3B · Chapter 15 · Lesson 5
Word Problems
Find cost, change, and amount remaining in multistep nonambiguous contexts.
Today's mathematical question
You have $20.00. You buy two items costing $3.30 and $0.71. What change do you receive?
Learning target
Find cost, change, and amount remaining in multistep nonambiguous contexts.
Before starting: Prior lesson: Subtracting Money. 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.
- P1
You have $11.11 and spend $2.69. How much remains?
Reveal explanation
Answer: $8.42
Subtract 269 cents from 1111 cents. The 842 cents remaining equal $8.42.
- P2
You have $10.87 and spend $2.93. How much remains?
Reveal explanation
Answer: $7.94
Subtract 293 cents from 1087 cents. The 794 cents remaining equal $7.94.
- P3
You have $11.18 and spend $3.27. How much remains?
Reveal explanation
Answer: $7.91
Subtract 327 cents from 1118 cents. The 791 cents remaining equal $7.91.
Learn and understand
A money word problem may require adding costs and then subtracting that total from the amount paid. Write the cost of each item first, calculate their combined cost, and decide whether the question asks for total cost or change. An estimate can check whether the final change is reasonable. A $10 bill pays for two items costing $2.35 and $3.40. First add the costs to $5.75, then subtract from $10.00 to find $4.25 change.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Use a bar for total budget divided into spent and remaining portions. Label every value with dollars and cents.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- budget
- money available
- total cost
- sum of prices
- change
- money left after payment
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
You have $20.00. You buy two items costing $3.30 and $0.71. What change do you receive?
- Identify the whole, the units, and what the question asks.
- Combine the costs: $3.30 + $0.71 = $4.01. Then subtract from $20.00 to get $15.99.
- Check that the answer uses the right units and makes sense.
Answer: $15.99
Check your understanding 1
You have $20.00. You buy two items costing $1.28 and $3.06. What change do you receive?
Reveal answer and explanation
$15.66 — Combine the costs: $1.28 + $3.06 = $4.34. Then subtract from $20.00 to get $15.66.
Worked example 2
Explore, calculate, verify
You have $20.00. You buy two items costing $4.17 and $1.03. What change do you receive?
- Identify the whole, the units, and what the question asks.
- Combine the costs: $4.17 + $1.03 = $5.20. Then subtract from $20.00 to get $14.80.
- Check that the answer uses the right units and makes sense.
Answer: $14.80
Check your understanding 2
You have $30.00. You buy two items costing $5.99 and $2.24. What change do you receive?
Reveal answer and explanation
$21.77 — Combine the costs: $5.99 + $2.24 = $8.23. Then subtract from $30.00 to get $21.77.
Worked example 3
Explore, calculate, verify
You have $30.00. You buy two items costing $2.37 and $1.55. What change do you receive?
- Identify the whole, the units, and what the question asks.
- Combine the costs: $2.37 + $1.55 = $3.92. Then subtract from $30.00 to get $26.08.
- Check that the answer uses the right units and makes sense.
Answer: $26.08
Check your understanding 3
You have $30.00. You buy two items costing $3.29 and $2.30. What change do you receive?
Reveal answer and explanation
$24.41 — Combine the costs: $3.29 + $2.30 = $5.59. Then subtract from $30.00 to get $24.41.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
You have $30.00. You buy two items costing $5.46 and $0.94. What change do you receive?
Reveal explanation
Answer: $23.60
Combine the costs: $5.46 + $0.94 = $6.40. Then subtract from $30.00 to get $23.60.
- G2
You have $20.00. You buy two items costing $6.24 and $0.71. What change do you receive?
Reveal explanation
Answer: $13.05
Combine the costs: $6.24 + $0.71 = $6.95. Then subtract from $20.00 to get $13.05.
- G3
You have $20.00. You buy two items costing $8.68 and $1.94. What change do you receive?
Reveal explanation
Answer: $9.38
Combine the costs: $8.68 + $1.94 = $10.62. Then subtract from $20.00 to get $9.38.
- G4
You have $30.00. You buy two items costing $2.36 and $2.25. What change do you receive?
Reveal explanation
Answer: $25.39
Combine the costs: $2.36 + $2.25 = $4.61. Then subtract from $30.00 to get $25.39.
- G5
You have $30.00. You buy two items costing $4.00 and $1.41. What change do you receive?
Reveal explanation
Answer: $24.59
Combine the costs: $4.00 + $1.41 = $5.41. Then subtract from $30.00 to get $24.59.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
You have $30.00. You buy two items costing $7.20 and $2.88. What change do you receive?
Reveal explanation
Answer: $19.92
Combine the costs: $7.20 + $2.88 = $10.08. Then subtract from $30.00 to get $19.92.
- I2
You have $30.00. You buy two items costing $5.77 and $2.59. What change do you receive?
Reveal explanation
Answer: $21.64
Combine the costs: $5.77 + $2.59 = $8.36. Then subtract from $30.00 to get $21.64.
- I3
You have $30.00. You buy two items costing $6.22 and $1.24. What change do you receive?
Reveal explanation
Answer: $22.54
Combine the costs: $6.22 + $1.24 = $7.46. Then subtract from $30.00 to get $22.54.
- I4
You have $30.00. You buy two items costing $4.91 and $1.82. What change do you receive?
Reveal explanation
Answer: $23.27
Combine the costs: $4.91 + $1.82 = $6.73. Then subtract from $30.00 to get $23.27.
- I5
You have $20.00. You buy two items costing $5.09 and $1.13. What change do you receive?
Reveal explanation
Answer: $13.78
Combine the costs: $5.09 + $1.13 = $6.22. Then subtract from $20.00 to get $13.78.
- I6
You have $20.00. You buy two items costing $6.60 and $3.80. What change do you receive?
Reveal explanation
Answer: $9.60
Combine the costs: $6.60 + $3.80 = $10.40. Then subtract from $20.00 to get $9.60.
- I7
You have $20.00. You buy two items costing $2.12 and $2.07. What change do you receive?
Reveal explanation
Answer: $15.81
Combine the costs: $2.12 + $2.07 = $4.19. Then subtract from $20.00 to get $15.81.
- I8
You have $30.00. You buy two items costing $5.77 and $3.36. What change do you receive?
Reveal explanation
Answer: $20.87
Combine the costs: $5.77 + $3.36 = $9.13. Then subtract from $30.00 to get $20.87.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
Explain why $7.05 is 7 dollars and 5 cents rather than 7 dollars and 50 cents.
Reveal explanation
Answer: $7.05
The first digit after the decimal is tens of cents, and the second is ones of cents.
- C2
You have $10.00 and spend $7.75. Find the change by counting up, explaining each jump.
Reveal explanation
Answer: $2.25
Count 25 cents to $8.00, then $2.00 more to $10.00, for $2.25 change.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
You have $30.00. You buy two items costing $1.64 and $2.48. What change do you receive?
Reveal explanation
Answer: $25.88
Combine the costs: $1.64 + $2.48 = $4.12. Then subtract from $30.00 to get $25.88.
- E2
You have $30.00. You buy two items costing $6.41 and $0.73. What change do you receive?
Reveal explanation
Answer: $22.86
Combine the costs: $6.41 + $0.73 = $7.14. Then subtract from $30.00 to get $22.86.
- E3
You have $30.00. You buy two items costing $3.57 and $2.41. What change do you receive?
Reveal explanation
Answer: $24.02
Combine the costs: $3.57 + $2.41 = $5.98. Then subtract from $30.00 to get $24.02.