Grade 3 Math Chapter 2: Teacher Guide and Answers
Download the teacher guide PDF. This guide is separate from the student materials. Use counters, drawings, and the worked examples. Record student progress privately and teach the prerequisite again when a misconception appears.
Lesson 1: Equal Groups and Multiplication
Target: Represent equal groups with multiplication and repeated addition.
Teaching note: Use counters to model 3 groups of 5. Write 3 × 5 = 15 and 5 + 5 + 5 = 15. Explain what each factor means. Ask the student to explain the operation and check with a new example.
Practice answers 1–12: 1. 8 | 2. 18 | 3. 20 | 4. 15 | 5. 12 | 6. 28 | 7. 24 | 8. 18 | 9. 28 | 10. 24 | 11. 0 | 12. 9
Advanced response: Examples: 3 groups of 8 and 4 groups of 6. Both contain 24; the numbers of groups and group sizes differ.
Lesson 2: Arrays and Multiplication Strategies
Target: Use rows, columns, and the distributive property to find products.
Teaching note: Draw 4 rows of 3 dots. Write 4 × 3 = 12 and 3 × 4 = 12. Explain why the total stays the same. Ask the student to explain the operation and check with a new example.
Practice answers 1–12: 1. 12 | 2. 24 | 3. 35 | 4. 18 | 5. 35 | 6. 32 | 7. 27 | 8. 36 | 9. 49 | 10. 48 | 11. 45 | 12. 16
Advanced response: Examples: (5 × 7)+(3 × 7)=56 or (4 × 7)+(4 × 7)=56.
Lesson 3: Division as Sharing and Grouping
Target: Interpret quotients and connect division to an unknown factor.
Teaching note: Share 20 counters among 5 groups. Then group 20 counters into groups of 5. Each gives 4, but the unknown describes something different. Ask the student to explain the operation and check with a new example.
Practice answers 1–12: 1. 4; 3 × 4 = 12 | 2. 6; 3 × 6 = 18 | 3. 5; 4 × 5 = 20 | 4. 4; 6 × 4 = 24 | 5. 7; 4 × 7 = 28 | 6. 6; 5 × 6 = 30 | 7. 8; 4 × 8 = 32 | 8. 6; 6 × 6 = 36 | 9. 6; 7 × 6 = 42 | 10. 8; 6 × 8 = 48 | 11. 7; 8 × 7 = 56 | 12. 7; 9 × 7 = 63
Advanced response: 24 items shared among 6 children gives 4 each; 24 items placed 6 per box gives 4 boxes.
Lesson 4: Missing Factors and Related Facts
Target: Solve unknown-factor equations and use fact families to verify.
Teaching note: Solve □ × 8 = 40 by asking 40 ÷ 8. Check 5 × 8 = 40. Ask the student to explain the operation and check with a new example.
Practice answers 1–12: 1. 6 | 2. 7 | 3. 7 | 4. 8 | 5. 6 | 6. 7 | 7. 8 | 8. 9 | 9. 9 | 10. 9 | 11. 9 | 12. 8
Advanced response: 4 × 9 = 36; 9 × 4 = 36; 36 ÷ 4 = 9; 36 ÷ 9 = 4.
Lesson 5: Word Problems and Choosing Operations
Target: Model one- and two-step situations using appropriate operations and units.
Teaching note: There are 3 trays of 8 cups. If 7 cups are used, 3 × 8 = 24 and 24 − 7 = 17 cups remain. Ask the student to explain the operation and check with a new example.
Practice answers 1–12: 1. 24 marbles | 2. 6 books per shelf | 3. 40 chairs | 4. 6 boxes | 5. 26 seeds | 6. 26 players | 7. 6 apples per basket | 8. 35 books | 9. 28 cups | 10. 6 boxes | 11. 26 rolls | 12. 28 occupied seats
Advanced response: Answers vary; check that the operations, numbers, units and result agree.
Chapter Check Answers
1. 28 | 2. 48 | 3. 9 | 4. 8 | 5. 7 | 6. 9 | 7. 32 | 8. 6 | 9. 34 | 10. 37
Check understanding as well as correctness. Review the missed objective, teach with objects or visual models, and assess again using different values. The ten-item check is an informal local assessment, not a state proficiency rating.