decimal concepts mood rings, part 2 1 · mood rings, part 2 writing math a decimal is another way...

$: Decimal Concepts Mood Rings, Part 2 1 · Mood Rings, Part 2 WRITING MATH A decimal is another way to write a fraction. Both decimals and fractions are ways to represent parts of a$
Unit 1 • Number Concepts 39

My Notes

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ACTIVITY

SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Look for a Pattern, Activating Prior Knowledge, Create Representations

Tyrell and his friends now all know their ring fi nger sizes. Th is table lists their fi nger sizes in inches from Activity 1.6.

Tyrell Bob Jose Nisha Ema

1 7 __ 8 2 1 __ 2 2 1 __ 4 1 3 __ 4 2 3 ___ 16

Now they must determine what size rings to buy. Look at this ring chart with the mood ring sizes.

Finger Measure (in.) 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7Mood Ring Size 4 5 6 7 8 9 10 11 12 13

1. What must the friends do to be able to use this chart?

Start by writing Bob’s fi nger size, 2 1 __ 2 , as a decimal.

You can do this because 2 1 __ 2 = 2 5 ___ 10 . Remember, in decimal

place value, 2.5 is read “two and fi ve tenths.”

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2. Look for a pattern in the chart above. Fill in the missing place values.

3. You can model the relationship between fractions and decimals with a grid. Th ree tenths means “3 out of 10.” Write a decimal and a fraction and shade the grid to represent three tenths.

Decimal:

Fraction:

1.7Decimal ConceptsMood Rings, Part 2

WRITING MATH

A decimal is another way to write a fraction. Both decimals and fractions are ways to represent parts of a whole.

039-044_SB_MS1_1-7_SE.indd 39039-044_SB_MS1_1-7_SE.indd 39 12/16/09 6:58:35 PM12/16/09 6:58:35 PM

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40 SpringBoard® Mathematics with Meaning Level 1

My Notes

Decimal Concepts ACTIVITY 1.7continued Mood Rings, Part 2Mood Rings, Part 2

SUGGESTED LEARNING STRATEGIES: Create Representations, Quickwrite, Discussion Group

4. Represent “1 whole and 55 out of 100” with numbers, words, and a model.

Mixed Number: Improper Fraction:

Decimal:

Word form:

Grid model:

5. Some fractions are not expressed in tenths, hundredths, thousandths, and so on.

a. How would you convert a fraction such as 2 __ 5 , to a decimal?

b. Use this method to convert Jose’s and Nisha’s fi nger sizes to decimals.

Jose: 2 1 __ 4

Nisha: 1 3 __ 4

c. Will this method work for a fraction like 3 __ 8 ? Explain.

6. Recall that 3 __ 8 means 3 divided by 8.

a. Use either long division or divide with your calculator to fi nd the decimal equivalent of 3 __ 8 .

b. Now convert Tyrell’s and Ema’s fi nger sizes to decimals.

Tyrell: 1 7 __ 8 Ema: 2 3 ___ 16

You may want to use a calculator to check your long division.

TECHNOLOGY


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My Notes

Decimal Concepts Mood Rings, Part 2Mood Rings, Part 2

ACTIVITY 1.7continued

SUGGESTED LEARNING STRATEGIES: Quickwrite, Discussion Group, Create Representations, Visualize, Summarize/Paraphrase/Retell

7. You learned in Activity 1.5 that fractions are rational numbers. Are decimals also rational numbers? Justify your answer.

8. Complete the table. Express the fi nger sizes in decimals.

Tyrell Bob Jose Nisha Ema

Fraction 1 7 __ 8 5 __ 2 9 __ 4 1 3 __ 4 2 3 ___ 16

Decimal

9. Here again is the chart of ring sizes. Use your table and the chart to determine Bob’s ring size.

FingerSize (in) 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7

RingSize 4 5 6 7 8 9 10 11 12 13

10. Can you use the chart for the others? Why or why not?

When rounding a decimal, think about its location on a number line and the place you want to round to. For example, when you round numbers between 7.2 and 7.3 to the tenths place:

• A number less than 7.25 is closer to 7.2, so it rounds to 7.2.

• A number greater than 7.25 is closer to 7.3 and rounds to 7.3.

• 7.25 is exactly halfway between 7.2 and 7.3 and rounds to 7.3.

7.27.21 7.22 7.23 7.24 7.267.25 7.27 7.28 7.29

7.3

Round to 7.2 Round to 7.3

7.27.21 7.22 7.23 7.24 7.267.25 7.27 7.28 7.29

7.3

Round to 7.2 Round to 7.3


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My Notes


SUGGESTED LEARNING STRATEGIES: Create Representations, Think Aloud

11. For each number line, label the middle if not given. Th en plot each number on its number line to help you round. Round each number to the underlined place value.

12. Look at the ring fi nger measurements for Nisha and Jose. Round their measurements to the nearest tenth. What size rings should Nisha and Jose order?

With small measurements, such as fi nger sizes, plotting numbers on number lines to help you round works well. It is more diffi cult, though, to use number lines to round decimals to the thousandths and ten-thousandths.

Tryrell and Ema wonder about a better way to round numbers. Th ey decide to consider only the decimal portion of a number, and then fi nd two numbers it falls between and the midpoint. For example:

Rounding to tenths:

2.364 0.300 0.350 0.400

0.364

364 rounds to 400, so 2.364 rounds to 2.4.

Rounding to hundredths:

2.364 0.360 0.365 0.370

0.364

0.364 is closer to 0.360 than 0.370, so 2.364 rounds to 2.36.

24

24.2

24.5 25

8.1

8.17

8.2

11.6

11.64

11.7

7

7.5

7.5 8

24

24.2

24.5 25

8.1

8.17

8.2

11.6

11.64

11.7

7

7.5

7.5 8

⎧ ⎨ ⎩⎧ ⎨ ⎩ ⎧ ⎨ ⎩⎧ ⎨ ⎩

⎧ ⎨ ⎩⎧ ⎨ ⎩ ⎧ ⎨ ⎩⎧ ⎨ ⎩

Considering the digit to the right of the place you are rounding to is a way to think about where the number is on a number line.


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My Notes

ACTIVITY 1.7continued

Decimal Concepts Mood Rings, Part 2Mood Rings, Part 2

13. Round Tyrell’s and Ema’s fi nger sizes to the nearest tenth.

14. Complete this table of mood ring sizes for the fi ve friends.

Mood Ring SizesTyrell Bob Jose Nisha Ema

15. Th e friends decide to order the decimal measurements on a number line. Place each rounded decimal on the number line below and label it with the person’s initial.

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6

16. Another way to order decimals is by comparing place values, as we do with whole numbers.

a. Tell how to order 250, 225, and 218 from least to greatest.

b. Use that process to order 1.875, 2.5, 2.25, 1.75, and 2.1875 from least to greatest. Use the place value chart to help you.

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c. Is this the same order that the friends found when ordering the fractions?

SUGGESTED LEARNING STRATEGIES: Create Representations, Think/Pair/Share, Activating Prior Knowledge


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My Notes


SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/Retell, Think/Pair/Share, Create Representations

Five other friends who were buying rings measured their fi nger sizes in centimeters, so they were expressed as decimals.

Abby Saaman Lela Eric Rafe5.9 cm 4.7 cm 6.6 cm 5.2 cm 5.4 cm

When they saw the ring size chart the salesperson gave them, the fi nger sizes were given in fractions.

Finger Size (cm) 4 7 ___ 10 4 9 ___ 10 5 1 __ 5 5 2 __ 5 5 7 ___ 10 5 9 ___ 10 6 1 __ 5 6 2 __ 5 6 3 __ 5 6 9 ___ 10

Ring Size 4 5 6 7 8 9 10 11 12 13

17. Th ese friends converted their decimal sizes to fractions.

a. When Lela did this, she did not fi nd her fi nger size on the chart. Why not?

b. Help Eric and Rafe determine their ring sizes.

c. Complete this table so that these friends can buy rings.

Ring SizesAbby Saaman Lela Eric Rafe

Write your answers on notebook paper. Show your work.

CHECK YOUR UNDERSTANDING

Write your answers on notebook paper. Show your work.

1. Convert each fraction to a decimal. a. 7 71 ____ 100 b. 98 3 _____ 1000 c. 6 ___ 25 d. 4 __ 5 2. Convert each decimal to a fraction in

simplest form. a. 3.049 b. 54.22 c. 218.6 d. 0.05 3. Put each of the following numbers in

order from least to greatest.5 __ 2 , 2.3, 2 2 __ 5 , 1.75, 2 13 ___ 25 , 9 __ 5

4. Th e table shows average gas prices in January 1978 for four diff erent regions of the U.S

Northeast West South Midwest0.655 0.664 0.634 0.650

Order these prices from most to least expensive.

5. Round each gas price in Item 4 to the nearest hundredth.

6. MATHEMATICAL R E F L E C T I O N

Which do you think are easier to order, decimals

or fractions? Explain the method you chose.


decimal concepts mood rings, part 2 1 · mood rings, part 2 writing math a decimal is another way...

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