Operations With Models

Overview

This is lesson 4 of 5 in the unit Number Sentences Make Sense. Students use concrete and visual models to check and complete addition, subtraction, multiplication and division number sentences, then explain how they know a sentence is true or false.

Learning intentions

• WALT check and complete number sentences involving the four operations.
• WALT choose a useful representation, such as a ten-frame, counters or a number line.
• WALT connect equal groups and sharing to multiplication and division.
• WALT explain our mathematical thinking clearly.

Success criteria

• I can choose a useful model for a number sentence.
• I can find a missing number or operation.
• I can use a model to check whether a sentence is true.
• I can explain my answer using words, pictures or materials.

Curriculum links

• Mathematics and Statistics — Number: using additive and multiplicative thinking to solve and explain problems.
• Mathematics and Statistics — reasoning with representations, including materials, diagrams and number lines.
• Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathsteasers / Alignment: selecting challenges that connect with familiar number knowledge and textbook learning.

Lesson structure (60 minutes)

1. 0–10 min · Skip-counting warm-up. Open with the warm-up question and counting visuals and lead the class in counting forwards and backwards in 2s, 5s and 10s, using actions or a number line. Students count together, identify patterns and solve quick oral prompts such as “What comes after 12 when we count in 2s?” and “How many groups of 2 make 8?”

2. 10–25 min · Teacher modelling. Use the worked-example slides and model one operation at a time, thinking aloud while building each example with counters. Students watch, predict and help complete:

• Addition: 18 + __ = 17 + 6. Build both sides and notice that the missing number is 5.
• Subtraction: 14 − __ = 9. Use a number line or counters to find the difference.
• Multiplication: __ × 2 = 6. Make equal groups and connect “3 groups of 2” with 3 × 2.
• Division: 6 ÷ __ = 2. Share 6 counters into equal groups and discuss that 3 groups of 2 are made.

Emphasise that the equals sign means “has the same value as”, not “the answer comes next”. Ask: “How could we prove this another way?”

3. 25–50 min · Operation stations. Arrange five groups of four students. Distribute the operations-with-models practice sheet and provide counters, number lines and the Twenty-frame Mats at the stations. Groups rotate every five minutes, or remain at a station long enough to complete the task:

• Build it: represent missing-addend and subtraction sentences on a twenty-frame or number line.
• Group it: make equal groups for multiplication sentences and draw or record the groups.
• Share it: share counters equally for division sentences and record the result.
• True or false: decide whether sentences such as 18 + 5 = 17 + 6 are true, then prove the answer with a model.
• Make one: complete a sentence with a missing number or operation and explain the choice to a partner.

Students record one example from each operation on the worksheet. The teacher moves between groups, asking: “What does each number represent?” “Why is your model useful?” and “How do you know both sides are equal?”

4. 50–55 min · Partner check. Display the partner-check prompts and ask pairs to choose one completed sentence from their worksheet. Students explain their model to a partner, who checks the calculation and asks one question. Partners may give an oral explanation, point to materials or draw a model.

5. 55–60 min · Sharing and exit check. Use the sharing and reflection slides to invite two or three students to share different representations for the same sentence. Students complete an oral or written exit response: “__ ÷ __ = 2. I know it is true because…” and show the answer with a drawing, counters or words. Collect worksheets and note who can complete and justify each operation.

Resources

• the Operations With Models teaching deck
• the operations-with-models practice sheet
• the Twenty-frame Mats
• Counters or small classroom objects
• Large floor or desk number lines
• Mini-whiteboards and pens
• Pencils and erasers
• Timer for station rotations

Assessment

• Observe whether students select an appropriate model and represent the quantities accurately.
• Question students during stations about the meaning of the equals sign, equal groups and sharing.
• Use the worksheet, partner explanation and exit response to identify students who can find a missing number or operation and justify whether a sentence is true.

Differentiation

• Model one operation at a time and keep worked examples visible. Use counters, equal-group mats, twenty-frames and large number lines before moving to abstract notation.
• Support learners with simpler facts within 10, pre-drawn number lines, reduced choices and visual vocabulary such as equal, groups, share, altogether, left and each. Provide sentence starters: “I used…”, “I know because…” and “There are ___ groups of ___.”
• Allow oral explanations, pointing, drawing or acting out a solution. Pair learners thoughtfully and provide additional adult support during multiplication and division.
• Challenge advanced learners to solve and create mixed-operation puzzles, including 2 + 2 + 2 = 3 × 2, and prove each answer in two ways—for example, with equal groups and a number line.