Name: ___________________________ Date: ______________ Class: ____________
LEVEL 2 · ENRICHMENT

End of Year Review & MCAP Prep

Standards: All Grade 6 domains — 6.RP · 6.NS · 6.EE · 6.G · 6.SP

Directions: These mixed-standard problems combine skills from the whole year. Show all work and label which domain each uses. For "Explain" prompts, write complete sentences. Finish with the Stretch Problem.

Mixed-Standard Challenge Set

1. A 5-pound bag of rice costs $6.25. A 12-pound bag costs $14.40. Which is the better unit price, and by how much per pound? 6.RPMULTI-STEP

2. A recipe needs ¾ cup of sugar per batch. You have 6 cups. How many full batches can you make, and how much sugar is left over? 6.NSREAL-WORLD

3. Simplify, then evaluate when x = 5: 3(2x − 1) + 4. 6.EEMULTI-STEP

4. A rectangular prism is 8 cm × 5 cm × 3 cm. Find its volume AND its surface area. 6.GMULTI-STEP

5. A data set is 4, 7, 7, 10, 12. Find the mean, median, and mean absolute deviation (MAD). 6.SPMULTI-STEP

6. Marisol scored 18 of 24 points. Liam scored 30 of 40. Are these scores equivalent ratios? Explain. 6.RPEXPLAIN

7. A triangle on the coordinate plane has vertices (0, 0), (8, 0), and (8, 6). Find its area. 6.G/6.NSREASONING

8. Solve the inequality and graph the solution: 2x + 3 ≤ 11. 6.EEMULTI-STEP

9. A store has a 30% off sale. A jacket is $50. What is the sale price? Show two different methods. 6.RPOPEN-ENDED

10. The mean of five test scores is 84. Four of the scores are 80, 88, 90, and 76. Find the fifth score. 6.SPREASONING

Hint: Work backward from the mean.

Explain Your Reasoning

11. A classmate says "dividing always makes a number smaller." Use ⅔ ÷ ¼ to explain why this is not always true. 6.NSWRITE

★ Stretch Problem

A garden is a rectangle 12 m long and 9 m wide. (a) Find its area and perimeter. (b) A path 1 m wide runs around the inside edge. Find the area of the inner planting region. (c) Seeds cost $0.40 per square meter for the planting region. What is the total seed cost? (d) Explain which Grade 6 domains you used.

Answer Key

  1. 5 lb: $1.25/lb; 12 lb: $1.20/lb. The 12-lb bag is better by $0.05 per pound
  2. 8 full batches — 6 ÷ ¾ = 6 × 4/3 = 8; uses exactly 6 cups, 0 left over
  3. 6x + 1; at x = 5: 6(5) + 1 = 31
  4. Volume = 120 cm³; Surface area = 2(40 + 24 + 15) = 158 cm²
  5. Mean = 8; Median = 7; MAD = (4+1+1+2+4)/5 = 12/5 = 2.4
  6. Yes — 18/24 = ¾ and 30/40 = ¾; both simplify to ¾
  7. 24 sq units — base 8, height 6, A = ½ × 8 × 6 = 24
  8. x ≤ 4 — 2x ≤ 8; closed circle on 4, shade left
  9. $35 — Method 1: 50 × 0.30 = $15 off, 50 − 15 = 35. Method 2: pay 70%, 50 × 0.70 = 35
  10. 86 — total must be 84 × 5 = 420; known four sum to 334; 420 − 334 = 86
  11. ⅔ ÷ ¼ = ⅔ × 4 = 8/3 ≈ 2.67, which is larger than ⅔; dividing by a number less than 1 makes the result bigger
  12. Stretch: (a) Area = 108 m², Perimeter = 42 m; (b) inner region 10 × 7 = 70 m²; (c) 70 × $0.40 = $28; (d) 6.G (area/perimeter), 6.RP/6.NS (unit cost, multiplication)