
28 + ____ = _______
78 + ____ = _______
4. Fill the missing addends. a.
8 + _____ = 10
b.
8 + _____ = 11 d.
7 + _____ = 10 7 + _____ = 12
13 + _____ = 20
c.
13 + _____ = 21 e.
18 + _____ = 20 18 + _____ = 22 22
67 + _____ = 70 67 + _____ = 71
f.
86 + _____ = 90 86 + _____ = 92
Math MammothAdd & Subtract 2-B (Blue Series)
5. Solve the problems. Write a number sentence for each problem, not just the answer. a.
Benjamin wants to buy a kite that costs $30. He has saved $22. How much more money will he need?
b.
Natasha had already saved $20. She earned $5 by selling eggs, and earned $5 more for selling fruit. How much money does she have now?
c.
Mom bought 28 fruit trees and has planted eight of them. How many still need planted?
d.
Thirty-seven people attended Uncle Sam's 50th birthday party. Thirty-two of them came before noon. How many came after noon?
e.
Dad bought a bunch of 40 grapes and ate half of them. Then, little sister ate seven grapes. How many are left now?
6. Continue the patterns. COMPARE the columns, and NOTICE what is the same. a.
9 + 1 = _______
b.
39 + 1 = _______
c.
59 + 1 = _______
9 + 2 = _______
39 + 2 = _______
59 + 2 = _______
9 + 3 = _______
39 + 3 = _______
59 + 3 = _______
9 + 4 = _______ 9 + ____ = _______
39 + 4 = _______ 39 + ____ = _______
59 + 4 = _______ 59 + ____ = _______
9 + ____ = _______
39 + ____ = _______
59 + ____ = _______
23
Math MammothAdd & Subtract 2-B (Blue Series)
Add with Two-Digit Numbers Ending in 9 Imagine that 29 wants to be 30... so it “grabs” one from 5. Then, 29 becomes 30, and 5 becomes 4. The addition problem is changed to 30 + 4 = 34.
1. Circle the nine dots and one more dot to form a complete ten. Add.
a.
19 + 5 = ______
b.
29 + 7 = ______
c.
49 + 5 = ______
d.
29 + 8 = ______
e.
39 + 6 = ______
f.
49 + 9 = ______
2. Add. For each problem, write a helping problem using the “ones” from the first problem. a.
19 + 7 = _______
b.
49 + 3 = _______
9 + 7 = ______
____ + _____ = ______
39 + 4 = _______
c.
____ + _____ = ______
3. Add. Compare the problems. a.
9 + 3 = ________ 19 + 3 = ________
d.
b.
9 + 6 = ________
c.
39 + 6 = ________ e.
9 + 4 = ________
49 + 4 = ________ f.
9 + 7 = ________ 39 + 7 = ________
9 + 9 = ________ 69 + 9 = ________
9 + 5 = ________ 19 + 5 = ________
29 + 7 = ________
79 + 9 = ________
59 + 5 = ________
24
Math MammothAdd & Subtract 2-B (Blue Series)
4. These problems review the basic facts with 9 and 8. By this time you should already remember these addition facts. Try to remember what number will fit, and not count.
a.
b.
c.
d.
9 + _____ = 14
4 + 9 = _____
8 + _____ = 15
7 + 8 = _____
9 + _____ = 15
8 + 9 = _____
8 + _____ = 17
8 + 8 = _____
9 + _____ = 13
2 + 9 = _____
8 + _____ = 12
5 + 8 = _____
9 + _____ = 18
5 + 9 = _____
8 + _____ = 14
6 + 8 = _____
9 + _____ = 12
6 + 9 = _____
8 + _____ = 13
3 + 8 = _____
9 + _____ = 17
9 + 9 = _____
8 + _____ = 18
9 + 8 = _____
9 + _____ = 16
7 + 9 = _____
8 + _____ = 16
4 + 8 = _____
5. Find the patterns and continue them! a.
+
40 b.
+
16 c.
+
+
+
48
53
61
+
+
+
27
34
21 +
_____
+
____
+
____
+
+
+
66
_____
+
+
42
+
_____
25
+
_____
_____ _____
+
_____
+
_____
+
_____ +
67
+
_____ _____
+
71
74
76
Math MammothAdd & Subtract 2-B (Blue Series)
Add in Columns Practice 1. Add in columns. a.
9 + 7 1
b.
2 4 + 6 7
c.
5 5 + 3 6
d.
4 5 + 2 5
e.
3 8 + 1 4
f.
3 4 9 + 3 5
g.
2 5 4 2 + 4 9
h.
5 8 3 0 + 6
i.
2 9 4 4 + 1 2
j.
1 6 1 4 + 1 9
2. Write the numbers so that the ones and tens are in their own columns. Add. a.
f.
45 + 27
6 + 31 + 25
b.
g.
8 + 56
40 + 7 + 9
c.
h.
40 + 32
46 + 8 + 20
26
d.
i.
25 + 45
5 + 8 + 13
e.
j.
47 + 9
5 + 4 + 57
Math MammothAdd & Subtract 2-B (Blue Series)
Here we have more than 10 tens. Ten tens make a hundred (100)! Add the tens: 8 + 7 = 14 tens. The “1” of the 14 goes in the hundreds' column, and the “4” stays in the tens column. The answer 149 is read “one hundred fifty-nine.” Another example. Add the tens normally: 1 + 5 + 6 = 12 tens. Write the 12 so that the “1” is in the hundreds' column, and the “2” is in the tens column. The 12 tens make 1 hundred and 2 tens. The answer 123 is read “one hundred twenty-three.” You will study more about hundreds later. 3. Add. You will have more than 10 tens. a.
27 + 80
b.
95 + 47
c.
29 + 75
d.
62 + 84
4. Add. a.
6 7 + 6 1
b.
9 0 + 6 5
c.
3 9 + 8 1
d.
8 5 + 6 2
e.
2 9 + 9 4
f.
6 5 1 8 + 2 6
g.
7 4 7 + 4 5
h.
6 8 4 7 + 3 2
i.
1 2 8 8 + 4 9
j.
8 5 0 + 7 9
27
Math MammothAdd & Subtract 2-B (Blue Series)
Add with Two-Digit Numbers Ending in 8 or 7 Imagine that 38 wants to be 40, so it “grabs” two from 7. Then, 38 becomes 40, and 7 becomes 5. The addition problem is changed to 40 + 5 = 45.
1. Circle the eight dots and two more dots to form a complete ten. Add.
a.
18 + 6 = ______
b.
28 + 7 = ______
c.
48 + 8 = ______
d.
38 + 4 = ______
e.
38 + 6 = ______
f.
48 + 5 = ______
2. Add. For each problem, write a helping problem using the “ones” from the top problem. a.
18 + 7 = _______
b.
38 + 6 = _______
8 + 7 = ______
____ + _____ = ______
58 + 5 = _______
c.
____ + _____ = ______
3. Add. Compare the problems. What is similar about the problems in each box? a.
8 + 3 = _______ 18 + 3 = _______
d.
8 + 2 = _______ 38 + 2 = _______ 28 + 2 = _______
b.
8 + 6 = _______
c.
38 + 6 = _______ e.
8 + 9 = _______ 68 + 9 = _______ 78 + 9 = _______ 28
8 + 4 = _______
78 + 4 = _______ f.
8 + 5 = _______ 18 + 5 = _______ 58 + 5 = _______
Math MammothAdd & Subtract 2-B (Blue Series)
4. Circle the seven dots and three more dots to make a new ten. Add.
a.
27 + 4 = ______
b.
47 + 5 = _______
37 + 7 = _______
c.
5. Add. For each problem, write a helping problem using the “ones” from the top problem. a.
75 + 7 = _______
b.
5 + 7 = ______
____ + _____ = ______
47 + 7 = _______
c.
57 + 6 = _______
____ + _____ = ______
6. Add. Compare the problems. What is similar about the problems in each box? a.
7 + 6 = ________
27 + 6 = ________ d.
7 + 9 = ________
b.
7 + 5 = ________
c.
77 + 5 = ________ e.
7 + 3 = ________
7 + 7 = ________
87 + 7 = ________ f.
7 + 10 = ________
67 + 9 = ________
37 + 3 = ________
17 + 10 = ________
87 + 9 = ________
77 + 3 = ________
47 + 10 = ________
7. Solve the word problems. a.
Jenny needed 24 eggs to make omelettes for her family. She already had 15 eggs. How many more does she need?
b.
Her large family eats lots of potatoes. Dad bought a 25-kilogram bag of potatoes. Now, only six kg are left. How many kilograms of potatoes have they eaten?
29
Math MammothAdd & Subtract 2-B (Blue Series)
Addition Practice 1. Break the second number into tens and ones, and then add mentally.
20 + 34 = _______
a.
70 + 18 = _______
b.
(20 + ______ + ____ )
50 + 27 = _______
c.
(70 + ______ + ____ )
(50 + ______ + ____ )
2. Add mentally. a.
17 + 10 = _______
b.
16 + 20 = _______
c.
50 + 14 = _______
26 + 10 = _______
34 + 30 = _______
60 + 23 = _______
42 + 10 = _______
67 + 20 = _______
30 + 45 = _______
3. Find the pattern and continue it. This pattern “grows” at each step. +
+
1
3
+
7
+
13
+
21
+
+
31
_____
+
_____ _____
4. Add. a.
4 4 + 4 8
b.
c.
3 2 + 5 9
1 6 + 4 7
d.
2 3 + 6 7
e.
5 5 + 2 9
5. Compare the expressions and write < , > , or = . a.
8+3
40 + 5
b.
8+54
9+53
d.
2 + 36
29 + 7
e.
46+8
48+5
30
c.
5+6+56
61+6
85+9
6+88
f.
Math MammothAdd & Subtract 2-B (Blue Series)
6. Explain why these are wrong:
33 + 48
55 + 39
711
814
7. Add. Compare the problems! a.
b.
c.
d.
7 + 8 = ______
4 + 9 = ______
8 + 4 = ______
7 + 9 = ______
17 + 8 = ______
14 + 9 = ______
48 + 4 = ______
57 + 9 = ______
37 + 8 = ______
44 + 9 = ______
78 + 4 = ______
37 + 9 = ______
8. Count in threes. a.
42, 45, _______, _______, _______, _______, _______, _______
b.
1, 4, _______, _______, _______, _______, _______, _______
9. Add. a.
b.
c.
d.
29 + 4 = _____
45 + 8 = _____
22 + 8 = _____
78 + 6 = _____
38 + 9 = _____
24 + 9 = _____
46 + 8 = _____
69 + 5 = _____
48 + 6 = _____
36 + 8 = _____
91 + 8 = _____
62 + 9 = _____
Figure out the missing numbers for these addition problems. a.
b.
+ 1
4
4
1
c.
+ 7
d.
e.
3
+ 2
5
+ 7
8
+ 2
6
1
5
1
9
1
6
1
31
Math MammothAdd & Subtract 2-B (Blue Series)
Many Addends When adding the ones, you may get two or even three tens. Regroup.
Adding the ones we get 8 + 7 + 8 = 23.
Write the new tens in the tens column.
Write the two new tens in the
2
4 8 2 7 + 1 8 9 3
tens column.
Adding the ones we get 9 + 9 + 7 + 6 = 31. Write the three new tens in the tens column.
3
1 1 2 + 2
9 9 7 6
9 1
1. Add mentally. First add the numbers that make 10 (if there are any).
8 + 4 + 5 = _______
a.
5 + 8 + 7 = _______
b.
9 + 9 + 9 = _______
9 + 2 + 6 = _______
c. 8
+ 5 + 6 + 4 = _______
4 + 9 + 5 + 6 = _______
2. Add. The answers are “hidden” in the list of numbers below the problems. a.
5 2 3 0 + 1 1
e.
i.
3 2 1 + 1
1 3 2 5
b.
c.
+ 5 4
6 7 8 6
f.
1 9
j.
+ 71 99
4 1 1 + 2
0 8 6 2
g.
5 6
k.
80
82
89
91
1 1 1 + 3
+ 1 9
5 7 8 9
h.
4 5
l.
+ 61 59
92
93
96
97
32
98
117
3 6 2 7
d.
+ 2 7
+ 32 29
74
3 3 3 8
1 2 2 + 1
2 9 5 4
5 1 + 17 59
117
122
129
145
Math MammothAdd & Subtract 2-B (Blue Series)
3. Solve the problems. Write an addition or subtraction sentence for each one. You can add in columns if you need to. a.
A bus can seat 30 people. There were already 23 people. Is there room for nine more people?
b.
The first bus had 22 people on it, and the second bus had 25. What is the total number of people on the buses?
d.
A bus was full, but then six people got off. How many people were on it now?
Yes/No, because
c.
How many buses do you need if you have 57 people?
How many buses do you need if you have 88 people?
e.
A bus was full. First it dropped off 13 people. Then it dropped off seven more people. How many people were left on the bus?
f.
A bus had some people in it, and then 13 more got on. Now there are 29 people on the bus. How many were on the bus srcinally?
g.
A bus had 20 people on it. Then it dropped off eight people. Then five people got on. Now how many people are on the bus?
h.
A bus had some people on it. It picked up 12 people, and then seven people more. Then it was full. How many people were on the bus srcinally?
33
Math MammothAdd & Subtract 2-B (Blue Series)
4. Add mentally. Try to find the easiest order. a.
30 + 2 + 40 + 8 = ________
c.
9 + 40 + 1 + 4 = ________
b.
50 + 4 + 10 + 7 = ________
d.
20 + 10 + 8 + 9 = ________
5. Add. Below each number, write “E” for an even number, and “O” for an odd number. a.
19 + 5 + 7 =3 1 OO
O
b.
25+ 7 + 3 =
e.
5 + 1 +1 1+ 9 =
_______
c.
7 + 11 + 23 =
_______
O
d.
57 + 21 =
g.
17 + 27 + 5 =
_______
_______
h.
_______
25 +1 3+ 3 + 1 =
_______
25 + 9 =
f.
i.
57+21=
_______
_______
Underline the correct choice in the sentences below. Can you think why it is that way? If I add two odd numbers, the answer is (even/odd). If I add three odd numbers, the answer is (even/odd). If I add four odd numbers, the answer is (even/odd). 4 7 + 2 9
5 2 1 7 + 1 4
6 0 + 1 6
Can you figure out how Mary is adding and why it works?
7 0 + 1 3
7 6
8 3 Use Mary's method with these problems: 1 3 1 5 + 4 8
2 7 2 8 + 3 1
1 6 2 5 + 4 7
34
4 6 2 5 + 1 2
3 6 2 7 + 3 4
Math MammothAdd & Subtract 2-B (Blue Series)
Subtracting in Columns tens
ones
1. a.
tens
ones
6
1
1. b.
–
3
2
–
Cross out 3 tens and 2 ones.
Cross out 6 tens and 1 one.
It's easy: subtract the tens and ones in their own column. 2. Subtract. a.
5 7 – 1 0
b.
6 6 – 2 4
c.
7 8 – 4 4
d.
8 7 – 2 0
e.
5 5 – 1 1
f.
9 5 – 3 5
g.
2 8 – 2 5
h.
6 7 – 3 3
i.
7 6 – 3 2
j.
8 8 – 6 6
9 6
d.
2 7
e.
3. Figure out what was subtracted.
5 7
a.
4 8
b.
–
– 3 7
c.
– 2 5
– 3 3
7 6 –
1 2
3 3
4. Subtract and add. Compare the problems. a.
b.
c.
72 + 20 = _______
29 + 10 = _______
63 + 30 = _______
72 + 10 = _______
29 + 50 = _______
63 – 40 = _______
72 – 30 = _______
29 + 30 = _______
63 – 60 = _______
35
Math MammothAdd & Subtract 2-B (Blue Series)
5. Kids gathered seashells on the beach, and counted how many each one got. Then they made a bar graph. a. Who gathered the least
seashells? __________________________ b. Who gathered the most?
__________________________ c. How many more did Luis gather than Linda? d. How many more did Annie gather than Mark? e. How many did Linda and Jane gather together?
________ more ________ more ________ seashells
f. Mark gave 10 of his to Linda.
Now how many does Linda have?
________ seashells
g. If Luis gives 10 of his to Annie,
will Luis and Annie have equal amount? ________________ 6. Count by six, seven, eight, and nine - and backwards by 5! a.
0, 6, ______, ______, ______, ______, ______, ______, ______
b.
0, 7, ______, ______, ______, ______, ______, ______, ______
c.
0, 8, ______, ______, ______, ______, ______, ______, ______
d.
0, 9, ______, ______, ______, ______, ______, ______, ______
e.
100, 95, ______, ______, ______, ______, ______, ______, ______
f.
77, 72, 67, ______, ______, ______, ______, ______, ______
36
Math MammothAdd & Subtract 2-B (Blue Series)
7. Solve the word problems. Write an addition or subtraction sentence for each one. a.
There were 36 birds sitting on the telephone line. 15 of them flew away. How many were left?
b.
The teacher needed 34 red sheets of paper for the crafts class. She already had 21. How many more did she need?
c.
The paper sheets are sold in packages of 12. How many packages did the teacher need to buy?
d. Jane
saw 38 birds sitting on the telephone line. A little later she counted only 30 birds on the line. How many had flown away?
Find the missing numbers in these addition and subtraction problems!
7 – 3
5 –
2 3
8 2
+ 3
4 2
+ 1
7 3
8 – 1 5 0
3 + 1 7 5 0
2
6 8
4
+
9 –
6 2
37
4
7
+ 9 3 4
4 1 5
+ 4 8 2
Math MammothAdd & Subtract 2-B (Blue Series)
Regrouping (Borrowing), Part 1 We will now study regrouping (“borrowing”) in subtraction.
Break a ten.
As a first step, we study breaking a ten-pillar into ten little cubes. This is called regrouping, 4 tens 5 ones because one ten “changes First we have 45. We groups” from the tens group “break” one ten-pillar into the ones. into little cubes. Here is another example. First we have 5 tens 3 ones. We “break” one ten-pillar into 10 little cubes. We end up with 4 tens 13 ones.
3 tens 15 ones Now we have 3 tens and 15 ones. It is still 45, but written in a different way.
Break a ten.
5 tens 3 ones
4 tens 13 ones
1. Break a ten into 10 ones. What do you get? Draw or use manipulatives to help.
a.
3 tens 0 ones
b.
___tens ____ones
___tens ___ones
c.
___tens ___ones
d.
___tens ____ones
___tens ___ones
e.
___tens ___ones
___tens ____ones
___tens ____ones
f.
___tens ____ones
___tens ___ones
38
___tens ____ones
Math MammothAdd & Subtract 2-B (Blue Series)
Let's study subtraction. The pictures on the right illustrate 45 – 17.
Break a ten.
First, a ten is broken into 10 ones. So, 4 tens 5 ones becomes 3 tens 15 ones. After that, cross out (subtract) 1 ten 7 ones.
4 tens 5 ones
3 tens 15 ones
Cross out 1 ten 7 ones (from the second picture). What is left? ____ tens ____ ones
The pictures on the right illustrate 52 – 39.
Break a ten.
First, a ten is broken into 10 ones. So, 5 tens 2 ones becomes 4 tens 12 ones. After that, cross out (subtract) 3 tens 9 ones.
5 tens 2 ones
4 tens 12 ones
Cross out 3 tens 9 ones (from the second picture). What is left? ____ tens ____ ones
2. Fill in. Always subtract (cross out some) from the second picture. Break a ten.
3 tens 6 ones a.
Break a ten.
___ tens ___ ones
2 tens 16 ones
Subtract 8 ones (from the second picture).
b.
Subtract 2 tens 7 ones.
What is left? ____ tens ____ ones
What is left? ____ tens ____ ones Break a ten.
___ tens ___ ones c.
___ tens ___ ones
Break a ten.
___ tens ___ ones
___ tens ___ ones
Cross out 2 tens 5 ones.
d.
What is left? ____ tens ____ ones
___ tens ___ ones
Cross out 4 tens 4 ones.
What is left? ____ tens ____ ones
39
Math MammothAdd & Subtract 2-B (Blue Series)
3. First, break a ten. Then subtract ones and tens separately. Look at the example. a.
b.
4 tens – 3 tens
5 tens 5 ones
3
tens
15 ones
___ te ns ___ ones
7 tens 2 ones
5 ones
8
–
5 ones
___ tens ___ ones
ones
c.
3 tens
d.
6 tens 0 ones
–
___ te ns ___ ones 2 tens
6 tens 4 ones
7 ones
–
___ tens ___ ones e.
___ te ns ___ ones 3 tens
8 ones
___ tens ___ ones f.
___ te ns ___ ones
7 tens 6 ones –
4 tens
___ te ns ___ ones
5 tens 0 ones
7 ones
–
___ tens ___ ones g.
2 tens
2 ones
___ tens ___ ones h.
8 tens 1 one –
___ tens ___ ones 6 tens
6 tens 3 ones
5 ones
–
___ tens ___ ones
___ te ns ___ ones 2 tens
8 ones
___ tens ___ ones
4. Jessica had 37 colored pencils. Then she gave 12 of them to her brother, and six to her sister. a.
How many pencils does Jessica have now?
b.
How many more pencils does Jessica have than her brother?
c.
How many more pencils does Jessica have than her sister?
40
Math MammothAdd & Subtract 2-B (Blue Series)
Regrouping (Borrowing), Part 2 In columns:
5 tens, 3 ones
4 tens, 13 ones
Cross out 1 ten 6 ones. What is left? ____ tens ____ ones
4
13
5
3
– 1
6
3
7
When the subtraction is done in columns:
We take (borrow) one ten from the 5 tens. There will be now only 4 tens in the tens column, so to show this, we cross the “5” in the tens column and write 4 above it. This new ten is now grouped with the ones. There were 3 ones, but with the 10 new ones there will be 13. To show this, we also cross the “3” in the ones column and write 13 above it. Then we subtract the tens and ones separately.
4 tens
3 tens, 10 ones
3
10
4
0
– 2
8
1
2
Cross out 2 tens 8 ones. What is left? ___ tens ___ ones Here is another example: 40 – 28.
We take (borrow) one ten from the 4 tens. There will be now only 3 tens in the tens column, so to show this, we cross the “4” in the tens column and write 3 above it. This new ten is now grouped with the ones. There were 0 ones, but with the 10 cross the “0”
new ones there will be and write 10 above it. 10. To show this, we also
in the ones column
Then we subtract the tens and ones separately in columns.
41
Math MammothAdd & Subtract 2-B (Blue Series)
2. Subtract. Check by adding the result and what was subtracted. a.
b.
Check:
4 16
1
5 6 – 2 7
2 9 + 2 7
2 9
5 6
Check:
Check:
9 0 – 2 8
c.
4 2 – 1 5
+ 2 8
d.
9 0 – 3 5
e.
8 2 – 2 5
f.
6 5 – 3 9
g.
5 2 – 1 4
h.
6 5 – 2 6
i.
7 0 – 4 8
.
5 5 – 1 7
k.
3 1 – 1 8
l.
6 6 – 2 8
+ 1 5
Figure out the missing numbers in these subtractions! You might need to regroup.
3 – 1 7
8 –
5
1
0 7
– 3
6
4
43
2
– 1
4
6
8
6
2
5
3
–
Math MammothAdd & Subtract 2-B (Blue Series)
Regrouping (Borrowing), Part 3 You can subtract
How do we know when to break a ten into 10 ones, and when not to? From six cubes, we can cross out 0, 1, 2, 3, 4, 5, or 6 cubes. We cannot cross out 7, 8, 9, etc. because
6–0 6–1 6–2
there are not that many cubes to begin with.
You would go into debt 6 – 7 6 – 11 6 – 8 6 – 12 6 – 9 6 – 13
6–3 6–4 6–5 6–6
6 – 10
etc.
1. Cross out the subtractions that would “make you go into debt”. Do you notice any patterns? (You can also write how much you would go into debt; for example –4 is a negative 4.) 3–0 3–1 3–2 3–3 3–4 3–5 3–6 3–7
4–0 4–1 4–2 4–3 4–4 4–5 4–6 4–7
5–0 5–1 5–2 5–3 5–4 5–5 5–6 5–7
6–0 6–1 6–2 6–3 6–4 6–5 6–6 6–7
7–0 7–1 7–2 7–3 7–4 7–5 7–6 7–7
8–0 8–1 8–2 8–3 8–4 8–5 8–6 8–7
3–8 3–9
4–8 4–9
5–8 5–9
6–8 6–9
7–8 7–9
8–8 8–9
2. Look at the ones' digits. Do you need to regroup (borrow a ten to ones' column)? a. Do you need
to regroup?
6 1 – 2 6
Y/N
d. to Doregroup? you need
Y/N
b. Do you need
to regroup?
7 4 – 2 3
Y/N
– 35 24
c. Do you need
to regroup?
5 0 – 2 5
Y/N
e. to Doregroup? you need
Y/N
– 58 62
f. Do you need to regroup?
– 29 70
Y/N
44
Math MammothAdd & Subtract 2-B (Blue Series)
If you subtract in columns and you don't have enough ones, you have regroup one ten to the ones' column. 3. Do you need to regroup? Find the answers in the line of numbers below.
a. Do you need
to regroup?
6 0 – 1 6
b. Do you need
to regroup?
Y/N
d. Do you need
to regroup?
to regroup?
c. Do you need
to regroup?
Y/N
8 0 – 2 8
to regroup?
9 7 – 2 5
f. Do you need
to regroup?
Y/N
5 0 – 1 0
8 8 – 7 7
Y/N
h. Do you need
to regroup?
Y/N
4 3 – 1 7
Y/N
e. Do you need
Y/N
g. Do you need
5 7 – 3 2
3 7 – 2 7
i. Do you need
to regroup?
Y/N
6 0 – 4 1
Y/N
35 44 26 19 25 11 63 22 72 49 10 26 51 52 78 30 25 40
4. Subtract. Regroup if necessary. Check by adding! a.
5 4 – 3 7
b.
9 4 – 3 4
c.
8 2 – 2 5
d.
6 2 – 2 9
e.
9 9 – 5 7
f.
4 0 – 2 3
45
Math MammothAdd & Subtract 2-B (Blue Series)
Graphs and Problems 1. The graph shows how many newspapers Jack sold at his newspaper stand from Monday through Sunday. a. For each day, find about how
many newspapers Jack sold. Look how tall each column is, and round to the nearest ten.
Day
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
about
about
about
about
about
about
about
______
______
______
______
______
______
______
Newspapers
b.
About how many newspapers did Jack sell on Saturday and Sunday together? ______
c.
About how many more newspapers did Jack sell on Sunday than on Monday? ______
2. The table lists the eye colors of a group of 50 children.
9
4
10
16
11
blue
green
gray
brown
hazel
a. Draw the bars for the bar
graph. b. How many children have
either brown or hazel eyes?
c. How many children have
either eyes? blue, green, or gray
46
Math MammothAdd & Subtract 2-B (Blue Series)
3. a. How many Arctic animals does the zoo have? How many rain forest birds? b.
How many European and Arctic animals does the zoo have together?
c.
How many more African animals does the zoo have than Australian animals?
4. Break the number you are subtracting into tens and ones, and subtract in parts. a.
45 – 23 / \ 45 – 20 – 3 = ______
b.
76 – 15 / \ 76 – 10 – 5 = ______
c.
47 – 15
5. Solve the word problems. Add or subtract in columns if you need to. a.
Jim has 62 marbles, Peter has 28, and Ed has 33 marbles. Peter and Ed put their marbles together. Now do they have more than Jim?
b.
You were on page 48 in a book that has a total of 95 pages. Then you read ten more pages. How many pages have you read now? How many pages do you have left to read?
47
Math MammothAdd & Subtract 2-B (Blue Series)
Adding 2-Digit Numbers Mentally Strategy 1: Break the second addend in parts
Break the 27 into tens and ones. First add 45 and 20. Then add 7.
45 +
27 / \ 45 + 20 + 7 65 + 7 = 72
1. Add by breaking the second addend into tens and ones. a.
52 +
b.
26
38 +
52 + 20 + 6 ____ +
35
6
= _____
57
25 + ____ + ____
____ + ____ = ____
____ + ____ = ____
e.
19
48 +
62 + ____ + ____
f.
36
54 +
48 + ____ + ____
____ + ____ = ____
39
54 + ____ + ____
____ + ____ = ____
g.
17 +
25 +
38 + ____ + ____
d.
62 +
c.
____ + ____ = ____
h.
64
44 +
17 + ____ + ____
i.
38
29 +
44 + ____ + ____
____ + ____ = ____
23
29 + ____ + ____
____ + ____ = ____
____ + ____ = ____
2. Add mentally. a.
b.
c.
d.
34 + 35 = ______
15 + 29 = ______
44 + 46 = ______
19 + 18 = ______
47 + 12 = ______
8 + 12 = ______
43 + 18 = ______
13 + 17 = ______
33 + 56 = ______
47 + 36 = ______
56 + 25 = ______
34 + 18 = ______
27 + 26 = ______
50 + 33 = ______
12 + 19 = ______
45 + 35 = ______
49
Math MammothAdd & Subtract 2-B (Blue Series)
Adding three numbers
The basic strategy is to simply break the numbers into parts, and add them little by little. You can add all the tens and ones separately. Or, you can add with rounded numbers, and lastly correct the rounding errors. Just do whatever works! Add tens and ones separately:
Add with rounded numbers. Then correct the final answer.
33 + 28 + 16 (30 + 20 + 10) + (3 + 8 + 6) 60 + 17 = 77
27 + 39 + 38 27 is 23 less less than than 40. 30. 39 is 1 less than 40. 38 is
Add first those numbers that form a ten:
So, 27 + 39 + 38 is exactly 6 less than 30 + 40 + 40, or 6 less than 110, which is 104.
15 + 27 + 45 (5 + 5 + 10 + 40) + 27 60 + 27 = 87
5. Add mentally, and find the answer to the riddle. Use any strategy. L
22 + 43 + 38 = ______
V
52 + 14 + 18 = ______
L
28 + 18 + 36 = ______
C
37 + 18 + 15 = ______
E 47
+ 32 + 21 = ______
E
50 + 15 + 16 = ______
E
22 + 44 + 38 = ______
L 19
+ 17 + 25 = ______
B
64 + 12 + 17 = ______
R
24 + 13 + 25 = ______
W
55 + 14 + 28 = ______
O
16 + 60 + 20 = ______
W
54 + 16 + 22 = ______
E
E
50 + 31 + 19 = ______
27 + 11 + 21 = ______
Father: “How were your test scores?” Son: “Underwater.” Father: “What do you mean underwater?” 97 100 62 59
93 81 103 96 92
70
82 104 84 100 61
Son: They...
51
Math MammothAdd & Subtract 2-B (Blue Series)
Mental Subtraction Methods Method 1:
Subtract in two parts
53 – 8 =5 3 – 3 – 5 = 50 – 5 = 45
72 – 6 = 72 – 2 – 4 = 70 – 4 = 66
Subtract 8 in two parts: first 3, then 5.
Subtract 6 in two parts: first 2, then 4.
(In other words, first subtract to the previous whole ten, then the rest.)
1. Subtract the elevated number in parts (first subtract to the previous whole ten; then the rest). −
5
/ a.
−
( 51 − 1 ) − 4 = ______ −
6
d.
−
5 \
( 92 − ____ ) − ____ = ______ −
\
/
( 75 − ____ ) − ____ = ______ /
g.
−
/
( 33 − ____ ) − ____ = ______ −
\
( 62 − ____ ) − ____ = ______
\
/ e.
b.
4
/ c.
7
/
\
f.
−
\
/ d.
\
( 63 − ____ ) − ____ = ______
7
( 35 − ____ ) − ____ = ______
7
5 \
( 74 − ____ ) − ____ = ______
2. First subtract the balls that are not in the ten-groups. a.
51 − 7 = _______
b.
−
42 − 4 = _______ −
51 5 = _______ 51 − 3 = _______
42 5 = _______ 42 − 3 = _______
51 − 6 = _______
42 − 6 = _______ 52
Math MammothAdd & Subtract 2-B (Blue Series)
Method 2:
Use known subtraction facts
Since 14 – 6 = 8, we know that the answer to 74 – 6 will end in 8, but it will be in the sixties (sixty-something). So it is 68. Since 15 – 8 = 7, we know that the answer to 55 – 8 will end in 7, but it will be in the forties (forty-something). So it is 47. 3. Subtract. The first problem in each box is a “helping problem” for the others. b.
f.
14 – 9 = _______
c.
d.
17 – 8 = _______
12 – 9 = _______
24 – 9 = _______
27 – 8 = _______
52 – 9 = _______
44 – 9 = _______
37 – 8 = _______
32 – 9 = _______
15 – 9 = _______
g.
13 – 8 = _______
h.
16 – 8 = _______
65 – 9 = _______
33 – 8 = _______
86 – 8 = _______
45 – 9 = _______
93 – 8 = _______
36 – 8 = _______
4. Use either method from this lesson to subtract. a.
b.
c.
d.
34 – 5 = ______
65 – 9 = ______
51 – 8 = ______
62 – 7 = ______
73 – 7 = ______
36 – 8 = ______
93 – 6 = ______
83 – 8 = ______
5. a. Terry is on page 56 of her book. The book has a total of 92 pages. How many pages does she have left to read? b. Terry reads nine pages more. Now how many
pages does she have left to read?
53
Math MammothAdd & Subtract 2-B (Blue Series)
Method 3:
Add.
You can “add backwards”. This works well if the two numbers are close to each other. Instead of subtracting, think how much you need to add to the number being subtracted (the subtrahend) in order to get the number you're subtracting from (the minuend). Think: 84 + ____ = 92
(84 and how many more makes 92?)
Think: 25 + ___ = 75
+____
(25 and how many more makes 75?)
92 – 84 = _____
+___ 75 – 25 = _____
6. To find these differences, think of adding more.
+ 8 a. 92
+____
– 84 =______
b. 51
(Think: 84 + ____ = 92)
+____
– 49 =______
c. 76
(Think: 49 + ___ = 51)
– 69 =______
(Think: 69 + ___ = 76)
g.
32 – 28 = ______
j.
90 – 83 = ______
m.
100 – 95 = ______
h.
22 – 14 = ______
k.
64 – 56 = ______
n.
64 – 55 = ______
i.
l.
53 – 46 = ______
o.
72 – 65 = ______
44 – 37 = ______
7. Fill in, and find what was subtracted. –
–
78
77
–
72
–
70
–
65
–
60
–
57
–
53
46
The triangle and square represent “mystery numbers.” Find them. Guess and check! Then change your guess. a.
+
+ 10 = 34
= ______
b.
c.
+ – = _____,
= 22 =4 = _____
54
+ + = _____,
= 22 = 36 = _____
Math MammothAdd & Subtract 2-B (Blue Series)
More Mental Subtraction 1. Break the number you are subtracting into two parts (tens and ones). Subtract in parts.
45 – 32 / \ 45 – 30 – 2 = _______
b.
81 – 45 / \ 81 – 40 – 5 = _______
c.
d.
e.
f.
a.
52 – 34 = _______
55 – 22 = _______
74 – 21 = _______
88 – 53 = _______
g.
70 – 34 = _______
h.
50 – 27 = _______
i.
66 – 27 = _______
j.
73 – 33 = _______
k.
94 – 27 = _______
l.
60 – 36 = _______
2. What is the difference? Solve whichever is easier.
35 + _____ = 42 42 − 35 = _______
a.
71 + _____ = 78 78 − 71 = _______
b.
3 + _____ = 42 42 − 3 = ______
d.
c.
10 + _____ = 33 33 − 10 = _______
3. Solve. a.
78 + _____ = 85
b.
63 − 55 = ______
c.
5 + ______ = 43
d.
76 − 69 = ______
e.
95 − 65 = ______
f.
8 + ______ = 96
g.
20 + ______ = 75
h. 11
+ ______ = 86
4. Subtract in the easiest order! a.
b.
c.
40 − 4 − 20 − 2 = ________
74 − 20 − 4 − 5 = _______
72 − 8 − 60 − 2 = _______
50 − 8 − 10 − 20 = _______
91 − 7 − 10 − 3 = _______
66 − 20 − 2 − 5 = _______
60 − 2 − 6 − 4 = ________
82 − 5 − 7 − 11 = _______
86 − 8 − 5 − 20 = _______
55
Math MammothAdd & Subtract 2-B (Blue Series)
5. Solve the word problems. a.
Mariana had 64 marbles. She gave 8 to her brother. Then her brother gave her 4 back. How many marbles does Mariana have now?
b.
In a store, one chair is 64 cm wide, and another is 55 cm wide. How much wider is the first chair?
c.
Mary had 50 cards, and Jack had 5. Mary gave 20 cards to Jack. How many cards does Jack have now?
d. Mary had 40 marbles, and Jack had 5.
Mary gave half of her marbles to Jack. How many marbles does Jack have now?
e.
Ken has collected 34 stamps. Bill has collected 57 stamps. Brian has collected 94 stamps. If Ken and Bill combine their collections, will they together have more than Brian?
6. Connect each problem to its answer with a line.
39 + _____ = 44
56 + _____ = 64
36 + _____ = 44
7
70 + _____ = 74
18 + _____ = 24
9
58 + _____ = 64
30 + _____ = 34
6
29 + _____ = 34
15 + _____ = 24
5
58 + _____ = 64
79 + _____ = 84
8
35 + _____ = 44
85 + _____ = 94
4
69 + _____ = 74
67 + _____ = 74
27 + _____ = 34
56
Math MammothAdd & Subtract 2-B (Blue Series)
Review 1. Complete the next ten. a.
b.
c.
16 + _____ = 20
47 + ____ = ______
75 + ____ = ______
64 + _____ = 70
38 + ____ = ______
92 + ____ = ______
2. Add. a.
4 3 + 2 8
b.
3 3 + 3 9
c.
2 4 + 4 7
d.
2 3 + 3 7
e.
5 5 +1 7
f.
3 8 1 3 + 4 2
g.
3 9 1 0 + 4 6
h.
4 1 1 4 + 3 6
i.
3 8 2 9 + 2 3
j.
1 8 1 9 +5 5
3. Add. a.
b.
c.
d.
25 + 8 = ______
76 + 5 = ______
88 + 3 = ______
82 + 8 = ______
81 + 8 = ______
72 + 7 = ______
42 + 9 = ______
54 + 9 = ______
24 + 9 = ______
50 + 6 = ______
34 + 7 = ______
10 + 9 = ______
4. Find the missing addends. a.
25 + _____ = 35 87 + _____ = 93
b.
44 + _____ = 51
c.
67 + _____ = 75
17 + _____ = 26 79 + _____ = 85
61
d.
34 + _____ = 41 21 + _____ = 30
Math MammothAdd & Subtract 2-B (Blue Series)
5. For each problem, write one where you subtract from 11, 12, 13, 14, 15, 16, 17, or 18. a.
55 – 7 = ____ 15 – 7 = 8
d.
72 – 7 = ____ ____ – ___ = ____
74 – 8 = ____
b.
c.
____ – ___ = ____ 51 – 3 = ____
e.
93 – 5 = ____ ____ – ___ = ____
f.
____ – ___ = ____
33 – 4 = ____ ____ – ___ = ____
6. Solve the problems. a.
There are some people in the bus. At the next bus stop, 13 people come in. Now there are 52 people in the bus. How many were there srcinally?
b. Molly
has 23 stuffed toys that she likes to play with, and 16 stuffed toys that she does not care for. Her little sister Annie has 17 stuffed toys. Molly gives the 16 toys to her little sister. How many does Annie have now? Who has more stuffed toys now? How many more?
c. There
are 24 hours in a day-night period. An elephant typically eats for about 16 hours a day, and sleeps for about 6 hours a day. How many hours a day can an elephant spend on other activities?
d. Andy
has $47 in his wallet. He earns $15 by selling lemonade. Can he now buy a remote-controlled toy car for $65? If yes, how much money would have have left after buying it? If not, how much more money would he need?
62
Math MammothAdd & Subtract 2-B (Blue Series)
7. Subtract. – 8
77
– 9
______
– 6
88
– 10
______
– 9
______
– 5
______
– 10
______
– 4
______
– 7
______
– 3
38
______
– 8
______
– 5
______
43
8. Subtract. Check by adding. a.
d.
Check:
8 8 – 5 4
b.
+ 5 4
6 6 – 1 7
e.
Check:
6 3 – 4 8
c.
+ 4 8
7 1 – 2 2
f.
Check:
6 9 – 2 7
+ 2 7
8 4 – 4 9
9. Compare the problems, and find a way to do them. Place a letter in the box next to each problem according to the right answer. Read the words vertically. a.
b.
c.
______ – 28 = 45
______ + 12 = 45
______ + 12 + 13 = 45
______ – 33 = 29
______ + 23 = 99
______ + 23 + 19 = 96
______ – 37 = 55
______ + 66 = 100
______ + 67 + 4 = 88
______ – 41 = 50
______ + 24 = 50
______ + 24 + 26 = 80
ADE
E HKM
NOORT
W W
62 20 30 99 91 26 73 17 54 76 34 92 85 33
63
Math MammothAdd & Subtract 2-B (Blue Series)
Subtracting Whole Tens, p. 10 1. a. 20 b. 20 c. 30 d. 27 e. 16 f. 25. The ones digit does not change. 2. a. 76, 66, 56, 46, 36, 26, 16 b. 72, 62, 52, 42, 32, 22, 12 c. 67, 57, 47, 37, 27, 17, 7 3. a. 13, 3
b. 28, 18
c. 46, 26
d. 65, 55
e. 21, 11
f. 41, 31
4. a. 88 – 10 = 78 88 – 20 = 68 88 – 30 = 58 88 – 40 = 48
b. 100 – 60 = 40 90 – 50 = 40 80 – 40 = 40 70 – 30 = 40
88 88 –– 50 60 = = 38 28 88 – 70 = 18
c. 34 – 10 = 24 44 – 20 = 24 54 – 30 = 24 64 – 40 = 24
60 50 –– 20 10 = = 40 40 40 – 0 = 40
74 84 –– 50 60 = = 24 24 94 – 70 = 24
5. a. 30 + 20 + 30 = 80. So they weigh about 80 kg. b. $30 + $30 + $30 = $90. No, he cannot. c. $50 – $10 – $10 – $10 = $20. He has about $20 left. Puzzle corner: Answers vary. There are many solutions for both puzzles. 40 + 50 =9 0 –
5 0 – 10 =4 0
–
10 + 20 = 30 = 30
= 30
= 80
30 + 60 =9 0 –– 0 = 30
+
+
30 –
0
= 30
= 10 45 –
5
= 40
++ + 30= = 30
30
35 – = 10
= 80
5
= 30
Adding in Columns, p. 12 1. a.
20 + 30
b.
50 2. a.
32 + 14 46
10 + 50
c.
60 b.
54 + 5 59
32 d. + 20 52
c.
41 d. + 27 68
43 + 33
e.
76 65 + 13 78
e.
35 f. + 12
57 g. + 22
26 h. + 51
47
79
77
31 f. + 40
43 + 34 77
25 + 33
71
58
3. a. 77 b. 98 c. 58 d. 69 e. 86 f. 86 g. 95 h. 87 i. 76 j. 89 k. 78 l. 97 m. 97 n. 88 o. 89
65
Math MammothAdd & Subtract 2-B (Blue Series)
Doubling, p. 14 1. a. 5 + 5 = 10
b. 30 + 30 = 60
c. 50 + 50 = 100
2. a. 2 2 + 2 2
b. 3 + 3
4 4
c. 1 + 1
3 3
d. 4 1 + 4 1
4 4
6
8
2
6
8 2
3. Double 6 is 6 + 6 = 12. Double 7 is 7 + 7 = 14 Double 8 is 8 + 8 = 16. Double 9 is 9 + 9 = 18. Double 10 is 10 + 10 = 20. Double 11 is 11 + 11 = 22. Double 12 is 12 + 12 = 24.
Double 13 is 13 + 13 = Double 14 is 14 + 14 = Double 15 is 15 + 15 = Double 16 is 16 + 16 = Double 17 is 17 + 17 = Double 18 is 18 + 18 = Double 19 is 19 + 19 =
26. 28. 30 32. 34. 36. 38.
4. Each child will make 8 sandwiches. 5. You each get 16 pieces of candy. 6. A double batch of brownies makes 32 brownies. 7. Each teacher will get 14 worksheets. 8. Mary moved 8 spaces. Andrea moved 12 spaces. 9. Each woman will make 10 dolls.
One-Half, p. 16 1. a.
b.
2.a.
b.
c.
d.
e.
3. a. 5 + 5 = 10
b. 20 + 20 = 40
c. 12 + 12 = 24
1 of 10 is 5. 2
1 of 40 is 20. 2
1 of 24 is 12. 2
4. 1
6 + 6 = 12
11 + 11 = 22
7 + 7 = 14
12 + 12 = 24
2 1 2
of 16 is 8. of 28 is 14.
1
8 + 8 = 16 9 + 9 = 18
13 + 13 = 26 14 + 14 = 28
2
10 + 10 = 20
15 + 15 = 30
1
1 2 2
of 26 is 13. of 30 is 15. of 22 is 11.
66
Math MammothAdd & Subtract 2-B (Blue Series)
5. b.
a. 1 of 26 is 13. 2
c. 1 of 48 is 24. 2
1 of 30 is 15. 2
6. a. Each one got $30.
d. 1 of 32 is 16. 2
10 + 10 = 20
b. Half of 60 minutes is 30 minutes.
20 + 20 = 40
c. 50 students were not sick.
30 + 30 = 60 40 + 40 = 80
d. Missie has $10 now.
50 + 50 = 100
e. Mom had 20 apples srcinally.
Regrouping with Tens, p. 18 1. a.
33 + 9 42
2. a.
13 + 29 42
2. g.
25 + 55 80
25 b. + 8 33 24 b. + 38 62
38 c. + 9 47
27 d. + 7 34
35 c. + 19 54
36 e. + 18 54
24 d. + 47 71
25 f. + 27 52
44 e. + 17 61
26 f. + 36 62
39 h. + 35 74
3. a. 57 b. 72 c. 91 d. 98 e. 53 f. 93 g. 57 h. 90 i. 87 j. 95 k. 58 l. 75 m. 94 n. 94 o. 40 4. a. 79 b. 87 c. 71
d. 93 e. 73
5. a. 0, 4, 8, 12, 16, 20, 24, 28, 32 b. 100, 96, 92, 88, 84, 80, 76, 72, 68
Going Over to the Next Ten, p. 21 1. a. 22 b. 23 c. 24 d. 31 e. 31 f. 46 g. 42 h. 52 i. 63 2. a. 28 + 8 / \ 28 + 2 + 6 30 + 6 = 36 d. 39 + 3 / \ 39 + 1 + 2 40 + 2 = 42
b. 47 + 5 / \ 47 + 3 + 2
c. 79 + 9 / \ 79 + 1 + 8
50 + 2 = 52 e. 27 + 5 / \ 27 + 3 + 2
80 + 8 = 88 f. 38 + 7 / \ 38 + 2 + 5
30 + 2 = 32
40 + 5 = 45
67
Math MammothAdd & Subtract 2-B (Blue Series)
3. a. 8 +1 = 9 8 + 2 = 10 8 + 3 = 11 8 + 4 = 12 8 + 5 = 13 8 + 6 = 14
28 28 28 28 28 28
b. + 1 = 29 + 2 = 30 + 3 = 31 + 4 = 32 + 5 = 33 + 6 = 34
c. 78 + 1 = 79 78 + 2 = 80 78 + 3 = 81 78 + 4 = 82 78 + 5 = 83 78 + 6 = 84
What do you notice? The two patterns are similar. The ones digits are the same. 4. a. 2, 3 b. 7, 8 c. 3, 4 d. 3, 5 e. 2, 4 f. 4, 6 5. a. $22 + $8 = $30 or $30 – $22 = $8. Benjamin needs $8 more. b. $20 + $5 + $5 = $30. Natasha has $3. c. 28 – 8 = 20 fruit trees left to plant. d. 37 – 32 = 5 came later. e. Half of 40 is 20. 40 – 20 – 7 = 13 grapes are left. 6. 9 9 9 9 9 9
a. + 1 = + 2 = + 3 = + 4 = +5 = + 6 =
10 11 12 13 14 15
39 39 39 39 39 39
b. + 1 = + 2 = + 3 = + 4 = + 5= + 6=
40 41 42 43 44 45
59 59 59 59 59 59
c. + 1 = + 2 = + 3 = + 4 = + 5 = + 6=
60 61 62 63 64 65
Add with Two-Digit Numbers Ending in 9, p. 24 1.
a. 19 + 5 = 24
b. 29 + 7 = 36
c. 49 + 5 = 54
d. 29 + 8 = 37
e. 39 + 6 = 45
f. 49 + 9 = 58
2. a. 19 + 7 = 26 9 + 7 = 16
b. 49 + 3 = 52 9 + 3 = 12
c. 39 + 4 = 43 9 + 4 = 13
3. a. 12, 22 b. 15, 45 c. 13, 53 d. 16, 46, 36 e. 18, 78, 88 f. 14, 24, 64 The answers to the problems in each box end in the same digit. 4. a. 5, 6, 4, 9, 3, 8, 7 b. 13, 17, 11, 14, 15, 18, 16 c. 7, 9, 4, 6, 5, 10, 8 d. 15, 16, 13, 14, 11, 17, 12
68
Math MammothAdd & Subtract 2-B (Blue Series)
5.
a.
+
8
40 b.
+
+ 32
5
48 5
16 c.
+
8
53 +
+
7
27 +
5
+
+
49
7
+
8
66 8
34
8
41
+
61
6
21 9
+
+
42 +
56
6 62
+
+
5
74
79
9
+ 10
51
61
5
+
67
+
8
+
87
92
+ 11
+ 12
72
4
+
71
5
84 3
+
74
2
76
Add in Columns Practice, p. 26 1. a. 80
b. 91
c. 91
d. 70
e. 52
f. 78
g. 116
h. 94
i. 85
j. 49
2. a. 72
b. 64
c. 72
d. 70
e. 56
f. 62
g. 56
h. 74
i. 26
j. 66
3. a. 107
b. 142
c. 104
d. 146
4. a. 128
b. 155
c. 120
d. 147
e. 123
f. 109 g. 126
h. 147
i. 149
j. 137
Add with Two-Digit Numbers Ending in 8 or 7, p. 28 1.
a. 18+ 6 = 24
b. 28 + 7 = 35
c. 48 + 8 = 56
d. 38 + 4 = 42
e. 38 + 6 = 44
f. 48 + 5 = 53
b. 38 + 6 = 44 8 + 6 = 14
c. 58 + 5 = 63 8 + 5 = 13
2. a. 18 + 7 = 25 8 + 7 = 15
3. a. 11, 21 b. 14, 44 c. 12, 82 d. 15, 95 e. 10, 40, 30 f. 17, 77, 87 g. 13, 23, 63 h. 16, 36, 96 The answers to the problems in each box end in the same digit. 4. a. 31 b. 52 c. 44 5. a. 75 + 7 = 82 5 + 7 = 12
b. 47 + 7 = 54 7 + 7 = 14
c. 57 + 6 = 63 7 + 6 = 13
6. a. 13, 33 b. 12, 82 c. 14, 94 d. 16, 76, 96 e. 10, 40, 80 f. 17, 27, 57 The answers to the problems in each box end in the same digit. 7. a. She needs nine eggs. b. They have eaten 38 pounds of potatoes.
69
Math MammothAdd & Subtract 2-B (Blue Series)
Addition Practice, p. 30 1. a. 20 + 34 = 54 (20 + 30 + 4)
b. 70 + 18 = 88 (70 + 10 + 8 )
2. a. 27, 36, 52 b. 36, 64, 87
c. 50 + 27 = 77 (50 + 20 + 7 )
c. 64, 83, 75
3. At each step, we add two more than we added in the previous step.
+ 2 1
+ 4 3
+ 6
+ 8
+ 10
1 3
21
31
7
+ 12
+ 14
4 3
57
+ 16
73
4. a. 92 b. 91 c. 63 d. 90 e. 84 5. a. <
b. =
c. =
d. > e. > f. =
6. The person did not carry to the tens, but instead wrote the sum of the ones down in its completeness, and then wrote the sum of the tens next to it. 7. a. 15, 25, 45 b. 13, 23, 53 c. 12, 52, 82 d. 16, 66, 46 8. a. 42, 45, 48, 51, 54, 57, 60, 63 b. 1, 4, 7, 10, 13, 16, 19, 22, 25 9. a. 33, 47, 54 b. 53, 33, 44 c. 30, 54, 99 d. 84, 74, 71 Puzzle corner. a.
b.
2 7 + 1 4
+
c.
6 8 3
4 1
d.
2 6 + 2 5
7 1
1 3 + 7 8
5 1
e.
3 5 + 2 6
9 1
6 1
Many Addends, p. 32 1. a. 17, 27 b. 20, 17 c. 23, 24 2. a. 93 b. 92 c. 98 d. 82 e. 97 f. 96 g. 89 h. 80 i. 117 j. 117 k. 129 l. 145 3. a. No, because 23 plus 9 is more than 30. It can only hold 7 more people. b. 47 people total. c. 2 buses for the 57 people and 3 buses for 88 people. d. 30 – 6 = 24. e. 30 – 13 – 7 = 10. f. 16 people g. 20 – 8 + 5 = 17, so there are 17 people now. h. 30 – 7 – 12 = 11, so there were 11 people on the bus srcinally. 4. a. 80 b. 71 c. 54 d. 47 5.a. 19 + 5 + 7 = 31 OO
O
d. 57 + 21 = 78 O
O
E
g. 17 + 27 + 5 = 49 OO
O
b. 25 + 7 + 3 = 35
O
O
O e. 5 O
+
O 1
O
c. 7 + 11 + 23 = 41
O
O
+ 11 +
OOO
9
=2 6
E
h. 25 + 13 + 3 + 1 = 42 OOO
O
E
OO
O
f. 25 +
9
O
O
= 34 E
i. 57 + 21 = 78 O
O
E
Underline the correct choice in the sentences below. Can you think why it is that way?
70
Math MammothAdd & Subtract 2-B (Blue Series)
If I add two odd numbers, the answer is (even/odd). If I add three odd numbers, the answer is (even/odd). If I add four odd numbers, the answer is (even/odd). Each odd number is actually some even number plus one. In other words, each odd number of items can be organized into pairs so that one item is left over. When we have two odd numbers, we can put those two items together to form another pair. That is why the sum of two odd numbers is even. If we have three odd numbers, from those we can form one pair but one item will be left over. So, the sum is odd. Similarly with adding two odd numbers, adding four odd numbers gives us an even sum. Puzzle Corner. Can you explain how Mary is adding and why it works? First she adds all of the tens and writes that under the line. Then she adds the ones and writes those under the tens' sum. Lastly, she adds the two sums. 13 27 16 46 15 28 25 25 + 48 + 31 + 47 + 12
36 27 + 34
60 + 16
70 + 16
70 + 18
70 + 13
80 + 17
76
86
88
83
97
Subtracting in Columns, p. 35 1. a. 55 –32 = 33. 2. a. 47
b. 42
b. 73 c. 34
– 61 = 12. d. 67
e. 44
f. 60
g. 3
h. 34
i. 44
j. 22
3. a. 20 b. 23 c. 63 d. 15 e. 43 4. a. 92, 82, 42 b. 39, 79, 59 c. 93, 23, 3 5. a. Linda b. Luis c. 33 more d. 3 more
e. 87 seashells f. 45
g. no
6. a. 0, 6, 12, 18, 24, 30, 36, 42, 48 b. 0, 7, 14, 21, 28, 35, 42, 49, 56 c. 0, 8, 16, 24, 32, 40, 48, 56, 64 d. 0, 9, 18, 27, 36, 45, 54, 63, 72 e. 100, 95, 90, 85, 80, 75, 70, 65, 60 f. 77, 72, 67, 62, 57, 52, 47, 42, 37, 32 7. a. 21 flew away b. She needed 13 sheets of paper. c. The teacher needed to buy 2 packages. d. 8 had flown away. Puzzle corner: –
5
7
3
4
–
5
4
1
2
2 3
–
6
8
1
8 5 0
+
3
8
3
5
4 2
+
3
3
1
7 5 0
+
5 1
3
4
2
8 6 2
+
2 6
6 8
7 3
+
4 4
–
9
9
8
4 1 5
71
7 6 9 3
+
3
4
4
8 8 2
Math MammothAdd & Subtract 2-B (Blue Series)
Regrouping (Borrowing), Part 1, p. 38 1. a. 3 tens 0 ones → 2 tens 10 ones b. 3 tens 6 ones → 2 tens 16 ones c. 5 tens 1 one → 4 tens 11 ones d. 5 tens 5 ones → 4 tens 15 ones e. 4 tens → 3 tens 10 ones f. 3 tens 7 ones → 2 tens 17 ones 2. a. What is left? 2 tens 8 ones b. 5 tens 4 ones → 4 tens 14 ones. What is left? 2 tens 7 ones. c. 4 tens 3 ones → 3 tens 13 ones. What is left? 1 ten 8 ones. d. 6 tens 1 one → 5 tens 11 ones. What is left? 1 ten 7 ones. 3. a.
b.
5 tens 5 ones –
4 tens 3 tens 1 tens
15ones 5 ones
7 tens 2 ones –
10 ones
c.
6 t ens 3 tens 3 tens
12 ones 5 ones 7 ones
d.
6 tens 0 ones –
5 tens 2 tens 3 tens
10 ones 7 ones
6 tens 4 ones –
3 ones
e.
5 tens 3 tens 2 tens
14 ones 8 ones 6 ones
f.
7 tens 6 ones –
6 tens 4 tens 2 tens
16 ones 7 ones
5 tens 0 ones –
9 ones
g.
4 tens 2 tens 2 tens
10 ones 2 ones 8 ones
h. 7 tens
8 tens 1 one –
6 tens 1 tens
11 ones
5 tens
6 tens 3 ones
5 ones
–
6 ones
2 tens 3 tens
13 ones 8 ones 5 ones
4. a. 19 pencils b. 7 more pencils c. 13 more pencils
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Math MammothAdd & Subtract 2-B (Blue Series)
Regrouping (Borrowing), Part 3, p. 44 1.
2. a. YES; 35 b. NO; 51 c. YES; 25
d. NO; 22 e. YES; 26 f. YES; 63
3. a. 44 h.b.NO; NO;10 25 i.c.YES; YES;1926 d. YES; 52 g. YES; NO; 40
e. NO; 72 f. NO; 11
4. a. 17 b. 60 c. 57 d. 33 e. 42 f. 17
Graphs and Problems, p. 46 1. a. Mon Tues Wed Thurs Fri
Day Newspapers
Sat
Sun
about about about about about about about 30 40 40 40 50 30 70
b. about 100
c. about 40 more.
2.
a.
b. 27 children c. 23 children
3. a. 35 Arctic animals, 90 rain forest birds b. 85 4. a. 22
b. 61
c. 35 more
c. 32
5. a. 28 + 33 = 61. No they don't have more than Jim. b. You have read now 48 + 10 = 58 pages. You have 95 – 58 = 37 pages left. 6. a. 14 books b. Annie, Lisa c. 8 more d. 9 more e. Books read Jan Feb Mar Apr Total Annie
13
21
18
14
66
Freddie
8
5
11
9
33
Lisa
8
13
16
18
55
Jonathan
10
8
14
15
47
f. 33
74
Math MammothAdd & Subtract 2-B (Blue Series)
Adding 2-Digit Numbers Mentally, p. 49 1. a. 78 b. 73 c. 82 d. 81 e. 84 f. 93 g. 81 h. 82 i. 52 2. a. 69, 59, 89, 53
b. 44, 20, 83, 83 c. 90, 61, 81, 31
d. 37, 30, 52, 80
3. a. 58 b. 90 c. 91 d. 79 e. 72 f. 110 g. 63 h. 95 4. WHITTLE BY WHITTLE 5. ...WERE BELOW C LEVEL.
Mental Subtraction Methods, p. 52 1. a. ( 51 − 1 ) − 4 = 46 −
b. ( 62
−
−
2 ) − 5 = 55
−
c. ( 33
−
−
3 ) − 1 = 29
−
e. ( 75 5 ) 1 = 69 f. ( 63 3 ) 4 = 56 2. a. 44, 46, 48, 45 b. 38, 37, 39, 36
g. ( 35
d. ( 92
−
5 ) 2 = 28
−
2 ) − 3 = 87
−
h. ( 74
−
4 )
2 = 68
3. a. 5, 15, 35 b. 9, 19, 29 c. 3, 43, 23 d. 6, 56, 36 e. 5, 25, 85 f. 8, 78, 28 4. a. 29; 66
b. 56; 28 c. 43; 87
d. 55; 75
5. a. 36 pages b. 27 pages 6. + 8
+2
+7
a. 92 – 84 = 8
b. 51 – 49 = 2
c. 76 – 69 = 7
(Think: 84 + 8 = 92)
(Think: 49 + 2 = 51)
(Think: 69 + 7 = 76)
d. 32 – 28 = 4 g. 22 – 14 = 8 j. 53 – 46 = 7
e. 90 – 83 = 7 h. 64 – 56 = 8 k. 72 – 65 = 7
f. 100 – 95 = 5 i. 64 – 55 = 9 l. 44 – 37 =7
7. –1, –5, –2, –5, –5, –3, –4, –7 Puzzle Corner: a.
= 12
b.
= 9,
= 13
c.
= 4,
= 18
More Mental Subtraction, p. 55 1. a. 13 b. 36 c. 53 d. 18 e. 33 f. 35 g. 36 h. 23 i. 39 j. 40 k. 67 l. 24 2. a. 7 b. 7 c. 39 d. 23 3. a. 7
b. 8
c. 38 d. 7 e. 30 f. 88
g. 55
h. 75
4. a. 14, 12, 48 b. 45, 71, 59 c. 2, 39, 53 5. a. 64 – 8 + 4 = 60. She has 60 marbles. b. 64 cm – 55 cm = 9 cm. The chair is 9 cm wider. c. 50 – 30 = 20. 5 + 20 = 25. Jack has 25 cards now. d. 1/2 of 40 is 20. 5 + 20 = 25. Jack has 25 marbles now. e. Ken's stamps plus Bill's stamps equal 34 + 57 = 91 stamps. 91 is less than 94. No, they will not have more than Brian.
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Math MammothAdd & Subtract 2-B (Blue Series)
6.
7. a. 54 – 45 = 9
b. 99 – 11 = 88
c. 100 – 50 = 50
63 – 36 = 27
88 – 22 = 66
99 – 51 = 48
72 – 27 = 45
77 – 33 = 44
98 – 52 = 46
81 – 18 = 63
66 – 44 = 22
97 – 53 = 44
90 – 09 = 81
55 – 55 = 0
96 – 54 = 42
8. Y O U ' R E A S U P E R S U B T R A C T E R!
Puzzle corner:
7 2
7 4
– 2 3
– 5 7
7 5 – 5 1
5 4 – 1 8
8 2 – 4 8
4 9
1 7
2 4
3 6
3 4
Euclid's Game, p. 58 1. No. 2. All the numbers that get marked are also even. 3. All the numbers that get marked will also be multiples of 5. 4. a. No. You cannot mark numbers that are greater than 90. b. Yes. c. No. You will only get to mark multiples of 10. d. Yes.
76
Math MammothAdd & Subtract 2-B (Blue Series)
Review, p. 61 1. a. b. c. 16 + 4 = 20 47 + 3 = 50 75 + 5 = 80 64 + 6 = 70 38 + 2 = 40 92 + 8 = 100 2. a. 71
b. 72
c. 71 d. 60 e. 72 f. 93
3. a. 33, 89, 33 b. 81, 79, 56 4. a. 10, 6 b. 7, 8
c. 9, 6
g. 95
h. 91
i. 90 j. 92
c. 91, 51, 41 d. 90, 63, 19
d. 7, 9
5. a. 55 – 7 = 48 b. 74 – 8 = 66 c. 93 – 5 = 88 15 – 7 = 8 14 – 8 = 6 13 – 5 = 8 d. 72 – 7 = 65 12 – 7 = 5
e. 51 – 3 = 48 f. 33 – 4 = 29 11 – 3 = 8 13 – 4 = 9
6. a. There were 39 people srcinally. b. Annie has now 33 toys. Annie has more toys; 10 more toys than Molly. c. about 2 hours d. He cannot buy the car. He needs $3 more. 7. 77 88
→
→
69 → 60 82
→
73
→
50
→
45
→
41
→
38
→
63
→
56
→
48
→
43
8. a. 34 b. 15 c. 42 d. 49 e. 49
f. 35
9. MATH WORK DONE. In set a., add the numbers. For example, to solve ___ – 28 = 45, add 28 and 45. In set b. and c., subtract. For example, to solve ___ + 12 = 45 , subtract 45 – 12. To solve ___ + 12 + 13 = 45, subtract 45 – 12 – 13.
77
Math MammothAdd & Subtract 2-B (Blue Series)
More from Math Mammoth Math Mammoth has a variety of resources to fit your needs. All are available as economical downloads, and most are also available as printed copies.
Math Mammoth Light Blue Series This is a complete curriculum for elementary grades. It includes two student worktexts (A and B), which contain all the instruction and exercises all in the same book, answer keys, tests, cumulative reviews, and a worksheet maker. www.MathMammoth.com/complete-curriculum.php Math Mammoth Blue Series Blue Series books are worktexts that each concentrate on a few interconnected topics, such as addition, clock,
measuring, money, division, multiplication, fractions, decimals, ratios & proportions, geometry, and more. They are not tied to grade levels, and are great for review, reinforcement, filling in gaps, or initial teaching. www.MathMammoth.com/blue-series.php
Math Mammoth Golden Series Best suited for teachers and tutors or parents who can explain math, Golden Series books are worksheet collections for grades 3-8. They work best as review or supplemental material. www.MathMammoth.com/worksheets/ Math Mammoth Green Series Best suited for teachers and tutors or parents who can explain math, Green Series books are worksheet collections by topics. They work best as review or supplemental material. www.MathMammoth.com/worksheets/green.php Make It Real Learning These activity workbooks concentrate on answering the question, "Where is math used in real life?" The exercises or activities in these books are taken from real life, and use real data. The series includes various workbooks for grades 3-12. www.MathMammoth.com/worksheets/mirl/
Learn more about Math Mammoth:
Advice for parents: www.MathMammoth.com/parents.php Advice for teachers: www.MathMammoth.com/teachers.php Frequently Asked Questions: www.MathMammoth.com/faq.php Math teaching videos: www.YouTube.com/MathMammoth Subscribe to receive free sample pages and worksheets: www.MathMammoth.com/worksheets/free.php About the author, Maria Miller: www.MathMammoth.com/about.php
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