Math // Measurement

Money word problems

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately

Ages
7 to 8
Type
Method
Builds on
1 topic
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Standards
1 code

Quick check

If the learner has 2 quarters, 1 dime, and 3 pennies, can they work out the total — and tell you whether that's enough to buy something costing 65 cents?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Determine the total value of a collection of coins
  • Solve a word problem about making change with US currency
  • Use $ and ¢ symbols correctly in answers

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

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Money word problems

Ages 7 to 8 // Method

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Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Children solve word problems with US coins and bills — totalling value, making change, and writing amounts with $ and ¢ correctly. The core difficulty is that a coin's value is abstract and matches neither its physical size nor the number of coins (a dime is smaller than a nickel yet worth more; three dimes beat five pennies). Money is best taught as a measure of value using proportional representations that make each coin's worth visible, introducing denominations a couple at a time, and first building the skip-counting and place-value number sense that totalling mixed coins depends on.

Common misconceptions

  • Value = size: a bigger coin is worth more (nickel > dime; five pennies > three dimes)
  • Value = count: each coin counts as one, or all coins are counted by ones regardless of denomination (unitary thinking)
  • Cannot switch counting patterns — counts 25, 50, 75 then cannot shift to +10 for a dime or +1 for a penny
  • Notation errors — mixing $ and ¢ ($0.50¢, or $5 for a nickel), or writing 5¢ as $5
  • Overusing one denomination (all dimes) because counting by tens is easiest, rather than realistic combinations

Useful representations

  • Proportional value strips / 'proportional dollar' (a coin laid over its worth in unit-squares)
  • A number line or hundred-square for skip-counting coin values
  • A coin-value reference (penny 1¢, nickel 5¢, dime 10¢, quarter 25¢, dollar 100¢)
  • A part-whole bar for making change (cost and amount paid)

Teaching practices

  • Treat money as measuring value — begin with barter and non-standard units so children feel why standard values are needed (Fanelli & Tracy)
  • Use PROPORTIONAL manipulatives (a dime shown as ten unit-squares) rather than realistic play coins, because a coin is not a concrete representation of its own value
  • Introduce coins two denominations at a time to reduce cognitive load and limit how often the counting pattern must switch
  • Build the underlying number sense first — skip-counting by 5s, 10s, 25s and place value — since totalling mixed coins is a skip-count-and-switch task
  • Teach 'counting on' from the largest coin; model correct $ and ¢ notation and when each is used (100¢ = $1)

Activities to try

  1. 1

    Proportional-coin workbench: build value and make change

    Why it works: A coin's worth is a number of cents you count on, separate from the coin's size or how many coins there are; proportional value makes 'smaller but worth more' visible and concrete.

    1. Place coins onto a mat; as each coin is placed, it opens into its worth shown as unit-squares (dime = 10 squares, nickel = 5, penny = 1, quarter = 25) while a running total counts on by value.
    2. Set the small dime beside the fatter nickel and compare the stacks of squares: the dime's 10 squares visibly outstretch the nickel's 5.
    3. Build a target amount such as 30¢ in more than one way (e.g. three dimes; or a quarter and a nickel) and compare the coins used.
    4. Switch to a make-change task: an item costs 40¢; pay with coins totalling 46¢ and count up the 6¢ change.
    5. Count a mixed handful (2 dimes and 3 pennies) by counting on from the largest coin: 10, 20, then 21, 22, 23.
  2. 2

    Coin denomination reference with the size/worth contradiction

    Why it works: Each coin has a fixed cents value that must be learned, and a coin's size does not tell you its worth.

    1. Reveal each coin's value and a short fact (e.g. the dime is 'smaller than a nickel, but worth more').
    2. Name each coin and state its cents value: penny 1¢, nickel 5¢, dime 10¢, quarter 25¢; then name the dollar bill (100¢) and state that 100¢ = $1.
    3. Point out at least one pair where the smaller coin is worth more.
  3. 3

    Comparison and totalling checks with diagnostic distractors

    Why it works: Judging worth by value — not by coin size or number of coins — and recording amounts in correct notation.

    1. Answer 'Which is worth more: three dimes or five pennies?' and explain the choice.
    2. Total a mixed set such as '2 dimes and 3 pennies — how many cents?' and show the count.
    3. Write the answer using ¢ (or $ with a decimal) without mixing the two symbols.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
2.MD.8

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