TEACHER GUIDE Includes Student Teacher Guide for the 36 ...

MATH

LEVEL 6

The vital resource for grading all assignments from the Math Level 6 course, which includes:

All the quizzes for the course, as well as quiz answers and worksheet solutions.

Cumulative reviews, final exam, and optional end of year student presentation.

OVERVIEW: This course was designed to present math concepts in the context of real life so students learn to apply the rules and techniques to solving everyday problems. It will help students review and master important skills as they prepare to move into more advanced coursework. A special note about quizzes and tests included in this book: If a teacher has used the previous books in this series, he or she will be aware that they contain very few quizzes or tests. This is because they are written in such a way that students consistently demonstrate what they know. Level 6 is also written in this way, BUT because quiz and test taking is a skill that students need in life, they have been added at the end of each lesson. If you, as the teacher, do not want your student to take every single lesson quiz, simply use the lesson practice and review, which is directly before most of the quizzes. You decide what your student needs and adjust this course to fit them.

FEATURES: The calendar provides daily sessions with clear objectives for the worksheets and quizzes.

Approximately 30 minutes per day, five days a week

Includes solutions manual for worksheets and quizzes

Quizzes are included to help reinforce learning and provide assessment opportunities

Designed for grade 6 in a one-year course

Teacher Guide for the 36-week, 6th grade math course!

TEAC

HER

GU

IDE

TEACHER GUIDE Includes Student Quizzes Weekly Lesson Schedule

QuizzesSolutions ManualLevel 6 Math

O’Dell

JUVENILE NONFICTION/Mathematics/GeneralSTUDY AIDS/General

ISBN-13: 978-1-68344-085-7 EAN

First printing: July 2017 Sixth printing: March 2021

Copyright © 2017 by Angela O’Dell and Master Books®. All rights reserved. No part of this book may be reproduced, copied, broadcast, stored, or shared in any form whatsoever without written permission from the publisher, except in the case of brief quotations in articles and reviews. For information write:

Master Books®, P.O. Box 726, Green Forest, AR 72638

Master Books® is a division of the New Leaf Publishing Group, Inc.

ISBN: 978-1-68344-085-7ISBN: 978-1-61458-599-2 (digital)

Printed in the United States of AmericaPlease visit our website for other great titles:

www.masterbooks.com

For information regarding author interviews, please contact the publicity department at (870) 438-5288.

Math Lessons for a

Living Education: Level 6

TEACHER GUIDE Includes Student Quizzes

Weekly Lesson Schedule

Quizzes

Solutions ManualLevel 6 Math

Permission is granted for copies of reproducible pages from this text to be made for use with immediate family members living in the same household. However, no part of this book may be reproduced, copied, broadcast, stored, or shared in any form beyond this use. Permission for any other use of the material must be requested by email from the publisher at [email protected].

MASTERBOOKSCurriculum

Author: Angela O’Dell

Master Books Creative Team:

Editor: Craig Froman

Design: Terry White

Cover Design: Diana Bogardus

Copy Editors: Judy Lewis

Craig Froman

Curriculum Review: Kristen Pratt Laura Welch Diana Bogardus

Author Bio: As a homeschooling mom and author, Angela O’Dell embraces many aspects of the Charlotte Mason method, yet knows that modern children need an education that fits the needs of this generation. Based upon her foundational belief in a living God for a living education, she has worked to bring a curriculum that will reach deep into the heart of home-educated children and their families. She has written over 20 books, including her history series and her math series. Angela’s goal is to bring materials that teach and train hearts and minds to find the answers for our generation in the never changing truth of God and His Word.

“Your reputation as a publisher is stellar. It is a blessing knowing anything I purchase from you is going to be worth every penny! —Cheri

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AffordableFlexibleFaith Building

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Table of Contents

Using This Course ...................................................................................................................................... 4Course Description .................................................................................................................................... 4Course Objectives ...................................................................................................................................... 5Suggested Daily Schedule ........................................................................................................................... 7Review and Quiz Section.......................................................................................................................... 15Solution Manual ...................................................................................................................................... 71Quiz Answers ......................................................................................................................................... 231Preview: Principles of Mathematics Book 1 (Chapter 1) ......................................................................... 255Preview: Principles of Mathematics Book 1 Teacher Guide (Chapter 1) .................................................. 281Multiplication Grid ................................................................................................................................ 303

4 Math Level 6

Using This Course

Features: The suggested weekly schedule enclosed has easy-to-manage lessons that guide the reading, worksheets, and all assessments. The pages of this guide are perforated and three-hole punched so materials are easy to tear out, hand out, grade, and store. Teachers are encouraged to adjust the schedule and materials needed in order to best work within their unique educational program.

Lesson Scheduling: Students are instructed to read the pages in their book and then complete the corresponding section provided by the teacher. Assessments that may include worksheets, activities, quizzes, and tests are given at regular intervals with space to record each grade. Space is provided on the weekly schedule for assignment dates, and flexibility in scheduling is encouraged. Teachers may adapt the scheduled days per each unique student situation.

Course DescriptionWelcome to the sixth course in the Math Lessons for a Living Education series! This math series is based on these unwavering realities: God does not separate our life lessons into subjects; everything touches something else. Likewise, His creation is woven together as a multifaceted, multi-dimensional display of His ingenious creativity. Any given element of the universe that He has created is fascinating to explore. You are challenged to look up and out in this study of mathematics. This course will help students review and master important skills as they prepare to move into more advanced coursework. Designed to present math concepts in the context of real life, the student learns to apply the rules and techniques to solving everyday problems.

Approximately 30 minutes per day, five days a week, for 36 weeks Quizzes are included to help reinforce learning and provide assessment opportunitiesWorksheets are included in the student book for each section

Designed for grade 6 in a one-year math course

Math Level 6 5

Course Objectives: Students completing this course will

D Investigate math through developing critical thinking skills DBecome familiar with whole numbers, averaging, rounding, and fractions D Identify decimal basics and using decimals in the real world DLearn how to work with percentages in the real world DStudy basics of geometry from pairs to polygons DDevelop maps, graphs and charts, units of measure, and more.

To the teacher: Mathematics and God’s relational character God teaches us through relationships. He is the One who set the example for this principle, using the perfect relationship between the members of the Trinity. He wants a relationship with us (John 3:16). Our children need a good relationship with us — not just for the sake of that relationship, but to lead them to Jesus. We cannot save our children’s souls, but our relationship with our children can build trust and lead them to the One who can. Our children need to know that everything they can learn about the world around them is already known by God.Think about this: the Alpha and the Omega, the Beginning and the End spoke, and His words created, and carried the power to set in motion everything in the world. God, the supreme architect, sent His words into the dark void and created the intricate, tiniest, most minute building blocks of matter, and then He taught them the secrets that keep them joining and bonding and creating larger building

blocks. And in the mix of all of this, He used the part of His wisdom and character that we humans call math. Psalm 19:1 says, “The heavens proclaim the glory of God. The skies display His craftsmanship.”Since God created it, math is a reflection of His character. God is absolute, consistent, and unchanging. No matter how many times His character and promises are tested, they come out true. As we learn about His creation (including operations with numbers!), our faith in His unwavering faithfulness is strengthened.Those of us who are His children can come and ask for wisdom. I hope you have chosen to accept Jesus as your Savior and Friend. If you have, you have the promise that God will help you and give you wisdom (James 1:5). “Fear of the Lord is the beginning of wisdom” (Prov. 9:10). This means that you can ask Him for help with learning!

6 Math Level 6

Math Level 6

Although this course was written mostly for the student, the story segments help the teacher build/strengthen a relationship with each student. The storyline of Math Lessons for a Living Education Book 6 is not merely written to introduce math concepts; it is meant to bring the element of character and relationship to the study of math. Children learn best when they can learn through relationship. The story in this course is prayerfully crafted to reach into many issues that children this age are facing . . . the question of a personal faith in God, the question of trust in God’s goodness even in the midst of hardship, the decision of letting God use pain for their good, etc. Read the story together, knowing that it is our tendency to push our children into independent learning at this age. Although a certain amount of independence is important, it is also extremely important that we maintain an element of closeness. Our children need contact with us more at this age than almost at any other time. Stay close. Stay plugged in. Stay involved.

• The concepts of math are a conversation between your student and the text. This Course is meant to grow your child’s faith in God, critical thinking ability, and confidence in their God-given ability.

• Quiz note: If you have used the previous courses in this series, you are aware that they contain very few quizzes or tests. This is because they are written in such a way that your child is consistently showing you what they know. Book 6 is also written in this way, BUT, because quiz and test taking is a skill that they need in life, they have been added in this teacher guide. If you, as the teacher, do not want your child to take every single lesson quiz, simply use the lesson practice and review. You decide what your student needs and adjust this course to fit them. Please also note that lesson 22 of this course is ten days worth of work on some additional, rather advanced concepts. Please preview this lesson and read the note at the beginning of it. Also note that there is an optional, but highly recommended, two-day student presentation at the end of the book. You may want to tell your student about it, so he or she can be thinking on what to present.

Note: There is a complete list of supplies in the student book.

Math Level 6 7

First Semester Suggested Daily Schedule

Date Day Assignment Due Date GradeFirst Semester-First Quarter

Week 1

Day 1Read Lesson 1: Working with Whole Numbers Pages 7-9 • Math Level 6 Student Book • (ML6) Complete Lesson 1 Exercise 1 • Pages 10-12 • (ML6)

Day 2 Complete Lesson 1 Exercise 2 • Page 13 • (ML6)

Day 3 Complete Lesson 1 Exercise 3 • Pages 14-15 • (ML6)



Week 2





Day 10 Complete Lesson 1 Exercise 10 Practice and Review Pages 27-28 • (ML6)

Week 3

Day 11 Complete Lesson 1 Quiz Pages 17-18 • Math Level 6 Teacher Guide • (TG)

Day 12Read Lesson 2: Whole Numbers in the Real World Pages 29-31 • (ML6) Complete Lesson 2 Exercise 1 • Page 32 • (ML6)




Week 4





Day 20 Complete Lesson 2 Quiz • Pages 19-20 • (TG)

Week 5

Day 21Read Lesson 3: Averaging, Rounding, and Roman Numerals Pages 49-50 • (ML6)Complete Lesson 3 Exercise 1 • Pages 51-53 • (ML6)





Week 6





Day 30 Read Lesson 4: Fractions • Pages 71-73 • (ML6)Complete Lesson 4 Exercise 1 • Pages 74-76 • (ML6)

8 Math Level 6

Date Day Assignment Due Date Grade

Week 7






Week 8



Day 38 Read Lesson 5: Working with Factors • Pages 91-92 • (ML6)Complete Lesson 5 Exercise 1 • Pages 93-94 • (ML6)



Week 9






First Semester-Second Quarter

Week 1


Day 47Read Lesson 6: More about Fractions - Mixed Numbers Page 111 • (ML6)Complete Lesson 6 Exercise 1 • Pages 112-114 • (ML6)




Week 2





Day 55Read Lesson 7: Using Factors and Multiples in Operations Pages 129-130 • (ML6)Complete Lesson 7 Exercise 1 • Pages 131-132 • (ML6)

Week 3






Math Level 6 9


Week 4



Day 63Read Lesson 8: Review of Fraction Concepts Pages 145-146 • (ML6)Complete Lesson 8 Exercise 1 • Pages 147-148 • (ML6)



Week 5




Day 69Read Lesson 9: Adding and Subtracting Fractions and Mixed Numbers • Pages 155-156 • (ML6)Complete Lesson 9 Exercise 1 • Pages 157-158 • (ML6)


Week 6






Week 7


Day 77Read Lesson 10: Multiplying and Dividing Fractions Pages 173-174 • (ML6)Complete Lesson 10 Exercise 1 • Pages 175-176 • (ML6)




Week 8



Day 83 Complete Lesson 10 Exercise 7 Practice and Review Page 188 • (ML6)


Day 85Read Lesson 11: Comprehensive Review of all Advanced Fractional Concepts • Pages 189-190 • (ML6)Complete Lesson 11 Exercise 1 • Pages 191-192 • (ML6)

Week 9




Day 89 Complete Lesson 11 Quiz • Page 39 • (TG)

Day 90 Read Lesson 12: Decimal Basics • Pages 201-202 • (ML6)Complete Lesson 12 Exercise 1 • Pages 203-204 • (ML6)

Mid-Term Grade

Math Level 6 11

Second Semester Suggested Daily Schedule

Date Day Assignment Due Date GradeSecond Semester-Third Quarter

Week 1






Week 2


Day 97Read Lesson 13: More Work with Decimals Pages 217-218 • (ML6) Complete Lesson 13 Exercise 1 • Pages 219-220 • (ML6)




Week 3






Week 4

Day 106Read Lesson 14: Using Decimals in the Real World Pages 239-240 • (ML6)Complete Lesson 14 Exercise 1 • Pages 241-243 • (ML6)





Week 5



Day 113 Read Lesson 15: Percents • Pages 259-260 • (ML6)Complete Lesson 15 Exercise 1 • Pages 261-262 • (ML6)



Week 6






12 Math Level 6


Week 7


Day 122Read Lesson 16: Using Decimals and Percents in the Real World — Savvy Shopping • Pages 277-278 • (ML6)Complete Lesson 16 Exercise 1 • Pages 279-280 • (ML6)




Week 8



Day 128Read Lesson 17: Comprehensive Review of Fractions, Decimals, and Percents • Pages 287-288 • (ML6)Complete Lesson 17 Exercise 1 • Pages 289-290 • (ML6)



Week 9


Day 132 Complete Lesson 17 Narration Quiz • Pages 51-52 • (TG)

Day 133 Read Lesson 18: Geometry • Page 295 • (ML6)Complete Lesson 18 Exercise 1 • Pages 296-298 • (ML6)



Second Semester-Fourth Quarter

Week 1






Week 2




Day 144 Read Lesson 19: Maps! • Page 325 • (ML6)Complete Lesson 19 Exercise 1 • Pages 326-328 • (ML6)


Week 3





Day 150 Read Lesson 20: Graphs and Charts • Page 337 • (ML6)Complete Lesson 20 Exercise 1 • Pages 338-339 • (ML6)

Math Level 6 13


Week 4






Week 5




Day 159 Read Lesson 21: Units of Measure • Page 355 • (ML6)Complete Lesson 21 Exercise 1 • Pages 356-357 • (ML6)


Week 6

Day 161 Complete Lesson 21 Exercise 3 • Pages 361-362 • (ML6) Day 162 Complete Lesson 21 Exercise 4 • Pages 363-364 • (ML6)


Day 164 Complete Lesson 21 Exercise 6 Practice and Review •Page 368 • (ML6)


Week 7

Day 166 Read Lesson 22: Additional Topics • Page 369 • (ML6) Complete Lesson 22 Exercise 1 • Pages 370-371 • (ML6)





Week 8




Day 174 Complete Lesson 22 Exercise 8 Practice and Review — Hands-on exploration of circles • Page 386 • (ML6)

Day 175 Complete Lesson 22 Narration Quiz • Page 63 • (TG)

Week 9

Day 176 Cumulative Review, part 1 • Page 15 • (TG)

Day 177 Cumulative Review, part 2 • Page 16 • (TG)

Day 178 Complete Final Exam • Pages 65-68 • (TG)

Day 179 Optional End of Year Show and Tell • Page 69 • (TG)

Day 180 Optional End of Year Show and Tell • Page 70 • (TG)

Final Grade

Math Level 6 15

Review & Quiz Section

Cumulative Review, part 1 You will need these materials: 1. Your math book or notebook if you have been removing the pages as you go

2. A white board / markers / eraser

3. Your teacher

Check off each one as you complete it. Look through each lesson carefully. If there are any areas of concern, take the time to work through the concept in question, using your whiteboard and discussing it thoroughly with your teacher.

Lesson 1: Working with Whole Numbers

Lesson 2: Whole Numbers in the Real World

Lesson 3: Averaging, Rounding, and Roman Numerals

Lesson 4: Fractions

Lesson 5: Working with Factors

Lesson 6: More About Fractions — Mixed Numbers

Lesson 7: Using Factors and Multiples in Operations

Lesson 8: Review of Fraction Concepts

Lesson 9: Adding and Subtracting Fractions and Mixed Numbers

Lesson 10: Multiplying and Dividing Fractions

16 Math Level 6

Cumulative Review, part 2You will need these materials: 1. Your math book or notebook if you have been removing the pages as you go

2. A white board / markers / eraser

3. Your teacher

Check off each one as you complete it. Look through each lesson carefully. If there are any areas of concern, take the time to work through the concept in question, using your whiteboard and discussing it thoroughly with your teacher.

Lesson 12: Decimal Basics

Lesson 13: More Work with Decimals

Lesson 14: Using Decimals in the Real World

Lesson 15: Percents

Lesson 16: Using Decimals and Percents in the Real World — Savvy Shopping

Lesson 18: Geometry

Lesson 19: Maps!

Lesson 20: Graphs and Charts

Lesson 21: Units of Measure

17Math Level 6 – Quiz Section

Quiz 1 Day 11

10 problems - 10 points each1. Write these numbers vertically and add them. Circle the one(s) that used carrying.

a. 342 + 652 + 702 = b. 892 + 128 + 286 =

2. Now round all of the numbers in the problems 1a and 1b and estimate the sum of each addition problem. Optional: auditory learners may do this orally.

3. Write these numbers vertically and subtract. Circle the one(s) that used borrowing. a. 672 – 599 = b. 76,984 – 33,218 =

4. Now round all of the numbers in the problems 3a and 3b and estimate the answer of each subtraction problem. Optional: auditory learners may do this orally.

5. Write these numbers vertically and multiply them. Circle the one(s) that used carrying. a. 419 x 503 = b. 7,891 x 888 =

6. Now round all of the numbers in the problems 5a and 5b and estimate the answer of each multiplication prob-lem. Optional: auditory learners may do this orally.

Name

18 Math Level 6 – Quiz Section

Quiz 1 Day 11

7. Divide. Next to each problem, use rounding to estimate the answer. a. 735 ÷ 23 = b. 9,451 ÷ 45 =

8. What are the three ways of writing a division problem? Show them using 9 as the dividend and 3 as the divisor.

9. Write the divisibility rules for: Dividing 2:

Dividing 5:

Dividing 9:

Dividing 3:

Dividing 4:

10. Multiplication facts! Complete your multiplication drill.

Name


Quiz 1 Day 168Quiz 1 Day 168Quiz 1 Day 168Quiz 2 Day

20

20 problems, 5 points each1. If you had a list of monthly expenses and bills, how would you find out what your monthly budget should be?

Why?

2. If you knew you had a certain amount of money in your bank account, how would you keep track of your current amount as you took money out to pay for your expenses? Why?

3. If you got a job that paid $15 for every hour you worked, how would you figure out what your paycheck should be after working 35 hours? Why?

4. Use the answer to problem 3 to solve. How much money would you have after working 4 weeks of work 35 hrs/week?

5. When you come across a story problem that has too much information, what are the four steps you would follow to find the answer?

What are the clue words for: 6. adding

7. multiplying

8. subtracting

9. dividing

10. Circle the number that you would enter into your calculator first to solve this problem. 81,918 ÷ 9 =

Solve each problem using regular calculation. Check with your calculator. Draw your calculator’s buttons next to each problem to show how you would enter the numbers to solve each problem. 11. 62,215 + 3,110 + 4,879 =

12. 3,862 - 2,998 =

13. 3,871 x 382 =

Name


Quiz 2 Day 20

14. The mountain climber was determined to climb Mount McKinley. In his first attempt, he climbed 16,385 feet before turning back. In his second attempt, he got dizzy at 14,310 feet and had to return to his base camp. Finally, in his final attempt, he reached the 20,310 foot summit. Write and solve equations showing how close he got to the summit in each of his first two attempts.

15. How many feet did he climb altogether?

16. If the family grocery budget is $7,200 per year, how much do they spend on groceries each month?

17. If their total monthly budget is $4,600, how much do they have left after the grocery budget is spent?

18. How much is their total yearly budget? If they save $300 per month, how much do they save a year?

19. Write your own multi-step story problem using clue words for addition and subtraction. Solve your problem.

20. Write your own multi-step story problem using clue words for multiplication and division. Solve your problem.

Name


Day 168Day 168Day 168Final Exam Day 178

25 problems - 4 points each1. Write 923,805,001 in number words. 2. Reduce these fractions by using factoring and cancellation.

(a) 320740 (b) 680

990 (c) 7001,100

3. Factor these numbers down to their prime factors by using factoring trees. (a) 615 (b) 850 (c) 384

4. 14 ÷ 37 = 5. 2 5

9 x 6 12 =

6. 3 14 + 1 4

5 – 4 310 =

7. Explain in detail when you should use GCF.

8. Explain in detail when you should use LCM.

9. What is 2% written as a decimal? _____________ as a fraction? ____________

Name


10. Write 65% as a reduced fraction.

11. Write 4.52 as a percent.

12. Percent means ______________ ___________________.

13. What is 30% of 550?

14. What is 10% of $75.69?

With your protractor, draw these angles. Label them. 15. Acute angle 80° 16. Obtuse angle 170°

17. Find the perimeter of these shapes: A square with 12-foot sides and a rectangle with sides that are 22 feet long and 16 feet long.

18. What is the difference between a line and a segment?

19. How are circles labeled?

20. What is the diameter of a circle that has a 9.5 feet radius?

Quiz 1 Day 168Quiz 1 Day 168Quiz 1 Day 168Final Exam Day 178 Name

71Math Level 6 – Solutions Manual

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72 Math Level 6 – Solutions Manual

13M

ath Level 6 – Lesson 1

Nam

e

E

xercise 2D

ay 2

Rounding tricks

When w

e work w

ith numbers, w

e often need to round them to m

ake it easier to do computations w

ith them. For

example, w

e may need to quickly estim

ate what several large num

bers are all together. It is important to know

the process of rounding and estim

ating. I am

going to teach you some fun tricks to rem

ember w

hen you are rounding, but first let’s review the steps of

rounding.

Example: Round 3

67 to the hundreds place.

Decide w

hat two “hundreds” 3

67 is betw

een. 30

0 and 40

0 U

nderline the digit in the place to which you are rounding. (3)

Trick #1: Ask the neighbor num

ber if you should round to the smaller hundred or the larger hundred. Is the

neighbor number to the right (6) five or bigger? If it is, round to the bigger hundred. If it is sm

aller than five, round to the sm

aller hundred. Trick #2: Turn all the neighbors to the right of the place to w

hich you are rounding into place holder zeros. 367

becomes 4

00

.

Now

you try it: Round these num

bers to the ten’s place. 1.

423 4

20

2. 4

5 50

3. 391 3

90

4. 56 6

0

5. 1,2

57 1,2

60

Round these numbers to the hundred’s place.

6. 23,4

90

23,5

00

7. 823 8

00

8. 12

7,94

7 127,9

00

9. 30

9 30

0

10. 989 1,0

00

Round these numbers to the thousand’s place.

11. 34

,980

35,0

00

12. 5,4

59 5

,00

0

13. 178,2

51 178

,00

0

14. 29,5

89 3

0,0

00

15. 1,474

,910

1,475

,00

0

16. Use Your W

ords! Explain the process of rounding.

14M

ath Level 614

Math Level 6 – Lesson 1

Nam

e

E

xercise 3D

ay 3

Addition (short and long)

Num

bers are amazing, aren’t they? Th

ey can show how

many socks w

e own, or they can show

how m

any socks our w

hole family ow

ns. When w

e want to com

bine two or m

ore numbers, w

e use an operation called adding. By adding tw

o numbers (addends) together, w

e come up w

ith an answer called the sum

. Remem

ber, addends may be added in

any order without changing the sum

. Let’s start w

ith a review of sim

ple addition. W

e can add horizontally.

1. 20

+ 6 = 2

6

2. 3

4 + 10

= 44

3. 4

2 + 8

= 50

4. 90

+ 6 = 9

6

5. 3

5 + 4

= 39

6. 12

+ 12 = 2

4

We can add vertically.

7.

46

+ 23

8.

85

+ 14

9.

13+ 14

10.

68

+ 11

11.

54

+ 14

12.

76+ 13

We can add w

ith carrying. In this problem

, when w

e add the one’s column, w

e end up with m

ore than what can fit in the one’s place (a num

ber larger than 9). Th

is means that w

e have to carry the group of ten up to the top of the ten’s column and add it to the

rest of the tens.

Example:

56

+ 1672 1

Example:

11367

134

+ 50

1

1,00

2

Add w

ith carrying.

13.

239

+ 34

14.

567

+ 189

15.

199

+ 1

16.

469

+ 11

17.

613

+ 18

18.

399

+ 10

69

99

27

7968

89

273

480

63

14

09

756

20

0

111

1

111

1



15M

ath

Leve

l 6 –

Les

son

1

Nam

e

E

xerc

ise

3D

ay

3

You

can

add

mor

e th

an tw

o nu

mbe

rs.

Hor

izon

tal a

dditi

on.

19. 1

2 +

34

+ 10

= 5

6

20

. 31 +

17 +

11 =

59

21

. 10

+ 5

+ 13 =

28

Vert

ical

add

ition

.

22.

124 12

+ 1

5

23.

56 13

+ 1

1

24

.

354

45

+ 1

0

You

can

use

roun

ding

to e

stim

ate

the

answ

er to

an

addi

tion

prob

lem

by

roun

ding

the

adde

nds b

efor

e ad

ding

. This

will

giv

e yo

u an

est

imat

ed a

nsw

er. F

or e

xam

ple:

610

+ 4

89

60

0+

50

0

1,10

0

Now

you

try

som

e:Ro

und

to e

stim

ate

the

sum

s. G

raph

ics,

thes

e ne

ed to

be

laid

out

like

the

sam

ple.

25.

439

+ 2

27

26.

98

1+

238

27.

56

1+

484

2

8.

735

+ 6

52

29.

Use

You

r Wor

ds! E

xpla

in th

e pr

oces

s of a

ddin

g w

ith c

arry

ing.

151

80

40

9

11

1

700

+ 70

0

1,4

00

40

0+

20

0

60

0

1,0

00

+ 20

0

1,20

0

60

0+

50

0

1,10

0

16M

ath

Leve

l 616

Mat

h Le

vel 6

– L

esso

n 1

Nam

e

E

xerc

ise

4D

ay

4

The

Shor

t and

Lon

g of

Sub

trac

tion

Wha

t hap

pens

whe

n yo

u lo

se a

pai

r of s

ocks

, and

you

r mom

ask

s you

how

man

y yo

u ha

ve le

ft? Y

ou k

now

you

use

d to

hav

e 10

pai

rs o

f soc

ks, b

ut y

ou lo

st o

ne, w

hen

you

cam

e in

from

pla

ying

in th

e sn

ow, o

nly

to re

aliz

e th

at y

our

boot

had

eat

en y

our f

avor

ite p

air,

and

now

ano

ther

pai

r has

bee

n lo

st fo

reve

r in

the

clut

ter u

nder

you

r bro

ther

’s be

d.

Thin

gs a

ren’

t loo

king

so g

ood

for y

our s

ock

draw

er! Y

ou st

op to

thin

k, I

used

to h

ave

10 p

airs

of s

ocks

, but

my

boot

s at

e 1

pair,

and

then

my

brot

her’s

clut

ter c

laim

ed a

noth

er p

air…

so th

at’s

10 m

inus

(tha

t mea

ns ta

ke aw

ay) 1

is 9

, and

9

min

us 1

is 8

. If t

his k

eeps

up,

I’m

goi

ng to

run

out o

f soc

ks b

efor

e th

e en

d of

the

win

ter!

But y

ou tr

y to

stay

pos

itive

as

you

ans

wer

you

r mom

, “I h

ave

8 pa

irs o

f soc

ks le

ft, M

om. A

t lea

st I

still

hav

e on

e fo

r eve

ry d

ay o

f the

wee

k, p

lus

one

mor

e ju

st in

cas

e…”

So, w

hat d

oes t

hat l

ook

like

on p

aper

?

Exam

ple:

10

- 1 =

9

9 -

1 =

8

We

can

subt

ract

hor

izon

tally

. 1.

26 –

4 =

22

2.

54

– 2

= 5

2

3. 4

9 –

8 =

41

4. 9

8 –

6 =

92

5. 6

7 –

4 =

63

6.

12 –

12 =

0

We

can

subt

ract

ver

tical

ly.

7.

56

– 2

2

8.

95

– 3

4

9.

32

– 1

1

10.

65

– 1

1

11.

54

– 2

4

12.

66

– 1

6

We

can

subt

ract

whe

re w

e ha

ve to

bor

row

a

grou

p of

ten

from

the

ten’s

pla

ce.

We

can

subt

ract

whe

re w

e ha

ve to

bor

row

a g

roup

of t

en

from

the

ten’s

pla

ce a

nd a

nd g

roup

of a

hun

dred

from

th

e hu

ndre

d’s p

lace

.

Exam

ple:

356

– 237

1191

4

Exam

ple:

823

– 6

54

1691

117

34

61

21

54

30

50



17M

ath Level 6 – Lesson 1

Nam

e

E

xercise 4D

ay 4

Subtract. Circle the problem

s in which you used borrow

ing.

13.

24

5– 2

31

14

14.

478

– 399

79

1613

15.

1123– 158

16.

798

11– 7

56

225

17.

61

67

11– 4

45

226

18.

387

– 222

165

Using the sam

e process, try these:

19.

512

111

6,2

311

– 4,9

99

1,232

20.

1 123,6

12– 19

,212

4,4

00

21.

99

91

11

10,0

00

– 999

9,0

011

22.

1210

491

51,3

09

– 24

,64

8

26

,66

11

23.

183,2

72

– 61,15

1

122

,1211

We can use rounding to estim

ate an answer in a subtraction problem

by rounding the minuend and the subtrahend

before finding the estimated difference.

For example:

910

– 750

90

0– 8

00

100

Now

you try it!

24.

823

– 189

25.

612

– 477

26.

952

– 899

27.

215

– 173

28. Use Your W

ords! Explain the process you used to solve problem 14 of this exercise.

Round to the nearest 10

0.

20

0– 2

000

80

0– 2

00

60

0

60

0– 5

00

100

1,00

0– 9

00

100

1

18M

ath Level 618


Nam

e

E

xercise 5D

ay 5

Multiplication Basics and M

ultiplication Facts Review

In your previous years of studying m

ath, you have learned that skip counting is another way to learn the factors in a

multiplication fam

ily. When you skip count by 2, you use this pattern:

2, 4

, 6, 8

, 10, 12

, 14, 16

, 18, 2

0…

(1x2) (2

x2) (3

x2) (4

x2) (5

x2) (6

x2) (7x2

) (8x2

) (9x2

) (10x2

)

As you can see, you are adding another group of 2 to each num

ber to get the next number. You are probably very

familiar w

ith counting by 2s . Explain to your teacher how

skip counting is related to multiplication. In the follow

ing problem

s, show how

skip counting and multiplication go together, like I did w

ith the 2s above. 1.

Skip count by 3 to 30: 3

, 6, 9

, 12, 15

, 18, 2

1, 24

, 27, 3

0

(1x3

) (2x3

) (3x3

) (4x3

) (5x3

) (6x3

) (7x3) (8

x3) (9

x3) (10

x3)

2. Skip count by 4

to 40: 4

, 8, 12

, 16, 2

0, 2

4, 2

8, 3

2, 3

6, 4

0

(1x4

) (2x4

) (3x4

) (4x4

) (5x4

) (6x4

) (7x4) (8

x4) (9

x4) (10

x4)

3. Skip count by 5 to 5

0: 5, 10

, 15, 2

0, 2

5, 3

0, 3

5, 4

0, 4

5, 5

0

(1x5) (2

x5) (3

x5) (4

x5) (5

x5) (6

x5) (7x5

) (8x5

) (9x5

) (10x5

)


0: 6, 12

, 18, 2

4, 3

0, 3

6, 4

2, 4

8, 5

4, 6

0

(1x6) (2

x6) (3

x6) (4

x6) (5

x6) (6

x6) (7x6

) (8x6

) (9x6

) (10x6

)

5. Skip count by 7 to 70: 7, 14

, 21, 2

8, 3

5, 4

2, 4

9, 5

6, 6

3, 70

(1x7) (2

x7) (3x7) (4

x7) (5x7) (6

x7) (7x7) (8x7) (9

x7) (10x7)


0: 8, 16

, 24

, 32, 4

0, 4

8, 5

6, 6

4, 72

, 80

(1x8

) (2x8

) (3x8

) (4x8

) (5x8

) (6x8

) (7x8) (8

x8) (9

x8) (10

x8)


0: 9, 18

, 27, 3

6, 4

5, 5

4, 6

3, 72

, 81, 9

0

(1x9) (2

x9) (3

x9) (4

x9) (5

x9) (6

x9) (7x9

) (8x9

) (9x9

) (10x9

)


0: 10, 2

0, 3

0, 4

0, 5

0, 6

0, 70

, 80

, 90

, 100

(1x10

) (2x10

) (3x10

) (4x10

) (5x10

) (6x10

) (7x10) (8

x10) (9

x10) (10

x10)

9. Review

your multiplication facts. C

omplete your lam

inated multiplication drill from

the appendix of this book. If there are any that you need to practice, m

ake flashcards to drill them until you know

them very w

ell.



19M

ath

Leve

l 6 –

Les

son

1

Nam

e

E

xerc

ise

6D

ay

6

Long

Mul

tiplic

atio

nN

ow th

at w

e ha

ve re

view

ed th

e ba

sics o

f mul

tiplic

atio

n, le

t’s m

ove

on a

nd re

ally

stre

tch

our m

inds

! Stu

dy th

e st

eps i

n th

e ex

ampl

e:

55

x 1

5

275

+ 5

50

825

Now

you

try

it:

1.

411

x 2

2

22

+ 8

80

90

2

1

2.

64

x 1

2

128

+ 6

40

76

8

3.

88

x 1

1

88

+ 8

80

96

8

1

4.

230

x 1

2

460

+ 2

,30

0

2,7

60

5.

30

11x

15

1,50

5+

3,0

10

4,5

15

6.

412

x 3

4

1,64

8+

12,3

60

14,0

08

11

Now

let’s

mak

e th

e nu

mbe

rs b

igge

r! Yo

u w

ill n

eed

to u

se c

arry

ing.

Stu

dy th

e ex

ampl

e:

24

5x

110

00

024

50

+ 2

450

0

26,9

50

Now

you

try

it!

7.

398

x 6

45

1,990

15,9

20

+ 2

38,8

00

256,7

10

112

8.

1,24

7x

40

9

11,2

23

00

,00

0+

498,8

00

510

,023

1

11

9.

723

x 5

79

6,5

07

50

,610

+ 3

61,50

0

418

,617

1

1

10.

1

3,6

22

x 1

,275

18,110

253,5

40

724

,40

0+

3,6

22,0

00

4,6

18,0

50

11

1

1. M

ultip

ly t

he top

fac

tor

by t

he n

umbe

r in t

he o

ne’s p

lace

of

the

bottom

fac

tor.

2. Place

a z

ero

to h

old

the

one’

s plac

e an

d th

en m

ultip

ly t

he top

fac

tor

by t

he

num

ber

in t

he ten

’s p

lace

of

the

bottom

fac

tor

3. A

dd b

oth

part

ial f

acto

rs tog

ethe

r to

com

plet

e th

e pr

oblem

.Th

is z

ero

is a

pl

ace

hold

er. Yo

u w

ill n

eed

2 pl

ace

hold

er z

eros

, one

for

the

one’

s pl

ace

and

one

for t

he te

n’s

plac

e.

Follo

w th

e sa

me

step

s as

bef

ore.

20

Mat

h Le

vel 6

20

Mat

h Le

vel 6

– L

esso

n 1

You

can

use

roun

ding

to e

stim

ate

in m

ultip

licat

ion

by ro

undi

ng e

ach

of th

e fa

ctor

s bef

ore

mul

tiply

ing

them

to fi

nd

the

estim

ated

pro

duct

. This

exam

ple

show

s a m

ultip

licat

ion

prob

lem

with

one

larg

e fa

ctor

(30

3) a

nd o

ne sm

alle

r fa

ctor

(4).

You

can

use

the

sam

e pr

oces

s with

larg

er p

robl

ems,

simpl

y by

roun

ding

bot

h nu

mbe

rs a

nd m

ultip

lyin

g lik

e us

ual.

Exam

ple:

30

3x

4

30

0x

4

1,20

0

You

try

a fe

w! Th

e fir

st o

ne is

don

e fo

r you

.

11.

12.

782

x

89

13

.

923

x

52

14. U

se Y

our W

ords

! Exp

lain

the

proc

ess y

ou w

orke

d th

roug

h in

pro

blem

9 o

f thi

s exe

rcise

. A

nsw

ers w

ill v

ary

but s

houl

d be

sure

to m

entio

n us

ing

plac

e ho

lder

zero

s whe

n ad

ding

to so

lve

a m

ultip

licat

ion

prob

lem

.

Nam

e

E

xerc

ise

6D

ay

6

80

0x

90

72,0

00

90

0x

50

45,0

00

54

4x

67

50

0x

70

35,0

00

Not

e: I

multip

lied

5 x

7

and

then

add

ed

the

num

ber

of z

eros

bot

h fa

ctor

s ha

d

(3 z

eros

).



21


Nam

e

E

xercise 7D

ay 7

Division basics

You have learned that addition and subtraction are related. In the space below, 1.

Use Your N

oodle — draw

a doodle! showing how

addition and subtraction go together. A

nswers w

ill vary.

2. N

ow, let’s quickly review the concept of division! If you have 6 cookies, and your m

om says, “Th

at’s way too

many! Share half of those w

ith your brother!” How

many cookies w

ill each of you have? 3 That’s division. H

ow

did you do it? Draw

a doodle below. Underneath that, draw

a doodle of how m

ultiplication and division are related. A

nswers w

ill vary.

3. D

o a quick review of your division facts! Study these m

ultiplication facts and write the m

atching division facts that go w

ith them.

Example:

12 x 12

= 144

division: 14

4 ÷ 12

= 12

3 x 4

= 12

division: 12 ÷

4 = 3

or 12 ÷

3 = 4

5 x 3

= 15

division: 15 ÷

3 = 5

or 15 ÷

5 = 3

9 x 3

= 27

division: 27 ÷

3 = 9

or 27 ÷

9 = 3

4 x 4

= 16

division: 16 ÷

4 = 4

5 x 6

= 30

division: 3

0 ÷

6 = 5

or 30

÷ 5 =

6

Now

you write three m

ultiplication equations and their matching division facts.

a. Answ

ers will vary.

b. Answ

ers will vary.

c. Answ

ers will vary.

22

Math Level 6

22


What if you w

anted to divide a dividend by a divisor and the quotient doesn’t come out even? W

hat if there is som

ething remaining? D

on’t worry —

when this happens, you have a rem

ainder! This can happen in sim

ple division equations, as w

ell as long division.Exam

ple: 1

1R.1

22

3

20321

–

2.

3R.2

41

4

12

02

–

3.

2R.2

51

2

10

02

–

4.

3R.2

62

0

18

02

–

5.

4R.2

73

0

28

02

–

6.

13

R.2

45

4

414

122

––

7.

6R.4

74

6

424

–

8.

15

R.4

57

9

529

244

––

9.

4R.1

2981

–

Use Your W

ords! Explain the process you worked through in problem

5 of this exercise.A

nswers w

ill vary but should include some m

ention of dividing and having a remainder left over.

Nam

e

E

xercise 7D

ay 7



23

Mat

h Le

vel 6

– L

esso

n 1

Nam

e

E

xerc

ise

8D

ay

8

Div

isio

n tr

icks

and

thre

e w

ays o

f wri

ting

divi

sion

You

may

hav

e le

arne

d in

you

r pre

viou

s yea

rs o

f mat

h st

udy

that

div

ision

has

a fe

w tr

icks

up

its sl

eeve

, whi

ch m

ake

it ea

sier t

o w

ork

out a

div

ision

equ

atio

n.

Stud

y th

em b

elow

:

872

231

3

28

9

0

810

3

3

54

765

Usin

g th

e nu

mbe

rs a

bove

, writ

e th

em o

n th

e lin

es b

elow

nex

t to

all t

he n

umbe

rs th

ey a

re d

ivisi

ble

by. Th

e fir

st o

ne is

do

ne fo

r you

.1.

D

ivisi

ble

by 2

: 872

3

28

90

81

0

54

2.

Div

isibl

e by

3: 2

31

90

81

0

33

765

3.

Div

isibl

e by

4: 8

72

328

5

4

4.

Div

isibl

e by

5: 9

0

810

76

5

5.

Div

isibl

e by

6: 9

0

810

54

6.

Div

isibl

e by

8: 8

72

328

7.

Div

isibl

e by

9: 9

0

810

54

7

65

8.

Div

isibl

e by

10:

90

81

0

Opt

iona

l: If

you

are

stru

gglin

g w

ith a

ny o

f the

div

isibi

lity

rule

s, ta

ke th

e tim

e no

w to

stud

y an

d re

view

them

. You

may

wan

t to

mak

e fla

sh c

ards

to k

eep

on h

and

thro

ugho

ut y

our s

choo

l yea

r. Re

view

of t

he th

ree

way

s of w

ritin

g a

divi

sion

prob

lem

.

÷

A n

umbe

r is

divisib

le b

y 2 if

it is

an

even

num

ber.

A n

umbe

r is

divisib

le b

y 5 if

the

one

’s d

igit

is 0

or

5.

A n

umbe

r is

divisib

le b

y 10

if t

he o

ne’s d

igit

is 0

.

A n

umbe

r is

divisib

le b

y 3 if

the

sum

of

the

digits

is d

ivisi

ble

by 3

.

A n

umbe

r is

divisib

le b

y 6 if

it is

divisi

ble

by 2

and

3.

Any

num

ber

is divisib

le b

y 8 if

the

last

thr

ee d

igits

are

divisi

ble

by 8

.

A n

umbe

r is

divisib

le b

y 9 if

the

sum

of

the

digits

is d

ivisi

ble

by 9

.

A n

umbe

r is

divisib

le b

y 4

if t

he la

st t

wo

digits

are

bot

h ze

ros,

or if

the

y ar

e divisib

le b

y 4

.

24

Mat

h Le

vel 6

24

Mat

h Le

vel 6

– L

esso

n 1

30

divided

by

5

30

÷5

30

53

05

You

try

it! W

rite

each

div

ision

sent

ence

in a

ll th

ree

way

s. 9.

65 d

ivided

by

5

65

÷5

65

56

55

10.

72 d

ivided

by

8

72

÷8

72

87

28

11.

56 d

ivided

2

56

÷2

56

25

62

12.

320

divided

by

3

32

0÷

3

32

0

33

20

3

13.

90

divided

by

10

90

÷1

0

90

10

90

1 0

14.

81 divide

d by

9

81

÷9

81

98

19

15.

40

divided

by

8

40

÷8

40

84

08

Nam

e

E

xerc

ise

8D

ay

8



25


Nam

e

E

xercise 9D

ay 9

Long divisionToday, w

e are going to tackle reviewing long division. To refresh your m

ind on the process, study the examples

below. The first one show

s a one-digit divisor, while the second one show

s a two-digit divisor. R

emem

ber: the steps of division are 1. divide 2. m

ultiply 3. subtract 4. bring down the next num

ber 5. repeat if needed. Exam

ples:

Now

you try it!

1.

15

2

34

58

315

150

8

062

R.2

––

–

2.

19

7

91

78

1

988

81

07

1

638

R.8

–

–

–

,

3.

,

–

18

02

47

21

0

432

320

101082

R.2

––

–

,

4. 5

34

12

64

12

604

1

365

2

484

–

–

R.4

–

,

5.

40

6

20

81

20

801

20

12

0

12

00

–

–– ,

6.

–

10

72

12

12

86

4

120

8086

842

4

240

–

–

– , ,

46

64

R.2

73

26

50

284

6

424

5

423

0

282

–

–

– , ,3

02

2R.3

22

66

48

7

660

4048

444

7

443

–

–

– , ,

26

Math Level 6

26


You can use rounding to estimate the quotient of a division problem

by first rounding both the dividend and the divisor before dividing. Exam

ple: 32

1 ÷ 31 =

30

0 ÷ 3

0 = 10

Now

you try it! Round the dividend and the divisor to quickly find the estimated answ

er of each problem.

7. 562 ÷ 12

=

8. 912

÷ 29 =

9. 1,178

÷ 63 =

60

0 ÷

10 = 6

0

90

0 ÷

30

= 30

1,2

00

÷ 6

0 = 2

0

10. 469 ÷ 4

6 =

11. 3

82 ÷ 4

1 =

50

0 ÷

50

= 10

40

0 ÷

40

= 10

Use Your W

ords! Explain the process you worked through in problem

2 of this exercise.A

nswers w

ill vary but should include discussion of long division.

Simply round each num

ber to the nearest largest place value. In this case you are rounding the dividend to the hundred’s place and the divisor to the ten’s place.

Nam

e

E

xercise 9D

ay 9



27

Mat

h Le

vel 6

– L

esso

n 1

Nam

e

E

xerc

ise 10

Day

10

Prac

tice

and

Rev

iew

Pl

ease

use

this

exer

cise

to p

ract

ice

any

conc

epts

with

whi

ch y

ou m

ay h

ave

diffi

culti

es, i

n pr

epar

atio

n fo

r you

r les

son

quiz

. A

dd:

1.

452

65

11+

714

1,8

17

1

2.

89

11+

662

1,553

1

3.

112

3,7

42

+ 72

3,9

47

84

7,689

Subt

ract

:

4.

317

181

34

,982

– 12

,999

21,

983

5.

216

101

723,1

74

– 4

12,9

99

310

,175

6.

98

112

6,8

90

,64

5–

101,

777,9

44

25,1

12,7

011

Mul

tiply

:

7.

823

x 28

6,5

84

+ 16

,460

23,0

44

11 1

8.

1

1 2

2,1

96

x 3

27

15,3

72

43,9

20

+ 658,8

00

718

,092

9.

11

11

32,8

90

x 6

31

32,8

90

986

,70

0+

19,7

34

,00

0

20

,753,5

90

Div

ide:

10.

54

12

65

2

60 5

2

48 4

R.4

–

–

1

1.

27

2

32

87

14

64

23

1

22

4 74

64

10

R.10

– –

–

12.

14

17

65

92

12

7

65

27

1

26

0

11

2

65

47

7

45

5

22

R.2

2

– –

–,

–

,

28

Mat

h Le

vel 6

28

Mat

h Le

vel 6

– L

esso

n 1

13. R

ound

ing:

In

this

spac

e, w

rite

the

first

pro

blem

of e

ach

of th

e pr

evio

us se

ctio

ns in

this

exer

cise

(pro

blem

s 1, 4

, 7, a

nd 1

0). U

se

roun

ding

to e

stim

ate

the

answ

er to

eac

h on

e.

1.

50

070

0+

700

1,90

0

4.

30

,00

0–

10,0

00

20

,00

0

7.

80

0x

30

24

,00

0

10.

700

÷ 10

= 7

0

Ora

l Rev

iew

: 14

. The

step

s of r

ound

ing

U

nder

line

the

digi

t to

whi

ch y

ou a

re ro

undi

ng. L

ook

at th

e di

git i

n th

e pl

ace

to th

e rig

ht o

f tha

t pla

ce. I

f it i

s 4 o

r les

s, ro

und

to th

e sa

mlle

r am

ount

. If i

t is 5

or m

ore,

roun

d to

the

larg

er a

mou

nt.

15. Th

e st

eps o

f add

ing

with

car

ryin

g an

d su

btra

ctin

g w

ith b

orro

win

g Ex

plai

ned

on p

ages

20

(add

ing)

and

22

(sub

trac

ting)

.

16. Th

e st

eps o

f mul

tiplic

atio

n w

ith c

arry

ing

Expl

aine

d on

pag

e 25

.

17. Th

e di

visib

ility

rule

s fro

m E

xerc

ise 8

Ex

plai

ned

on p

age

29.

18. Th

e st

eps o

f lon

g di

visio

n, th

e th

ree

way

s of w

ritin

g a

divi

sion

prob

lem

Ex

plai

ned

on p

age

30.

19. Th

e m

ultip

licat

ion

tabl

e to

12

x 12

C

orre

ct w

ith th

e co

mpl

eted

char

t in

the

appe

ndix

.

Nam

e

E

xerc

ise 10

Day

9


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