Build Equal Groups

Overview

Lesson 23 of 30 in Building Mathematical Thinking. Students connect multiplication to equal groups and repeated addition by building, drawing, and explaining small multiplication facts. The lesson uses concrete materials before moving to arrays and equations.

Learning intentions

• Students will be able to represent multiplication as equal groups.
• Students will be able to connect equal groups to repeated addition.
• Students will be able to match a model to a multiplication equation.
• Students will be able to explain what each factor represents.

Success criteria

• I can build equal groups with counters.
• I can write repeated addition for my groups.
• I can match my model to a multiplication equation.
• I can explain how an array, drawing, and equation show the same fact.

Curriculum links

• Operations and Algebraic Thinking — interpret products of whole numbers.
• Multiplication — describe a total as equal groups of objects.
• Mathematical practices — model with mathematics and explain thinking using representations.

Lesson structure (30 minutes)

1. 0–4 min · Hook and connect. Open with the equal-groups introduction slide and display 3 groups of 2 dots. Ask, “How many dots are there altogether? What do you notice about the groups?” Students count, turn and talk, and share that the groups are equal.

2. 4–9 min · Direct teach. Use the multiplication model slides to build 3 groups of 2 with counters, record 2 + 2 + 2 = 6, and introduce 3 × 2 = 6 as three groups of two. Students build the model with counters, repeat the language orally, and identify the number of groups, objects in each group, and total.

3. 9–16 min · Guided practice. Show one small factor pair at a time on the guided-practice slides: 2 groups of 4, 4 groups of 3, and 5 groups of 2. Students work with a partner to build each fact, draw or arrange an array, say the repeated addition sentence, and share one explanation. Pause after each example to check that groups contain the same number.

4. 16–24 min · Independent practice. Distribute the equal-groups practice worksheet. Students complete tasks by building with counters first, then drawing equal groups or an array, writing repeated addition, and matching each model to a multiplication equation. Confer with students and ask, “What does this factor tell you?” and “How do you know the groups are equal?”

5. 24–28 min · Share and compare. Return to the representation discussion slide and display one fact, such as 4 × 3 = 12. Invite two students to show different representations. Students compare an array, drawing, repeated-addition sentence, and equation, explaining how each represents the same total.

6. 28–30 min · Exit check. Show 3 groups of 4 on the closing and exit slide. Students independently draw or build the groups, write a multiplication equation and repeated-addition sentence, then briefly explain what the factors mean.

Resources

• Counters or small connecting cubes
• Grid paper or blank paper for arrays
• Pencils, crayons, and erasers
• the equal-groups and multiplication slide deck
• the equal-groups practice worksheet
• Small whiteboards or response cards
• Document camera or board space

Assessment

• During guided practice, check whether students build equal-sized groups and accurately identify the number of groups and objects in each group.
• Review worksheet models, repeated addition, and equations; provide immediate feedback when students reverse or misinterpret the factors.
• Use the exit check to identify whether each student can represent one product with a model and equation. Record students needing additional concrete practice.

Differentiation

• Support: Use counters, tactile grouping, small factors from 2–5, and pre-drawn circles or array frames. Model one group at a time and use the sentence frame, “I have __ groups of __. The total is __.”
• Dyslexia-friendly options: Keep visual arrays and equations together, use large clear print and generous spacing, read directions aloud, allow oral rehearsal before writing, and provide equation frames such as “__ + __ + __ = ” and “ × __ = __.”
• Communication and learning support: Pair students strategically, offer choice between building, drawing, pointing, or explaining orally, and check understanding with one-step directions and frequent repetition of key language.
• Extension: Students choose one multiplication fact and represent it with an array, an equal-groups drawing, repeated addition, and an equation. They explain how the representations are connected and create a matching fact using the same total.

Extension

• Challenge advanced learners to show the same total using a different number of equal groups, such as 3 × 4 and 4 × 3, and explain what changes in the model.
• Ask students to create a short classroom context for their fact, such as equal groups of objects, and have a partner identify the equation.