From Groups to Arrays

Overview

In this second lesson of the “Share, Group, Array” unit, students connect concrete equal sharing with the structure of an array. They rearrange counters from equal groups into rows and columns, then communicate their thinking using an equal-sharing sentence.

Learning intentions

• WALT rearrange equal groups to make arrays.
• WALT describe arrays using rows, columns and equal groups.
• WALT record an equal-sharing sentence to match a practical problem.
• WALT explain how an array shows that quantities have been shared equally.

Success criteria

• I can make equal groups with counters.
• I can rearrange the groups into rows and columns.
• I can describe how many rows and how many counters are in each row.
• I can record a sentence such as “12 shared between 3 is 4” and explain what each number means.

Curriculum links

• Number — multiplication and division using equal grouping, arrays, repeated addition and partitioning.
• Number — modelling practical sharing and grouping problems, representing solutions and explaining them in context.
• Algebra — using doubling and halving to support facts for twos and related division facts.
• Mathematical proficiencies — understanding, fluency, problem-solving and reasoning through concrete representation and oral explanation.

Lesson structure (50 minutes)

1. 0–7 min · Warm-up: Share the counters. Teacher opens with the sharing warm-up slide and presents: “12 counters are shared equally between 3 children. How many does each child get?” Students use counters to share one at a time, discuss with a partner and complete the oral sentence, “12 shared between 3 is ___.” Ask: “How do we know the groups are equal?” Record a drawing and sentence, without introducing arrays yet.

2. 7–15 min · From groups to an array. Teacher models 12 counters in 3 loose groups of 4, then physically moves them into 3 rows of 4. Use the groups-to-array modelling slides to show the same counters as groups and as an array. Students help identify the rows, columns and total, using gestures: sweep across for a row and point down for a column. Model the language: “3 rows of 4 make 12” and “12 shared between 3 is 4.” Show a non-example with unequal rows and ask why it does not show equal sharing.

3. 15–27 min · Build and describe. Teacher places students in pairs and distributes counters and the groups-to-arrays recording sheet. Give each pair a prepared problem, such as 8 shared between 2, 10 shared between 5 or 12 shared between 4. Students first make equal groups, then slide the counters into an array. They draw or trace the array and complete: “___ shared between ___ is ___.” Partners rehearse the explanation aloud: “I made ___ equal groups. Each group has ___.”

4. 27–38 min · Array investigation. Teacher displays the array investigation instructions and gives pairs totals of 6, 8, 10 or 12. Students create an array, rotate or rearrange it where possible, and record the rows and columns. Ask selected pairs to show their array and explain whether “3 rows of 4” and “4 rows of 3” represent the same total. Support students to connect the physical arrangement to repeated addition, for example, 4 + 4 + 4 = 12.

5. 38–46 min · Solve, record and justify. Teacher displays two prepared examples and two non-examples on the solve-and-justify slides. Students independently solve two sharing problems on the worksheet, using counters or an array template if needed. They circle the number that tells how many groups there are and underline the number in each group. Invite students to justify one answer using “I know it is equal because …”

6. 46–50 min · Plenary and exit check. Teacher shows 10 counters arranged in 2 equal rows on the reflection and exit prompt. Students complete an exit response: draw or describe the array and finish “10 shared between 2 is ___.” Ask one or two students to explain what the 2 and 5 represent. Collect responses to identify who is ready to work with larger totals next lesson.

Resources

• the complete groups-to-arrays slide deck
• the groups-to-arrays recording sheet
• Connecting cubes or counters, approximately 20 per pair
• Small hoops, paper plates or mats for making groups
• Array templates with marked rows and columns
• Prepared example and non-example cards
• Mini-whiteboards and markers
• Pencils and coloured pencils

Assessment

• Observe whether students make equal groups, physically rearrange them into rows and columns, and use accurate mathematical language.
• Question students during pair work: “What does this number tell us?” and “How can you prove the groups are equal?”
• Use the exit response to assess accurate representation, sharing sentence structure and interpretation of the answer.

Differentiation

• Support students with pre-counted sets, smaller totals within 10, array templates, marked rows and columns, and a worked example kept visible.
• Provide oral rehearsal and sentence frames: “I made ___ groups of ”; “ shared between ___ is ___”; and “The groups are equal because ___.”
• Use gestures, real objects, clear modelling and partner talk for EAL learners; accept pointing, drawing and oral explanations before written recording.
• For students requiring additional support, work with a teacher-led group and share counters one at a time. Check understanding after each step rather than requiring independent recording immediately.

Extension

• Students create more than one array for the same total, such as 12 as 3 rows of 4 and 4 rows of 3.
• Students describe the rows, columns and equal groups, then record both sharing sentences and a related repeated-addition sentence.
• Challenge students to find a total that cannot make an array with more than one row arrangement and explain why.