MathMammoth_Grade4A

(1)

(2)

EDITION 1.25

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/

(3)

Foreword

Math Mammoth Grade 4-A and Grade 4-B worktexts comprise a complete math curriculum for the fourth grade mathematics studies.

In the fourth grade, students focus on multidigit multiplication and division, learning to use bigger numbers, solving multi-step word problems that involve several operations, and get started in studying fractions and decimals. This is of course accompanied by studies in geometry and measuring.

The year starts out with review of addition and subtraction, graphs, and money. We illustrate word problems with bar diagrams and study finding missing addends, which teaches algebraic thinking. Children also learn addition and subtraction terminology, the order of operations, and statistical graphs. Next come large numbers -- up to millions, and the place value concept. At first the student reviews thousands and some mental math with them. Next are presented numbers till one million, calculations with them, place value concept and comparing. In the end of the chapter we find more about millions and an introduction to multiples of 10, 100, and 1000.

The third chapter is all about multiplication. After briefly reviewing the concept and the times tables, the focus is on learning multidigit multiplication (multiplication algorithm). The children also learn why it works when they work on multiplying in parts. We also study the order of operations again, touch on proportional reasoning, and do more money and change related word problems.

The last chapter in part A is about time, temperature, length, weight, and volume. Students will learn to solve more complex problems using various measuring units and to convert between measuring units. In part B, we first study division. The focus is on learning long division and using division in word problems. The geometry chapter introduces students to measuring angles, and we do lots of drawing of different shapes and circles. Area and perimeter are other important topics in geometry.

Fractions and decimals are presented last in the school year. These two chapters practice only some of the basic operations with fractions and decimals. The focus is still on the conceptual understanding, building a good foundation towards 5th grade math, where fractions and decimals will be in focus.

When you use these books as your only or main mathematics curriculum, they can be like a “framework”, but you do have some liberty in organizing the study schedule. Chapters 1, 2, and 3 should be studied in this order, but you can be flexible with chapters 4 (Time and Measuring) and 6 (Geometry) and schedule them somewhat earlier or later if you so wish. Chapter 3 (Multiplication) needs to be studied before long division in Chapter 5. Many topics from chapters 7 and 8 (Fractions and Decimals) can also be studied earlier in the school year; however finding parts with division should naturally be studied only after mastering division.

This product also includes an HTML page that you can use to make extra practice worksheets for computation.

I wish you success in your math teaching! Maria Miller, the author

(7)

Concerning Challenging Word Problems

I would heartily recommend supplementing this program with regular practice of challenging word problems and puzzles. You could do that once a week to once every two weeks. The goal of challenging story problems and puzzles is to simply develop children's logical and abstract thinking and mental discipline. Fourth grade is a good place to start such a practice because students are able to read the problems on their own and have developed mathematical knowledge in many different areas. Of course I am not discouraging people from doing such in earlier grades, either.

I have made lots of word problems for the Math Mammoth curriculum. Those are for the most part multi-step word problems. I have included several lessons that utilize the bar model for solving problems and tried to vary the problems.

Even so, the problems I've created are usually tied to a specific concept or concepts. I feel children can also benefit from problem solving practice where the problems require “out of the box” thinking, or are puzzle-type in nature, or are just different from the ones I have made. Additionally, I feel others are more capable of making very different, very challenging problems.

So I'd like for you to use one or several of the resources below for some different problems and puzzles. Choose something that fits your budget (most of these are free) and that you will like using.

Math Kangaroo Problem Database

Easily made worksheets of challenging math problems based on actual past Math Kangaroo competition problems.

http://www.kangurusa.com/clark/pdb/

Primary Grade Challenge Math by Edward Zaccaro

The book is organized into chapters, with each chapter presenting a type of problem and the ways to think about that problem. And then there is a series of related story problems to solve, divided into 4 levels. $25, ISBN 978-0967991535

You can find this at Amazon.com or various other bookstores.

http://www.amazon.com/Primary-Grade-Challenge-Edward-Zaccaro/dp/0967991536/

Problem Solving Decks from North Carolina public schools

Includes a deck of problem cards for grades 1-8, student sheets, and solutions. Many of these problems are best solved with calculators. All of these problems lend themselves to students telling and writing about their thinking.

http://community.learnnc.org/dpi/math/archives/2005/06/problem_solving.php

Math Stars Problem Solving Newsletter (grades 1-8)

These newsletters are a fantastic, printable resource for problems to solve and their solutions.

(8)

Mathematics Enrichment - nrich.maths.org

Open-ended, investigative math challenges for all levels from the UK. Find the past issues box down in the left sidebar. Use Stage 2, 1-star or 2-star problems for 4th grade.

http://nrich.maths.org/public/

http://nrich.maths.org/public/themes.php lets you find problems organized by mathematical themes. Figure This! Math Challenges for Families

Word problems related to real life. They don't always have all the information but you have to estimate and think. For each problem, there is a hint, other related problems, and interesting trivia. Website supported by National Council of Teachers of Mathematics.

http://www.figurethis.org/

MathStories.com

Over 12,000 interactive and non-interactive NCTM compliant math word problems, available in both English and Spanish. Helps elementary and middle school children boost their math problem solving and critical-thinking skills. A membership site.

http://www.mathstories.com/

“Problem of the Week” (POWs)

Problem of the week contests are excellent for finding challenging problems and for motivation. There exist several:

z Math Forum: Problem of the Week

Five weekly problem projects for various levels of math. Mentoring available.

http://mathforum.org/pow/

z Math Contest at Columbus State University Elementary, middle, algebra, and “general” levels.

http://www.colstate.edu/mathcontest/ z Aunty Math

Math challenges in a form of short stories for K-5 learners posted bi-weekly. Parent/Teacher Tips for the current challenge explains what kind of reasoning the problem requires and how to possibly help children solve it.

http://www.auntymath.com/

z Grace Church School's ABACUS International Math Challenge This is open to any child in three different age groups.

http://www.gcschool.org/pages/program/Abacus.html z MathCounts Problem of the Week Archive

Browse the archives to find problems to solve. You can find the link to the current problem on the home page.

http://mathcounts.org/Page.aspx?pid=355 z Math League's Homeschool Contests

Challenge your children with the same interesting math contests used in schools. Contests for grades 4, 5, 6, 7, 8, Algebra Course 1, and High School are available in a non-competitive format for the homeschoolers. The goal is to encourage student interest and confidence in mathematics through solving worthwhile problems and build important critical thinking skills. By subscription only.

(9)

Chapter 1: Addition, Subtraction,

Graphs and Money

Introduction

The first chapter of Math Mammoth Grade 4-A Complete Worktext covers addition and subtraction topics, word problems, graphs, and money problems.

At first, we review the “technical aspects” of adding and subtracting: mental math techniques plus adding and subtracting in columns. If these are fairly easy for your student(s), you can choose to skip some problems.

Going beyond those, the chapter includes lessons in addition and subtraction terminology. These lessons are already preparing your child for algebraic thinking.

In the next lessons, the student reviews the addition/subtraction connection, and solves word problems with the help of bar models. Next, we solve simple missing addend equations using subtraction, such as x + 20 = 60. We use bar models to illustrate these and connect them with fact families.

The lesson on the order of operations contains some review but it goes beyond that. In many of the problems, the student builds the mathematical expression (calculation) needed for a certain real-life situation.

Going towards applications of math, the chapter contains lessons on bar graphs, line graphs, rounding, estimating, and money problems.

The Lessons in Chapter 1

page span

Addition Review ... 12 3 pages Adding in Columns ... 15 1 pages Subtraction Review ... 16 3 pages Subtract in Columns ... 19 3 pages Mental Math Workout and

Pascal's Triangle ... 22 3 pages Subtraction Terms ... 25 2 pages Word Problems and Bar Models ... 27 3 pages Missing Addend Solved With Subtraction ... 30 4 pages Order of Operations ... 33 2 pages Bar Graphs ... 35 3 pages Line Graphs ... 38 3 pages Rounding ... 41 4 pages Estimating ... 45 2 pages Reviewing Money ... 47 3 pages Review ... 50 1 page

(10)

Helpful Resources on the Internet

Calculator Chaos

Most of the keys have fallen off the calculator but you have to make certain numbers using the keys that are left.

http://www.mathplayground.com/calculator_chaos.html

ArithmeTiles

Use the four operations and numbers on neighboring tiles to make target numbers.

http://www.primarygames.com/math/arithmetiles/index.htm

Choose Math Operation

Choose the mathematical operation(s) so that the number sentence is true. Practice the role of zero and one in basic operations or operations with negative numbers. Helps develop number sense and logical thinking.

http://www.homeschoolmath.net/operation-game.php

MathCar Racing

Keep ahead of the computer car by thinking logically, and practice any of the four operations at the same time.

http://www.funbrain.com/osa/index.html

Fill and Pour

Fill and pour liquid with two containers until you get the target amount. A logical thinking puzzle.

http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html

Estimate Addition Quiz

Scroll down the page to find this quiz plus some others. Fast loading.

http://www.quiz-tree.com/Math_Practice_main.html

Mental Addition and Subtraction

A factsheet, quiz, game, and worksheet about basic mental addition and subtraction.

http://www.bbc.co.uk/skillswise/numbers/wholenumbers/addsubtract/mental/

Shop 'Til You Drop

Get as many items as you can and be left with the least amount of change, and practices your addition skills. The prices are in English pounds and pennies.

http://www.channel4.com/learning/microsites/P/puzzlemaths/shop.shtml

Change Maker

Determine how many of each denomination you need to make the exact change. Good and clear pictures! Playable in US, Canadian, Mexican, UK, or Australian money.

http://www.funbrain.com/cashreg/index.html

Cash Out

Give correct change by clicking on the bills and coins.

(11)

Piggy bank

When coins fall from the top of the screen, choose those that add up to the given amount, and the piggy bank fills.

http://fen.com/studentactivities/Piggybank/piggybank.html

Bar Chart Virtual Manipulative

Build your bar chart online using this interactive tool.

http://nlvm.usu.edu/en/nav/frames_asid_190_g_1_t_1.html?from=category_g_1_t_1.html

An Interactive Bar Grapher

Graph data sets in bar graphs. The color, thickness and scale of the graph are adjustable. You can put in your own data, or you can use or alter pre-made data sets.

(12)

Addition Review

1. Add mentally. You can add in parts (tens and ones separately).

2. Write the numbers as a sum of whole thousands, whole hundreds, whole tens, and ones.

3. Solve the problems.

a. Two of the addends are 56 and 90. The sum is 190. What is the third addend?

b. Four of the addends equal 70 and five other addends equal 80. What is the sum?

Remember addition?

You can write any number

as a SUM of the different units such as whole thousands, whole hundreds, whole tens, and ones.

5,248 = 5,000 + 200 + 40 + 8

thousands hundreds tens ones

You can add in parts:

56 + 124

= 100 + 50 + 20 + 6 + 4

= 100 + 70 + 10 = 180

Add in any order:

7 + 90 + 91 + 3

= 7 + 3 + 90 + 91

= 10 + 90 + 91 = 191

Trick: add first a bigger number, then subtract to correct the error:

76 + 89

= 76 + 90 − 1

= 166 − 1 = 165

a.

70 + 80 = ___

77 + 80 = ___

77 + 82 = ___

b.

140 + 50 = ___

141 + 50 = ___

144 + 55 = ___

c.

50 + 60 = ___

54 + 65 = ___

58 + 62 = ___

d.

80 + 90 = ___

82 + 93 = ___

88 + 91 = ___

a.

487 =

c.

8,045 =

b.

2,103 =

d.

650 =

(13)

4. Add and compare the results. The addition problems are “related”!

5. Write here four different addition problems that are “related” to the problem 5 + 8 = 13. See examples above!

6. Add in parts.

7. Explain an easy to way to add 99 to any number. For example, explain how to do easily 56 + 99 and 487 + 99.

8. Add in parts, or use other “tricks”.

9. Continue the patterns. a.

7 + 8 = ___

57 + 8 = ___

70 + 80 = ____

700 + 800 = ____

b.

4 + 9 = ___

34 + 9 = ___

40 + 90 = ____

240 + 90 = ____

c.

6 + 8 = ___

16 + 8 = ___

600 + 800 = ____

560 + 80 = ____

a.

80 + 5 + 2 + 30 + 4 + 44

b.

127 + 500 + 4 + 3 + 9 + 90

a.

71 + 82 = ____

37 + 42 = ____

57 + 64 = ____

b.

42 + 47 = ____

64 + 64 = ____

12 + 99 = ____

c.

89 + 92 = ____

82 + 19 = ____

51 + 98 = ____

a.

600 + 600 =____

+ 600 =____

b.

900 + 900 =____

+ 900 =____

c.

100 + 75 =____

+ 75 =____

d.

500 + 45 =____

+ 45 =____

(14)

10. Double and halve the numbers.

11. a. There are five people in the Brill family and they went to a concert. Children's tickets were $20 each and the two parents' tickets were $28 a piece.

What was the total cost of the tickets for the family?

b. In another concert, adult ticket cost $30 and children's tickets were half that price. What was the total cost for the Brill family?

12. Fill in the table - add 999 each time.

Half the number

10

Number

20

90

110

120

480

500

900 1,600

4,010

Its double

40

n

56

69 125 156 287 569 788 950 999

n + 999

John is writing very simple “missing addend” problems for first graders. For example, he wrote the problem 2 + ___ = 8. The first addend is given, and the second addend is missing.

John uses whole numbers from 0 on up to the number that is the sum. a. How many such problems can he write when the sum is 8? b. How many such problems can he write when the sum is 10? c. How many such problems can he write when the sum is 20?

d. You should see a pattern in the above answers. Now use the pattern to solve this: How many such problems could he write when the sum is 100 (for second-graders)?

(15)

Adding in Columns

1. Add in columns. Check by adding the numbers in each column in different order (for example from down up).

2. Write the numbers under each other carefully, and add in columns. a.

5,609 + 1,388 + 89 + 402

b.

$8.05 + $0.29 + $38.40 + $293 + $203.20 + $46.49 + $94

3. The map shows some Kentucky cities and distances between them. For example, from Louisville to Frankfort is 54 miles. The one distance not marked is written below the map: from Frankfort to Lexington is 28 miles.

Calculate the total driving distance, if a family goes on a field trip like this:

a. Covington - Lexington - Paducah - Lexington - Covington

b. A round trip from Lexington via Covington, Louisville, and Frankfort, and back to Lexington.

a.

3 8 4

2 9 1 2

2 0 0 8

2 0 9

+ 2 6

b.

$1.8 2

4 0.5 9

9.9 7

1 0.2 9

1.0 9

+ 0.4 3

c.

_{2 4 5}

1 3 9

3 0

2 9 3 1

5 9 4

9 5 9 3

+ 5 2 6

d.

_{1 7 3 8}

2 3 9 0

1 0 7 8

3 6 4

2 8 0 3

2 1 1

+ 9 9

(16)

Subtraction Review

1. Subtract from whole hundreds. You can subtract in parts.

2. Subtract. Use the helping problem.

3. Subtract and compare the results. The problems are “related” – can you see how?

4. Write here four different subtraction problems that are “related” to the problem 14 – 8 = 6. See the examples above!

Compare the methods.

Marie: “I subtract in parts: first to the previous whole ten, then the rest.”

35 − 7

= (35 − 5) − 2

= 30 − 2 = 28

John: “I use a helping problem.” 15 − 7 = 8 is the helping problem for 35 − 7.

The answer to 35 − 7 also ends in “8” and is in the previous ten (the twenties). So, 35 − 7 is 28. a.

100 – 2 = ____

100 – 20 = ____

100 – 22 = ____

b.

200 – 4 = ____

200 – 40 = ____

200 – 45 = ____

c.

500 – 5 = ____

500 – 50 = ____

500 – 56 = ____

d.

400 – 7 = ____

400 – 70 = ____

400 – 71 = ____

a.

13 – 7 = ____

63 – 7 = ____

b.

15 – 9 = ____

150 – 90 = ____

c.

12 – 6 = ____

82 – 6 = ____

d.

16 – 8 = ____

1,600 – 800 = ____

a.

12 – 8 = ____

42 – 8 = ____

120 – 80 = ______

520 – 80 = ______

b.

15 – 9 = ____

75 – 9 = ____

150 – 90 = ______

650 – 90 = ______

c.

13 – 7 = ____

73 – 7 = ____

1300 – 700 = ______

430 – 70 = ______

(17)

5. Fill in the table - subtract 99 each time.

6. Subtract in parts, use a helping problem, add up to find the difference, or use other “tricks”.

Trick: subtract first a bigger number, then add back some to correct the error:

705 − 99

= 705 − 100 + 1

= 605 + 1 = 606

140 − 88

= 140 − 90 + 2

= 50 + 2 = 52

n 125 293 346 404 487 510 640 849 n – 99

Strategy: Add up to find the difference of two numbers.

To solve 93 – 28, start at 28 and add until you reach 93. However much you added is the difference.

93 – 28 = (2 + 60 + 3) = 65

+ 2 + 60 + 3 2 8 3 0 9 0 9 3

420 – 160 = (40 + 200 + 20) = 260

+ 40 + 200 + 20 16 0 2 00 4 00 4 20 a.

91 – 82 = ______

42 – 37 = ______

77 – 64 = ______

b.

100 – 82 = ______

100 – 56 = ______

96 – 48 = ______

c.

56 – 29 = ______

61 – 39 = ______

84 – 38 = ______

d.

250 – 180 = ______

440 – 390 = ______

730 – 290 = ______

e.

1,000 – 555 = ______

1,000 – 56 = ______

1,000 – 208 = ______

f.

500 – 82 = ______

612 – 70 = ______

540 – 48 = ______

n 120 140 160 180 200 n – 27

(18)

8. Subtract the same number repeatedly. Multiplication tables can help!

Repeated Subtraction Game!

Jane and Jim are playing a repeated subtraction game. Each player has various number cards. A player pairs his cards together, two by two. With each two cards, the player subtracts the smaller number as many times as possible from the bigger number.

For example, Jane pairs together cards 20 and 4. Jane subtracts 20 – 4 – 4 – 4 – 4 – 4 = 0.

Jim pairs the cards 45 and 11, and subtracts 45 – 11 – 11 – 11 – 11 = 1. He can't subtract any more. Each player gets as many “points” as is the “remainder” number (the final difference).

Above, Jane got 0 points and Jim got 1. The player who first accumulates 25 points loses the game. Write the subtractions that Jane does with these cards:

With four cards, you need to choose which two will make a pair. Pair the cards for subtractions so that you will get the least possible points. Then write the subtractions.

e. Play the game yourself! Try number cards from 2-30 for an easier game. Try numbers from 2 to 60 for a challenge. Give each player 4-8 cards, depending on the difficulty level you wish to have.

a.

240 – 40 = 200

– 40 = 160

– 40 = ______

b.

1600

– 200 = ______

c.

540 – 60 = ______

– 60 = ______

d.

490 – 70 = ______

– 70 = ______

The table of 4 has a similar pattern.

The table of ____ has a similar pattern.

a. b.

(19)

Subtract in Columns

1. This is review. Subtract in columns. Check by adding!

It is time to review borrowing over zeros!

2. Subtract in columns. Check by adding! a.

5 1 9

− 3 4 6

Add to check:

+ 3 4 6

b.

7 2 8

− 5 1 9

Add to check:

+ 5 1 9

c.

1 3 5 0

− 7 8 2

Add to check:

+ 7 8 2

You can't subtract 3 from 0. You can't borrow a ten - there are none!

First borrow one hundred. You get 10 tens in the tens column.

Then borrow 1 ten into the ones column. Now you can subtract.

8 0 0

–

2 5 3

7 10

8 0 0

–

2 5 3

7 9 10 10

8 0 0

–

2 5 3

5 4 7

You can't borrow from the tens nor from the hundreds. So borrow 1 thousand.

Next, borrow one hundred into the tens column.

Then borrow one ten into the ones column. You're ready to subtract! 6 10

7 0 0 2

–

4 9 3 3

6 9 10 10

7 0 0 2

–

4 9 3 3

6 9 10 9 10 12

7 0 0 2

–

4 9 3 3

2 0 6 9

a.

7 0 0

− 3 5 6

Add to check:

+ 3 5 6

b.

5 0 0 0

− 1 2 3 6

Add to check:

+ 1 2 3 6

c.

6 0 0 4

− 6 7 8

Add to check:

+ 6 7 8

(20)

3. Subtract in columns. Check by adding!

4. Look again at the Kentucky map. How many miles longer is

a. a round trip from Lexington to Ashland and back than a round trip from

Lexington to Covington and back?

b. a trip from Lexington to Paducah and back than a triangular trip from Lexington via Covington, Louisville, Frankfort, and back to Lexington?

a.

5 0 6

− 2 8 9

Add to check:

+ 2 8 9

b.

4 0 9 0

− 3 7 8 5

Add to check:

+ 3 7 8 5

c.

9 0 0 0

− 3 4 2 0

Add to check:

+ 3 4 2 0

d.

5 0 7 0

− 2 3 5 6

+

e.

$ 8 0 . 0 0

− 5 6 . 7 0

+

f.

$ 6 0 0 . 0 0

− 2 3 0 . 5 0

+

g.

4 0 0 5

− 2 3 9 1

+

h.

$ 4 0 0 . 0 0

− 1 9 8 . 9 9

+

i.

$ 1 0 9 . 4 0

− 7 8 . 6 5

+

(21)

5. Write the numbers under each other carefully, and subtract in columns. a. 4,400 − 2,745 − 493 b. 5,604 − 592 − 87 c. $45.60 − $12.36 − $1.69

6. You can solve the problem 5,200 − 592 − 87 − 345 − 99 by subtracting the numbers one at a time. That means four separate subtractions. Can you find a quicker way?

8120 – 2653 – 754 = ?

When subtracting two numbers, you can continue the subtraction under your first answer.

Check by adding the answer and all the numbers you subtracted. 7 10 11 10

8 1 2 0

–

2 6 5 3

5 4 6 7

–

7 5 4

4 7 1 3

Check:

4 7 1 3

7 5 4

+

2 6 5 3

8 1 2 0

Little Hannah has almost learned to read the (analog) clock, but she can't remember which hand is the hour hand and which is the minute hand. So when the time is 1:15, she might say, “It is 3:05”, mixing the hours and the minutes.

One day mom was lying in bed, sick, and she asked Hannah what time it was. Hannah said, “It is 2:20.” Just a few minutes later mom asked again for the time. Hannah claimed it was now 4:25.

Remembering that each time Hannah either tells the time right, or mixes the hour and minute hands, mom was able to figure out what time it was in reality. Can you?

(22)

Mental Math Workout and Pascal's Triangle

1. Fill in the table - add 29 each time.

3. Subtract - and be careful!

4. Figure out the patterns and continue them.

n

9

18

27

36

45

54 n + 29

n

660

600

540

480

420 n – 39

a.

500 – 3 =

500 – 30 =

500 – 300 =

500 – 33 =

500 – 303 =

b.

600 – 2 =

600 – 20 =

600 – 200 =

600 – 22 =

600 – 202 =

c.

300 – 3 =

400 – 40 =

500 – 5 =

600 – 60 =

700 – 7 =

d.

1,000 – 7 =

1,000 – 70 =

1,000 – 700 =

1,000 – 77 =

1,000 – 707 =

+ + + + + + + +

5 28 51 74

____

__

____

– – – – – – – –

1000

900 810 730

660 ____

____

(23)

5. Continue the patterns.

6. This will be a Pascal's triangle but you need to fill it in. On the left and right sides are ones. Any other number is gotten by adding the two numbers right above it (slightly to the right and to the left). For example, the colored number 3 comes from adding the 1 and 2 above it.

+ 300 + 300 + 300 + + + + +

3,000

___ ___ ____ ____ ____ ____ ____ ___

– 400 – 400 – 400 – – – – –

(24)

7. a. After filling the triangle, add the numbers in each row and make a list. For example, the first row just has 1. In the second row, add 1 + 1 = 2. In the third row, add 1 + 2 + 1 = 4.

The row sums are: 1, 2, 4, ____, ____, ____, ____, ____, ____, ____, ____, ____. What do you notice about these numbers?

b. Can you find a diagonal with the numbers 1, 2, 3, 4, 5, 6, 7? c. Can you find a diagonal with triangular numbers?

(Triangular numbers start like this:)

Read more about Pascal's triangle and its patterns at http://ptri1.tripod.com/

Below you will find an empty Pascal's triangle to explore with. You can fill it with some other number on all the sides, such as 2, 3, or 20.

(25)

Subtraction Terms

1. The minuend is missing! Find a general idea that always works to solve these kind of problems.

2. The subtrahend is missing! Find a general idea that always works to solve these kind of problems.

3. a. Write three subtraction problems where the difference is 10.

b. The subtrahend is 12 and the difference is 58. What is the minuend? c. The minuend is 55 and the difference is 17. What is the subtrahend? 4. Explain an easy to way to subtract 999 from any number mentally. For example, explain how to do easily 1,446 – 999.

5. The difference of two numbers is 20, and one of the numbers is 25. What can the other number be?

Remember subtraction terms?

Just like “m” comes before “s” in the alphabet, the minuend comes before the subtrahend.

a.

____ − 8 = 7

____ − 4 = 20

b.

____ − 15 = 17

____ − 24 = 48

c.

____ − 22 − 7 = 70

____ − 300 − 50 = 125

a.

20 −

____ = 12

6 −

____ = 5

b.

55 −

____ = 34

100 −

____ = 72

c.

234 −

____ = 100

899 −

____ = 342

(26)

6. Solve the problems. You will need addition AND subtraction. a. A package of cheese costs $6 and a package of ham costs $2 less. How much do the two cost together?

b. One alarm clock costs $11 and another costs $8 more. How much would the two cost together?

c. Of the 45 students, 18 are girls. How many are boys? How many more boys are there than girls?

d. Jack gave the clerk $50 for his purchases, and got $13 as his change. How much did his purchases cost?

e. It rained five days in June and six days in July.

How many non-rainy days did those two months have? f. Amy is 134 cm tall and her mom is 162 cm tall.

What is the difference in their heights?

g. Jack bicycled his favorite 28 km route on Tuesday and on Wednesday. On Thursday and Saturday he bicycled along a route that was 6 km shorter. How many kilometers did he bicycle all totalled?

Subtraction is used: z To find the difference

z In “less than” or “more than” situations

z In “take away” situations

z To find one part when you have a “whole” and several “parts”.

Find the missing numbers.

a.

200 − 45 − ____ − 70 = 25

b.

_____ − 5 − 55 − 120 = 40

(27)

Word Problems and Bar Models

Mark the numbers given in the problem in the diagram. Mark what is asked with “?”. Then solve the problem.

Bar models help you see how the numbers in a problem relate to each other. Whenever you get stumped by a word problem, try drawing a bar model.

On Monday, Dad drove 277 miles, and on Tuesday he drove 25 miles more than he did on Monday. How many miles did he drive in the two days?

On Tuesday he drove 277 + 25 = 302 miles. Altogether he drove 277 + 302 = 579 miles.

The bracket “}” means addition or the total of the two bars. We do not know the total or the sum of the two days' journey, so it is marked with a question mark.

Monday Tuesday

After driving 20 miles, Dad says, “I still have 15 more miles to go to the half-way point.” How long is the trip?

20 mi + 15 mi = 35 miles, and that is the first half of the trip. So, the total trip is 2 × 35 = 70 miles.

We do not know the total length, so it is marked with “?”.

1. Jake worked for 56 days on a farm, and Ed worked for 14 days less.

How many days did Ed work?

2. Of his paycheck, Dad paid $250 on taxes, and spent $660 on other bills and purchases. Then, half of his paycheck was gone. How much was his paycheck?

3. Dad bought two hammers. One cost $18 and the other cost $28 more.

(28)

Mark the numbers given in the problem in the diagram. Mark what is asked with “?”. Then solve the problem.

6. Eric and Angela did yard work together. They earned $80 and split it so that Eric got $12 more

than Angela. How much did each one get? Draw a bar diagram.

To solve it, you can think this way. If you took away (subtracted) the “additional” $10, then the total would be $90, and we would only have the two equal parts (the two green parts). So, $90 ÷ 2 = $45 gives us the amount Rebecca got, and then Angi got $45 + $10 = $55.

Angi and Rebecca split a $100 paycheck so that Angi got $10 more than Rebecca.

How much did each one get?

The bar diagram shows the situation. Angi got $10 more than Rebecca, and together they earned $100.

We can then see Angi got $50 + $5 = $55 and Rebecca got $50 − $5 = $45. Here's another way of looking at the same situation.

We draw just one bar for the paycheck, and divide it into two halves in the middle (the dashed line). Then we draw half of the $10, or $5, on either side of that middle line.

4. Mary and Luisa bought a $46 gift together. Mary spent $6 more on it than Luisa. How many dollars did each spend?

5. Henry bought two circular saws. One saw was $100 cheaper than the other.

(29)

You can solve the rest of the problems any way you like best. 7. Mark bought four towels for $7 each, and a blanket for $17. He paid, and the clerk handed him back $5.

What denomination was the bill Mark used to pay?

8. One plain yogurt costs $2.40, strawberry yogurt costs $0.15 less than plain yogurt, and plum yogurt costs $0.30 more than plain yogurt.

What is your total bill if you buy all three?

9. Erica was 132 cm tall when she was 9 years old. In the next year, she grew 6 cm, and the next year 2 cm less than the previous year. How tall was she at the age of 11?

10. John's monthly phone service bill is $48. John said that with the money he earned on his summer job, he could pay his phone service for two months, spend $120 for a bike, and still have half his money left. How much did he earn?

11. Melissa found a nice shirt for $11.50, another for $2.55 less, and yet another for $2 less. If she buys all three, what will her total bill be?

(30)

Missing Addend Solved with Subtraction

1. The missing addend is solved with subtraction. Solve.

2. Write a missing addend sentence using x, and a subtraction sentence to solve it. From this simple diagram, we can write

two addition and two subtraction sentences. Those four form a fact family.

x stands for a number, too. We just don't know it yet. Which fact in the family makes it easy to

find the value of x?

z x + 15 = 56 z 15 + x = 56

z 56 – x = 15 z 56 – 15 = x

Here is missing addend problem: 769 + x = 1,510.

You can solve it by subtracting

the one part (769) from the total (1,510): x = 1,510 – 769 = 741 a.

78 + x = 145

x = 145 – 78 = _____

b.

128 + x = 400

x = – = _

c.

x + 385 = 999

x = – = _

a. A car costs $1,200 and dad has $890. How much more does he need?

b. The school has 547 students, of which

265 are girls. How many are boys?

(31)

3. a. Write a fact family using these three numbers: x, 59, 124.

(Remember, x stands for a number too.)

b. Solve for x.

4. Write a missing addend sentence with x. Solve.

5. Which number sentence fits the problem? Find x. a. A school's teachers and students

filled a 450-seat auditorium. If the school had 43 teachers, how many students did it have?

x =

students + teachers = total ______ + ______ = ______

b. Mom went shopping with $250 and came back home with $78. How much did she spend?

x =

spent + left = had originally ______ + ______ = ______

c. Janet had $200. She bought an item for $54 and another for $78.

How much is left?

x =

item 1 + item 2 + left = total ______ + ______ + ______ = ______

d. Jean bought one item for $23 and another for $29, and she had $125 left. How much did she have

initially? _{x =}

______ + ______ + ______ = ______

a. Jane had $15. Dad gave Jane her allow- ance (x) and afterwards Jane had $22. $15 + x = $22 OR $15 + $22 = x

b. Mike had many drawings. He put 24 of them in the trash. Then he had 125 left. 125 – 24 = x OR x – 24 = 125

c. Jill had 120 marbles, but some of them got lost. Now she has 89 left.

120 – x = 89 OR 120 + 89 = x

d. Dave gave 67 of his stickers to a friend and now he has 150 left.

150 – 67 = x OR x – 67 = 150

(32)

6. Pick a number sentence that you can use to find x. Then solve for x.

7. Solve for x.

8. Write the numbers and x to the picture. Write a missing addend sentence. Solve. a. Problem: 253 + x = 2056 2056 – 253 = x OR x – 253 = 2056 b. Problem: x + 148 = 397 148 – 397 = x OR 397 – 148 = x c. Problem: x – 23 = 45 45 – 23 = x OR 45 + 23 = x d. Problem: 120 – x = 55 120 – 55 = x OR 120 + 55 = x |⎯⎯⎯⎯⎯⎯ 4,900 ⎯⎯⎯⎯⎯| a. x 1,750 b. 23 + 56 + x = 110

a. The Jones' family had traveled 420 miles of their 1,200-mile journey. How many miles were left to travel?

|⎯⎯⎯⎯⎯⎯|⎯⎯⎯⎯⎯⎯⎯⎯|

b. The store is expecting a shipment of 4,000 blank CDs. Two boxes of 500 arrived. How many are still to come?

|⎯⎯⎯|⎯⎯⎯|⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯|

c. A 250 cm board is divided into three parts:

two 20 cm parts at the ends and a part in the middle. How long is the middle part?

|⎯⎯|⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯|⎯⎯|

d. After traveling 56 miles, Dad said, “We have 118 miles left.”

How long is the journey?

|⎯⎯⎯⎯⎯⎯|⎯⎯⎯⎯⎯⎯⎯⎯|

(33)

Order of Operations

1. Do the calculations in the right order.

2. Calculate in the right order.

3. Match the description with the right number sentence. Then calculate.

1. Do operations within ( ) first.

2. Then multiply & divide, from left to right. 3. Then add & subtract, from left to right. Make sure you understand

the examples on the right.

30 − 6 − 11 + 5

= 24 − 11 + 5

= 13 + 5 = 18

4 + 3 × (6 − 2)

= 4 + 3 × 4

= 4 + 12 = 16

7 + 3 × 5

= 7 + 15 = 22

70 + (80 − 5)

= 70 + 75 = 145

a.

500 – 30 – 30 =

500 – (30 – 30) =

500 – 30 + 30 =

500 – (30 + 30) =

b.

250 + (100 – 50) + (100 – 50) =

250 + 100 – 50 + 100 – 50 =

(250 + 100) – (50 + 100) – 50 =

250 + 100 – (50 + 100 – 50) =

a.

2 × (5 + 3) =

20 – 3 × 3 =

50 – 1 – 2 × 10 =

b.

2 × 5 + 3 × 1 =

(10 – 3) × 3 + 1 =

50 – 1 × 7 + 2 × 3 =

c.

2 × 5 + 3 × 0 =

(20 – 16) × 3 + 2 =

2 × (2 + 2) – 3 =

First multiply 5 times 10 and subtract from the result 7. Add to 10 the difference of 100 and 20.

First subtract 7 from 10, and then multiply the result by 5. From 100 subtract the sum of 20 and 10.

5 × (10 – 7)

5 × 10 – 7

100 – (20 + 10)

(100 – 20) + 10

4. You cut off two 20-cm pieces of a 90-cm piece of wood. Which calculation tells you the piece that is left?

90 – 20 + 20

90 – 2 × 20

(90 – 20) × 2

(34)

5. A clerk in the store rings up all the items the customer buys, gets the customer's money, and figures out the change.

6. Describe a shopping situation where you need to do these calculations:

a. $10 + $2.10 + $45

b. 4 × $1.20

c. $10 – 4 × $1.20

7. Put operation symbols +, – , or × into the number sentences so that they become true.

8. Every day, James feeds the kennel dogs 5 kg of dog food. He bought a 100-kg bag of dog food. How many kilograms are left after four days? Write a single number sentence to solve that.

9. Parking costs $2 per hour during the day and $3 per hour during the night. Write a single number sentence that tells you the cost of parking a car for 5 daytime hours and

2 nighttime hours. Solve it.

10. Write a single number sentence that tells you the change if you buy a book for $7, a ball for $5, and pay with a $20 bill.

See also the Choose Two Operations game at http://www.homeschoolmath.net/operation-game.php

a. Which of the calculations on the right best matches figuring out the change? b. Which calculation of the three would give you the wrong answer for the change?

i. $50 – $1.26 – $6.55 – $0.22 – $5 ii. $50 + $1.26 + $6.55 + $0.22 + $5 iii. $50 – ($1.26 + $6.55 + $0.22 + $5) a.

4

1 8 = 12

50

5 10 = 0

b.

2

10

1

2 =

14

100 (15

17)

1 =

68

c.

3

3 3 = 6

(2

5 )

2 = 14

(35)

Bar Graphs

1. Beverly asked her classmates how many hours they watch the TV each day. The results are below; she already organized them in order.

0 0 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 5 5 6

Each number above is someone's answer to Beverly's question. So two people answered that they watched TV for 0 hours. Quite a few answered that they watch TV about 1 hour per day. With such a bunch of numbers, we need to make first a frequency table. In a frequency table, we count how frequently or how often a certain number was in our list of data. After counting all that, we can make a bar graph.

In Beverly's data above, the number zero (0 hours TV) appeared two times. The number two (2 hours TV) appeared four times. Finish the frequency table and the bar graph.

b. How many classmates did Beverly question?

c. What was the most common response to Beverly's question? d. How many of these kids watch TV 1 hour or less?

e. How many kids watch TV 3 hours or more?

f. Are there more kids who watch TV 3 hours a day than kids who watch TV 2 hours a day? g. Are there more kids watching TV 2 hours or more, than kids watching TV less than 2 hours?

Hours of TV Frequency

0 h

2 1 h

(36)

2. a. Beverly also asked some people about their favorite color. Make a bar graph.

b. How many people did Beverly question?

c. Were the “warm” colors or the “cold” colors more popular?

(Warm colors are red, orange, and yellow. Cold colors are green, blue, and purple.) 3. The numbers are students' quiz scores. 1 3 5 3 6 4 9 8 6 4 8 7 5 3 9 8 6 2 1 8 9 10 2 9 7 6 a. Make a frequency table and a bar graph.

b. What was the most common quiz score? How many students got that score? c. What was the least common quiz score? How many students got that score? d. How many students got a score from 5 to 8?

e. How many students did excellent (got a score of 9 or 10)?

f. The teacher said after the test, “Anyone with a score of 4 or less will need to retake the test, and anyone with a score of 5 or 6 will get extra homework.”

How many students need to do the test again? How many will get extra homework?

Color Frequency red 2 orange 1 yellow 4 green 5 blue 7 purple 4 black 2 white 2

(37)

b. How many people were short (less than 140 cm tall)? c. How many were very tall (180 cm or taller)?

d. Most adults are 160 cm tall or taller. Use this fact to guess (estimate) how many children and how many adults were in this group.

e. Could this data come from

z a group of elementary school children?

z a group of people who were at the swimming pool at 5 pm on a certain Tuesday? z a group of elderly women in an old people's home?

Explain your reasoning. 4. a. Make a bar graph out of the data

in the frequency table on the right.

Height in cm Number of people

120...129 4

130...139 10

140...149 41

150...159 82

Height in cm Number of people

160...169 95

170...179 61

180...189 39

(38)

Line Graphs

1. Look at the line graph about Amy's savings. a. How many dollars had Amy saved in May? b. How many dollars had Amy saved in August? c. How many dollars had Amy saved in September? d. In which month had she saved up $75?

e. In September Amy used up her savings to buy a used bike. How much did the bike cost?

b. What is the first day that the puppy weighed 600 g or more? c. What is the first day that the puppy weighed 700 g or more?

A line graph shows how something changes over time, such as over several hours, days, weeks, months, or years.

The data values are often drawn as dots. Then the dots are connected with lines. The x-axis and the y-axis are the

two lines that frame the picture. The time units are written under the x-axis.

To read a line graph, look “up” from the time unit until you find the dot. Then draw an imaginary line from that dot to the y-axis For example, in July Amy had saved $90.

2. The graph shows a puppy's weight for 10 days after birth.

Notice how the two axes are named as “day” and “grams”. a. About how many grams did the puppy weigh on day 1? ________ Day 2? ________ Day 3? ________ Day 4? ________

(39)

3. Look at the graph about the monthly retail prices of strawberries in 2004, given in dollars per pound. The retail price is the price you see in a grocery store or the price the customers pay.

4. Becca's mom wrote down an “x” mark for every bad behavior she did during the day. The table shows the list of her x-marks.

a. Make a line graph. Remember to name one axis as “days” and the other as “x-marks”. b. Did Becca's behavior improve?

a. Describe the price changes as the year progresses. Do you know why the price is lower in the summer?

b. Find the highest price per pound and the lowest price per pound. What is the difference of these two?

c. How much did it cost to buy 2 lb of strawberries in August? In November? Month Price ($ per lb) Jan 2.48 Feb 2.33 Mar 2.12 Apr 1.66 May 1.67 Jun 1.85 Jul 1.63 Aug 1.82 Sep 1.84 Oct 2.60 Nov 3.19 Dec 3.60 Day x-marks Mon 10 Tue 8 Wed 9 Thu 6 Fri 3 Sat 4 Sun 2

(40)

a. Make a line graph. Three values are already done for you. b. What are the coldest months?

c. What are the warmest months?

d. What is the difference in maximum temperature between the coldest and the warmest month?

6. Do a line graph from some data that you gather yourself! Just remember, it has to be something that changes over time. You can also “make up” data from your own head. Here are some ideas:

z outside temperature from the morning till the evening

z your savings in the past 6 months, or an imaginary child's savings in 6 or 8 or 12 months z how many hours of schoolwork (or housework or playing etc.) you do each day of the week z how many pages of a book you read each day of the week

z your height from year 0 to year 9 of your life

You can also use this neat online tool for creating your graph: http://nces.ed.gov/nceskids/createagraph/

To use it, you need to have your data ready. It will not give you any data. It just draws the graph. 5. The table gives the average

maximum temperatures for each month in New York.

Month Max. Temp. Jan 3°C Feb 3°C Mar 7°C Apr 14°C Month Max. Temp. May 20°C Jun 25°C Jul 28°C Aug 27°C Month Max. Temp. Sep 26°C Oct 21°C Nov 11°C Dec 5°C

(41)

Rounding

1. Round the numbers to the nearest ten. The number line can help.

2. Round these numbers to the nearest ten. When you are rounding to the nearest ten, look at the ONES DIGIT.

z If the ones digit is 0, 1, 2, 3, or 4, then round down. z If the ones digit is 5, 6, 7, 8, or 9, then round up. z If you round up, the tens digit increases by one. The sign “ ≈ ” is read “is about”, or “is approximately”.

When the number is exactly in the middle, round up. 85 ≈ 90.

(This is just a convention.)

You can draw a line after the digit whose place you are rounding to. The digit or digits after the line will become zeros.

25 6 ≈ 26 0 (up) 8 4 ≈ 8 0 (down) 3,28 7 ≈ 3,29 0 (up) 9,85 4 ≈ 9,85 0 (down) Notice carefully: If you are rounding up, and the tens digit is already 9, look at the two digits just before your line, and increase that “number” by one:

3,29 7 ≈ 3,30 0 (up) 79 5 ≈ 80 0 (up) 3,09 8 ≈ 3,10 0 (up) It is as if the “29” formed by the hundreds and

tens changes into “30” - exactly one more. (In reality it is “29” tens changing to “30” tens.)

The “79” changes to “80”. The “09” changes to “10”. a.

294 ≈ ______

b.

315 ≈ ______

c.

278 ≈ ______

d.

285 ≈ ______

e.

315 ≈ ______

f.

296 ≈ ______

g.

304 ≈ ______

h.

207 ≈ ______

a.

526 ≈ ______

b.

34 ≈ ______

c.

181 ≈ ______

d.

197 ≈ ______

e.

705 ≈ ______

f.

392 ≈ ______

g.

440 ≈ ______

h.

5,971 ≈ ______

i.

9,568 ≈ ______

j.

4,061 ≈ ______

k.

2,282 ≈ ______

l.

4,003 ≈ ______

(42)

3. Round the numbers to the nearest hundred.

4. Round these numbers to the nearest hundred.

Find the whole hundred that is nearest to 539. Rounded to the nearest hundred, 539 ≈ _________. When you are rounding to the nearest hundred, look at the TENS DIGIT.

z If the tens digit is 0, 1, 2, 3, or 4, then round down. z If the tens digit is 5, 6, 7, 8, or 9, then round up.

z The rounded result is a whole hundred so it ends in two zeros. z The hundreds digit changes by one if you round up.

You can draw a line after the digit whose place you are rounding to. The digits after the line will become zeros.

5 62 ≈ 6 00 2 48 ≈ 2 00 (down) 1,2 90 ≈ 1,3 00 (up) 5,4 28 ≈ 5,4 00 (down) Notice carefully: If you are rounding up, and the hundreds digit is already 9, look at the two digits just before your line, and increase that “number” by one:

5,9 92 ≈ 5,5 00 (up) 6,9 71≈ 7,0 00 (up) 12,9 61≈ 13,0 00 (up) It is as if the “59” formed by the thousands and

hundreds changes into “60” - exactly one more.

The “69” changes to “70”. The “29” changes to “30”. a.

3,520 ≈ ______

b.

3,709 ≈ ______

c.

3,935 ≈ ______

d.

3,541 ≈ ______

e.

3,962 ≈ ______

f.

3,425 ≈ ______

g.

3,847 ≈ ______

h.

3,656 ≈ ______

a.

526 ≈ ______

b.

54 ≈ ______

c.

761 ≈ ______

d.

197 ≈ ______

e.

706 ≈ ______

f.

365 ≈ ______

g.

2,907 ≈ ______

h.

5,971 ≈ ______

i.

7,543 ≈ ______

j.

3,032 ≈ ______

k.

2,959 ≈ ______

l.

4,014 ≈ ______

(43)

5. Round the numbers to the nearest thousand.

6. Round these numbers to the nearest thousand.

7. Round these numbers to the nearest ten, nearest hundred, and nearest thousand. Rounded to the nearest thousand, 4,772 ≈ ________.

When you are rounding to the nearest thousand, look at the HUNDREDS DIGIT. z If the hundreds digit is 0, 1, 2, 3, or 4, then round down.

z If the hundreds digit is 5, 6, 7, 8, or 9, then round up.

z The rounded result is a whole thousand so it ends in three zeros. z The thousands digit changes by one if you round up.

You can draw a line after the thousands digit. The digits after the line will become zeros. 2, 723 ≈ 3,000 (up) 9, 804 ≈ 10,000 (up) 7 288 ≈ 7,000 (down) 457 ≈ 0 (down)

a.

3,520 ≈ ______

b.

6,709 ≈ ______

c.

5,499 ≈ ______

d.

7,230 ≈ ______

e.

2,800 ≈ ______

f.

4,087 ≈ ______

g.

3,602 ≈ ______

h.

4,555 ≈ ______

a.

526 ≈ ______

b.

54 ≈ ______

c.

761 ≈ ______

d.

4,197 ≈ ______

e.

5,672 ≈ ______

f.

3,099 ≈ ______

g.

2,907 ≈ ______

h.

5,502 ≈ ______

i.

9,397 ≈ ______

j.

9,605 ≈ ______

k.

2,553 ≈ ______

l.

1,047 ≈ ______

n

55 2,602

9,829 3,199 495 709 5,328 rounded to nearest 10 rounded to nearest 100 rounded to nearest 1000

(44)

The rounding rules remain the same even with money amounts.

8. Round these numbers to the nearest dollar.

9. Round these numbers to the nearest ten dollars.

10. Round these numbers to the nearest one, nearest ten, and nearest hundred.

11. Round the prices, and use the rounded prices to estimate the total bill. a. pencils $2.28, paper $5.90, notebook $4.76, books $12.75.

b. Chairs $126.70, table $195.99, bed $256, mattresses $346.60. Rounding to the nearest dollar, look at

the ten-cents DIGIT (tenth of a dollar). z If it is 0, 1, 2, 3, or 4, then round down. z If it is 5, 6, 7, 8, or 9, then round up. z The rounded result is in whole dollars

so omit the decimal point and the cents. $12. 72 ≈ $13

$452. 34 ≈ $452

$59. 92 ≈ $60 $3,480. 55 ≈ $3,481

Rounding to the nearest ten dollars, look at the dollars DIGIT (ones digit).

z If it is 0, 1, 2, 3, or 4, then round down. z If it is 5, 6, 7, 8, or 9, then round up. z The ones digit becomes zero.

Omit the decimal point and the cents. $4 7.26 ≈ $50 $39 5.60 ≈ $400 $56 2.94 ≈ $560 $4,53 9.50 ≈ $4,540 a.

$3.17 ≈ ______

b.

$97.99 ≈ ______

c.

$3.29 ≈ ______

d.

$1,680.25 ≈ ______

e.

$47.38 ≈ _____

f.

$125.59 ≈ ______

g.

$13.70 ≈ ______

h.

$977.50 ≈ ______

a.

$45.70 ≈ ______

b.

$7.99 ≈ ______

c.

$73.78 ≈ ______

d.

$6,289.40 ≈ ______

e.

$43.27 ≈ ______

f.

$169.49 ≈ ______

g.

$255.55 ≈ ______

h.

$564.00 ≈ ______

n

$129.78

$455.09

$69.42

$591.95

$1,285.38

$6,089.90

rounded to nearest dollar rounded to nearest ten dollars rounded to nearest hundred dollars

(45)

Estimating

1. First estimate by rounding the numbers to the nearest hundred. Then find the exact answer.

2. The table lists the costs of running the student recess time snack bar. Estimate the total cost over these five weeks by rounding

the numbers to the nearest ten.

You can estimate the result of a calculation. Round the numbers, and then calculate (add or subtract) using the rounded numbers. Your result is not exact. That is why it's called an estimate.

Use the symbol “≈” (is approximately) instead of equality “=” when you change from exact numbers to rounded numbers.

567 + 89 – 413

≈ 600 + 100 – 400 = 300.

$4.12 + $27.90 + $5.99

≈ $4 + $28 + $6 = $38.

a.

967 + 231 + 4,792

Estimation: b.

320 + 405 + 587

Estimation: c.

1,029 – 372 – 105

Estimation: d.

3,492 – 1,540 – 211

Estimation:

Week 37 Week 38 Week 39 Week 40 Week 41

(46)

3. Mary's family is going to rent an apartment for a 3-week vacation. They have two choices: one apartment costs $289 per week, and the other costs $327 per week.

a. Estimate the cost of each one.

b. How much approximately would the family save by choosing the cheaper rental?

4. Solve these problems with estimation. You don't need to find the exact answer!

5. The chart lists the number of loans that Charleston library had on the weeks of May and June. From this chart, you cannot read the exact numbers of loans, but you can find the approximate numbers of loans. Estimate to the nearest ten, the total number of loans for a) weeks 18-21 b) weeks 22-25.

a. Each bus can take 47 passengers. About how many passengers are in four buses?

b. A gallon of gas is $2.87. How many gallons can you get with $20?

c. A book is $4.87 and another is $6.95. What is the total approximately?

d. You have $10. How many ice creams could you buy that cost $1.97 each?

(47)

Reviewing Money

1. Write the dollar amounts as cents or vice versa.

2. Round to the nearest dollar.

3. You bought items for $1.50, $12, and for $2.20. You paid with a 20-dollar bill. How much was your total?

How much was your change?

4. Make change. Mark how many of each bill/coin you need.

5. Make change. Mark how many of each bill or coin you need.

a. $0.25 = _____ ¢ b. $0.70 = ______ ¢ c. $1.25 = _______ ¢ d. $5.60 = ______ ¢ e. $31.55 = ______ ¢ f. $_______ = 76¢ g. $_______ = 20¢ h. $______ = 154¢ i. $_______ = 859¢ j. $______ = 419¢ k. $80.34 = _______¢ l. $_______ = 104¢ a. $1.05 ≈ ______ b. $7.72 ≈ ______ c. $35.17 ≈ ______ d. $165.83 ≈ _______ e. $94.90 ≈ ______ f. $99.09 ≈ ______ g. $99.90 ≈ ______ h. $100.56 ≈ _______ Item cost Money given Change needed

$50 bill $20 bill $5 bill $1 bill

a. $56 $70 b. $29 $50 c. $78 $100 d. $129 $200

Item cost Money

given Change needed $5 bill $1 bill 25¢ 10¢ 5¢ 1¢ a. $2.56 $5 b. $8.94 $10 c. $7.08 $10 d. $3.37 $10

(48)

6. Solve. Write a number sentence for each problem.

7. Match the situations (a), (b), and (c) with number sentences (i), (ii), and (iii). Then solve for the unknown number x in each situation.

8. Solve the word problems.

a. Mike had $99. He spent $34 , and he has $56 left. b. Dad had ______. He spent $250, and has $170 left. c. Mom had $280. She spent $45, and now has ______ left. d. Greg bought a $45-tool and now he has $15 left.

Originally he had _______.

e. Alice had $12. She bought an item, and now she has $3.56. The item cost ________.

a. $99 − $34 = $56. b. c. d. e.

a. Andy had $60 and he bought a tool set for $48. How much does he have left?

i. $60 − x = $48

b. Elisa bought food for $60 and now has $48 left. How much money did she have initially?

ii. $60 − $48 = x

c. Greg had $60 when he went to the store. He came back home with $48. How much did he spend?

iii. x − $60 = $48.

a. Mike had $38, and after Grandma's gift, he had $158.

How much did Grandma give him?

b. Ashley spent half of her $88 in town. How much does she have now?

c. Greg bought two $15 books with his birthday money ($60).

How much did he have left?

d. Jill bought three $4 magazines with her birthday money, and now she has $28. How much was the birthday money?

e. You bought 4,000 marker pens at $0.98 each, and 1,000 whiteboard erasers at $1.02 each, Estimate the total using rounded numbers.

f. Dad bought a $0.60 ice cream cone for each of the three kids, and an $0.80 ice cream cone for himself. How much was the total?

What was his change from $10?

MathMammoth_Grade4A

Contents

Chapter 1: Addition, Subtraction, Graphs and

Money

Chapter 2: Place Value

Chapter 3: Multiplication

Chapter 4: Time and Measuring

Foreword

Concerning Challenging Word Problems

Chapter 1: Addition, Subtraction,

Graphs and Money

Introduction

The Lessons in Chapter 1

Helpful Resources on the Internet

Addition Review

5,248 = 5,000 + 200 + 40 + 8

56 + 124

= 100 + 50 + 20 + 6 + 4

= 100 + 70 + 10 = 180

7 + 90 + 91 + 3

= 7 + 3 + 90 + 91

= 10 + 90 + 91 = 191

76 + 89

= 76 + 90 − 1

= 166 − 1 = 165

70 + 80 = ___

77 + 80 = ___

77 + 82 = ___

140 + 50 = ___

141 + 50 = ___

144 + 55 = ___

50 + 60 = ___

54 + 65 = ___

58 + 62 = ___

80 + 90 = ___

82 + 93 = ___

88 + 91 = ___

487 =

8,045 =

2,103 =

650 =

7 + 8 = ___

57 + 8 = ___

70 + 80 = ____

700 + 800 = ____

4 + 9 = ___

34 + 9 = ___

40 + 90 = ____

240 + 90 = ____

6 + 8 = ___

16 + 8 = ___

600 + 800 = ____

560 + 80 = ____

80 + 5 + 2 + 30 + 4 + 44

127 + 500 + 4 + 3 + 9 + 90

71 + 82 = ____

37 + 42 = ____

57 + 64 = ____

42 + 47 = ____

64 + 64 = ____

12 + 99 = ____

89 + 92 = ____

82 + 19 = ____

51 + 98 = ____

600

+ 600 =____

+ 600 =____

+ 600 =____

+ 600 =____

+ 600 =____

+ 600 =____

900

+ 900 =____

+ 900 =____

+ 900 =____

+ 900 =____

+ 900 =____

+ 900 =____

100

+ 75 =____

_{2 4 5}

_{1 7 3 8}