Sharing and Grouping

Overview

In lesson 4 of the 10-lesson unit “Build, Model, Solve,” students model division as sharing equally and grouping into equal sets. They use counters, tape diagrams, and multiplication facts to solve one- and two-step problems, explain remainders, and build readiness for dividing larger numbers.

Learning intentions

Students will be able to:

• Represent division situations using counters, drawings, and tape diagrams.
• Explain the difference between sharing into equal groups and grouping by a known amount.
• Connect division equations to related multiplication facts.
• Solve one- and two-step word problems and interpret remainders in context.

Success criteria

• I can show a division problem with counters or a tape diagram.
• I can write a related multiplication equation to check my answer.
• I can explain what a remainder means in the problem.
• I can solve and explain a one- or two-step division situation.

Curriculum links

• Number and Operations in Base Ten — whole-number quotients and remainders using place value, multiplication, arrays, and area models.
• Number and Operations in Base Ten — multiplication using properties and place value.
• Number and Operations in Base Ten — reading, writing, and comparing multi-digit whole numbers.
• Number and Operations in Base Ten — understanding the relationship between adjacent place values.

Lesson structure (60 minutes)

1. 0–7 min · Hook and connect. Display a situation from the division hook and introduction slides: “35 counters are shared equally among 5 teams. How many does each team get?” Students estimate, solve mentally or with a sketch, and turn-and-talk about whether they shared or grouped. Invite two strategies and record both division and multiplication equations.

2. 7–17 min · Model sharing and grouping. Use counters and the sharing and grouping model slides to demonstrate 24 ÷ 4. First, share 24 counters equally among 4 groups; then make groups of 4 until all counters are used. Draw a tape diagram for each model and connect 24 ÷ 4 = 6 with 4 × 6 = 24. Students model one example with a partner and explain which quantity is known and which is unknown.

3. 17–22 min · Remainders mini-lesson. Model 26 ÷ 4 with counters and a tape diagram. Ask, “What does the 2 left over mean?” Discuss that a remainder must be less than the divisor and that its meaning depends on the situation: leave some items, share only complete groups, or round up when every person must receive an item. Students complete a quick whiteboard response: 26 ÷ 4 = __ R __ and one sentence interpreting the remainder.

4. 22–42 min · Collaborative stations. Organize 7 groups of 5 students and provide counters, grid paper, pencils, and the group role cards to clarify responsibilities. Groups rotate through three stations approximately every 6 minutes, with 2 minutes for transitions. Station A: model division with counters and draw a tape diagram. Station B: match division equations to related multiplication facts and check using multiplication. Station C: solve a word problem, decide what the remainder means, and explain the choice. Students record their work on the division sharing and grouping worksheet. Circulate, question, and select examples for discussion.

5. 42–53 min · Two-step problem solving. Open the two-step problem-solving slides and read: “A school has 4 boxes with 18 pencils in each box. The pencils are shared equally among 6 tables. How many pencils does each table receive?” Students identify the steps, solve independently, compare with a partner, and represent the work with equations and a tape diagram. Discuss how multiplication and division are both needed.

6. 53–60 min · Debrief and exit ticket. Use the discussion and closing slides to revisit the question, “How are sharing, grouping, and multiplication connected?” Students complete the final section of the division sharing and grouping worksheet: solve 43 ÷ 5, draw a model, and explain the remainder. Collect responses as students leave.

Resources

• the division hook, modeling, station directions, problem-solving, and closing slides
• the division sharing and grouping worksheet
• Counters or linking cubes, one set per group
• Small cups, hoops, or paper circles for making equal groups
• Grid paper and blank paper
• Pencils, erasers, and dry-erase boards
• Timer and station signs
• the group role cards

Assessment

• During modeling, check whether students distinguish the dividend, divisor, quotient, and remainder and can represent division with equal groups.
• At stations, listen for explanations connecting division and multiplication; record students needing support with remainders or tape diagrams.
• Use the exit response to assess accurate computation, a valid model, and interpretation of the remainder.

Differentiation

• Provide counters, pre-drawn tape-diagram templates, multiplication charts, and sentence frames such as “I made ___ groups of ___” and “The remainder means ___.”
• Pair students strategically and assign supportive roles; read word problems aloud and clarify vocabulary such as share, each, groups, total, and left over for English learners and students with language needs.
• For students needing additional support, use divisors of 2, 3, 4, or 5 and model one step at a time before moving to two-step problems.
• Challenge early finishers to create two different stories for 29 ÷ 4 that require different interpretations of the remainder, then prove each answer with multiplication.