Math Mammoth Grade 4-A 2020

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Edition 1/2020

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Contents

Foreword ........................................................................... 6

Chapter 1: Addition, Subtraction, Patterns

and Graphs

Introduction ...................................................................... 7

Addition Review ............................................................... 11

Adding in Columns .......................................................... 14

Subtraction Review .......................................................... 15

Subtract in Columns ........................................................ 18

Patterns and Mental Math .............................................. 21

Patterns in Pascal’s Triangle .......................................... 23

Bar Models in Addition and Subtraction ...................... 25

Order of Operations ........................................................ 29

Making Bar Graphs ........................................................ 31

Line Graphs ..................................................................... 33

Rounding .......................................................................... 36

Estimating ........................................................................ 39

Money and Discounts ...................................................... 41

Calculate and Estimate Money Amounts ..................... 44

Review Chapter 1 ............................................................ 47

Chapter 2: Large Numbers and Place Value

Introduction ..................................................................... 49

Thousands ........................................................................ 51

At the Edge of Whole Thousands .................................. 54

More Thousands ............................................................. 56

Practicing with Thousands ............................................ 58

Place Value with Thousands .......................................... 60

Comparing with Thousands .......................................... 62

Adding and Subtracting Big Numbers ......................... 65

Rounding and Estimating with Large Numbers .......... 69

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Multiples of 10, 100, and 1000 ...................................... 73

Mixed Review Chapter 2 ............................................... 76

Review Chapter 2 ........................................................... 78

Chapter 3: Multi-Digit Multiplication

Introduction .................................................................... 80

Understanding Multiplication ...................................... 84

Multiplication Tables Review ....................................... 87

Scales Problems ............................................................. 90

Multiplying by Whole Tens and Hundreds ................ 94

Multiply in Parts 1 ........................................................ 98

Multiply in Parts 2 ........................................................ 101

Multiply in Parts—Area Model .................................... 103

Multiplying Money Amounts ....................................... 105

Estimating in Multiplication ........................................ 107

Multiply in Columns - the Easy Way .......................... 109

Multiply in Columns - the Easy Way, Part 2 ............. 112

Multiply in Columns - the Standard Way .................. 115

Multiplying in Columns, Practice ............................... 119

Order of Operations Again .......................................... 121

Money and Change ....................................................... 124

So Many of the Same Thing ......................................... 127

Multiplying Two-Digit Numbers in Parts ................... 130

Multiply by Whole Tens in Columns ........................... 135

Multiplying in Parts: Another Way ............................. 137

The Standard Multiplication Algorithm

with a Two-Digit Multiplier ......................................... 139

Mixed Review Chapter 3 ............................................... 143

Review Chapter 3 ........................................................... 145

Chapter 4: Time and Measuring

Introduction .................................................................... 148

Time Units ...................................................................... 153

Elapsed Time 1 ............................................................... 156

The 24-Hour Clock ........................................................ 159

Elapsed Time 2 .............................................................. 161

Elapsed Time 3 .............................................................. 164

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Measuring Temperature: Celsius ............................... 167

Measuring Temperature: Fahrenheit ......................... 171

Temperature Line Graphs ........................................... 173

Measuring Length ........................................................ 175

More Measuring in Inches and Centimeters ............. 178

Feet, Yards, and Miles ................................................. 180

Metric Units For Measuring Length .......................... 185

Customary Units of Weight ......................................... 188

Metric Units of Weight ................................................ 192

Customary Units of Volume ........................................ 195

Metric Units of Volume ............................................... 198

Mixed Review Chapter 4 ............................................. 201

Review Chapter 4 ......................................................... 203

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Foreword

Math Mammoth Grade 4 comprises a complete math curriculum for the fourth grade mathematics studies. The

curriculum meets and exceeds the Common Core standards.

The main areas of study in Math Mammoth Grade 4 are:

1. Students develop understanding and fluency with multi-digit multiplication, and use efficient

multiplication procedures to solve problems.

2. They develop understanding of division to find quotients involving multi-digit dividends (long division),

and they solve word problems involving division, including division with a remainder.

3. Students develop an understanding of fraction equivalence and some operations with fractions. They learn

to add and subtract fractions with same denominators, and to multiply a fraction by a whole number.

4. Students learn the concept of angle. They draw and identify lines and angles, and classify shapes by

properties of their lines and angles.

Additional topics we study are place value, time, measuring, graphs, and decimals.

This book, 4-A, covers addition and subtraction and graphs (chapter 1), place value (chapter 2), multi-digit

multiplication (chapter 3), and time and measuring (chapter 4). The rest of the topics are covered in the 4-B

worktext.

Some important points to keep in mind when using the curriculum:

• The two books (parts A and B) are like a “framework”, but you still have a lot of liberty in planning the

child’s studies. Chapters 1, 2, and 3 should be studied in order, and Chapter 3 (multiplication) should be

studied before Chapter 5 (division). However, you can be flexible with chapters 4 (time and measuring)

and 6 (geometry), and schedule them earlier or later. Also, most lessons from chapters 7 and 8 (fractions

and decimals) can be studied earlier; however the topic of finding parts with division should naturally be

studied only after mastering division.

Math Mammoth is mastery-based, which means it concentrates on a few major topics at a time, in order to

study them in depth. However, you can still use it in a spiral manner, if you prefer. Simply have the child

study in 2-3 chapters simultaneously. This type of flexible use of the curriculum enables you to truly

individualize the instruction for the child.

• Don’t automatically assign all the exercises. Use your judgment, trying to assign just enough for the

child’s needs. You can use the skipped exercises later for review. For most children, I recommend to start

out by assigning about half of the available exercises. Adjust as necessary.

• For review, the curriculum includes a worksheet maker (Internet access required), mixed review lessons,

additional cumulative review lessons, and the word problems continually require usage of past concepts.

Please see more information about review (and other topics) in the FAQ at

https://www.mathmammoth.com/faq-lightblue.php

I heartily recommend that you view the full user guide for your grade level, available at

https://www.mathmammoth.com/userguides/

And lastly, you can find free videos matched to the curriculum at https://www.mathmammoth.com/videos/

I wish you success in teaching math!

Maria Miller, the author

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Chapter 1: Addition, Subtraction,

Patterns, and Graphs

Introduction

The first chapter of Math Mammoth Grade 4 covers addition and subtraction, problem solving, patterns, graphs,

and money.

At first, we review the “technical aspects” of adding and subtracting: mental math techniques and adding and

subtracting in columns. We also study some patterns. The lesson on Pascal’s triangle is intended to be fun and

fascinating—after all, Pascal’s triangle is full of patterns!

In the next lesson, students use bar models (visual models with one or more horizontal “bars”) to help them write

addition and subtraction sentences with unknowns and to solve them. They are actually learning algebraic

thinking and how to write and solve simple equations.

The lesson on the order of operations contains some review. We also connect this topic with real-life situations,

such as shopping. The student writes simple expressions (number sentences) for word problems, which, again,

practices algebraic thinking, and also helps students learn how to show their work in math problems. As

applications of math, the chapter then contains straightforward lessons on bar graphs, line graphs, rounding,

estimating, and money problems.

Keep in mind that the specific lessons in the chapter can take several days to finish. They are not “daily lessons.”

Instead, use the general guideline that fourth graders should finish about 2 pages daily or 9-11 pages a week.

Also, I recommend not assigning all the exercises by default, but that you use your judgment, and strive to vary

the number of assigned exercises according to the student’s needs.

Please see the user guide at https://www.mathmammoth.com/userguides/ for more guidance on using and pacing

the curriculum.

I also offer free videos matched to the curriculum at https://www.mathmammoth.com/videos/.

The Lessons in Chapter 1

page span

Addition Review ......................................................... 11 3 pages

Adding in Columns ..................................................... 14 1 page

Subtraction Review .................................................... 15 3 pages

Subtract in Columns ................................................... 18 3 pages

Patterns and Mental Math ........................................... 21 2 pages

Patterns in Pascal's Triangle ....................................... 23 2 pages

Bar Models in Addition and Subtraction .................... 25 4 pages

Order of Operations .................................................... 29 2 pages

Making Bar Graphs .................................................... 31 2 pages

Line Graphs ................................................................ 33 3 pages

Rounding .................................................................... 36 3 pages

Estimating ................................................................... 39 2 pages

Money and Discounts ................................................. 41 3 pages

Calculate and Estimate Money Amounts .................... 44

3 pages

Review Chapter 1 .....................

.................................. 47 2 pages

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Helpful Resources on the Internet

THE BASIC OPERATIONS

Add Like Mad

Click on single-digit numbers that add up to the given sum as quickly as you can, clearing the board.

http://www.mathnook.com/addlikemad.html

Sum Tracks

The game board shows square and round tiles with numbers. Drag the square number tiles over the round tiles,

so that the sum of the round tiles equals the number on the square tile.

http://www.coolmath-games.com/0-sum-tracks

A Maze'n Math

Move the red piece through the maze and use it to eliminate the other numbers, according to certain rules relating

to addition and difference.

http://www.hoodamath.com/games/amazenmath.html

Minus Mission

Practice subtraction facts within your chosen range, such as 0-12 or 0-20 while destroying green slime.

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

Pop the Balloons

Pop the balloons in the order of their value. You need to use all four operations.

http://www.sheppardsoftware.com/mathgames/numberballoons/BalloonPopMixed.htm

Math Mahjong

Match tiles with the same value. The game uses all four operations and has three levels.

http://www.sheppardsoftware.com/mathgames/mixed_mahjong/mahjongMath_Level_1.html

PATTERNS AND PASCAL'S TRIANGLE

Crack the Code

Find the missing numbers in the patterns, and unlock the safe.

http://www.sciencekids.co.nz/gamesactivities/math/numberpatterns.html

Pascal's Triangle at Maths Is Fun

Learn fascinating facts and patterns in Pascal's triangle!

http://www.mathsisfun.com/pascals-triangle.html

Coloring Multiples

Color various multiples (such as multiples of 6 or 10) in Pascal's Triangle, and see the patterns!

http://www.shodor.org/interactivate/activities/ColoringMultiples/

BAR MODELS AND PROBLEM SOLVING

Thinking Blocks - Addition and Subtraction

Model and solve word problems.

https://www.mathplayground.com/tb_addition/index.html

Jugs Puzzle

Fill and pour the water out of the two jugs until you get the desired quantity. Drag the jugs to empty or fill them.

A puzzle using logical thinking.

https://www.mathsisfun.com/games/jugs-puzzle.html

Algebra Puzzle

Figure out the values of the objects so that they add up to the target numbers.

https://www.mathplayground.com/algebra_puzzle.html

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Calculator Chao

Most of the keys have fallen off the calculator. “Make” numbers using the keys that are left.

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

ORDER OF OPERATIONS

Addition Mystery Picture

Reinforce your addition skills while uncovering a hidden picture.

https://www.mathmammoth.com/practice/mystery-picture#min=20&max=100

Subtraction Mystery Picture

Practice subtraction of two-digit numbers while uncovering a hidden picture.

https://www.mathmammoth.com/practice/mystery-picture-subtraction#min=11&max=100

Choose Math Operation

Choose the operation(s) so that the given number sentence becomes true.

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

Order of Operations Quiz

A 10-question online quiz that includes two different operations and possibly parentheses in each question. You

can also modify the quiz parameters yourself.

http://www.thatquiz.org/tq-1/?-j8f-la

Order of Ops

Choose the expression to be solved in each step, and solve it. The program uses a visual representation of steps

to show how the expression gets shorter at each step.

https://mrnussbaum.com/order-ops-online-game

The Order of Operations Millionaire

Answer multiple-choice questions that have to do with the order of operations, and win a million.

http://www.math-play.com/Order-of-Operations-Millionaire/order-of-operations-millionaire.html

Exploring Order of Operations (Object Interactive)

Click on the operation to be done first in the given expression. The program then solves that, and you click on

the next operation to be performed, etc., until it is solved. The resource also includes a game.

http://www.learnalberta.ca/content/mejhm/html/object_interactives/order_of_operations/use_it.html

Order of Operations Practice

A simple online quiz of 10 questions. Uses parentheses and the four operations.

http://www.onlinemathlearning.com/order-of-operations-practice.html

ROUNDING AND ESTIMATING

Online Rounding Practice

Practice rounding to the nearest ten, hundred, or thousand.

https://www.mathmammoth.com/practice/rounding#number-range=0to10000&round-

to=ten,hundred,thousand

Rounding Sharks Game

Round numbers to the nearest hundred by clicking the shark with the correct rounded number.

http://www.free-training-tutorial.com/rounding/sharks.html

Brain Racer Rounding

Round numbers as fast as you can to beat two other walkers in the walking race. Choose to round either to the

nearest ten, nearest hundred, or nearest thousand.

http://www.mathnook.com/math/brain-racer-rounding.html

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Ice Ice Maybe

Fast estimation game. Help penguins migrate across a perilous ocean patrolled by hungry killer whales. The

game uses all operations; addition and subtraction are most appropriate for this level. Start the game from the

circular button near the top.

https://www.mangahigh.com/en/games/iceicemaybe

Estimation Games

Find the answer fast! You also get points for being close. Choose “Add 100s” or “Add Tens” “Subtract Tens”, or

“Subtract 100s” for 4th graders.

https://www.mathsisfun.com/numbers/estimation-game.php

MONEY

Change Maker

Determine how many of each denomination you need to make the exact change. Choose the “hard” level for 4th

graders. Playable in US, Canadian, Mexican, UK, or Australian money.

https://www.funbrain.com/games/change-maker

Cash Out

Give correct change by clicking on the bills and coins. It has three levels of difficulty.

https://mrnussbaum.com/cash-out-online-game

DATA AND GRAPHS

Bar Charts

Interactive questions about bar charts. First, choose a topic for the graph. Next, choose how the vertical axis is

presented; for example, “20 intervals, 10 marked”. Lastly, choose the type of questions asked.

http://www.topmarks.co.uk/Flash.aspx?f=barchartv2

Graphs Quiz

A 10-question online quiz that involves a variety of types of questions on line graphs, bar graphs, and

pictograms. You can also easily change the quiz parameters to your liking.

http://www.thatquiz.org/tq-5/?-j50f15-l5-p0

Line Graphs at Maths Is Fun

A simple tutorial on line graphs, followed by ten interactive practice questions.

https://www.mathsisfun.com/data/line-graphs.html

An Interactive Bar Grapher

Graph data sets in bar graphs. The color, thickness and scale of the graph are adjustable. You can input your own

data or use or alter pre-made data sets.

http://illuminations.nctm.org/Activity.aspx?id=4091

Graph Master

Create a graph from your own data (you can even make it up). The interactive activity creates the graph, and also

makes up multiple-choice questions from your data for you to answer.

https://mrnussbaum.com/graphmaster

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Chapter 1: Addition Review

Addition Review

The numbers to be added are

addends. The result is a sum.

You can write any number as a sum of its different parts:

whole thousands, whole hundreds, whole tens, and ones.

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

thousands hundreds tens ones

2,019 = 2,000 + 0 + 10 + 9

You can add in parts

(hundreds, tens, ones):

56 + 124

= 100 + 50 + 20 + 6 + 4

= 100 + 70 + 10 = 180

You can add in any order:

7 + 90 + 91 + 3

= 7 + 3 + 90 + 91

= 10 + 90 + 91 = 191

Trick: first add a bigger but

easier number, then subtract

to correct the error:

76 + 89

= 76 +

90 − 1

= 166 − 1 = 165

1. Add mentally. Compare the problems in each box!

70 + 80 = _______

77 + 80 = _______

77 + 82 = _______

140 + 50 = _______

141 + 50 = _______

144 + 55 = _______

50 + 60 = _______

54 + 65 = _______

58 + 62 = _______

80 + 90 = _______

82 + 93 = _______

88 + 91 = _______

2. Write each number as a sum of its parts: thousands, hundreds, tens, and ones.

a. 487 = b. 2,103 =

c. 8,045 = d. 650 =

3. Solve.

a. Emma added three numbers. Two of them were 56 and 90. The sum was 190.

What was the third number she added?

b. The sum of four numbers is 70 and the sum of five other numbers is 80.

What is the sum of all nine numbers?

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Chapter 1: Adding in Column

Adding in Columns

1. Add in columns. Check

by adding the numbers

in each column in a

different order (for

example, starting at the

bottom and working up).

3 8 4

2 9 1 2

2 0 0 8

2 0 9

+ 2 6

2 4 5

1 3 9

3 0

2 9 3 1

5 9 4

4 5 9 3

+ 5 2 6

1 7 3 8

2 3 9 0

1 0 7 8

3 6 4

2 8 0 3

2 1 1

+ 9 9

2. Add. Write the numbers under each other,

carefully aligning the ones, tens, hundreds,

and thousands. You may use a separate

piece of paper if you prefer.

a. 5,609 + 1,388 + 89 + 402 + 837

b. 67 + 504 + 1,298 + 492 + 3,288 + 8

3. The map shows some Kentucky cities

and distances between them.

The two distances that may be hard to read are:

from Louisville to Frankfort is 54 miles;

from Frankfort to Lexington is 28 miles.

Calculate the total driving distance, if

a family goes on a trip like this:

a. Covington - Lexington - Paducah - Lexington - Covington

b. A trip from Lexington via Covington,

Louisville, and Frankfort, and back to Lexington.

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Chapter 1: Subtraction Review

Subtraction Review

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.

1. Subtract.

13 − 7 = ______

63 − 7 = ______

12 − 6 = ______

82 − 6 = ______

15 − 9 = _______

150 − 90 = ______

16 − 8 = _______

1,600 − 800 = _______

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

100 − 2 = _______

100 − 20 = ______

100 − 22 = ______

200 − 4 = _______

200 − 40 = ______

200 − 45 = ______

500 − 5 = _______

500 − 50 = ______

500 − 56 = _______

400 − 7 = _______

400 − 70 = ______

400 − 71 = ______

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

a. 12 − 8 = _______

42 − 8 = _______

120 − 80 = _______

520 − 80 = _______

b. 15 − 9 = _______

75 − 9 = _______

150 − 90 = _______

650 − 90 = _______

c. 13 − 7 = _______

73 − 7 = _______

1,300 − 700 = ______

430 − 70 = _______

4. Write here four different subtraction problems

that are “related” to the problem 14 − 8 = 6.

See the examples above!

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Chapter 2: Large Numbers and Place Value

Introduction

The second chapter of Math Mammoth Grade 4 covers large numbers (up to 1 million) and place value.

The first lessons only deal with thousands, or numbers with a maximum of four digits. These are for review and

for deepening the student’s understanding of place value, as understanding place value with four-digit numbers

is crucial before moving on to larger numbers. After that we go on to numbers with five and six digits (numbers

till one million). Students write them in expanded form, compare them, add and subtract them, and learn more

about rounding.

Lastly, we briefly study the multiples of 10, 100, and 1000. This lesson prepares the way for some very

important ideas in the next chapter (multi-digit multiplication).

Please recall that it is not recommended to assign all the exercises by default. Use your judgment, and strive to

vary the number of assigned exercises according to the student’s needs.

The Lessons in Chapter 2

page span

Thousands ................................................................. 51 3 pages

At the Edge of Whole Thousands ............................. 54 2 pages

More Thousands ....................................................... 56 2 pages

Practicing with Thousands ....................................... 58 2 pages

Place Value with Thousands .................................... 60 2 pages

Comparing with Thousands ..................................... 62 3 pages

Adding and Subtracting Big Numbers ..................... 65 4 pages

Rounding and Estimating with Large Numbers ...... 69 4 pages

Multiples of 10, 100, and 1000 .................................73 3 pages

Mixed Review Chapter 2 .......................................... 76 2 pages

Review Chapter 2 ..................................................... 78 2 pages

Helpful Resources on the Internet

Teaching Place Value

What is the value of the red underlined digit? Answer the questions in this online quiz.

http://www.softschools.com/math/place_value/teaching_place_value/TeachingPlaceValue.swf

Can You Say Really Big Numbers?

Enter a really big number, try to say it out loud, and see it written.

http://www.mathcats.com/explore/reallybignumbers.html

Place Value Payoff

Match numbers written in standard form with numbers written in expanded form in this game.

http://www.quia.com/mc/279741.html

Base Ten Blocks

Click on buttons to make blocks appear. Show a problem to challenge yourself to match the correct number of

blocks with a written number. The level of difficulty can be adjusted.

http://www.hoodamath.com/mobile/games/basetenblocks.html

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Place Value Puzzler

Place value or rounding game. Click on the asked place value in a number, or type in the rounded version of the

number.

https://www.funbrain.com/games/place-value

Fruit Splat — Compare Numbers (Choose Level 3)

Compare numbers by picking >, <, or = .

http://www.sheppardsoftware.com/mathgames/placevalue/FSCompareNumbers.htm

Balloon Pop Math—Order Numbers

Pop the balloons in order from the smallest one to the largest one. Choose the number range 1-10,000.

http://www.sheppardsoftware.com/mathgames/placevalue/BPOrder1000.htm

Addition Quiz

Practice adding in columns in this 10-question online quiz.

http://www.thatquiz.org/tq-1/?-jg41-l34-p0

Complements of 1,000 Interactive Mad Maths

Answer as many questions as you can in this interactive timed addition quiz.

http://www.snappymaths.com/addition/make1000/interactive/make1000imin/make1000imin.htm

Adding and Subtracting Powers of Ten

Practice adding and subtracting powers of ten up to 1,000,000 in this interactive online quiz.

http://www.snappymaths.com/addsub/addsubp10/interactive/addsubpowers10/addsubpowers10.htm

ROUNDING AND ESTIMATING

Online Rounding Practice

Reinforce your rounding skills with this interactive online exercise

https://www.mathmammoth.com/practice/rounding#number-range=0to1000000&round-to=any-place

Online Addition Practice

Practice adding large numbers in expanded form with this interactive online exercise.

https://www.mathmammoth.com/practice/place-value#mode=write-number&max-digits=6&question-

number=10

Missing Addend Addition Practice

Find the missing number in each addition problem in this interactive online exercise.

https://www.mathmammoth.com/practice/place-value#mode=missing-part&max-digits=6&question-

number=10

Rounding Sharks

Round numbers to the nearest hundred. Click on the shark that has the correctly rounded number.

http://www.free-training-tutorial.com/rounding/sharks.html

Rounding Quiz

Practice rounding large numbers with this interactive 10-question quiz.

https://www.thatquiz.org/tq-c/?-jg020-l5-mpnv600-p0

Money Word Problems Worksheets: Addition and Subtraction

Practice addition and subtraction of various amounts of money with these printable worksheets.

https://www.dadsworksheets.com/worksheets/money-word-problems-addition-and-subtraction.html

Rounding to Thousands, Ten Thousands, or Hundred Thousands

Practice your rounding skills with this online multiple-choice quiz.

https://www.tutorialspoint.com/ordering_rounding_and_order_of_operations/rounding_to_thousands_ten_thousand_or_hundred_thousand_

Place Value Worksheets, Riddles, and Challenges

This page offers a variety of printable activities that practice place value on a fourth grade level.

https://www.math-salamanders.com/4th-grade-place-value.html

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Chapter 2: More Thousand

More Thousands

On this number line we see whole thousands marked from one thousand to fifteen thousand.

In the numbers on the right, the colored digits tell us

the number of whole thousands. A comma separates

those digits from the rest of the number.

Read the colored digits as a number by itself, and

when you come to the comma, say the word “thousand.”

We continue with whole thousands until we reach

a thousand thousands. That number has a new name:

one million.

7 8, 0 0 0 Read: 78 thousand

1 5 3, 0 0 0 Read: 153 thousand

8 0 2, 0 0 0 Read: 802 thousand

9 9 0, 0 0 0 Read: 990 thousand

9 9 9, 0 0 0 Read: 999 thousand

1,0 0 0, 0 0 0 Thousand thousand

= 1 million

The rest of the digits (not colored)

tell us the hundreds, tens, and ones

just like you have learned in the past.

1 7, 5 4 4 Read: 17 thousand five hundred forty four

6 0 9, 2 3 0 Read: 609 thousand two hundred thirty

7 0, 0 8 0 Read: 70 thousand eighty

9 0 2 , 0 0 5 Read: 902 thousand five

1. Place a comma in the number to separate the thousands. Fill in the missing parts.

a. 1 6 4 0 0 0

______ thousand

b. 9 2 0 0 0

______ thousand

c. 3 0 9 0 0 0

______ thousand

d. 3 4 0 0 0

______ thousand

e. 7 8 0 0 0 0

______ thousand

2. Place a comma in the number. Fill in missing parts. Read the numbers aloud.

a. 1 6 4,4 5 3

164 thousand 453

b. 9 2 9 0 8

______ thousand ______

c. 3 2 9 0 3 3

______ thousand ______

d. 1 4 0 0 4

______ thousand ______

e. 5 5 0 0 5 3

______ thousand ______

f. 7 2 0 0 1

______ thousand ______

g. 8 0 0 0 0 4

______ thousand ______

h. 3 0 0 3 6

______ thousand ______

3. Read these numbers aloud.

456,098

e. 78,304

b. 950,050

f. 266,894

c. 23,090

g. 1,000,000

d. 560,008

h. 306,700

Sample worksheet from

https://www.mathmammoth.com

Chapter 2: More Thousand

4. Think in whole thousands and add!

a. 30,000 + 5,000 =

think: 30 thousand + 5 thousand

b. 200,000 + 1,000 =

c. 400,000 + 30,000 = d. 710,000 + 40,000 =

e. 300,000 + 700,000 = f. 700,000 + 70,000 =

5. Add and subtract, thinking in whole thousands.

a. 35,000 + 5,000 = b. 711,000 + 10,000 =

c. 420,000 + 30,000 = d. 700,000 − 70,000 =

e. 300,000 − 60,000 = f. 1,000,000 − 200,000 =

g. 30,000 − 5,000 = h. 200,000 − 6,000 =

i. 723,000 − 400,000 = j. 500,000 − 1,000 =

6. The numbers 510,000 and 520,000 are marked on the number line below (at the “posts”).

Write the numbers that correspond to the dots.

7. Make a number line from 320,000 to 340,000 with tick-marks at every whole thousand, similar

to the one above. Then mark the following numbers on the number line:

323,000 328,000 335,000 329,000 330,000

Sample worksheet from

https://www.mathmammoth.com

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Sample worksheet from

https://www.mathmammoth.com

Chapter 3: Multi-Digit Multiplication

Introduction

The third chapter of Math Mammoth Grade 4 covers multi-digit multiplication and some related topics.

This is one of the focus areas of 4th grade math. For further help in teaching these topics, check out the

free videos matched to the curriculum at https://www.mathmammoth.com/videos/.

The first lessons briefly review the multiplication concept and the times tables. The next lesson, where

students solve scales or pan balance problems, is intended to be somewhat fun and motivational. The

balance problems are actually equations in disguise.

The focus of the chapter is multi-digit multiplication. We start out by multiplying numbers by whole

tens and hundreds (such as 20 × 4 or 500 × 6). After this, students learn multiplication part-by-part

(also called partial products) — a very important concept. It means that we calculate, for example,

4 × 63 in two parts: first we solve 4 × 60 and 4 × 3, and then we add the two results (240 + 12 = 252).

This principle underlies the standard multiplication algorithm and it also allows us to calculate the

result of a multiplication mentally, so it is very important to master. Additionally, multiplying in parts

is tied in with an area model — which also is important to learn.

Before learning the traditional form of the multiplication algorithm, students encounter a simplified

form of that algorithm in the lesson Multiply in Columns—the Easy Way. At your discretion, you may

skip that lesson or skim through it quickly, if your student is ready to understand the standard form of

the algorithm, which is taught next.

Students also study estimation, the order of operations, and multiplying with money. These lessons

have numerous word problems. Students are instructed to write a number sentence or several for each

word problem, which helps them learn how to show their work for math problems.

The idea in the lesson So Many of the Same Thing is very simple, yet it actually prepares students to

study proportions (in middle school math). In this lesson, students fill in values for two quantities in

tables (for example, the quantity of the items and the total cost).

Nearing the end of the chapter, we study 2-digit by 2-digit multiplication (e.g. 52 × 63). Again, we first

use partial products, including in the context of an area model. The lesson Multiplying in Parts:

Another Way presents an alternate way to multiply and is optional. After that we end the chapter with

the standard algorithm for multiplying a two-digit number by a two-digit number.

The Lessons in Chapter 3

page span

Understanding Multiplication ............................... 84 3 pages

Multiplication Tables Review ............................... 87 3 pages

Scales Problems .................................................... 90 4 pages

Multiplying by Whole Tens and Hundreds .......... 94 4 pages

Multiply in Parts, 1 ............................................... 98 3 pages

Multiply in Parts, 2 ............................................... 101 2 pages

Multiply in Parts—Area Model ............................ 103 2 pages

Multiplying Money Amounts ................................ 105 2 pages

Sample worksheet from

https://www.mathmammoth.com

page span

Estimating in Multiplication ................................... 107 2 pages

Multiply in Columns - the Easy Way ..................... 109 3 pages

Multiply in Columns - the Easy Way, Part 2 ......... 112 3 pages

Multiplying in Columns - the Standard Way ......... 115 4 pages

Multiplying in Columns, Practice .......................... 119 2 pages

Order of Operations Again ..................................... 121 3 pages

Money and Change ................................................ 124 3 pages

So Many of the Same Thing .................................. 127 3 pages

Multiplying Two-Digit Numbers in Parts.............. 130 5 pages

Multiply by Whole Tens in Columns .................... 135 2 pages

Multiplying in Parts: Another Way ....................... 137 2 pages

The Standard Multiplication Algorithm

with a Two-Digit Number Multiplier .................... 139 4 pages

Mixed Review Chapter 3 ....................................... 143 2 pages

Review Chapter 3 ................................................... 145 3 pages

Helpful Resources on the Internet

Multiplication tables — online practice

Ad-free online practice of the multiplication tables at MathMammoth.com website. Also works as an offline

program in most browsers. Includes the option for both timed and non-timed practice.

https://www.mathmammoth.com/practice/multiplication.php

Multiplication games for the multiplication tables

Improve your multiplication skills with these fun games!

http://www.multiplication.com/games/all-games

http://www.hoodamath.com/games/multiplication.html

Interactive Pan Balance

Each of the four shapes is assigned a certain (unknown) weight. You need to figure out their weights by placing

them on the two sides of the pan balance in different configurations.

http://illuminations.nctm.org/Activity.aspx?id=3531

Stable Scales Quiz

In each picture, the scales are balanced. Can you find the weight of the items on the scales?

https://www.transum.org/Software/SW/Starter_of_the_day/Students/Stable_Scales_Quiz.asp

MULTIPLYING IN PARTS (PARTIAL PRODUCTS)

Mental Multiplication of Multiples of 10 and 100

This activity allows you to rehearse the mental multiplication of multiples of 10 and 100, e.g. 30 × 400 etc. Play

against the clock and see what level you can get up to before you run out of time!

https://www.studyzone.tv/game86-code3dc5617c60ff2ca509aabc60944162d1

Sample worksheet from

https://www.mathmammoth.com

Multiply by Multiples of 10 Bicycle Race

Answer the multiplication problems correctly to help the bicycle rider win the race.

https://www.studyladder.com/games/activity/multiply-by-multiples-of-10-22221

Open Array Multiplication Tool

This interactive tool shows the partial products algorithm and an area model for multi-digit multiplication,

allowing students to easily link the two. The model accommodates 2-digit × 2-digit problems and 1-digit × 1, 2,

3, or 4-digit problems.

https://www.conceptuamath.com/app/tool/open-array-multiplication

Partial Products Finder App

An interactive app that illustrates multiplication (up to 30 x 30) with an area model.

https://apps.mathlearningcenter.org/partial-product-finder/

Amoeba Multiplication Game (Choose Beginner or Medium Level)

Practice multiplication by splitting numbers. Choose Beginner or Medium Level for this chapter.

http://www.bbc.co.uk/skillswise/game/ma12pape-game-written-multiplication

MULTIPLICATION ALGORITHM

One-Digit by Two-Digits Multiplication Game

Students will multiply one-digit numbers by two-digit whole numbers, then get to try to shoot a basket.

http://www.math-play.com/one-digit-by-two-digit-multiplication-game.html

Multiplication Jeopardy Game

You get to solve multi-digit multiplication questions of 1-digit by 1-digit, 1-digit by 2-digit, and 1-digit by

3-digit numbers in this game.

http://www.math-play.com/Multiplicaton-Jeopardy/Multiplication-Jeopardy.html

Canoe Penguins

Answer the multiplication problems quickly and correctly to help your penguins win the race!

http://www.arcademics.com/games/canoe-penguins/canoe-penguins.html

Batter's Up Baseball

Answer the multiplication problems correctly to help the home team beat the visiting team. Choose “Double” or

“Homerun” level.

http://prongo.com/baseball-multiply/

Multi-Digit Multiplication Number Battle Card Game (page 18 of PDF file)

Arrange your cards to make the highest product possible.

http://www.pepnonprofit.org/uploads/2/7/7/2/2772238/acing_math.pdf

Multiplication Quiz

Practice multiplying by one digit in this 10-question online quiz.

http://www.thatquiz.org/tq-1/?-jg24-la-p0

Math FROG MultipliACTION

Practice 2 by 2 digit multiplication online. Enter one digit in each box.

http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/mult5.shtml

Sample worksheet from

https://www.mathmammoth.com

Math Computation Practice: Multiply Two digits by Two Digits

Practice two-digit multiplication in columns.

http://www.mathplayground.com/multiplication05.html

ORDER OF OPERATIONS

Choose Math Operation

Choose the operation(s) so that the number sentence is true. Helps develop number sense and logical thinking.

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

Order of Ops

Save seven members of a Royal Family from prison by using your order of operation skills. Choose the

expression to be solved in each step, and solve it. The program uses a visual representation of a stairway to

show how the expression gets shorter at each step.

https://mrnussbaum.com/order-ops-online-game

Order of Operations Quiz

A 10-question online quiz that includes two different operations and possibly parentheses in each question. You

can also modify the quiz parameters yourself.

http://www.thatquiz.org/tq-1/?-j8f-la

Exploring Order of Operations (Object Interactive)

Click on the operation to be done first in the given expression. The program then solves that, and you click on

the next operation to be performed, etc., until it is solved. The resource also includes a game.

http://www.learnalberta.ca/content/mejhm/html/object_interactives/order_of_operations/use_it.html

Order of Operations Practice

A simple online quiz of 10 questions. Uses parentheses and the four operations.

http://www.onlinemathlearning.com/order-of-operations-practice.html

MISCELLANEOUS

Multiplication Matching Game

Practice the multiplication tables while also uncovering a hidden picture in this fun matching game!

https://www.mathmammoth.com/practice/multiplication-matching

Matching Rates

Match each rate to its unit rate. Get a 1,000 point bonus for each round in which you don't make mistakes!

http://www.sheppardsoftware.com/mathgames/ratios/MatchingRates.htm

Thinking Blocks

Thinking Blocks is an engaging, interactive math tool that helps students learn how to solve multi-step word

problems. Scroll down to Multiplication and Division.

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

Multiplication Word Problem Quiz

This 10-question quiz focuses on using multiplication to solve word problems.

http://www.softschools.com/quizzes/math/multiplication_word_problems/quiz1059.html

Mental Math Tricks for Multiplication

Includes some basic common-sense tricks, such as multiplying by 9 or multiplying by doubling and halving.

http://wildaboutmath.com/2007/11/11/impress-your-friends-with-mental-math-tricks

Sample worksheet from

https://www.mathmammoth.com

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Sample worksheet from

https://www.mathmammoth.com

Chapter 3: Multiplying by Whole Tens and Hundred

Multiplying by Whole Tens and Hundreds

We have studied the SHORTCUTS for multiplying any number by 10, 100, or 1,000:

To multiply any number by 10, just tag ONE zero to the end.

To multiply any number by 100, just tag TWO zeros to the end.

To multiply any number by 1,000, just tag THREE zeros to the end.

10 × 481 = 4,810 100 × 47 = 4,700 1000 × 578 = 578,000

Note especially what happens when the number you multiply already ends in a zero or zeros.

The rule works the same way, and you still have to tag the zero or zeros.

10 × 800 = 8000 100 × 6,600 = 660,000 1 000 × 40 = 40,000

1. Multiply.

a. 10 × 315 = _______

3,560 × 10 = _______

35 × 100 = _______

b. 100 × 6,200 = _______

10 × 1,200 = _______

100 × 130 = _______

c. 1,000 × 250 = _______

38 × 1,000 = _______

10 × 5,000 = _______

Shortcut for multiplying by 20 or 200 (You can probably guess this one!)

What is 20 × 14?

First solve the problem without the zero in 20:

2 × 14 = 28. Next, tag a zero to the answer,

28, and you get 280. So, 20 × 14 = 280.

What is 200 × 31?

First solve the problem without the zeros:

2 × 31 = 62. Next, just two zeros to the

result, 62, to get 6,200. In other words,

200 × 31 = 6,200.

2. Now try it! Multiply by 20 and 200.

20 × 8 = ______

4 × 20 = ______

20 × 5 = ______

200 × 7 = _______

5 × 200 = _______

11 × 200 = _______

20 × 12 = _______

35 × 20 = _______

200 × 9 = _______

20 × 16 = _________

42 × 200 = _________

54 × 20 = _________

Sample worksheet from

https://www.mathmammoth.com

Hint: To calculate

the area of a

rectangle, multiply

its two sides.

Chapter 3: Multiplying by Whole Tens and Hundred

Why does the shortcut work? It is based on the fact that we can multiply numbers in any order.

When multiplying any number by 20, we

can write the 20 as 10 × 2. For example:

20 × 14 = 10 × 2 × 14

In that problem, first multiply 2 × 14 = 28.

Then the problem becomes 10 × 28, which

equals 280. Notice again how we did it:

20 × 14

= 10 × 2 × 14

= 10 × 28

= 280

Let's try the same idea with 200. We will write

200 as 100 × 2. For example:

200 × 31 = 100 × 2 × 31

In that problem, first multiply 2 × 31 = 62.

The problem now becomes 100 × 62, which

is 6,200. Notice again how it was done:

200 × 31

= 100 × 2 × 31

= 100 × 62

= 6,200

3. Try it yourself! Fill in.

a. 20 × 7

= ______ × 2 × 7

= 10 × ______

= _________

b. 20 × 5

= ______ × 2 × 5

= 10 × ______

= _________

c. 200 × 8

= ______ × 2 × 8

= 100 × ______

= _________

d. 200 × 25

= ______ × 2 × 25

= 100 × ______

= _________

4. Mark’s shed measures 20 ft by 15 ft. Write and solve a number sentence

for its area. (“A” means area.)

A = __________________________________

5. Write a number sentence to find the area

of Mark’s driveway, and solve it.

A = __________________________________

6. Mark was told he needed four truckloads of gravel to cover his driveway.

One truckload costs 5 × $20 plus $30 for the delivery. How much will

it cost him to cover the driveway with gravel?

Sample worksheet from

https://www.mathmammoth.com

Chapter 3: Multiplying by Whole Tens and Hundred

SHORTCUT for multiplying by whole tens and whole hundreds

The same principle works if you multiply by whole tens (30, 40, 50, 60, 70, 80, or 90):

simply multiply by 3, 4, 5, 6, 7, 8, or 9, and then tag a zero to the result.

Similarly, if you multiply by some whole hundred, first solve the multiplication without

the two zeros of the hundreds, and then tag two zeros to the result.

50 × 8 = 400 90 × 11 = 990 300 × 8 = 2,400 12 × 800 = 9,600

7. Multiply.

a. 40 × 3 = ________

8 × 20 = ________

b. 70 × 6 = _________

50 × 11 = ________

c. 80 × 9 = _________

30 × 15 = _________

d. 60 × 11 = _________

12 × 40 = _________

e. 200 × 9 = ________

7 × 400 = ________

f. 700 × 6 = ________

600 × 11 = ________

g. 200 × 12 = ________

15 × 300 = ________

h. 3 × 1100 = ________

8 × 900 = ________

i. 11 × 120 = ________

8 × 300 = ________

It even works this way:

To multiply 40 × 70, simply

multiply 4 × 7, and tag two

zeros to the result:

40 × 70 = 2,800

To multiply 600 × 40, simply

multiply 6 × 4, and tag three

zeros to the result:

600 × 40 = 24,000

To multiply 700 × 800, simply

multiply 7 × 8, and tag four

zeros to the result.

700 × 800 = 560 ,000

8. Multiply.

a. 20 × 90 = _________

70 × 300 = _________

b. 60 × 80 = _________

30 × 900 = _________

c. 400 × 50 = _________

200 × 200 = _________

d. 80 × 800 = _________

200 × 500 = _________

e. 100 × 100 = _________

40 × 30 = _________

f. 800 × 300 = _________

90 × 1100 = _________

Sample worksheet from

https://www.mathmammoth.com

Chapter 3: Multiplying by Whole Tens and Hundred

Write a number sentence for each question.

9. One hour has ______ minutes.

How many minutes are in 12 hours? ____________________________________________

How many minutes are in 24 hours? ____________________________________________

10. One hour has ______ minutes, and one minute has ______ seconds.

How many seconds are there in one hour? __________________________________________

11. Ed earns $30 per hour.

a. How much will he earn in an 8-hour workday? _____________________________________

b. How much will he earn in a 40-hour workweek? ___________________________________

c. How many days will he need to work in order to earn more than $1,000?

_________________________________________________________________________

12. Find the missing factor. Think “backwards”: how many zeros do you need?

a. _______ × 3 = 360

_______ × 50 = 450

b. 40 × _______ = 320

5 × ________= 600

c. ________ × 40 = 400

________ × 2 = 180

d. ________ × 30 = 4,800

________ × 200 = 1,800

e. 40 × ________ = 2,000

6 × _________= 4,200

f. _______ × 800 = 56,000

________ × 20 = 12,000

John wanted to prove that 40 × 70 is indeed 2,800 by breaking the

multiplication into smaller parts. He wrote 40 as 4 × 10 and 70

as 7 × 10, and then multiplied in a different order:

40 × 70 = 4 × 10 × 7 × 10

= 10 × 10 ×

(4 × 7) = 100 × 28 = 2,800.

Do the same, and prove that 600 × 50 is indeed 30,000.

Sample worksheet from

https://www.mathmammoth.com

(This page intentionally left blank.)

Sample worksheet from

https://www.mathmammoth.com

Chapter 3: Multiplying in Columns, the Standard Wa

Multiplying in Columns, the Standard Way

The standard algorithm of multiplication is based on a principle you already know: multiplying in

parts (partial products). We simply multiply ones, tens, and hundreds of the number separately, and

then add.

However, in the standard algorithm, the additions are done at the same time as the multiplications –

not afterwards. That way, the calculation looks more compact and takes less space.

The standard way to multiply “The easy way”

6 3

2 5 2

Multiply the ones: 4 × 3 = 12.

Place 2 in the ones place, but

write the tens digit (1) above

the tens column as a little

memory note. You are

regrouping (carrying).

Then multiply the tens, adding

the 1 ten that was regrouped:

4 × 6 + 1 = 25

Write 25 in front of the 2.

Note: This 25 means 25 tens

or 250!

6 3

× 4

1 2

+ 2 4 0

2 5 2

In the “easy way,” we

multiply in parts, and

the adding is done

separately.

The standard way to multiply “The easy way”

7 5

5 2 5

Multiply the ones: 7 × 5 = 35

Regroup the 3 tens.

Multiply & add the tens:

7 × 7 + 3 = 52

7 5

× 7

3 5

+ 4 9 0

5 2 5

1. Multiply using both methods: the standard way and the easy way.

a. b.

115

Sample worksheet from

https://www.mathmammoth.com

Chapter 3: Multiplying in Columns, the Standard Wa

2. Multiply using both methods: the standard way and the easy way.

3. Multiply. Be careful with the regrouping.

a. b. c. d.

e. f. g. h.

i. j. k. l.

4. Write number sentences (additions, subtractions, multiplications) on the lines, and solve.

a. What is the cost of buying three chairs for $48 each?

_________________________________________________

And the cost for six chairs? ___________________________________

b. You earn $77 a day. How much do you earn in five days?

_________________________________________________

How much in ten days? _____________________________________

116

Sample worksheet from

https://www.mathmammoth.com

(This page intentionally left blank.)

Sample worksheet from

https://www.mathmammoth.com

Chapter 4: Time and Measuring

Introduction

The fourth chapter of Math Mammoth Grade 4 includes lessons on time, temperature, length, weight,

and volume. The focus is no longer on the actual act of measuring, but on conversions between the

units and on word problems that involve conversions.

We start out studying clock and time, with a focus on elapsed time. In contrast to third grade, the time

intervals can now include the change from AM to PM, and the given times do not follow five-minute

increments. The lessons give several strategies for finding the elapsed time. Students also make

schedules and solve a variety of word problems involving time.

Conversions between measurement units is a big focus point of the chapter. Students may have

difficulties with this, and that is why this topic will also be studied in 5th grade. At this point, students

should be able to easily convert a bigger unit into a smaller unit (such as converting 3 feet into 36

inches or 2 kg into 2,000 grams).

While the Common Core standards do not include them for fourth grade, I have also included some

problems where we convert from a smaller unit to a bigger unit (such as 4,500 ml into 4 L 500 ml or 12

feet into 4 yards) because I feel most children are capable of doing these in fourth grade. If you feel

your child has difficulty with converting from a smaller unit to a bigger one, feel free to omit those

particular exercises. They are intermixed though, and not marked in any special way.

The chapter includes separate lessons for customary and metric units. Each lesson dealing with

measuring units includes a table that lists the units we are studying and the conversion factors. For

metric units, those tables always include all the units, even when they are not in common usage. For

example, for metric units of volume, the chart looks like this:

1 L = 1,000 ml

liter L for larger amounts of liquid

deciliter dl (for medium amounts of liquid)

centiliter cl (for small amounts of liquid)

milliliter ml for small amounts of liquid

The lesson deals only with milliliters and liters. However, the chart also shows the other two units

(deciliters and centiliters) in order to help students become familiar with those basic units of the metric

system:

1. The units always differ by a factor of ten;

2. The units are named consistently with the same prefixes (milli-, centi-, deci-, deka-, hecto-, and

kilo-). These prefixes and their meanings are not yet studied in detail in fourth grade. You may,

at your discretion, explain them to the student.

148

Sample worksheet from

https://www.mathmammoth.com

The Lessons in Chapter 4

page span

Time Units ........................................................ 153 3 pages

Elapsed Time 1................................................. 156 3 pages

The 24-Hour Clock .......................................... 159 2 pages

Elapsed Time 2 ................................................ 161 3 pages

Elapsed Time 3 ................................................ 164 3 pages

Measuring Temperature: Celsius ..................... 167 4 pages

Measuring Temperature: Fahrenheit ............... 171 2 pages

Temperature Line Graphs ................................ 173 2 pages

Measuring Length ............................................ 175 3 pages

More Measuring in Inches and Centimeters .... 178 2 pages

Feet, Yards and Miles ...................................... 180 5 pages

Metric Units for Measuring Length ................ 185 3 pages

Customary Units of Weight ........................... 188 4 pages

Metric Units of Weight ................................... 192 3 pages

Customary Units of Volume ........................... 195 3 pages

Metric Units of Volume .................................. 198 3 pages

Mixed Review Chapter 4 ................................. 201 2 pages

Review Chapter 4 ............................................ 203 2 pages

Helpful Resources on the Internet

ELAPSED TIME

Elapsed Time

Find how much time passes between two different given times (elapsed time or time intervals) in this

customizable online exercise.

https://www.mathmammoth.com/practice/clocks

Elapsed Time

Click “New Time”. Then click the buttons that advance the time on the clock, until the time matches

the “End” time. Choose difficulty levels 1 and 2 for this grade level.

http://www.shodor.org/interactivate/activities/ElapsedTime/

Elapsed Time Worksheets

Generate printable worksheets for elapsed time. You can practice the elapsed time, finding the starting

time, or finding the ending time.

http://www.mathnook.com/elapsedtimegen.html

149

Sample worksheet from

https://www.mathmammoth.com

Find the Start Tim

Word problems about starting times with multiple-choice answers. Choose “full screen”, then “Find the

start time”. Next, choose option 4 or 5.

http://mathsframe.co.uk/en/resources/resource/119/find_the_start_time

Time for Crime—Elapsed Time Mystery

A single mystery problem which can be solved by thinking of the elapsed time: who is the thief?

http://teacher.scholastic.com/maven/timefor/index.htm

ThatQuiz—Elapsed time

A ten-question quiz on Elapsed Time

http://www.thatquiz.org/tq-g/?-j4-l4-p0

Adding Time Word Problems

Read the time and then answer a word problem involving adding a given time.

http://mathsframe.co.uk/en/resources/resource/118/adding_time_word_problems

Converting Units of Time Quiz

Practice converting between various units of time with this multiple-choice quiz.

https://www.turtlediary.com/quiz/converting-units-of-time.html

24-hour Snap Game

Snap together the matching times, one given with the 24-hour clock, and another with AM/PM.

http://www.bbc.co.uk/skillswise/game/ma25time-game-24-hour-snap

Interactivate: Elapsed Time

Practice calculating elapsed time with analog or digital clocks.

http://www.shodor.org/interactivate/activities/ElapsedTime/

Elapsed Time Quiz

A 10-question online quiz that practices elapsed time in hours and minutes.

https://www.thatquiz.org/tq-g/?-j4-l3-mpnv600-p0

TEMPERATURE

Thermo Quiz

Select the box that contains the temperature the thermometer is showing.

http://www.mathnook.com/math/thermo-quiz.html

Fun Physics from NASA: Temperature

Practice matching different things to their temperature. You can choose Celsius, Fahrenheit, or Kelvin

degrees (the Kelvin scale is not studied in this curriculum). When you are done, you can compare the

temperature scales, learn more about temperature, or click on one of the objects to learn more about it.

https://funphysics.jpl.nasa.gov/adventures/temperature-game.html

Hot Stuff

Practice estimating temperatures in Fahrenheit.

http://www.beaconlearningcenter.com/WebLessons/HotStuff/default.htm

Be a Scientist

Practice estimating temperatures in Celsius.

http://www.beaconlearningcenter.com/WebLessons/BeAScientist/default.htm

150

Sample worksheet from

https://www.mathmammoth.com

Temperature

Practice reading thermometers with different scales.

http://www.topmarks.co.uk/Flash.aspx?f=Temperaturev2

Temperature Quiz

Answer questions about reasonable temperatures in Fahrenheit and Celsius in this interactive multiple-choice

quiz.

http://www.softschools.com/quizzes/math/temperature_measurement/quiz2112.html

Line Graph Quiz

Read the line graph and answer 5 questions in this simple quiz.

http://www.mcwdn.org/Graphs/LineGraphQuiz.html

LENGTH

The Ruler Game

Click on the measurements on the ruler that correspond with the measurements that appear.

http://www.rulergame.net/

Reading a Ruler by Eighths

Practice reading a ruler by eighths with a matching exercise and a game of Concentration.

https://www.quia.com/jg/1364429.html

Measure It!

Practice measuring lines with either centimeters or inches. Multiple choice questions.

https://www.funbrain.com/games/measure-it

Sal's Sub Shop

Cut the subs to the given measurements—sometimes in metric units, sometimes in inches.

https://mrnussbaum.com/sal-s-sub-shop-online-game

Reading a Tape Measure Worksheets

Worksheet generator—choose to measure in inches, or inches and feet.

http://themathworksheetsite.com/read_tape.html

Feet to Yards and Feet

Match the correct conversions. Get a 1,000-point bonus per round if you get all correct.

http://www.sheppardsoftware.com/mathgames/measurement/MeasurementYards.htm

Metric Length Matching

Match the conversions as fast as you can!

http://www.sheppardsoftware.com/mathgames/measurement/MeasurementMeters.htm

Quiz on metric units of length

Practice converting between metric units of length in this 10-question quiz.

http://www.thatquiz.org/tq-n/?-j147-l2-p0

WEIGHT

Matching Math: Customary Weight

Practice converting between pounds and ounces in this matching game.

http://www.sheppardsoftware.com/mathgames/measurement/MeasurementOunces.htm

Reading Scales

Illustrate how to read a variety of measuring devices, such as scales, measuring cup, thermometer. You can

generate examples using different scales on different devices.

http://www.teacherled.com/resources/dials/dialsload.html

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Ounces, Pounds, and Ton

Answer questions about customary units of weight in this jeopardy-style game.

https://www.quia.com/cb/426998.html

VOLUME

Artie Ounces Soda Jerk

Practice standard units of volume with this fun soda jerk game. Fill the client orders as fast as you can!

https://mrnussbaum.com/artie-ounces-soda-jerk-online-game

Standard Liquid Volume Matching Game

Match standard liquid volumes with equivalent volumes

https://www.quia.com/mc/126277.html

GENERAL

Matching Math: Customary Measuring Units

Match each item with its best estimate of capacity, weight, or length.

http://www.sheppardsoftware.com/mathgames/measurement/BestMeasure2.htm

Measures

An online activity about metric measuring units and how to read scales, a measuring cup, and a ruler.

Note: You will need to use the British spellings “centimetres” and “millilitres” in the activity.

http://flash.topmarks.co.uk/674

A Dictionary of Units of Measurement

This resource explains the common measuring systems and their history.

http://www.ibiblio.org/units/

Measuring

Worksheets, fact sheets, and quizzes that practice various measuring concepts in both metric and imperial units.

http://www.bbc.co.uk/skillswise/topic-group/measuring

Conversion Quizzes - ThatQuiz.org

A customizable online quiz about conversions between measuring units. The options include both metric and

customary systems and six different difficulty levels.

http://www.thatquiz.org/tq-n/science/metric-system/

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Chapter 4: Metric Units for Measuring Length

Metric Units for Measuring Length

The basic unit for measuring length in the

metric system is the meter. All the other

units are based on the meter, and in fact,

have the word “meter” in them.

Each unit in the metric system is 10 times

the smaller unit. For example, 1 kilometer

is 10 hectometers and 1 centimeter is 10

millimeters. However, we don’t commonly

use hectometers, dekameters, or decimeters.

You need to learn only the units that are

bolded in the chart.

Units of length in the metric system

kilometer km

“Kilo” means 1,000.

hectometer hm (not used)

dekameter dam (not used)

meter m

the basic unit

decimeter dm (not used much)

centimeter cm

This is 1/100 of a meter.

millimeter mm

This is 1/10 of a centimeter.

Remember also that 1 meter is very close to 1 yard. One meter is just a bit longer than one yard.

1. Draw two lines at least 4 m long that start at the same place (outside, in a hallway, or a large room).

a. On the one line, make marks

for 1 m, 2 m, 3 m, and 4 m.

Then try to take “hops”

one meter long.

1 meter 1 meter 1 meter 1 meter

b. On the second line make marks at each foot, from 1 to 13 feet.

Then take 1-yard hops.

Do the two kinds of hops feel about the same?

2. Measure how tall you and other people are in centimeters.

Write it also using whole meters and centimeters.

Name Height

_______ cm = 1 m _____ cm.

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Chapter 4: Metric Units for Measuring Length

Conversions between units

Remember what millimeters look like on a ruler. They are tiny! Ten millimeters make 1 cm.

Then verify from a measuring tape that 100 centimeters makes one meter. “Centi” means one

hundred (from the Latin word centum). That is why 1 dollar has 100 cents, and 1 meter has 100

centimeters.

Lastly, 1 kilometer is 1,000 meters, because “kilo” means one thousand.

1 km = 1,000 m 1 m = 100 cm 1 cm = 10 mm

3. One meter is 100 cm. Convert between meters and centimeters.

a. 5 m = _________ cm

8 m = _________ cm

12 m = _________ cm

b. 4 m 6 cm = _______ cm

9 m 19 cm = _______ cm

10 m 80 cm = _______ cm

c. 800 cm = _______ m

239 cm = ____ m ______ cm

407 cm = ____ m ______ cm

4. One centimeter is 10 mm. Convert between centimeters and millimeters.

a. 5 cm = _______ mm

8 cm = _______ mm

14 cm = _______ mm

b. 2 cm 8 mm = _______ mm

7 cm 5 mm = _______ mm

10 cm 4 mm = _______ mm

c. 50 mm = ____ cm _____ mm

72 mm = ____ cm _____ mm

145 mm = ____ cm _____ mm

5. One kilometer is 1,000 m. Convert between kilometers and meters.

a. 5 km = ___________ m

23 km = ____________ m

1 km 200 m = __________ m

b. 2 km 800 m = _________ m

6 km 50 m = __________ m

13 km 579 m = __________ m

c. 2,000 m = _______ km

4,300 m = ____ km _______ m

18,700 m = ____ km _______ m

6. Calculate. Give your answer using whole kilometers and meters.

a. 5 km 200 m + 8 km 900 m

b. 3 km 600 m + 2 km 800 m

c. 1,500 m + 2 km 600 m

d. 6 × 700 m

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Chapter 4: Metric Units for Measuring Length

7. Solve.

a. Find the perimeter of this rectangle.

80 cm

2 m

b. Find the perimeter of this rectangle.

1 cm 5 mm

7 mm

c. One side of a square measures 5 cm 6 mm. What is its perimeter?

d. A challenge. A square has a perimeter of 6 cm. How long is its side?

8. Solve the problems.

a. How many millimeters are in a meter?

b. John jogs around a track 1 km 800 m long twice a day, five days a week.

How long a distance does he jog in a day?

In a week?

c. Gary is 1 m 34 cm tall and Jared is 142 cm tall.

How much taller is Jared?

Kathy’s wallpaper has butterflies that are 8 cm wide. She will

put the wallpaper in her room. How many complete butterflies

can she have on a wall that is 1 meter long?

How about if the wall is 3 meters long?

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