Array Strategy Challenge

Overview

Students investigate multiplication by building arrays with counters and recording them on grid paper. Working in mixed Year 2–3 pairs, they choose an accessible product, represent it in at least two ways, compare strategies, and design a related challenge for another pair.

Learning intentions

• WALT represent multiplication using equal groups and arrays.
• WALT connect arrays with multiplication equations and repeated addition.
• WALT explain and compare different strategies.
• WALT create and solve a related multiplication challenge.

Success criteria

• I can build an array with equal rows and columns.
• I can record my array as a multiplication equation and repeated addition.
• I can show the same product in at least two ways.
• I can explain how I know my answer is correct and solve another pair’s challenge.

Curriculum links

• Te Mātaiaho Mathematics and Statistics — Mathsteasers: higher-order thinking and challenging mathematical questions.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers / Alignment: connecting the investigation with multiplication and representation learning.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: extending learners through open-ended problem solving.
• Mathematical competencies: reasoning, communicating mathematical thinking, representing ideas, and working collaboratively.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Display a picture of 12 objects arranged in rows using the opening array image and notice-and-wonder prompt. Ask, “How many objects are there? How could we organise them so they are easy to count?” Students quietly notice, then share possible rows, columns, skip-counting, or addition strategies.

2. 5–10 min · Model the mathematics. Build 3 rows of 4 counters where all students can see. Model the language: “3 groups of 4 is 3 × 4, which equals 12”; connect this to 4 + 4 + 4 and explain that turning the array gives 4 × 3. Use the array modelling slides to show rows, columns, equation, and repeated addition. Students rehearse one explanation with a partner.

3. 10–13 min · Set up the investigation. Pair students from different year levels, aiming for supportive partnerships and shared decision-making. Show the task on the investigation instruction slide and distribute the array investigation recording sheet. Each pair chooses a product they can access, such as 6, 8, 10, 12, 15, 18, 20, 24, or 30, then builds it with counters and records at least two different representations on grid paper or the worksheet.

4. 13–28 min · Investigate and record. Circulate, asking, “What does each row represent?”, “How do you know your groups are equal?”, and “Can you show the same product another way?” Students build an array, draw or shade it on the grid, write a multiplication equation and repeated addition, then find a second array or representation for the same product. Encourage pairs to label rows and columns clearly.

5. 28–36 min · Compare strategies. Invite pairs to place their work where another mixed-year pair can view it, or conduct a paired explanation. Students use the discussion prompts on the compare-and-explain slides: “Our product is…”, “We represented it by…”, “Our strategies are alike/different because…”, and “We know it is correct because…”. Partners ask one clarifying question and identify whether the arrays show a commutative pair, such as 3 × 4 and 4 × 3.

6. 36–42 min · Create and solve a challenge. Each pair creates a related challenge for another pair using their chosen product or a nearby product. For example: “I have 24 counters. Make two different arrays and write the matching equations.” Pairs swap challenges, build or draw a solution, and check it against the creator’s intended answer. Students record the challenge and solution on the challenge and response section.

7. 42–45 min · Plenary and exit check. Use the final reflection slide to revisit the learning intentions. Students complete a quick oral or written exit response: “Show 12 in two array ways. Write one multiplication equation and explain which number tells the rows.” Select two contrasting examples to celebrate clear reasoning and representation.

Resources

• the complete array investigation slide deck
• the array investigation recording sheet
• Counters, linking cubes, or small classroom objects
• Grid paper
• Pencils, coloured pencils, and rulers
• Large paper or mini-whiteboards for pair sharing
• Prepared mixed Year 2–3 pairings
• Optional visualiser or document camera

Assessment

• Observe whether students make equal rows and columns, count efficiently, and connect the array to a correct equation.
• Listen for precise mathematical language, including groups, rows, columns, altogether, multiplication, and product.
• Check the investigation sheet and challenge response for two representations, a valid equation, and an explanation. Use the exit response to identify learners needing further work with equal groups or multiplication notation.

Differentiation

• Support learners with a smaller choice of products, such as 6, 8, 10, or 12; provide pre-counted groups of counters and sentence starters: “I made __ rows of __. This is __ × __ = __.”
• Allow dyslexia-friendly access through uncluttered worksheets, a clear sans-serif font, large spacing, short instructions read aloud, visual examples, and the option to explain orally rather than write lengthy responses.
• Pair thoughtfully across year levels, but ensure both learners build, record, explain, and make decisions. Use role cards such as builder, recorder, checker, then swap roles.
• Extend advanced learners by asking them to find all possible rectangular arrays for a product, explain why some products have more factors, or create a challenge with a missing row, column, or product.

Extension

• Ask learners to investigate a product such as 24 or 30 and prove that they have found every possible rectangular array.
• Invite pairs to create a “Which array am I?” clue challenge using rows, columns, and product, then solve another pair’s clues.