Fair Shares Across Aotearoa

Overview

In this 60-minute lesson, Year 4 learners connect equal groups, arrays, multiplication and division facts with tenths and decimal notation. They use concrete materials and visual representations before recording and explaining their thinking in different ways.

Learning intentions

• WALT represent multiplication as equal groups and arrays.
• WALT connect multiplication facts with related division facts.
• WALT represent tenths as fractions and decimals.
• WALT explain mathematical thinking using materials, drawings, words or equations.

Success criteria

• I can model 6 groups of 4 and write the matching multiplication equation.
• I can solve 24 ÷ 6 using equal groups, an array or a related fact.
• I can show that 3/10 is 0.3 and explain what the digits mean.
• I can explain why 0.30 and 0.3 have the same value.

Curriculum links

• Mathematics and Statistics — multiplicative thinking through equal groups, arrays, multiplication and division.
• Mathematics and Statistics — fractions and decimal notation, including tenths.
• Mathsteasers — higher-order thinking, reasoning and explaining strategies for advanced learners.
• Te Mātaiaho emphasis on communicating mathematical ideas through concrete, visual and symbolic representations.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Open with the hook and learning intention slides and show 24 counters arranged as 4 groups of 6. Ask, “How many altogether? How could we share them fairly?” Students quietly notice, then discuss with a partner and share multiplication or division ideas. Record 4 × 6 = 24 and 24 ÷ 4 = 6.

2. 7–17 min · Explicit modelling. Use counters and an array to model 6 groups of 4, then connect the model to 6 × 4 = 24, 4 × 6 = 24, 24 ÷ 6 = 4 and 24 ÷ 4 = 6. Refer to the equal-groups and related-facts slides and the Division Facts Strategy Mat for vocabulary and strategy prompts. Students build the model, sketch an array and explain one related fact to a partner.

3. 17–25 min · Tenths and decimals. Shade 3 parts of a ten-frame or fraction strip to represent 3/10. Model the language “three tenths”, the decimal 0.3 and the equivalence 3/10 = 0.3 using the tenths and decimal notation slides. Students make 3/10 with materials, draw it and complete the sentence: “___ tenths is ___, written as ___.”

4. 25–45 min · Fair Shares activity. Organise learners into five groups of five and provide counters, arrays, fraction strips and ten-frames. Distribute the Fair Shares practice worksheet. Students rotate through or select tasks: build and draw 6 groups of 4; solve 24 ÷ 6; show 3/10 as a fraction and decimal; and solve the key fact family, 5 × 7 = 35 and 35 ÷ 5 = 7. Learners may build, draw, explain orally or write equations. Display the Fair Shares instructions and task slides to keep the activity moving.

5. 45–54 min · Reasoning challenge and discussion. Present the statement, “0.30 is greater than 0.3 because it has more digits.” Students use a ten-frame, place-value representation or drawing to decide whether the statement is true. Pairs prepare an explanation, then share. Guide learners to see that both represent 3 tenths; the zero in the hundredths place does not change the value. Use the reasoning discussion slide to collect explanations.

6. 54–60 min · Plenary and exit check. Revisit the learning intentions on the plenary slide. Students complete the final section of the Fair Shares practice worksheet independently: draw or describe 6 groups of 4, solve 24 ÷ 6, write 7/10 as a decimal, and explain why 0.30 = 0.3. Invite two learners to share different representations.

Resources

• the complete lesson slide deck
• the Fair Shares practice worksheet
• Counters or linking cubes, approximately 30 per group
• Array grids or squared paper
• Fraction strips marked into tenths
• Ten-frames
• Mini-whiteboards and pens
• Pencils and colouring tools
• the Division Facts Strategy Mat

Assessment

• Observe whether learners build equal groups accurately and connect the model to multiplication and division equations.
• During partner talk, listen for correct use of “groups of”, “shared equally”, “tenths”, “fraction” and “decimal”; ask learners to justify rather than guess.
• Use the independent final worksheet questions to identify who can represent 7/10 as 0.7 and explain the equivalence of 0.30 and 0.3.

Differentiation

• Support learners with pre-organised counters, partially completed arrays, a ten-frame and sentence starters such as “I can see ___ groups of ” and “ tenths is written as ___.”
• Allow learners to demonstrate understanding by building, drawing, speaking or writing; pair learners strategically and rehearse explanations before whole-class sharing.
• For EAL learners, explicitly model gestures and visuals for “group”, “share”, “equal”, “tenths” and “same value”; provide a word bank and accept labelled diagrams.
• Extend confident learners by asking them to create another multiplication-division fact family and prove, using a representation, that 0.40 = 0.4 and 4/10 = 0.4.