Activity 01
Pairs: Double Dominoes
Provide dominoes and cards showing doubles up to 20. Pairs match each domino to its double card, then explain the link to 2x table. Swap sets and record three new matches in maths books.
Compare how doubling and halving are like a mirror image of each other.
Facilitation TipDuring Double Dominoes, circulate and ask each pair to justify one match aloud to ensure language practice.
What to look forPresent students with a set of 10 counters. Ask them to show you double the amount, then halve the original amount back. Observe their strategies and accuracy.
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Activity 02
Small Groups: Halving Arrays
Groups use counters to build arrays for even numbers like 12 or 16, then halve into two equal parts two ways. Try odd numbers like 15 and discuss remainders. Draw findings on mini-whiteboards.
Critique whether every whole number can be halved to make another whole number.
Facilitation TipIn Halving Arrays, remind groups to rotate the array to check the halving from both directions.
What to look forGive each student a card with a number. Ask them to write down the double of their number and half of their number (if it's even). For example, if they have 8, they write 'Double is 16, Half is 4'.
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Activity 03
Whole Class: Mirror Relay
Call a number; teams send one student to board to double it, next halves it back, third quadruples using double-double. Rotate roles. Correct as class and vote on clearest explanations.
Explain how knowing the double of a number helps us find the quadruple.
Facilitation TipFor the Mirror Relay, keep the pace brisk so students stay alert and transfer their understanding between doubling and halving smoothly.
What to look forAsk students: 'If you have 7 sweets, can you share them equally between two people without breaking any sweets? Why or why not?' Listen for their reasoning about odd and even numbers.
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Activity 04
Individual: Number Line Doubles
Students mark numbers 1-20 on personal number lines, then jump doubles and halves with counters. Label quadruples and note even-odd patterns. Share one discovery with partner.
Compare how doubling and halving are like a mirror image of each other.
Facilitation TipOn individual Number Line Doubles, have students mark both the jump and the label so they can later halve the same jumps back.
What to look forPresent students with a set of 10 counters. Ask them to show you double the amount, then halve the original amount back. Observe their strategies and accuracy.
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Generate Complete Lesson→A few notes on teaching this unit
Teach doubling and halving as actions first, then symbols second. Use consistent language: say ‘two groups of five’ and ‘split five into two equal parts’ before introducing 2 × 5 and 5 ÷ 2. Avoid rushing to formal algorithms; let children discover the quadruple shortcut through repeated doubling with real items.
Successful learning looks like students using objects or drawings to double and halve correctly, explaining why odd numbers cannot be halved evenly, and applying doubling twice to find quadruples. They will speak in sentences such as ‘Double seven is fourteen, double fourteen is twenty-eight, so four times seven is twenty-eight.’
Watch Out for These Misconceptions
During Halving Arrays, watch for students who split odd totals into unequal parts or ignore remainders.
Have them recount the counters and draw the split; the leftover counter must be placed to one side, prompting a class discussion on even versus odd numbers.
During Double Dominoes, listen for learners who claim doubling and halving are unrelated operations.
Ask them to show the domino’s total as two equal rows, then split those rows in half, naming each step so the mirror image becomes explicit.
During Mirror Relay, notice if students skip the quadruple connection and compute 4 × n directly.
Pause the relay and ask the team to build the first double with cubes, then double again, so the link to 4 × n is physically demonstrated before resuming.
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