Sharing Fairly

Overview

This is lesson 24 of 30 in Building Mathematical Thinking. Students use counters and drawings to understand division as equal sharing, then connect a fair-sharing situation to a division equation. The lesson builds on students’ prior experience with equal groups and multiplication.

Learning intentions

• I can share objects equally among groups.
• I can describe what a division problem means.
• I can write or explain a division equation for a fair-sharing story.
• I can use drawings, objects, or words to show my thinking.

Success criteria

• I can solve a fair-sharing problem with no objects left over.
• I can identify the number of objects in each group.
• I can explain that division can show how a total is shared equally.
• I can match a story, model, and equation such as 12 ÷ 3 = 4.

Curriculum links

• Operations and Algebraic Thinking — interpreting whole-number quotients.
• Students interpret division as partitioning a total into equal shares.
• Students represent word problems with objects, drawings, spoken explanations, and equations.

Lesson structure (30 minutes)

1. 0–4 min · Hook: What is fair? Teacher opens the fair-sharing hook slide and shows 12 counters being shared among 3 children; ask, “How can we make sure everyone gets the same amount?” Students act out or discuss how they would share the objects and predict the amount each child will receive.

2. 4–10 min · Model equal sharing. Teacher uses 12 counters and three labeled hoops or spaces, placing one counter in each group at a time while thinking aloud: “I am sharing 12 objects equally into 3 groups. Each group gets 4. We can write 12 ÷ 3 = 4.” Teacher revisits the division model and equation slide and models the language “12 divided by 3 equals 4.” Students copy the sharing action with their own counters and say the equation with the teacher.

3. 10–16 min · Guided practice: story and model. Teacher reads aloud the picture-supported stories on the guided practice slides, such as, “There are 10 apples shared equally among 2 baskets. How many apples go in each basket?” Students work in pairs with counters, draw the groups on the fair-sharing practice worksheet, and explain their answer to a partner. Teacher checks that students share one object at a time and asks, “How many are in each group?”

4. 16–23 min · Supported independent practice. Teacher distributes the fair-sharing practice worksheet and assigns problems appropriate to each student, using quantities from 6 to 20 and only equal-share situations. Students solve by using counters, drawings, numbers, or oral explanation. Teacher circulates and repeatedly models with students who need support, asking, “What is the total? How many groups? Is each group equal?”

5. 23–27 min · Share and clarify. Teacher displays the discussion and comparison slides and selects two student models to compare. Students explain how their objects or drawings show the total, the number of groups, and the number in each group. Teacher emphasizes that in a problem such as 15 ÷ 3 = 5, 15 is the total, 3 is the number of equal groups, and 5 is the number in each group.

6. 27–30 min · Exit check. Teacher displays the exit question slide: “Share 8 counters equally between 2 children. How many does each child get? Show or explain your thinking.” Students complete the final item on the worksheet or respond orally with a model. Teacher collects responses and asks one or two students to explain how they know the sharing is fair.

Resources

• the Understand Division slide deck
• the fair-sharing practice worksheet
• Connecting cubes, counters, or small classroom objects
• Three hoops, paper plates, or drawn group spaces
• Pencils, crayons, and blank paper
• Optional number cards from 6 to 20
• Document camera or board for modeling

Assessment

• Observe whether students distribute one object at a time and create equal groups during guided and independent practice.
• Ask individual students to identify the total, number of groups, and number in each group in a modeled problem.
• Use the exit check to determine whether students can solve and explain a basic equal-sharing problem; accept a correct model or oral explanation as evidence.

Differentiation

• Support: Use small quantities first, three clearly marked group spaces, physical counters, and a “share one to each group” routine. Model the same problem several times before changing the numbers.
• Communication and dyslexia-friendly access: Read every story aloud, provide picture-supported problems, reduce written directions, use large clear print with generous spacing, and allow students to answer by pointing, building, drawing, or speaking.
• Special education access: Pair students strategically, provide a visual sequence—total, groups, share, count—and give extra processing time. Check understanding privately and offer hand-over-hand demonstration only when appropriate.
• Extension: Students compare two interpretations of the same division equation. For 12 ÷ 3 = 4, they explain both “12 objects shared among 3 groups gives 4 in each group” and “12 objects made into groups of 3 makes 4 groups,” using a drawing for each.

Extension

• Challenge students to create their own fair-sharing story for 18 ÷ 3 or 20 ÷ 4 and exchange it with a partner to solve.
• Ask advanced learners to explain how multiplication can check their division answer, such as 3 × 4 = 12.