A team has 32 points and scores 9 more. Roughly, what is their new total? You already know how to count on in ones, so think about how you would get there. Would you count on nine ones from 32, or is there a faster route hiding in those numbers?
Counting on is our familiar route from before. Today we add two brand-new routes that can be even faster, and we pick the one that saves us the most steps.
The number line will show four additions, each jumped a different way. Counting on is the route you already know, so watch how a big jump, partitioning and a near-double can be quicker. Before each jump is revealed, predict the landing number in your head.
Today we work through these additions together on the number line: 33 + 8, 42 + 30, 26 + 27, and 23 + 24. One pupil works at the board for each addition while the rest of the class follows along and predicts the landing number before it is confirmed. For each one, we choose a route first, then draw the jumps to land on the total.
In your maths copy, show your strategy for these two additions. Beside each one, draw a quick jotting on a number line: a jump for counting on, a split for partitioning, or a near-double if the numbers are close.
A scoreboard is adding up totals: 43 + 6, 38 + 20, 27 + 28, and 49 + 49. We work through these together at the board. For each one, choose the route that saves the most steps, then draw the jumps and check.
When does counting on in ones become the slow way, and a partition or a near-double the smart way? For which of today's additions would counting on in ones be the slow way?
Now look at a new pair: 36 + 28. Are these two close numbers? No, so a near-double is not the smart route. The second number has tens and units, so we partition: jump 20 from 36 to 56, then jump 8 to land on 64. Compare that with today's near-doubles like 27 + 28, where the numbers sit side by side.
So: a big tidy number wants one jump; two close numbers want a near-double; tens and units that are not close want a partition.
Next we turn this thinking around and look at smart ways to subtract within 100: counting back, and counting up to find the gap.
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