Reference / Curriculum / 3B / Chapter 15

3B · Chapter 15 · Lesson 2

Making $10

Find complements to ten dollars using dollars/cents and benchmark sums.

MATH-3B-C15-L02Independent and tutor-supported

Today's mathematical question

You have $5.19. How much more money do you need to make exactly $10.00?

Learning target

Find complements to ten dollars using dollars/cents and benchmark sums.

Before starting: Prior lesson: Dollars and Cents. Try the warm-up independently.

Prerequisite · 3 questions

Check earlier skills first

These are earlier ideas you need for today; revisit them if they are difficult.

  1. P1

    Write 867 cents as dollars and cents.

    Reveal explanation

    Answer: $8.67

    There are 100 cents in one dollar; 867 cents = 8 dollars and 67 cents.

  2. P2

    Write 837 cents as dollars and cents.

    Reveal explanation

    Answer: $8.37

    There are 100 cents in one dollar; 837 cents = 8 dollars and 37 cents.

  3. P3

    Write 380 cents as dollars and cents.

    Reveal explanation

    Answer: $3.80

    There are 100 cents in one dollar; 380 cents = 3 dollars and 80 cents.

Learn and understand

Making $10 uses the same missing-part reasoning as making 100 in whole-number arithmetic. Find the complement: if you have $6.45, the missing amount is $3.55. Count up to the next dollar and then to ten dollars if that is easier. For $6.85, count 15 cents to $7.00 and then $3.00 to $10.00. You need $3.15 in all. Counting up is another way to subtract.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Draw a ten-dollar total bar and label one known part. Split the missing section using friendly dollar boundaries.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

complement
missing part needed to reach a total
change
money returned after payment
dollar
100 cents

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

You have $5.19. How much more money do you need to make exactly $10.00?

  1. Identify the whole, the units, and what the question asks.
  2. 10 dollars is 1,000 cents. Subtract 519 cents to get 481 cents, or $4.81.
  3. Check that the answer uses the right units and makes sense.

Answer: $4.81

Check your understanding 1

You have $1.27. How much more money do you need to make exactly $10.00?

Reveal answer and explanation

$8.73 — 10 dollars is 1,000 cents. Subtract 127 cents to get 873 cents, or $8.73.

Worked example 2

Explore, calculate, verify

You have $4.97. How much more money do you need to make exactly $10.00?

  1. Identify the whole, the units, and what the question asks.
  2. 10 dollars is 1,000 cents. Subtract 497 cents to get 503 cents, or $5.03.
  3. Check that the answer uses the right units and makes sense.

Answer: $5.03

Check your understanding 2

You have $5.12. How much more money do you need to make exactly $10.00?

Reveal answer and explanation

$4.88 — 10 dollars is 1,000 cents. Subtract 512 cents to get 488 cents, or $4.88.

Worked example 3

Explore, calculate, verify

You have $4.55. How much more money do you need to make exactly $10.00?

  1. Identify the whole, the units, and what the question asks.
  2. 10 dollars is 1,000 cents. Subtract 455 cents to get 545 cents, or $5.45.
  3. Check that the answer uses the right units and makes sense.

Answer: $5.45

Check your understanding 3

You have $5.08. How much more money do you need to make exactly $10.00?

Reveal answer and explanation

$4.92 — 10 dollars is 1,000 cents. Subtract 508 cents to get 492 cents, or $4.92.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    You have $8.29. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $1.71

    10 dollars is 1,000 cents. Subtract 829 cents to get 171 cents, or $1.71.

  2. G2

    You have $1.72. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $8.28

    10 dollars is 1,000 cents. Subtract 172 cents to get 828 cents, or $8.28.

  3. G3

    You have $4.93. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $5.07

    10 dollars is 1,000 cents. Subtract 493 cents to get 507 cents, or $5.07.

  4. G4

    You have $2.13. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $7.87

    10 dollars is 1,000 cents. Subtract 213 cents to get 787 cents, or $7.87.

  5. G5

    You have $8.19. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $1.81

    10 dollars is 1,000 cents. Subtract 819 cents to get 181 cents, or $1.81.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    You have $3.44. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $6.56

    10 dollars is 1,000 cents. Subtract 344 cents to get 656 cents, or $6.56.

  2. I2

    You have $8.40. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $1.60

    10 dollars is 1,000 cents. Subtract 840 cents to get 160 cents, or $1.60.

  3. I3

    You have $5.68. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $4.32

    10 dollars is 1,000 cents. Subtract 568 cents to get 432 cents, or $4.32.

  4. I4

    You have $3.56. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $6.44

    10 dollars is 1,000 cents. Subtract 356 cents to get 644 cents, or $6.44.

  5. I5

    You have $1.89. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $8.11

    10 dollars is 1,000 cents. Subtract 189 cents to get 811 cents, or $8.11.

  6. I6

    You have $3.85. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $6.15

    10 dollars is 1,000 cents. Subtract 385 cents to get 615 cents, or $6.15.

  7. I7

    You have $6.58. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $3.42

    10 dollars is 1,000 cents. Subtract 658 cents to get 342 cents, or $3.42.

  8. I8

    You have $7.48. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $2.52

    10 dollars is 1,000 cents. Subtract 748 cents to get 252 cents, or $2.52.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    Explain why $4.05 is 4 dollars and 5 cents rather than 4 dollars and 50 cents.

    Reveal explanation

    Answer: $4.05

    The first digit after the decimal is tens of cents, and the second is ones of cents.

  2. C2

    You have $10.00 and spend $4.75. Find the change by counting up, explaining each jump.

    Reveal explanation

    Answer: $5.25

    Count 25 cents to $5.00, then $5.00 more to $10.00, for $5.25 change.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    You have $3.64. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $6.36

    10 dollars is 1,000 cents. Subtract 364 cents to get 636 cents, or $6.36.

  2. E2

    You have $2.74. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $7.26

    10 dollars is 1,000 cents. Subtract 274 cents to get 726 cents, or $7.26.

  3. E3

    You have $8.66. How much more money do you need to make exactly $10.00?

    Reveal explanation

    Answer: $1.34

    10 dollars is 1,000 cents. Subtract 866 cents to get 134 cents, or $1.34.

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