Lesson Plan: Using Repeated Subtraction to Understand Multiplication

Repeated subtraction gives children a practical way to see how multiplication and division are connected. Instead of memorising a times-table fact in isolation, students remove equal groups again and again and observe how many groups fit into a total.

This lesson suits early primary learners who are building confidence with equal groups, skip counting, multiplication facts and sharing problems. It can be adapted for Australian Foundation to Year 3 classrooms, small tutoring groups, homeschool sessions or a short maths intervention.

The central example might be 18 − 3 − 3 − 3 − 3 − 3 − 3 = 0. Children can identify six groups of three, connect the calculation to 6 × 3 = 18, and explain that 18 ÷ 3 = 6. The focus is on meaning rather than speed.

Use counters, linking cubes, small classroom objects or drawings before moving to numbers and symbols. A hands-on approach works well during a morning maths rotation, a whole-class lesson or a quiet practice session at home.

Set The Learning Goal

Begin by explaining that multiplication can describe equal groups, while repeated subtraction shows those groups being removed from a total. A suitable learning intention is: “We are learning to use repeated subtraction to find how many equal groups are in a number.”

Share success criteria in child-friendly language. Students should be able to subtract the same number several times, record the number of subtractions, draw or build the equal groups, and write a related multiplication or division fact.

Start with a familiar context. For example, a class in Melbourne could imagine packing 20 tennis balls into bags of four, while a group in Brisbane might arrange counters into teams for a school sports activity. The context should make the equal group size clear without distracting from the mathematics.

Build Equal Groups With Materials

Give each pair of students 12 counters and ask them to remove groups of two until none remain. Encourage them to say the calculation aloud: “12 take away 2 is 10, take away 2 is 8…” Record each step where everyone can see it.

Next, ask children to count how many groups they removed. Connect their actions to 12 ÷ 2 = 6 and 6 × 2 = 12. Explain that the repeated subtraction answers the division question, while the number of equal groups becomes the first factor in the multiplication fact.

Repeat with totals such as 15, 20 and 24, using group sizes of three, four and six. Children may work on mini-whiteboards or place counters on a large sheet of paper. In a composite classroom, provide smaller totals for students who need support and larger totals for learners ready to extend their thinking.

Link Subtraction To Skip Counting

Once students are comfortable with physical groups, show how repeated subtraction connects to skip counting backwards. For 30 and groups of five, write 30, 25, 20, 15, 10, 5, 0. The six jumps show that six groups of five make 30.

A hundreds chart can make this relationship visible. When students investigate multiples on a hundreds chart, they can compare forward skip counting with backward jumps and identify patterns in the rows and columns.

Invite learners to circle every fifth number, then start at 30 and trace backwards by fives. Discuss how the same sequence supports multiplication, division and subtraction. Australian students may recognise these patterns from counting coins, sharing fruit at recess or grouping classroom materials for a school fete.

Move From Models To Equations

Display a worked example such as 28 − 4 − 4 − 4 − 4 − 4 − 4 − 4 = 0. Ask students to identify the repeated number, the starting total and the number of times the subtraction occurred. Then write 7 × 4 = 28 and 28 ÷ 4 = 7 beside it.

Include examples with remainders, such as 14 − 3 − 3 − 3 − 3 = 2. Explain that four complete groups of three can be removed, with two left over. This prepares children for division with remainders and helps them understand why some sharing problems do not divide evenly.

Use sentence frames to support mathematical language: “I subtracted ___ each time,” “I made ___ equal groups,” and “There are ___ left over.” Encourage students to explain their method to a partner before recording an equation. This is useful in a Year 2 or Year 3 classroom where verbal reasoning is part of everyday maths learning.

Practise And Check Understanding

Provide a short set of problems that moves from concrete to abstract. Students might solve 16 using groups of four, 21 using groups of three, and 32 using groups of eight. Add one word problem, such as sharing 24 lamingtons equally among groups of six for a class gathering.

Ask students to draw jumps on a number line, write a repeated-subtraction equation and state the matching multiplication fact. A quick exit task could show 25 − 5 − 5 − 5 − 5 − 5 = 0 and ask children to complete 5 × 5 = 25 and 25 ÷ 5 = 5.

Assess understanding by listening for accurate explanations rather than relying only on completed answers. Watch for students who subtract different amounts, count the starting number as a group, or confuse the number in each group with the number of groups. Counters, number lines and multiplication grids can remain available as supports.

Print a suitable worksheet from the Gialdini Worksheets library for independent practice, tutoring or a homeschool maths session. Pair the page with counters and a pencil so students continue to connect written calculations with equal groups. Revisit the activity during a later Term lesson, then gradually remove the concrete materials as fluency develops.

Use this lesson as a foundation for multiplication facts, factors, multiples and division strategies. Select a few problems, model the thinking clearly, and give learners time to represent every answer in more than one way.