Build Equal Arrays

Overview

Students investigate multiplication as equal groups and arrays using counters. They will build, move and describe groups in practical situations, developing the language of “groups of”, “rows” and “columns” without recording number sentences. The lesson assumes students can count reliably and recognise small quantities.

Learning intentions

• WALT make equal groups using concrete materials.
• WALT move equal groups to form arrays.
• WALT describe an array using groups, rows and columns.
• WALT solve practical multiplication problems by counting equal groups.

Success criteria

• I can make groups with the same number of counters.
• I can rearrange my groups into an array with equal rows.
• I can explain how many groups I made and how many are in each group.
• I can check that my groups and rows are equal.

Curriculum links

• Number — multiplication and division through equal grouping, arrays and repeated addition.
• Number — modelling practical multiplicative situations and explaining solutions in context.
• Algebra — developing understanding of groups of two through doubling and equal groups.

Lesson structure (50 minutes)

1. 0–5 min · Hook and prior knowledge. Open with the opening question and array image and show a picture of 3 plates with 4 counters on each; students discuss what they notice, count the counters and explain why the groups are fair or equal.

2. 5–12 min · Teacher modelling. Give each pair a small collection of counters and model making 3 equal groups of 2, then physically slide the counters into 3 rows of 2; students copy the model and practise saying, “I made 3 equal groups, with 2 in each group” and “I made 3 rows of 2.”

3. 12–20 min · Guided construction. Display group prompts on the equal-groups modelling slides and call out examples such as 2 groups of 5, 4 groups of 2 and 3 groups of 3; pairs build each example with counters, move the counters into an array, and check that every row has the same number.

4. 20–35 min · Worded problem investigation. Distribute the equal-groups problem worksheet and read each problem aloud, pausing to clarify vocabulary and demonstrate the first one; pairs use counters to act out, build and rearrange each situation, then draw the groups or array and write the answer in words or as a numeral, but do not write number sentences.

• Problem 1: Four children each have 2 counters for a game. How many counters are there altogether?
• Problem 2: There are 3 plates with 5 biscuits on each plate. How many biscuits are there altogether?
• Problem 3: A gardener plants 2 rows of 4 flowers. How many flowers are planted?
• Problem 4: Five toy cars are placed in each of 2 equal lines. How many toy cars are there?
• Problem 5: A teacher puts 3 pencils in each of 4 pots. How many pencils are there altogether?

5. 35–43 min · Share and compare. Invite selected pairs to display one counter model and its array using the discussion and comparison slides; students explain how they know the groups are equal and compare arrangements such as 2 groups of 4 and 4 groups of 2, focusing on what stays the same without requiring formal notation.

6. 43–50 min · Plenary and assessment. Show two final challenges on the plenary slides: “Make 3 equal groups with 12 counters” and “Move them to show equal rows”; students build independently, explain their model to a partner and complete a brief teacher check before packing away.

Resources

• the equal-groups and arrays slide deck
• the equal-groups problem worksheet
• Counters, approximately 20 per pair
• Small plates, hoops or sorting circles
• Mini-whiteboards and markers
• Pencils and coloured pencils
• Large demonstration counters or magnetic counters
• Word cards: equal, group, row, column, altogether
• Classroom display space or document camera

Assessment

• During modelling, check whether students make equal groups rather than simply placing counters randomly.
• Question pairs during the investigation: “How many groups are there?”, “How many are in each group?” and “How can you prove the rows are equal?”
• For the final check, each student must build 3 equal groups of 4 and rearrange them into an array, then explain the model orally or by pointing and using the word cards.

Differentiation

• Support students, including EAL learners, with a smaller range of numbers, sorting circles, demonstration counters and sentence frames: “I made ___ groups of ___” and “Each row has ___.”
• Use gestures and repeated modelling for “group”, “row” and “equal”; pair students strategically and allow students to explain through drawing, pointing or home-language discussion before sharing in English.
• For students needing additional support, provide pre-counted groups or work with 2 groups of 2, 2 groups of 3 and 3 groups of 2. Confirm understanding one problem at a time.
• Extension: ask advanced learners to make two different arrays using the same total number of counters, explain how the groups and rows change, and find all possible equal arrangements for 12 counters.