Level 2 · Enrichment

Reveal Math · Unit 1 · Supplemental

Foundation Math Skills

Grade 6 · Multi-step operations, factors, divisibility, reasoning & problem solving

Name: Date:

Challenge Problems

Directions: Solve each problem and show your strategy. For "Explain" prompts, write a complete sentence justifying your reasoning.
  1. A train travels 234 miles in the morning and 178 miles in the afternoon, then returns 156 miles. How far is the train from its starting point? Multi-step
  2. A factory makes 1,248 widgets per day. How many are made in a 5-day week? In a 4-week month? Multi-step
  3. You have $500. You buy 3 shirts at $24.50 each and 2 pairs of shoes at $67.25 each. How much money is left? Real-world
  4. Find all pairs of whole numbers whose product is 72. Open-ended
    Explain: how do you know you found every pair?
  5. A theater has 32 rows with 28 seats per row. If 647 people attend, how many seats are empty?
  6. The sum of three consecutive numbers is 312. Find the three numbers. Reasoning
    Explain: why does dividing the sum by 3 give the middle number?
  7. What is the smallest number greater than 100 that is divisible by both 6 and 8?
    Explain: how does the least common multiple help you?
  8. Using the digits 1, 3, 5, 7 each exactly once, form two 2-digit numbers whose product is as large as possible. Open-ended
    Explain: what placement strategy makes the product largest?
  9. A clock chimes once at 1:00, twice at 2:00, and so on up to 12 times at 12:00. How many chimes in a full 12-hour cycle? Reasoning
  10. A rectangular garden is 24 ft long and 18 ft wide. A 3-ft-wide path is built around the outside. Find the area of just the path. Multi-step

Stretch Problem

Real-world application: You are planning a class supply budget of $75 for 28 students. Each student needs 2 pencils ($0.25 each), 1 notebook ($1.50), and 1 folder ($0.75). Will $75 cover everyone? If not, how much more is needed, and what is one change you could make to stay within budget? Show all calculations and explain your reasoning.

Answer Key

  1. 234 + 178 = 412 forward; 412 − 156 = 256 miles from start.
  2. Week: 1,248 × 5 = 6,240. Month: 6,240 × 4 = 24,960 widgets.
  3. Shirts $73.50 + shoes $134.50 = $208.00; $500 − $208 = $292 left.
  4. 1×72, 2×36, 3×24, 4×18, 6×12, 8×9 (6 pairs). Stop at √72 ≈ 8.5 since pairs repeat after that.
  5. 32 × 28 = 896 seats; 896 − 647 = 249 empty.
  6. 312 ÷ 3 = 104 (middle); numbers are 103, 104, 105. The middle term is the mean of evenly spaced numbers.
  7. LCM(6, 8) = 24; multiples 24, 48, 72, 96, 120 → answer 120.
  8. 71 × 53 = 3,763 (largest). Put the largest digits in the tens places.
  9. 1+2+…+12 = (12 × 13) ÷ 2 = 78 chimes.
  10. Outer 30 × 24 = 720 sq ft; garden 24 × 18 = 432; path = 720 − 432 = 288 sq ft.
  11. Stretch: pencils 28×2×$0.25 = $14; notebooks 28×$1.50 = $42; folders 28×$0.75 = $21; total $77 → $2 over. Answers vary on the cut (e.g., drop folders or buy 1 pencil each).