What is a Decimal? A Decimal Number ( based on the number 10, tenth - - PDF document

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5th Grade

Decimal Concepts

2015-11-16 www.njctl.org

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What is a Decimal? Identify Place Values Read and Write Decimals Compare & Order Decimals Round Numbers to Designated Place Values

Table of Contents

Click on a topic to go to that section. Glossary & Standards

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What is a Decimal? Identify Place Values Read and Write Decimals Compare & Order Decimals Round Numbers to Designated Place Values

Table of Contents

Click on a topic to go to that section. Glossary & Standards

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Teacher Notes

Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end

• f the presentation with the

word defined on it.

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Return to Table

• f Contents

What is a Decimal?

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A Decimal Number (based on the number 10, tenth parts, and powers

• f ten) contains a Decimal Point.

Click to find out!

What is a decimal number?

Decimals

SLIDE 2

Slide 6 / 192 Where do we see decimals being used?

Click on the photo to find out! In races to show speed. The women's record for the fastest 100 meter dash is 10.88 seconds. In baseball, batting averages are in

• decimals. Miguel

Cabrera has a batting average of 0.387 Music Stations that show their radio frequency in decimals. With money to show dollars and change. This shows $6.91. And many other places!

Slide 7 / 192 Why do we need decimals?

Decimals are used in situations when more precision is needed. For instance, when two people cross the finish line, someone will win by a fraction of a second. We show those fractions as decimals. If you are spending money, many things are not worth an exact dollar amount.

Slide 7 (Answer) / 192 Why do we need decimals?

Decimals are used in situations when more precision is needed. For instance, when two people cross the finish line, someone will win by a fraction of a second. We show those fractions as decimals. If you are spending money, many things are not worth an exact dollar amount.

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Math Practice

MP.6 - Attend to precision. Ask the students to think, pair, share to come up with another example of when a more precise number is needed. MP.7 - Look for and make use of structure. Ask them to compare that with a situation that does not require as much precision. Ask, "Why is it important to round _____ decimal place in this situation/problem?

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Lets take a look at decimals on a number line. Click on the picture below for an interactive number line.

Decimals on a Number Line

Teacher Notes

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Return to Table

• f Contents

Identify Place Values

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• nes

tenths

hundredths

.

tens

hundreds

thousands

Our place value chart is almost like a mirror image, with a line between the ones place and the decimal point. Everything to the left ends in "s" and everything to the right ends in "ths"

thousandths

Place Value Chart

SLIDE 3

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• nes

tenths

hundredths

.

tens

hundreds

thousands

Our place value chart is almost like a mirror image, with a line between the ones place and the decimal point. Everything to the left ends in "s" and everything to the right ends in "ths"

thousandths

Place Value Chart

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Teacher Notes The words: place value tenths hundredths thousandths are linked to a vocabulary page in the glossary.

Slide 11 / 192 Place Value Chart Slide 11 (Answer) / 192 Place Value Chart

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Teacher Notes This chart can be printed for student use. Use this chart to practice identifying place value of digits in a decimal number. If needed, this chart can be used to practice reading and writing decimal numbers in standard, word and expanded forms.

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1 What digit is in the thousandths place? 987,654.0123 A 7

B

2 C 3 D 8

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1 What digit is in the thousandths place? 987,654.0123 A 7

B

2 C 3 D 8

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Answer

B Slide 13 / 192

2 What digit is in the tenths place? 987,654.0123 A 1

B

4 C D 5

SLIDE 4

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2 What digit is in the tenths place? 987,654.0123 A 1

B

4 C D 5

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Answer

C Slide 14 / 192

3 What digit is in the hundredths place? 987,654.0123 A 5

B

C 1 D 2

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3 What digit is in the hundredths place? 987,654.0123 A 5

B

C 1 D 2

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Answer

C Slide 15 / 192

What is the value of a yellow rod? one-tenth (0.1) Blue Block How many yellow rods are needed to fill the blue block? 10 Yellow Rod One Unit (1)

click click

Tenths Slide 15 (Answer) / 192

What is the value of a yellow rod? one-tenth (0.1) Blue Block How many yellow rods are needed to fill the blue block? 10 Yellow Rod One Unit (1)

click click

Tenths

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Teacher Notes

Use this page for students to gain an understanding

• f what tenths and

hundredths look like.

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Think of it in terms of money. How many dimes does it take to make a dollar? _________ dimes = 1 dollar So, a dime is one tenth of a whole dollar.

Money and Decimals

SLIDE 5

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Blue Block Red Block Yellow Rod How many red blocks are needed to fill the blue block? 100 (Hint: Fill a yellow rod with red blocks) What is the value of a red block?

• ne-hundredth (0.01)

One Unit (1)

click click

Hundredths Slide 17 (Answer) / 192

Blue Block Red Block Yellow Rod How many red blocks are needed to fill the blue block? 100 (Hint: Fill a yellow rod with red blocks) What is the value of a red block?

• ne-hundredth (0.01)

One Unit (1)

click click

Hundredths

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Teacher Notes

Use this page for students to gain an understanding

• f what tenths and

hundredths look like.

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Think of it in terms of money. How many pennies does it take to make a dollar? _________ pennies = 1 dollar So, a penny is one hundredth of a whole dollar.

Money and Decimals Slide 19 / 192

So a dollar is a whole. A dime is a tenth. And a penny is a hundredth.

• ne

tenth

hundredth

.

What if we had a coin that was smaller than a penny? How many times smaller than a penny do you think it would be? What would you call it?

Money and Decimals Slide 20 / 192

Blue = One Unit 3 yellow rods = 0.3 three tenths

Representing Units Slide 21 / 192

23 red blocks = 0.23 twenty three hundredths Blue = One Unit

Representing Units

SLIDE 6

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Interactive Number Grid - Use to Show Decimals

Click to Go to Interactive Site

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Interactive Number Grid - Use to Show Decimals

Click to Go to Interactive Site

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Teacher Notes

This site requires Flash 5 Plugin

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4 If the square equals one whole, what does the shaded area represent?

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4 If the square equals one whole, what does the shaded area represent?

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Answer

.33 Slide 24 / 192

5 If the square equals one whole, what does the shaded area represent?

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5 If the square equals one whole, what does the shaded area represent?

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Answer

.45

SLIDE 7

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6 If the square equals one whole, what does the shaded area represent?

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6 If the square equals one whole, what does the shaded area represent?

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Answer

.62 Slide 26 / 192

7 If the square equals one whole, what does the shaded area represent?

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7 If the square equals one whole, what does the shaded area represent?

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Answer

.4 Slide 27 / 192

8 If the square equals one whole, what does the shaded area represent?

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8 If the square equals one whole, what does the shaded area represent?

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Answer

.7

SLIDE 8

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• nes

tenth

hundredth

.

tens

hundreds

dime penny

thousands

Lets look at place value using money again. ______ pennies = 1 dime ______ dimes = 1 dollar bill ______ 1 dollar bills = 1 ten dollar bill ______ ten dollar bills = 1 hundred dollar bill What do you notice about place value?

Money and Decimals Slide 29 / 192 Place Value

As you look at the place value chart, how many times does the value of the number decrease as you go to the right?

Each place has a value that is one tenth of the value of its place to its left.

Click to reveal

Slide 29 (Answer) / 192 Place Value

As you look at the place value chart, how many times does the value of the number decrease as you go to the right?

Each place has a value that is one tenth of the value of its place to its left.

Click to reveal

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Math Practice

MP.2 - Reason Abstractly and Quantitatively By recognizing that as you move to the right in place value, the numbers decrease by a tenth, the students are making meaning of quantities and of relationships between quantities.

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10 ones = ten 10 tens = 1 hundred

• ne x 10 = ten x 10 = 1 hundred x 10 = 1 thousand...

Lets take a closer look at what happens as we move to the left on the place value chart.

Representing Units

Teacher Notes

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• nes

tenth

hundredth

.

tens

hundreds

dime penny

thousands

Lets look at place value using money again. A hundred dollars is ____ times as much as ten dollars A ten dollars is ____ times as much as a dollar A dollar is ____ times as much as a dime A dime is ____ times as much as a penny What do you notice about place value?

Money and Decimals Slide 31 (Answer) / 192

• nes

tenth

hundredth

.

tens

hundreds

dime penny

thousands

Lets look at place value using money again. A hundred dollars is ____ times as much as ten dollars A ten dollars is ____ times as much as a dollar A dollar is ____ times as much as a dime A dime is ____ times as much as a penny What do you notice about place value?

Money and Decimals

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Math Practice

MP.4 - Model with mathematics. For this standard, students should solve real life & society related questions and represent real life scenarios mathematically. Using money to solve problems comparing place value gives students an opportunity to do this.

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Slide 32 / 192 Place Value

As you look at the place value chart, how many times does the value of the number increase as you go to the left?

Each place has a value that is 10 times the value of its place to the right.

Click to reveal

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ten 10 = one 1 hundred 10 = ten 1 thousand 10 = 1 hundred 10 = ten 10 = 1 Lets take a closer look at what happens as we move to the right on the place value chart.

Representing Units Slide 33 (Answer) / 192

ten 10 = one 1 hundred 10 = ten 1 thousand 10 = 1 hundred 10 = ten 10 = 1 Lets take a closer look at what happens as we move to the right on the place value chart.

Representing Units

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Teacher Notes

Use the moveable pieces to show that ten is "one tenth" of 100, and one is "one tenth" of ten.

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Lets use place value to compare decimal #s.

.

tenths hundredths

33

.

0.3 + 0.03 The 3 in the tenths place is ten times as much as the 3 in the hundredths place. expanded form standard form thirty-three hundredths word form

Place Value Slide 34 (Answer) / 192

Lets use place value to compare decimal #s.

.

tenths hundredths

33

.

0.3 + 0.03 The 3 in the tenths place is ten times as much as the 3 in the hundredths place. expanded form standard form thirty-three hundredths word form

Place Value

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Teacher Notes

Writing numbers in word, standard and expanded form has been addressed

• previously. Take note if

you have students who need extra instruction/ practice with this skill. The words are also linked to vocabulary slides.

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.

tenths hundredths

44

.

0.4 + 0.04 The 4 in the hundredths place is

• ne tenth the 4 in the tenths place.

expanded form standard form word form forty-four hundredths

Place Value

SLIDE 10

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9 In the number 3.33, the digit in the tenths place is one tenth of the digit in the hundredths place. True False

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9 In the number 3.33, the digit in the tenths place is one tenth of the digit in the hundredths place. True False

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Answer

False Slide 37 / 192

10 In the number 11.111, the digit in the thousandths place is one tenth of the digit in the ________ place. A ones B tenths C hundredths

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10 In the number 11.111, the digit in the thousandths place is one tenth of the digit in the ________ place. A ones B tenths C hundredths

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Answer

C Slide 38 / 192

11 A digit in the ones place is 100 times as much as a digit in the ______ place. A ones B tenths C hundredths

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11 A digit in the ones place is 100 times as much as a digit in the ______ place. A ones B tenths C hundredths

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Answer

C

SLIDE 11

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12 The value of the 6 in 26.495 is _______________ the value of the 6 in 17.64. A 1/10 B 10 times C 1/100

From PARCC EOY sample test #18

D 100 times

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12 The value of the 6 in 26.495 is _______________ the value of the 6 in 17.64. A 1/10 B 10 times C 1/100

From PARCC EOY sample test #18

D 100 times

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Answer

A Slide 40 / 192

13 The value of the 3 in 0.931 is _______________ the value of the 3 in 0.384 A 1/10 B 10 times C 1/100

From PARCC EOY sample test #18

D 100 times

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13 The value of the 3 in 0.931 is _______________ the value of the 3 in 0.384 A 1/10 B 10 times C 1/100

From PARCC EOY sample test #18

D 100 times

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Answer

A Slide 41 / 192 Decimals on the Number Line

2 3

What does each line, between the whole numbers 2 and 3, represent on this number line ? Label the number line.

Slide 41 (Answer) / 192 Decimals on the Number Line

2 3

What does each line, between the whole numbers 2 and 3, represent on this number line ? Label the number line.

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Teacher Notes

Use the interactive number line if further exploration is needed.

SLIDE 12

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32 33

What does each line, between the whole numbers 32 and 33, represent on this number line ? Label the number line.

Decimals on the Number Line Slide 43 / 192

4.3 4.4

What does each line, between the decimal numbers 4.3 and 4.4, represent on this number line ? Label the number line.

Decimals on the Number Line Slide 44 / 192

0.63 0.64

What does each line, between the decimal numbers 0.63 and 0.64, represent on this number line? Label the number line.

Decimals on the Number Line Slide 45 / 192 National Library of Virtual Manipulatives

Click to go to web site. Change Places to "Decimals" at the bottom left.

Zoom in to drag the dot more precisely.

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14 Which letter corresponds to the number 4.4 on this number line? 10

A B C D

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14 Which letter corresponds to the number 4.4 on this number line? 10

A B C D

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Answer

C

SLIDE 13

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15 Which letter corresponds to the number 6.8 on this number line? 10

A B C D

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15 Which letter corresponds to the number 6.8 on this number line? 10

A B C D

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Answer

C Slide 48 / 192

16 Which letter corresponds to the number 0.8 on this number line? 1

A B C D

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16 Which letter corresponds to the number 0.8 on this number line? 1

A B C D

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Answer

C Slide 49 / 192

17 Which letter corresponds to the number 7.2 on this number line? 7 8

A B C D

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17 Which letter corresponds to the number 7.2 on this number line? 7 8

A B C D

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Answer

B

SLIDE 14

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18 Which letter corresponds to the number 19.3 on this number line? 19 20

A B C D

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18 Which letter corresponds to the number 19.3 on this number line? 19 20

A B C D

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Answer

C Slide 51 / 192

19 Which letter corresponds to the number 324.5 on this number line? 3 2 4 325

A B C D

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19 Which letter corresponds to the number 324.5 on this number line? 3 2 4 325

A B C D

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Answer

B Slide 52 / 192

20 Which letter corresponds to the number 5.35 on this number line?

A B C D

5.3 5.4

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20 Which letter corresponds to the number 5.35 on this number line?

A B C D

5.3 5.4

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Answer

C

SLIDE 15

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21 Which letter corresponds to the number 1.08 on this number line?

A B C D

Not plotted on this number line 1 1.1

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21 Which letter corresponds to the number 1.08 on this number line?

A B C D

Not plotted on this number line 1 1.1

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Answer

B Slide 54 / 192

22 Which letter corresponds to the number 6.23 on this number line?

A B C

6.2 6.3

D

Not plotted on this number line

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22 Which letter corresponds to the number 6.23 on this number line?

A B C

6.2 6.3

D

Not plotted on this number line

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Answer

B Slide 55 / 192

23 Which letter corresponds to the number 17.4 on this number line?

A B C

17.1 17.2

D

Not plotted on this number line

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23 Which letter corresponds to the number 17.4 on this number line?

A B C

17.1 17.2

D

Not plotted on this number line

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Answer

D

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Return to Table

• f Contents

Read & Write Decimals

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In this unit, we will be working with numbers written in standard, word, and expanded form. Lets review each.

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.

and

• nes

1 10 1 100 1 1,000 tenths hundredths thousandths

1

10

and and

3

4

three and four hundredths Word Form 2 3 5

1

two and three hundred fifty-one thousandths

8

eight tenths

Word Form

Word form is simply the number written using words instead of digits, commas, and a period when needed.

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To read decimal numbers we:

• 1. Read the number to the left of the decimal
• 2. Say "and" for the period
• 3. Read the number to the right of the decimal
• 4. State the place value of the last digit.

Reading Decimals Slide 60 / 192

Remember the place values after the decimal point start with tenths

million hundred thousand ten thousand thousand hundred ten

• ne

and tenth hundredth thousandth ten thousandth

9, 8 7 5, 6 1 0 . 4 7 9

This number is read: Nine million, eight hundred seventy-five thousand, six hundred ten AND four hundred seventy-nine thousandths

Reading Decimals Slide 61 / 192

. 7 5 4 6 . 2 5 9 8 . 3 . 8 9 . 1 1 2 3 5 4 . 6 9 . 7

Can You Read the Number?

thousands hundreds tens

• nes

and tenths hundredths thousandths

SLIDE 17

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Click on the the dice, and then read the number.

Dice Reading Slide 62 (Answer) / 192

Click on the the dice, and then read the number.

Dice Reading

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Teacher Notes

Click on the double arrows for the first dice and fill in whole

• numbers. Then click on the

double arrows for the second dice and fill in decimal numbers.

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• 1. Look to see if there is a number to the left of the decimal; if so

write it out. If there is no number to the left of the decimal, skip to step 3.

• 2. Write an and for the decimal point.
• 3. Write the number in the decimal part.
• 4. Write the word for the place value of the rightmost digit.

Writing Decimals in Words

Write 13.24 in words Thirteen and twenty-four hundredths

The numbers twenty-one through ninety-nine are always hyphenated.

Click to reveal

Click to reveal

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How does a comma help when writing a decimal number? The place value before the comma is always stated. For example: 1,547 is written One THOUSAND, five hundred forty-seven 6,547,100 is written 6 MILLION, five hundred forty-seven THOUSAND,

• ne hundred

Writing Decimals Slide 65 / 192 Write the Decimal in Words

1) 5.04 Five and four hundredths 2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths 3) .0009 Nine ten-thousandths 4) 6,345.149 Six thousand, three hundred forty-five and one hundred forty-nine thousandths

Slide 65 (Answer) / 192 Write the Decimal in Words

1) 5.04 Five and four hundredths 2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths 3) .0009 Nine ten-thousandths 4) 6,345.149 Six thousand, three hundred forty-five and one hundred forty-nine thousandths

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Math Practice

MP.1 - Make sense of problems and persevere in solving them.

Some students may not know where to

• begin. Sketching a place value chart, and

using comas and the decimal point as benchmarks may help. Ask: How could you start this problem? How could you make it easier to solve? What are you having trouble with? To guide them to using these strategies.

SLIDE 18

Slide 66 / 192 Slide 67 / 192 Web Site Practice Slide 67 (Answer) / 192 Web Site Practice

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Teacher Notes

Practice I gives a decimal in standard form, and has the students identify the word form. Practice II gives the decimal number verbally, and has the students identify the number given. (This can be saved for the next set of practice problems)

To use responders with these problems, start a multiple- choice instant question.

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24 What is 4.36 in word form? A

four and thirty-six

B

four and thirty-six tenths

C

four, thirty-six

D

four and thirty-six hundredths

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24 What is 4.36 in word form? A

four and thirty-six

B

four and thirty-six tenths

C

four, thirty-six

D

four and thirty-six hundredths

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Answer

D Slide 69 / 192

25 What is 63.067 in word form? A

sixty-three and sixty-seven hundredths

B

sixty-three and sixty-seven thousandths

C

sixty-three and sixty-seven

D

sixty-three, sixty-seven thousandths

SLIDE 19

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25 What is 63.067 in word form? A

sixty-three and sixty-seven hundredths

B

sixty-three and sixty-seven thousandths

C

sixty-three and sixty-seven

D

sixty-three, sixty-seven thousandths

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Answer

B Slide 70 / 192

26 What is 0.419 in word form? A

zero and four hundred nineteen

B

four hundred nineteen hundredths

C

four hundred nineteen thousandths

D

four one nine

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26 What is 0.419 in word form? A

zero and four hundred nineteen

B

four hundred nineteen hundredths

C

four hundred nineteen thousandths

D

four one nine

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Answer

C Slide 71 / 192

27 What is 0.09 in

word form?

A nine and nine B nine hundredths C nine and nine hundredths D nine and zero nine tenths

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27 What is 0.09 in

word form?

A nine and nine B nine hundredths C nine and nine hundredths D nine and zero nine tenths

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Answer

B Slide 72 / 192

28 What is 407.021 in

word form? A four zero seven zero two one B four hundred seven twenty-one C four hundred seven and twenty-one thousandths D four hundred seven and twenty-one hundredths

SLIDE 20

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28 What is 407.021 in

word form? A four zero seven zero two one B four hundred seven twenty-one C four hundred seven and twenty-one thousandths D four hundred seven and twenty-one hundredths

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Answer

C Slide 73 / 192 Standard Form

Standard form is the way we usually see numbers written, using digits, commas and a period when needed. Standard Form 10.88 0.387 92.3 6.91

Slide 74 / 192 Standard Form

• 1. If there is a ths, there will be a decimal
• 2. If there is an and, there will be a whole number to the left of

the decimal

• 3. Note the ending - this is the place where the decimal number

will end

• 4. Use the decimal chart to help you!

Slide 75 / 192

Use the chart as a guide to write the decimal numbers in standard form.

• 1. two hundred sixteen and 2 tenths
• 2. thirty-two and nine thousandths
• 3. four thousand, five hundred six and twenty-four hundredths
• 4. nine hundred and eight hundredths

thousands hundreds tens

• nes

and tenths hundredths thousandths

Standard Form Chart Slide 76 / 192 Web Site Practice Slide 76 (Answer) / 192 Web Site Practice

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Teacher Notes

Practice I gives a decimal in standard form, and has the students identify the word form. Practice II gives the decimal number verbally, and has the students identify the number given. (This can be saved for the next set of practice problems)

To use responders with these problems, start a multiple- choice instant question.

SLIDE 21

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29 What is fifty-two and eighteen hundredths?

A 52,18 B 52.018 C 52.18 D 52.0018

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29 What is fifty-two and eighteen hundredths?

A 52,18 B 52.018 C 52.18 D 52.0018

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Answer

C Slide 78 / 192

30 What is five thousand, fifty and five hundredths?

A 550.5 B 5,050.5

C

5,050.05

D

5,500.05

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30 What is five thousand, fifty and five hundredths?

A 550.5 B 5,050.5

C

5,050.05

D

5,500.05

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Answer

C Slide 79 / 192

31 What is six hundred three and four thousandths?

A 603.4 B 603.004 C 603.04 D 603.0004

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31 What is six hundred three and four thousandths?

A 603.4 B 603.004 C 603.04 D 603.0004

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Answer

B

SLIDE 22

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32 What is thirty-four hundredths?

A 340 B 34 C 0.34 D 0.034

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32 What is thirty-four hundredths?

A 340 B 34 C 0.34 D 0.034

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Answer

C Slide 81 / 192

33 What is four hundred ninety-five thousandths? A 495 B 495.000 C 0.0495 D 0.495

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33 What is four hundred ninety-five thousandths? A 495 B 495.000 C 0.0495 D 0.495

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Answer

D Slide 82 / 192

To write a number in expanded form, the number is written as a sum of the value of each digit. Place value charts make it easy to write numbers in expanded form, because it helps us see the value of each digit. 3 + 0.04 2 + 0.3 + 0.04 + 0.001 0.8

.

and

• nes

1 10 1 100 1 1,000 tenths hundredths thousandths

1

10

and and

3

4

Expanded Form 2 3 5

1 8

Expanded Form Slide 83 / 192

0.008

0.03 0.5

2

SLIDE 23

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0.008

0.03 0.5

2

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Teacher Notes

Use this tool as a place value visual to model expanded form to the

• students. (Pull the

numbers apart.) Show how it breaks down to 2 + 0.5 + 0.03 + 0.008

Slide 84 / 192

100 + 20 + 9 + 0.2 + 0.04 This interactive game will help you practice writing numbers in expanded form. As a class, select the correct building blocks for each place value, then write the number in expanded form. Check your work as a class.

Decimal Place Value Game Slide 85 / 192 Slide 86 / 192

34 What is 80 + 0.2 + 0.03 in standard form?

Slide 86 (Answer) / 192

34 What is 80 + 0.2 + 0.03 in standard form?

[This object is a pull tab]

Answer

80.23 Slide 87 / 192

35 What is 0.5 + 0.004 in standard form?

SLIDE 24

Slide 87 (Answer) / 192

35 What is 0.5 + 0.004 in standard form?

[This object is a pull tab]

Answer

0.504 Slide 88 / 192

36 Which is equivalent to 30.53? A 30+0.5+0.3 B 3+0.05+0.03 C 0.3+0.05+0.003 D 30+0.05+0.003

Slide 88 (Answer) / 192

36 Which is equivalent to 30.53? A 30+0.5+0.3 B 3+0.05+0.03 C 0.3+0.05+0.003 D 30+0.05+0.003

[This object is a pull tab]

Answer

C Slide 89 / 192

37 Which is equivalent to 0.873? A 0.8+0.07+0.03 B 8+0.7+0.3 C 0.8+0.07+0.3 D 0.8+0.07+0.003

Slide 89 (Answer) / 192

37 Which is equivalent to 0.873? A 0.8+0.07+0.03 B 8+0.7+0.3 C 0.8+0.07+0.3 D 0.8+0.07+0.003

[This object is a pull tab]

Answer

D Slide 90 / 192

38 Which number is equivalent to 0.08? A eight tenths B 0.8 + 0.08 C eight hundredths

SLIDE 25

Slide 90 (Answer) / 192

38 Which number is equivalent to 0.08? A eight tenths B 0.8 + 0.08 C eight hundredths

[This object is a pull tab]

Answer

C Slide 91 / 192

39 Which number is equivalent to 0.3 + 0.004 A 3.04 B 0.34 C three hundred four thousandths

Slide 91 (Answer) / 192

39 Which number is equivalent to 0.3 + 0.004 A 3.04 B 0.34 C three hundred four thousandths

[This object is a pull tab]

Answer

C Slide 92 / 192

40 Which number is equivalent to sixteen hundredths? A 0.016 B .1 + 0.06 C .01 + 0.06

Slide 92 (Answer) / 192

40 Which number is equivalent to sixteen hundredths? A 0.016 B .1 + 0.06 C .01 + 0.06

[This object is a pull tab]

Answer

B Slide 93 / 192

SLIDE 26

Slide 93 (Answer) / 192 Slide 94 / 192

Return to Table

• f Contents

Compare & Order Decimals

Slide 95 / 192

One number goes on the left of the symbol and another number goes on the right of the symbol. The number on the left of the ">" shows the larger number. For example: 2 > 1 2 is "greater than" 1 The number on the left of the "<" shows the smaller number. For example: 1 < 2 1 is "less than" 2

Inequalities

There are two symbols we use to compare numbers when they are not equal. We call these number sentences inequalities. > (greater than) < (less than)

Slide 96 / 192

Symbols and Words to remember when comparing numbers SYMBOL WORDS > < = greater than/largest less than/ smallest equal

Inequality Symbols Slide 97 / 192 Comparing Decimals

· Line up the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number

Slide 98 / 192

0.045 0.210 Compare 0.045 and 0.21 · Line up the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number

put zero

• n the

end Compare left to right. 2 is greater than 0, so 0.21 is greatest.

0.045 < 0.21

Click to reveal

Comparing Decimals

SLIDE 27

Slide 99 / 192

0.360 0.312 Compare 0.36 and 0.312 · Line up the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number

put zero

• n the

end Compare left to right. 6 is greater than 1, so 0.36 is greatest.

0.36 > 0.312

Click to reveal

Comparing Decimals Slide 100 / 192

0.009 0.020 Compare 0.009 and 0.02 · Line up the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number

put zero

• n the

end Compare left to right. 2 is greater than 0, so 0.02 is greatest.

0.009 < 0.02

Click to reveal

Comparing Decimals Slide 101 / 192 Decimal Squares Interactive Games

Click for link.

Game could also be played with two students having a spinner and writing down their decimal number. In this game the robot won, because 0.7950 is greater than 0.5021.

Slide 102 / 192

42 Choose the correct symbol.

0.41 0.049

A > B < C =

Slide 102 (Answer) / 192

42 Choose the correct symbol.

0.41 0.049

A > B < C =

[This object is a pull tab]

Answer

A Slide 103 / 192

43 Choose the correct symbol. A > B <

0.301 three hundred eleven thousandths

C =

SLIDE 28

Slide 103 (Answer) / 192

43 Choose the correct symbol. A > B <

0.301 three hundred eleven thousandths

C =

[This object is a pull tab]

Answer

B Slide 104 / 192

44 Choose the correct symbol. A > B <

0.007 0.05

C =

Slide 104 (Answer) / 192

44 Choose the correct symbol. A > B <

0.007 0.05

C =

[This object is a pull tab]

Answer

B Slide 105 / 192

45 Choose the correct symbol. A > B < 0.179 twenty-four hundredths C =

Slide 105 (Answer) / 192

45 Choose the correct symbol. A > B < 0.179 twenty-four hundredths C =

[This object is a pull tab]

Answer

B Slide 106 / 192

46 Choose the correct symbol. A > B <

forty-six hundredths 0.6

C =

SLIDE 29

Slide 106 (Answer) / 192

46 Choose the correct symbol. A > B <

forty-six hundredths 0.6

C =

[This object is a pull tab]

Answer

B Slide 107 / 192

47 Select from the choices to correctly complete the comparison. A > B <

4.408 four and forty-eight thousanths

C =

From PARCC PBA sample test #3

Slide 107 (Answer) / 192

47 Select from the choices to correctly complete the comparison. A > B <

4.408 four and forty-eight thousanths

C =

From PARCC PBA sample test #3

[This object is a pull tab]

Answer

A Slide 108 / 192

48 Select from the choices to correctly complete the comparison. A > B < six hundred ninety-one and five hundredths 6 x 100 + 9 x 10 + 1 + 8 x 11,000 C =

From PARCC PBA sample test #3

Slide 108 (Answer) / 192

48 Select from the choices to correctly complete the comparison. A > B < six hundred ninety-one and five hundredths 6 x 100 + 9 x 10 + 1 + 8 x 11,000 C =

From PARCC PBA sample test #3

[This object is a pull tab]

Answer

B Slide 109 / 192

Teachers: Use this Mathematical Practice Pull Tab for the next slide.

Teacher Note

SLIDE 30

Slide 109 (Answer) / 192

Teachers: Use this Mathematical Practice Pull Tab for the next slide.

Teacher Note

[This object is a pull tab]

Math Practice MP.3 - Construct viable arguments and critique the reasoning of others. If the answer is not unanimous, give the students an opportunity to justify their response and evaluate the reasoning of others. Ensure that they are listening to and questioning other students. Ask: How was your answer different than some of your classmates? How did you reach that conclusion? Why is that true? Who would like to share a different way of answering the problem?

Slide 110 / 192

49 In a paper airplane contest, Marcel's plane travels 3.345

• meters. Salvador's plane travels 3.35 meters. Based on

the measurements, whose plane traveled the farthest distance? On your paper, explain how you know. A Marcel

Derived from

( (

B Salvador

Slide 110 (Answer) / 192

49 In a paper airplane contest, Marcel's plane travels 3.345

• meters. Salvador's plane travels 3.35 meters. Based on

the measurements, whose plane traveled the farthest distance? On your paper, explain how you know. A Marcel

Derived from

( (

B Salvador

[This object is a pull tab]

Answer

B

If you have struggling students, this is a good

• pportunity to utilize

"think, pair, share." This will provide students with a platform to learn from each other.

Slide 111 / 192 Ordering Decimals

· Line up all of the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number Example: 910.800 085.007 910.801 911.900 085.070 What digit tells us this is the largest number? 1 Why is this the smallest number? Compare the digits

click

Slide 112 / 192

50 The number with the least value is:

A

61.005

B

61.3

C

61.05

D

61.04

Slide 112 (Answer) / 192

50 The number with the least value is:

A

61.005

B

61.3

C

61.05

D

61.04

[This object is a pull tab]

Answer

A

SLIDE 31

Slide 113 / 192

51 The number with the least value is: A 0.005 B 0.5 C 0.05 D 0.0005

Slide 113 (Answer) / 192

51 The number with the least value is: A 0.005 B 0.5 C 0.05 D 0.0005

[This object is a pull tab]

Answer

D Slide 114 / 192

52 The number with the greatest value is: A 9.888 B 9.8 C 9.008 D 9.088

Slide 114 (Answer) / 192

52 The number with the greatest value is: A 9.888 B 9.8 C 9.008 D 9.088

[This object is a pull tab]

Answer

A Slide 115 / 192

53 The number with the greatest value is: A 0.67 B 0.067 C 0.0067 D 0.00067

Slide 115 (Answer) / 192

53 The number with the greatest value is: A 0.67 B 0.067 C 0.0067 D 0.00067

[This object is a pull tab]

Answer

A

SLIDE 32

Slide 116 / 192

54 How much money would you like to win?

A

$150.59

B

$140.99

C

$150.82

D

$140.50

Slide 116 (Answer) / 192

54 How much money would you like to win?

A

$150.59

B

$140.99

C

$150.82

D

$140.50

[This object is a pull tab]

Answer

C Slide 117 / 192

55 Using the following digits, create the largest number you can between 0 and 1.

1 7 2 , , , Slide 117 (Answer) / 192

55 Using the following digits, create the largest number you can between 0 and 1.

1 7 2 , , ,

[This object is a pull tab]

Answer

.7210 Slide 118 / 192

56 Using the following digits, create the smallest number you can between 0 and 1.

1 7 2 , , , Slide 118 (Answer) / 192

56 Using the following digits, create the smallest number you can between 0 and 1.

1 7 2 , , ,

[This object is a pull tab]

Answer

.0127

SLIDE 33

Slide 119 / 192

Order the numbers from least to greatest. Move the numbers to put them in order.

Ordering Decimals

15 1.5 0.015 0.15

Slide 119 (Answer) / 192

Order the numbers from least to greatest. Move the numbers to put them in order.

Ordering Decimals

15 1.5 0.015 0.15

[This object is a pull tab]

Math Practice

MP.5 - Use appropriate tools strategically. Ask students to share their method for comparing the numbers. Did they use mental math, a place value chart, lining up the decimals without needing a chart. Ask: What strategy did you use? Could you do this mentally?

Slide 120 / 192

Order the numbers from greatest to least. Move the numbers to put them in order.

Ordering Decimals

0.709 0.009 0.68 0.08 0.07

Slide 121 / 192

57 Which of the following is ordered least to greatest? A 0.3, 0.03, 0.33, 3.3 B 0.03, 0.3, 0.33, 3.3 C 0.03, 0.33, 0.3, 3.3

Slide 121 (Answer) / 192

57 Which of the following is ordered least to greatest? A 0.3, 0.03, 0.33, 3.3 B 0.03, 0.3, 0.33, 3.3 C 0.03, 0.33, 0.3, 3.3

[This object is a pull tab]

Answer

B Slide 122 / 192

58 Which of the following is ordered least to greatest? A 0.008, 0.06, 0.5 B 0.5, 0.06, 0.008 C 0.06, 0.5, 0.008

SLIDE 34

Slide 122 (Answer) / 192

58 Which of the following is ordered least to greatest? A 0.008, 0.06, 0.5 B 0.5, 0.06, 0.008 C 0.06, 0.5, 0.008

[This object is a pull tab]

Answer

A Slide 123 / 192

59 Which of the following is ordered greatest to least? A 8.07, 0.008, 0.087, 0.87 B 0.008, 0.087, 0.87, 8.07 C 8.07, 0.87, 0.087, 0.008

Slide 123 (Answer) / 192

59 Which of the following is ordered greatest to least? A 8.07, 0.008, 0.087, 0.87 B 0.008, 0.087, 0.87, 8.07 C 8.07, 0.87, 0.087, 0.008

[This object is a pull tab]

Answer

C Slide 124 / 192

60 Which of the following is not correct? A 0.23 > 0.08 > 0.009 B 0.23 > 0.009 > 0.08 C 0.009 < 0.08 < 0.23

Slide 124 (Answer) / 192

60 Which of the following is not correct? A 0.23 > 0.08 > 0.009 B 0.23 > 0.009 > 0.08 C 0.009 < 0.08 < 0.23

[This object is a pull tab]

Answer

B Slide 125 / 192

61 Which of the following is correct? A 0.8 < 0.32 < 0.41 < 0.701 B 0.8 > 0.701 > 0.41 > 0.32 C 0.32 > 0.41 > 0.701 > 0.8

SLIDE 35

Slide 125 (Answer) / 192

61 Which of the following is correct? A 0.8 < 0.32 < 0.41 < 0.701 B 0.8 > 0.701 > 0.41 > 0.32 C 0.32 > 0.41 > 0.701 > 0.8

[This object is a pull tab]

Answer

B Slide 126 / 192

62 In a paper airplane contest, Marcel's plane travels 3.345

• meters. Salvador's plane travels 3.35 meters. Jennifer's

plane travels 3.3 meters. Based on the measurements, who won the contest? On your paper, explain your answer. A Marcel B Salvador

Derived from

( (

C Jennifer

Slide 126 (Answer) / 192

62 In a paper airplane contest, Marcel's plane travels 3.345

• meters. Salvador's plane travels 3.35 meters. Jennifer's

plane travels 3.3 meters. Based on the measurements, who won the contest? On your paper, explain your answer. A Marcel B Salvador

Derived from

( (

C Jennifer

[This object is a pull tab]

Answer

B

If you have struggling students, this is a good

• pportunity to utilize

"think, pair, share." This will provide students with a platform to learn from each other.

Slide 127 / 192

Return to Table

• f Contents

Round Numbers to Designated Place Values

Slide 128 / 192

• 1. Roll the die.
• 2. Click the yellow arrow to pop out the number.
• 3. Move the number to the correct place on the number

line.

• 4. Determine whether the number is closer to 0 or 10.

The dotted line shows the halfway mark between 0 and 10. Instructions for the next slide: This can be repeated six times.

Number Line Investigation Slide 129 / 192

10

Number Line Investigation

SLIDE 36

Slide 129 (Answer) / 192

10

Number Line Investigation

[This object is a pull tab]

Math Practice

MP.8 - Look for and express regularity in repeated reasoning. Student think, pair, share. Ask: What rule can you use to determine whether any given number is closer to 0 or 10? After share-out. Ask: How can you use this to tackle similar problems?

Slide 130 / 192

Rounding makes numbers easier to work with in your head. · Rounded numbers are only approximate. · An exact answer generally can not be obtained using rounded numbers. · Use rounding to get an answer that is close and does not have to be exact.

Rounding Slide 131 / 192

• 1. Put your pencil point under the digit in the tens place.

Look to the right.

• 2. Is the digit 5 or more?

Yes OR No

• 3. What happens to the digit?

Increases by 1 OR remains the same

• 4. What happens to everything to the left of the tens place?

Those digits always remain the same.

• 5. What happens to everything to the right of the tens place?

Those digits become zero.

Round 8,749 to the nearest ten.

Review

Slide 131 (Answer) / 192

• 1. Put your pencil point under the digit in the tens place.

Look to the right.

• 2. Is the digit 5 or more?

Yes OR No

• 3. What happens to the digit?

Increases by 1 OR remains the same

• 4. What happens to everything to the left of the tens place?

Those digits always remain the same.

• 5. What happens to everything to the right of the tens place?

Those digits become zero.

Round 8,749 to the nearest ten.

Review

[This object is a pull tab]

Teacher Notes

Move pencil under the digit that is being rounded to

Slide 132 / 192

Round 8,749 to the nearest hundred.

Review

• 1. Put your pencil point under the digit in the tens place.

Look to the right.

• 2. Is the digit 5 or more?

Yes OR No

• 3. What happens to the digit?

Increases by 1 OR remains the same

• 4. What happens to everything to the left of the hundreds place?

Those digits always remain the same.

• 5. What happens to everything to the right of the hundreds place?

Those digits become zero.

Slide 132 (Answer) / 192

Round 8,749 to the nearest hundred.

Review

• 1. Put your pencil point under the digit in the tens place.

Look to the right.

• 2. Is the digit 5 or more?

Yes OR No

• 3. What happens to the digit?

Increases by 1 OR remains the same

• 4. What happens to everything to the left of the hundreds place?

Those digits always remain the same.

• 5. What happens to everything to the right of the hundreds place?

Those digits become zero.

[This object is a pull tab]

Teacher Notes

Move pencil under the digit that is being rounded to

SLIDE 37

Slide 133 / 192

63 Round

143 to the nearest ten.

Slide 133 (Answer) / 192

63 Round

143 to the nearest ten.

[This object is a pull tab]

Answer

140 Slide 134 / 192

64 Round

4,561 to the nearest hundred.

Slide 134 (Answer) / 192

64 Round

4,561 to the nearest hundred.

[This object is a pull tab]

Answer

4,600 Slide 135 / 192

65 Round

564,012 to the nearest

hundred thousand.

Slide 135 (Answer) / 192

65 Round

564,012 to the nearest

hundred thousand.

[This object is a pull tab]

Answer

600,000

SLIDE 38

Slide 136 / 192

66 Round

7,399 to the nearest thousand.

Slide 136 (Answer) / 192

66 Round

7,399 to the nearest thousand.

[This object is a pull tab]

Answer

7,000 Slide 137 / 192

67 Round

63,752 to the nearest hundred.

Slide 137 (Answer) / 192

67 Round

63,752 to the nearest hundred.

[This object is a pull tab]

Answer

63,800 Slide 138 / 192

What happens in this case? Round 697 to the nearest ten. The 7 to the right of the 9 tells us to increase the 9 by 1. What happens? Answer ____________

Rounding Slide 139 / 192

68 Round 3,972 to the nearest hundred.

SLIDE 39

Slide 139 (Answer) / 192

68 Round 3,972 to the nearest hundred.

[This object is a pull tab]

Answer

4,000 Slide 140 / 192

69 Round 98 to the nearest ten.

Slide 140 (Answer) / 192

69 Round 98 to the nearest ten.

[This object is a pull tab]

Answer

100 Slide 141 / 192

70 Round 399,238 to the nearest ten thousand.

Slide 141 (Answer) / 192

70 Round 399,238 to the nearest ten thousand.

[This object is a pull tab]

Answer

400,000 Slide 142 / 192

71 Round 9,521 to the nearest thousand.

SLIDE 40

Slide 142 (Answer) / 192

71 Round 9,521 to the nearest thousand.

[This object is a pull tab]

Answer

10,000 Slide 143 / 192

72 Round 9,983 to the nearest hundred.

Slide 143 (Answer) / 192

72 Round 9,983 to the nearest hundred.

[This object is a pull tab]

Answer

10,000 Slide 144 / 192

• 1. Roll the die.
• 2. Click the yellow arrow to pop out the number.
• 3. Position the number in the correct place on the number line.
• 4. Determine whether the number is closer to 1 or 2. The dotted line

shows the halfway mark between 1 and 2. Instructions for the next slide: This can be repeated six times.

Number Line Investigation Slide 145 / 192

1 2 Think, Pair, Share: What rule can you use to determine whether any given number is closer to 1 or to 2?

Number Line Investigation Slide 146 / 192

Let's learn how to round decimals using the following examples: Round 687.268 to the nearest tenths place. When rounding decimals, put your pencil point under the place value that you are rounding to DO NOT MOVE IT

687.268

Rounding Decimals

SLIDE 41

Slide 147 / 192

• 1. Put your pencil point under the digit in the tenths

place. Look to the right.

• 2. Is the digit 5 or more?

Yes OR No

• 3. What happens to the digit?

Increases by 1 OR remains the same

• 4. What happens to everything to the left of the tenths

place? Those digits always remain the same.

Round 687.268 to the nearest tenth. Slide 148 / 192

• 5. What happened to the digits to the right of the tenths place?

Remember, we are rounding. The place values to the right of the tenths place have zero value, so now the digits 6 and 8 become zeroes. 687.300 = 687.3 However we leave the zeros off when they are at the end of a number to the right of the decimal point.

Rounding Decimals Slide 149 / 192

• 1. Put your pencil point under the digit in the hundredths place.

Look to the right.

• 2. Is the digit 5 or more?

Yes OR No

• 3. What happens to the digit?

Increases by 1 OR remains the same

• 4. What happens to everything to the left of the hundredths place?

Those digits always remain the same.

• 5. What happens to everything to the right of the hundredths place?

Those digits become zero (and we leave them

• ff since they are to the right of the decimal).

Round 8.73258 to the hundredths place. Slide 150 / 192 Slide 151 / 192

Try this: Round 687.4953 to the nearest hundredths place Answer: 687.50

Click to reveal

Rounding Practice Slide 152 / 192

73 Round 6874.6479 to the nearest hundredth.

SLIDE 42

Slide 152 (Answer) / 192

73 Round 6874.6479 to the nearest hundredth.

[This object is a pull tab]

Answer

6874.65 Slide 153 / 192

74 Round 6874.6479 to the nearest ten.

Slide 153 (Answer) / 192

74 Round 6874.6479 to the nearest ten.

[This object is a pull tab]

Answer

6870 Slide 154 / 192

75 Round 6874.6479 to the nearest hundred.

Slide 154 (Answer) / 192

75 Round 6874.6479 to the nearest hundred.

[This object is a pull tab]

Answer

6,900 Slide 155 / 192

76 Round 6874.6479 to the nearest tenth.

SLIDE 43

Slide 155 (Answer) / 192

76 Round 6874.6479 to the nearest tenth.

[This object is a pull tab]

Answer

6874.6 Slide 156 / 192

77 Round 6874.6479 to the nearest thousand.

Slide 156 (Answer) / 192

77 Round 6874.6479 to the nearest thousand.

[This object is a pull tab]

Answer

7,000 Slide 157 / 192

78 Round 6874.6479 to the nearest thousandth.

Slide 157 (Answer) / 192

78 Round 6874.6479 to the nearest thousandth.

[This object is a pull tab]

Answer

6874.648 Slide 158 / 192

When rounding to a specific place, your answer MUST have a digit in that place. Example: Round 23.97 to the nearest tenth Answer: 24.0 There must be a digit in the tenths place, since we were to round to the tenths place.

Caution!

SLIDE 44

Slide 159 / 192

79 Round 678.97 to the nearest tenth.

Slide 159 (Answer) / 192

79 Round 678.97 to the nearest tenth.

[This object is a pull tab]

Answer

679.0 Slide 160 / 192

80 Round 6.304 to the nearest hundredth.

Slide 160 (Answer) / 192

80 Round 6.304 to the nearest hundredth.

[This object is a pull tab]

Answer

6.30 Slide 161 / 192

81 Round 5.03 to the nearest tenth.

Slide 161 (Answer) / 192

81 Round 5.03 to the nearest tenth.

[This object is a pull tab]

Answer

5.0

SLIDE 45

Slide 162 / 192

82 Round 0.3497 to the nearest thousandth.

Slide 162 (Answer) / 192

82 Round 0.3497 to the nearest thousandth.

[This object is a pull tab]

Answer

0.350 Slide 163 / 192

83 Round 84.951 to the nearest tenth.

Slide 163 (Answer) / 192

83 Round 84.951 to the nearest tenth.

[This object is a pull tab]

Answer

85.0 Slide 164 / 192

84 A decimal number has two digits to the right of its decimal

• point. If we round it to the nearest tenth, the result is

18.6. What is the maximum possible value of this decimal? On your paper, use words and the number line to explain your reasoning.

Problem derived from

( (

Slide 164 (Answer) / 192

84 A decimal number has two digits to the right of its decimal

• point. If we round it to the nearest tenth, the result is

18.6. What is the maximum possible value of this decimal? On your paper, use words and the number line to explain your reasoning.

Problem derived from

( (

[This object is a pull tab]

Answer

18.64

SLIDE 46

Slide 165 / 192

85 A decimal number has two digits to the right of its decimal

• point. If we round it to the nearest tenth, the result is

18.6. What is the minimum possible value of this decimal? On your paper, use words and the number line to explain your reasoning.

Problem derived from

( (

Slide 165 (Answer) / 192

85 A decimal number has two digits to the right of its decimal

• point. If we round it to the nearest tenth, the result is

18.6. What is the minimum possible value of this decimal? On your paper, use words and the number line to explain your reasoning.

Problem derived from

( (

[This object is a pull tab]

Answer

18.55 Slide 166 / 192

86 Jules reads that one pint is equivalent to 0.473 liters. He asks his teacher how many liters there are in a pint. His teacher responds that there are about 0.47 liters in a

• pint. He asks his parents, and they say there are about

0.5 liters in a pint. Who is correct? On your paper, explain your answer. A His teacher B His parents

Problem derived from

( (

C Both of them

Slide 166 (Answer) / 192

86 Jules reads that one pint is equivalent to 0.473 liters. He asks his teacher how many liters there are in a pint. His teacher responds that there are about 0.47 liters in a

• pint. He asks his parents, and they say there are about

0.5 liters in a pint. Who is correct? On your paper, explain your answer. A His teacher B His parents

Problem derived from

( (

C Both of them

[This object is a pull tab]

Answer

A

Consider having students write their explanations, submit their answers, then pair-share with a partner or their group, before discussing it as a class. Or have them choose a corner of the room (assign a letter to each of 3 corners) and justify their answer. Students can then persuade each

• ther to arrive at the correct answer.

Slide 167 / 192

87 Rainfall collected in a rain gauge was found to be 3.4 cm when rounded to the nearest tenth of a centimeter. Select all the measurements below that could be the actual measurement of the rainfall. A 3.251 cm B 3.349 cm C 3.352 cm D 3.295 cm

Slide 167 (Answer) / 192

87 Rainfall collected in a rain gauge was found to be 3.4 cm when rounded to the nearest tenth of a centimeter. Select all the measurements below that could be the actual measurement of the rainfall. A 3.251 cm B 3.349 cm C 3.352 cm D 3.295 cm

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Answer

C

SLIDE 47

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88 Annual rainfall total for cities in New York are listed below. Rochester 0.97 meters Ithaca 0.947 meters Saratoga Springs 1.5 meters New York City 1.268 meters Round the smallest total rainfall to the nearest tenth.

Derived from

( (

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88 Annual rainfall total for cities in New York are listed below. Rochester 0.97 meters Ithaca 0.947 meters Saratoga Springs 1.5 meters New York City 1.268 meters Round the smallest total rainfall to the nearest tenth.

Derived from

( (

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Answer

0.9 meters Slide 169 / 192

Drag and drop one number into each box. When you are finished, the number inside each box should match the number below the box when rounded to the nearest hundredth.

Drag and Drop

From PARCC EOY sample test #6

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Use rounding to estimate answers to problems. At a restaurant, a burger is $5.99, fries are $3.85 and a small drink is $1.29. Round to the nearest dollar to estimate the cost to purchase all three items. Cost Estimate $5.99 $6 $3.85 $4 $1.29 $1 It would cost about $11 to purchase all three items.

Estimating Answers Slide 171 / 192

89 Round the following items, to the nearest dollar, to figure out the approximate cost if all of the items were bought.

pens $2.99 pencils $2.20 book bag $15.75

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89 Round the following items, to the nearest dollar, to figure out the approximate cost if all of the items were bought.

pens $2.99 pencils $2.20 book bag $15.75

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Answer

$3+$2+$16 =$21.00

SLIDE 48

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90 Round the following items to the nearest dollar to figure

• ut the approximate cost if all of the items were bought.

jeans $24.99 t-shirt $6.79 hat $12.31

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90 Round the following items to the nearest dollar to figure

• ut the approximate cost if all of the items were bought.

jeans $24.99 t-shirt $6.79 hat $12.31

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Answer

$25+$7+$12 =$44.00 Slide 173 / 192

91 Round the following items to the nearest dollar to figure

• ut the approximate cost if all of the items were bought.

milk $3.79 bread $2.15 juice $2.40

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91 Round the following items to the nearest dollar to figure

• ut the approximate cost if all of the items were bought.

milk $3.79 bread $2.15 juice $2.40

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Answer

$4+$2+$2 = $8 Slide 174 / 192

92 Round the following items to the nearest half dollar to figure out the approximate cost if all of the items were bought.

chicken $8.60 potatoes $2.45 peas $0.99

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92 Round the following items to the nearest half dollar to figure out the approximate cost if all of the items were bought.

chicken $8.60 potatoes $2.45 peas $0.99

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Answer

$9.00+$2.50+$1.00 =$12.50

SLIDE 49

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93 Round the following items to the nearest half dollar to figure out the cost if all of the items were bought.

apples $4.60 bananas $1.90

• ranges $3.10

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93 Round the following items to the nearest half dollar to figure out the cost if all of the items were bought.

apples $4.60 bananas $1.90

• ranges $3.10

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Answer

$5.00+$2.00+3.00= $10.00 Slide 176 / 192

94 Round the following items to the nearest ten dollars to figure out the approximate cost if all of the items were bought.

sneakers $36.21 sweatshirt $13.99 socks $6.00

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94 Round the following items to the nearest ten dollars to figure out the approximate cost if all of the items were bought.

sneakers $36.21 sweatshirt $13.99 socks $6.00

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Answer

$40.00+$10.00+$10.00= $60.00 Slide 177 / 192

95 Round the following items to the nearest hundred dollars to figure out the approximate cost if all of the items were bought.

computer$688.23 printer $213.50 desk $175.89

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95 Round the following items to the nearest hundred dollars to figure out the approximate cost if all of the items were bought.

computer$688.23 printer $213.50 desk $175.89

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Answer

$700+$200+$200= $1100

SLIDE 50

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96 Which numbers show 1,034.17 rounded correctly to different place values? Select the three correct answers. A 1,000 B 1,030 C 1,035 D 1,100 E 1,034.1 F 1.034.2

From PARCC PBA sample test #12 Part B

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96 Which numbers show 1,034.17 rounded correctly to different place values? Select the three correct answers. A 1,000 B 1,030 C 1,035 D 1,100 E 1,034.1 F 1.034.2

From PARCC PBA sample test #12 Part B

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Answer

A, B, F Slide 179 / 192

Return to Table

• f Contents

Glossary & Standards

Slide 179 (Answer) / 192

Return to Table

• f Contents

Glossary & Standards

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Teacher Notes

Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end

• f the presentation with the

word defined on it.

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Standards for Mathematical Practices MP8 Look for and express regularity in repeated reasoning. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure.

Click on each standard to bring you to an example of how to meet this standard within the unit.

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Back to Instruction

A Decimal Number (based on the number 10, tenth parts, and powers of ten) contains a Decimal Point.

Decimal Number

SLIDE 51

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Back to Instruction

Expanded Form

When a number is written as a sum of the value of each digit.

0.456= 0.4 + 0.05 + 0.006

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Back to Instruction

Greater Than

A symbol that shows that the number on the left is larger than the number on the right. .4 > .2

four tenths is greater than two tenths

the alligator eats the bigger number

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0.01

Back to Instruction

Hundredths

A part of one whole that has been divided into 100 equal parts. Also, a part of one tenth that has been divided into 10 equal parts.

0.01

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Back to Instruction

Inequality

A number statement that shows that two numbers are not equal. .4 > .2

four tenths is greater than two tenths

.2 < .4

two tenths is less than four tenths

.2 = .4

two tenths is not equal to four tenths

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Back to Instruction

Less Than

A symbol that shows that the number on the left is smaller than the number on the right.

the alligator will not eat the smaller #

.2 < .4

two tenths is less than four tenths

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Back to Instruction

Place Value

The value of a digit depending

• n its position in a number.

SLIDE 52

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Standard Form

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Standard form is the way we usually see numbers written, using digits, commas and a period when needed.

2.35

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0.1

Back to Instruction

Tenths

A part of one whole that has been divided into 10 equal parts.

0.3

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Thousandths

A part of one whole that has been divided into 1,000 equal parts. Also, a part of one tenth that has been divided into 100 equal parts, and a part of one hundredth that has been divided into 10 equal parts.

Back to Instruction

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$2.99 for 16 oz 18.7 for 1 oz

(1 unit) Unit

Back to Instruction

Unit

A unit is used to describe one of something. In place value, a unit is the ones place.

1

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Word Form

Back to Instruction

Word form is a number written using words instead of digits, commas, and a period when needed.

$3.44

three dollars and forty-four cents 8:24pm Eight twenty-four pm

3.45

three and forty-five hundredths