Blaine’s Fractions & Decimals Challenge

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Date:

Part 1: Warm-up and Fraction Connections

Learning intention: We are learning to represent, compare and connect fractions and decimals.

Success criteria: I can match equivalent representations, find equivalent fractions, compare values and explain my reasoning using place value.

1. Match each fraction to its decimal and description. Write the matching letter beside each number.

1. 1/2

2. 3/4

3. 2/5

4. 1/4

A. 0.25 — 1 of 4 equal parts shaded

B. 0.50 — 2 of 4 equal parts shaded

C. 0.40 — 2 of 5 equal parts shaded

D. 0.75 — 3 of 4 equal parts shaded

2. Complete each equivalent fraction puzzle.

a) 3/5 = ______ / 20

b) 7/8 = 21 / ______

c) ______ / 12 = 2/3

3. Insert <, > or =.

a) 5/8 ______ 0.6

b) 0.7 ______ 2/3

c) 9/10 ______ 0.90

Part 2: Compare, Convert and Reason

4. Order these values from least to greatest: 0.45, 2/5, 3/4, 0.7.

Answer: __________________________________________________________

5. Convert each familiar fraction to a decimal.

a) 1/4 = ______

b) 3/5 = ______

c) 7/10 = ______

6. Place-value challenge: Write one decimal with 3 decimal places that is greater than 0.46 but less than 0.47. Explain how the hundredths and thousandths digits prove your answer.

7. Number-line reasoning: The points 0.25, 1/2 and 0.75 are equally spaced on a number line. What decimal belongs halfway between 0.25 and 1/2? Explain your strategy.

Part 3: Real-world Challenge and Show-off Extension

8. Blaine has $20. He spends 3/8 of the money on a book and 0.2 of the original amount on a snack. How much money does he have left? Show all steps.

9. A 2.5 m ribbon is cut into pieces measuring 3/5 m and 0.75 m. How much ribbon remains? Give your answer in metres and explain your calculation.

10. Show-off challenge: Find a fraction and a decimal, both between 0.4 and 0.5, that are equal. Prove that they are equal and explain how you know they fit between 0.4 and 0.5.

Answer Key

1. 1–B, 2–D, 3–C, 4–A.

2. a) 12, because 5 × 4 = 20 and 3 × 4 = 12. b) 24, because 7 × 3 = 21 and 8 × 3 = 24. c) 8, because 2 × 4 = 8 and 3 × 4 = 12.

3. a) 5/8 = 0.625, so >. b) 2/3 is approximately 0.667, so 0.7 > 2/3. c) 9/10 = 0.90, so =.

4. 2/5, 0.45, 0.7, 3/4. Convert 2/5 to 0.4 and 3/4 to 0.75.

5. a) 0.25. b) 0.6. c) 0.7.

6. Answers may include 0.461, 0.465 or 0.469. The number has 4 tenths, 6 hundredths and more than 0 thousandths, but remains below 0.470.

7. 0.375. Halfway between 0.25 and 0.50 is 0.375, because each interval is 0.125.

8. 3/8 of $20 = $7.50. 0.2 of $20 = $4.00. $20 − $7.50 − $4.00 = $8.50.

9. 3/5 m = 0.6 m. Used: 0.6 + 0.75 = 1.35 m. Remaining: 2.5 − 1.35 = 1.15 m.

10. Example: 3/7 and approximately 0.428571 are equal, but a terminating decimal example is 9/20 = 0.45. Both are between 0.4 and 0.5 because 0.40 < 0.45 < 0.50.

Excellent work, Blaine! Keep explaining your mathematical thinking and looking for efficient strategies.