Arrays Equal Groups

Overview

Lesson 1 of 8 in the unit Multiplication and Division Facts. Students use concrete materials, drawings and equations to represent multiplication as equal groups and arrays, focusing on facts for 3, 4, 5 and 10.

Learning intentions

Students will:

• Represent multiplication using equal groups and arrays.
• Connect equal groups, repeated addition and multiplication equations.
• Describe rows, columns, factors and products.
• Begin developing efficient recall of multiplication facts for 3, 4, 5 and 10.

Success criteria

• I can make equal groups.
• I can build and describe an array.
• I can write a matching multiplication sentence.
• I can explain what each factor represents.

Curriculum links

• Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10, and use these facts to develop related division facts.
• Represent and solve multiplication situations using equal groups, arrays, materials, drawings and number sentences.
• Use mathematical language to explain strategies and communicate reasoning.
• Develop the proficiencies of understanding, fluency, problem-solving and reasoning within the Tasmanian Mathematics curriculum.

Lesson structure (50 minutes)

1. 0–5 minutes – Hook and connect

Display an image or quick arrangement of 12 counters and ask: “How could we organise these so every group is equal?” Open with the hook and learning intention slides. Invite students to share possible groupings, without confirming all answers immediately.

Explain that today’s focus is representing multiplication, and introduce the words equal groups, array, row, column, factor, product, multiplication and groups of. Use the multiplication vocabulary cards to support the introduction and classroom word wall.

2. 5–15 minutes – Explicit teaching

Model 3 groups of 4 using counters and three hoops or paper plates. Say: “Three groups of four makes twelve.” Record the repeated addition, 4 + 4 + 4 = 12, then connect it to 3 × 4 = 12.

Rearrange the same 12 counters into an array. Identify three rows of four and four columns of three. Explain that the factors are the numbers being multiplied and the product is the answer. Emphasise that students must count rows and columns consistently. Refer to the modelling and vocabulary slides.

3. 15–30 minutes – Guided practice in pairs

Place students in pairs, with one student building and the other describing before swapping roles. Provide counters, linking cubes and hoops or paper plates. Call out arrays such as 3 groups of 4, 4 groups of 3, 5 groups of 2 and 10 groups of 3. Include examples connected to the 3, 4, 5 and 10 facts.

Students build each model, describe it using the frame “___ groups of ___ makes ___”, and record the matching multiplication equation on a mini-whiteboard. Circulate and ask: “What does this factor tell us?” and “How do you know the groups are equal?” Use the guided practice instructions and sentence-frame slide.

4. 30–40 minutes – Independent practice

Distribute the arrays and equal groups worksheet. Students draw and label four arrays, match each array to a multiplication equation and write a word description for each. Encourage students to label rows and columns and show repeated addition for at least one example.

Confer with students who reverse the number of groups and the number in each group. Prompt them to physically build the array before drawing it. Students who finish early can write both turn-around facts for an array and explain why the products are equal.

5. 40–47 minutes – Reasoning discussion

Display an array, such as 3 rows of 4, and ask: “How can the same array show two multiplication facts?” Students turn and talk, then share equations such as 3 × 4 = 12 and 4 × 3 = 12. Clarify that the arrangement shows different rows and columns, but the total number of objects remains twelve.

Use the reasoning and discussion slide. Check that students are not simply stating that the facts are equal; ask them to explain using the array.

6. 47–50 minutes – Exit ticket and review

Students complete an exit ticket: draw 4 groups of 3 and write the matching equation. On the reverse or beneath the drawing, label the number of groups, the number in each group and the product.

Collect responses as students leave. Use the reflection and exit-ticket slide to revisit the success criteria and ask students to self-assess with a thumbs up, sideways or down.

Resources

• the complete lesson slide deck with hook, modelling, guided practice, reasoning prompts and plenary
• the arrays and equal groups worksheet
• Counters, linking cubes and small hoops or paper plates
• Grid paper, pencils and erasers
• Mini-whiteboards and markers
• Prepared array cards
• the multiplication vocabulary cards
• Word wall or board space

Assessment

• Observe whether students create equal groups, build arrays accurately and distinguish the number of groups from the number in each group.
• Listen for correct use of row, column, factor, product and the sentence frame during paired practice.
• Analyse the worksheet and exit ticket for accurate models, equations and explanations. Record students needing further support with arrays or multiplication facts.

Differentiation

• Support students with smaller totals, pre-drawn grids, concrete materials and prepared array cards. Rehearse descriptions with a partner before recording.
• Provide visual sentence frames: “___ groups of ___ makes ” and “ rows of ___ is ___.”
• For EAL learners and students requiring additional support, keep vocabulary cards visible, demonstrate each term with gestures or labelled examples, and accept oral explanations before written responses.
• Extend confident students by asking them to write both turn-around facts, connect an array to repeated addition and explain why both multiplication facts have the same product.