Worked solutions using the default input values for both project versions. For teachers only.
For teachers — worked solutions using the default values. Students who change inputs get different but similarly-structured answers. Each phase shows: default inputs used, step-by-step arithmetic, the correct final answer, and the exact quick-check answer. Sample expert responses and rubric guidance are included for scoring.
"I bought my item for $40.00 and applied a 25% markup. The markup amount is $40.00 × 0.25 = $10.00, so my selling price is $40.00 + $10.00 = $50.00. Setting the price at $50.00 gives me a $10.00 profit on every item I sell at full price."
4 (Expert): Markup amount ($10.00) and selling price ($50.00) both correct; shows the two-step process (percent × cost, then add); explains the profit in context.
3 (Proficient): Selling price $50.00 correct.
2 (Developing): Partial work shown; may have computed the markup but added incorrectly, or confused markup with the selling price.
"This weekend my $50.00 item is 20% off. The discount is $50.00 × 0.20 = $10.00, so the sale price is $50.00 − $10.00 = $40.00. Shoppers save $10.00 compared to the regular price. I notice this equals my original cost price, so I break even on sale-day purchases."
4 (Expert): Discount amount ($10.00) and sale price ($40.00) both correct; notes that savings equals the markup amount (showing deeper reasoning); or computes an alternative check using 80% × $50 = $40.
3 (Proficient): Sale price $40.00 correct.
2 (Developing): Attempted; common error is subtracting the percent (50 − 20 = 30) instead of computing percent of the price first.
Part A — Sales Tax
Part B — Percent Conversion
"After my 20% weekend discount the sale price is $40.00. The state adds 8% sales tax: $40.00 × 0.08 = $3.20, making the checkout total $43.20. I also converted 35% to its decimal (0.35) and simplified fraction (7/20) by dividing numerator and denominator by GCF = 5."
4 (Expert): Tax amount ($3.20) and final total ($43.20) both correct; fraction 7/20 shown with GCF simplification; decimal 0.35 confirmed; student may cross-check with 7 ÷ 20 = 0.35.
3 (Proficient): Final total $43.20 correct; fraction and decimal forms both accurate.
2 (Developing): Tax or conversion has one error (e.g., fraction left as 35/100 unsimplified, or tax computed on selling price $50 instead of sale price $40).
"Welcome to my pop-up shop! I bought my item for $40.00 and marked it up 25% ($10.00 markup) to sell it for $50.00. This weekend it is on sale for 20% off, so you pay only $40.00 — saving $10.00. After 8% sales tax, your total is $43.20. My best promo deal is Promo A (30% off a $60 item for $42.00) because it saves customers $18.00, which beats Promo B's flat $15.00 off by $3.00!"
4 (Expert): Storefront sign cites all four numeric results (cost $40, markup $10, selling price $50, discount $10, sale price $40, tax $3.20, total $43.20); Promo A identified as better with both final prices compared ($42 vs $45); reasoning is clear and customer-focused.
3 (Proficient): Sign uses most numbers; correct promo choice stated.
2 (Developing): Missing key numbers (e.g., no mention of tax total or promo comparison).
"Package A costs $3.60 for 12 units, giving a unit price of $0.30 per unit ($3.60 ÷ 12). Package B costs $5.25 for 20 units, giving a unit price of $0.2625 per unit ($5.25 ÷ 20). Even though Package B has a higher sticker price, its unit price is lower by about $0.04, making it the better buy for a budget-conscious shopper."
4 (Expert): Both unit prices computed correctly ($0.30 and $0.2625); Package B identified as better buy with explicit comparison ("$0.2625 < $0.30"); explains the apparent paradox that the bigger, more expensive package is cheaper per unit.
3 (Proficient): Both unit prices correct; better buy correctly identified.
2 (Developing): One unit price correct or a minor division error; may choose Package A because its total cost is lower (misunderstanding unit price).
"Store 1 sells the item for $80.00 with a 25% discount: $80 × 0.75 = $60.00 after the sale. Store 2 sells for $75.00 with a 15% discount: $75 × 0.85 = $63.75 after the sale. Store 1 is the better deal at $60.00 — $3.75 cheaper than Store 2, despite having a higher original price."
4 (Expert): Both final prices correct ($60.00, $63.75); Store 1 identified as cheaper with the savings amount ($3.75); explains the counterintuitive result (higher original price, deeper discount → lower final price).
3 (Proficient): Both prices correct; cheaper store identified.
2 (Developing): One price correct or minor percent-computation error (e.g., computed 15% of $80 instead of $75).
Part A — Tip Calculation
Part B — Measurement Conversion (default: 5 feet → inches)
"After shopping I had lunch and left a 15% tip on a $20.00 bill: $20 × 0.15 = $3.00 tip, for a $23.00 total. Using rate reasoning, I also converted 5 feet to inches by multiplying by the rate (12 inches per foot): 5 × 12 = 60 inches. The foot units canceled, confirming the conversion."
4 (Expert): Tip ($3.00) and total ($23.00) both correct; conversion shown as a unit-fraction multiplication (5 × 12 in/ft = 60 in) with units explicitly canceling; connects method to "rate reasoning."
3 (Proficient): Tip and conversion both numerically correct.
2 (Developing): Tip correct but conversion set up without the unit-fraction framework; or conversion answer correct but tip computation contains arithmetic error.
"Based on my unit price research, Package B is the better buy at $0.2625 per unit vs. Package A's $0.30 per unit — a savings of $0.0375 per unit. For the item I compared between stores, Store 1 is cheaper at $60.00 after a 25% discount, beating Store 2's $63.75 after a 15% discount. At the restaurant I tipped 15%, which came to $3.00, for a total of $23.00; and I converted 5 feet to 60 inches using rate reasoning (5 × 12 in/ft). My overall shopping strategy: always compute the unit price before choosing a package, and compare post-discount prices — not original sticker prices — when comparing stores."
4 (Expert): Verdict cites all four phase results (Package B unit price $0.2625, Store 1 final price $60.00, tip $3.00 and total $23.00, conversion 60 inches); gives a general shopping strategy drawn from the math; reasoning is clear and uses correct mathematical vocabulary (unit price, discount, rate reasoning).
3 (Proficient): Uses most numbers; package and store choices correctly stated.
2 (Developing): Verdict is vague or missing phase results (e.g., no unit prices mentioned, or store chosen without showing the post-discount prices).