Grade 3 Mathematics: Chapter 2 Student Text
Five lessons: equal groups, arrays, sharing and grouping, related facts, and word problems. Read one lesson, practice the model with counters or drawings, then open the separate workbook. Children may work at a different level when they show prerequisite mastery. This chapter is part of a developing course, not a complete annual textbook.
Download the student text PDF | Open the fillable practice workbook and online exercises | Parent and teacher guide.
Lesson 1: Equal Groups and Multiplication
Learning target: Represent equal groups with multiplication and repeated addition.
Learn: A product gives the total number in equal groups. In 4 groups of 3, the expression 4 × 3 means 3 + 3 + 3 + 3, or 12. The first factor can name the groups and the second the number in each. Both factors matter. Zero groups contain zero objects.
Worked example: Use counters to model 3 groups of 5. Write 3 × 5 = 15 and 5 + 5 + 5 = 15. Explain what each factor means.
Practice together: Explain the example using counters, a drawing or an equation. Then complete the 12 questions for this lesson in the workbook.
Advanced extension: Draw two different equal-group arrangements for 24. Explain what changes and what stays the same.
Lesson 2: Arrays and Multiplication Strategies
Learning target: Use rows, columns, and the distributive property to find products.
Learn: An array arranges objects in equal rows and columns. An array of 3 rows with 6 in each row has 18 objects. Rotate it to see 6 rows of 3, also 18. You can split an array: 7 × 6 = (5 × 6) + (2 × 6) = 30 + 12 = 42.
Worked example: Draw 4 rows of 3 dots. Write 4 × 3 = 12 and 3 × 4 = 12. Explain why the total stays the same.
Practice together: Explain the example using counters, a drawing or an equation. Then complete the 12 questions for this lesson in the workbook.
Advanced extension: Show two ways to split 8 × 7 into smaller products.
Lesson 3: Division as Sharing and Grouping
Learning target: Interpret quotients and connect division to an unknown factor.
Learn: Division can mean sharing a total equally or finding how many equal groups fit. With 24 counters in 6 equal groups, each group has 4. With 24 counters grouped in fours, there are 6 groups. Because 6 × 4 = 24, both 24 ÷ 6 = 4 and 24 ÷ 4 = 6.
Worked example: Share 20 counters among 5 groups. Then group 20 counters into groups of 5. Each gives 4, but the unknown describes something different.
Practice together: Explain the example using counters, a drawing or an equation. Then complete the 12 questions for this lesson in the workbook.
Advanced extension: Write a sharing story and a grouping story for 24 ÷ 6, then explain the different unknowns.
Lesson 4: Missing Factors and Related Facts
Learning target: Solve unknown-factor equations and use fact families to verify.
Learn: In 7 × □ = 42, ask how many groups of 7 make 42, or use 42 ÷ 7 = 6. The missing factor is 6. For 6, 7 and 42 the related facts are 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7, and 42 ÷ 7 = 6. Division by zero is undefined.
Worked example: Solve □ × 8 = 40 by asking 40 ÷ 8. Check 5 × 8 = 40.
Practice together: Explain the example using counters, a drawing or an equation. Then complete the 12 questions for this lesson in the workbook.
Advanced extension: Create the complete related fact family for 4, 9 and 36.
Lesson 5: Word Problems and Choosing Operations
Learning target: Model one- and two-step situations using appropriate operations and units.
Learn: Read what the problem asks and decide what is known. Equal groups can be modeled with multiplication; sharing or finding the number of groups can use division. In a two-step problem, label the intermediate quantity. For 4 boxes of 6 crayons with 5 used, (4 × 6) − 5 = 19 crayons remain.
Worked example: There are 3 trays of 8 cups. If 7 cups are used, 3 × 8 = 24 and 24 − 7 = 17 cups remain.
Practice together: Explain the example using counters, a drawing or an equation. Then complete the 12 questions for this lesson in the workbook.
Advanced extension: Write your own two-step equal-groups story, solve it and explain the units.
Standards reference and evidence
This chapter provides instruction and partial practice related to 2019 Alabama Mathematics Course of Study, Grade 3 standards 1–8, including equal groups, division, unknown factors, operations, and word situations. It is not a complete crosswalk: broader instruction and varied independent evidence are needed for every component, including multiplication fact fluency and automaticity.