Financial Literacy: Coin Combinations to 100 Cents
Warm-up
Show a handful of mixed coins. How do we count these efficiently? Students suggest strategies. Introduce sort-then-skip-count: sort by denomination, skip-count each group, add the subtotals. Practice with 2 examples together.
Explore
Coin combination challenge: each pair receives a total (e.g., 65 cents) and must find 3 different coin combinations that make that total. Record each. How many ways did you find? Is there a combination that uses the fewest coins? (Always use the largest coins possible.)
Formalize
Spending and saving scenario: you earn 4. How many weeks must you save? (4 weeks.) A snack costs 75 cents each day. How much do you spend in 5 days? ($3.75.) Which is a want and which is a need? The mathematical reasoning is identical; the values dimension adds meaning.
Financial Literacy: Coin Combinations to 100 Cents
Coin equivalences: build a class equivalence chart. 1 quarter = ? dimes + ? nickels (2 dimes + 1 nickel). 1 dollar = ? quarters = ? dimes = ? nickels. This is proportional reasoning: 100 = 4 x 25 = 10 x 10 = 20 x 5. Connect to multiplication preview: the times tables hidden inside money.
Practice
Students count 6 mixed coin combinations and record the total. Find 2 equivalent combinations for 50 cents and 75 cents. Solve a savings goal problem. Exit ticket: show two different ways to make 60 cents.
Exit ticket
Students count 6 mixed coin combinations and record the total. Find 2 equivalent combinations for 50 cents and 75 cents. Solve a savings goal problem. Exit ticket: show two different ways to make 60 cents.
Step 1: Sort the coins largest value first — this is the counting strategy, not just tidiness: quarter (25), dimes (10, 10), nickel (5), penny (1).
Step 2: Count on, switching the skip-size at each coin type: 25 → 35 → 45 (dimes) → 50 (nickel) → 51 (penny).
Step 3: Say the total like a shopper: "51 cents."
Step 4: The strategy sentence to post: "biggest coins first, then count on." Starting with pennies buries you in ones; starting big means the hard counting happens with the fewest coins.
Watch for: students who switch skip-sizes late or early (counting the nickel as 10). Touch each coin as its value is added, and pause deliberately at every switch: "now we're counting by fives."
Step 1: Pose it as a puzzle: using ONLY quarters and dimes, make exactly one dollar (100 cents). Find every way.
Step 2: Work systematically by quarter-count: 4 quarters = 100 ✓ (zero dimes). 3 quarters = 75, need 25 more — but dimes make 10s, and 25 isn't reachable by 10s ✗. 2 quarters = 50, need 50 → 5 dimes ✓. 1 quarter = 25, need 75 ✗ (not a multiple of 10). 0 quarters → 10 dimes ✓.
Step 3: Collect the solutions: {4Q}, {2Q + 5D}, {10D}. Exactly three ways.
Step 4: The reasoning worth naming: we didn't hunt randomly — we marched the quarter-count down from 4 to 0 and CHECKED each case. The impossible cases had a reason (leftover 25 or 75 can't be built from tens). Systematic case-checking is a genuine proof technique, here disguised as coin play.
The offer on the table: 3 nickels for 1 quarter. A student is tempted — three coins for one feels like winning.
Step 1: Value both sides before judging: 3 nickels → 5, 10, 15 cents. The quarter → 25 cents.
Step 2: Compare: 15 < 25. The trade is NOT fair — the quarter-owner would lose 10 cents of value while gaining two extra coins.
Step 3: Repair the deal: what WOULD be fair for the quarter? 5 nickels (25 ✓), or 2 dimes and a nickel (25 ✓), or 25 pennies. Multiple fair offers exist; all are worth exactly 25 cents.
Step 4: The principle, which is the whole financial-literacy lesson in one line: fairness is measured in VALUE, not in number of coins. Run a trading-post centre where every proposed trade must be value-checked aloud by both traders before it's allowed to happen.