Here is a sum: 47 + 38. No paper, no columns. How could you work this out in your head? There is more than one way, and some ways are quicker than others depending on the numbers.
Give five seconds of quiet think-time before any hands go up, then take three hands-up answers, not open call-outs.
Don't reveal the answer yet. Listen for the different routes pupils describe (some add the 30 first, some round up to 40) — you'll name these as strategies in the next step.
We will take the same sum, 47 + 38, three different ways, then a bigger sum at the end. Notice where each set of jumps lands and see what stays the same.
Take each one slowly; the point is one sum, three routes.
Partition 47+38: +30 to 77, then +8 to 85. Say split 38 into 30 and 8.
Compensate 47+38: +40 to 87, overshoots, jump back 2 to 85. Stress +40 is easier than +38.
Bridge 47+38: +3 to the friendly 50, then +35 to 85. Round ten first makes the next jump easier.
Point out all three land on 85.
235+198: +200 to 435, back 2 to 433. Ask why adding 200 was easier than 198 — this is where compensating clearly wins.
Today we explore one sum together: 56 + 27. First we choose a strategy, then we draw the jump arcs to land on the answer.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Let the class decide the strategy before a pupil draws. For 56 + 27, some will partition (+20, +7); others will bridge to 60 (+4, +23). Both land on 83 — revoice that different routes reach the same answer.
If time allows, reset the line and let the class call a fresh two-digit sum to try the same way; the focus is matching strategy to numbers, not copying a worked example.
In your maths copy, take the sum 47 + 38 and work it three ways, one under the other: once by partitioning, once by compensating, once by bridging to fifty. Write the jumps you used beside each one. Then decide which way you would choose if you had to do it quickly.
Walk the room glancing at whether each pupil's three routes all land on 85 — this is whole-class copybook practice, not marking. If a route lands somewhere else, the jumps don't yet add to 38.
Today we work through these sums and reach each target in the fewest jumps you can: 47 + 38, then 56 + 27, then 235 + 198, then 268 + 197. The numbers get bigger, so think about which strategy keeps your jumps to a minimum each time.
These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
Each challenge targets the fewest possible jumps (two). For the three-digit sums, compensating usually wins (235 + 198 in two jumps: +200, −2; 268 + 197 in two jumps: +200, −3). If a pupil reaches the answer in more jumps, accept it, then ask the class if there's a shorter route.
One pupil says partitioning is always best. Another says compensating is best for 235 + 198. Who is right, and how would you settle it? Which strategy fits 47 + 38, and which fits 235 + 198?
Listen for pupils tying the strategy to the numbers, not picking a single favourite. Revoice: 'so the numbers decide — when one number is just under a round ten or hundred, compensating wins.'
Head off the misconception that one strategy is always best. The whole point of the lesson is choosing to fit the numbers.
Next we move from mental jumps to the written column method, where we line up the units and add column by column with regrouping.
Keep this brief. Reinforce the one big idea: mental strategy is a choice that fits the numbers, not a single rule to memorise.
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