Here is a quick one to do in your head: what is 1,998 + 2,005?

Now the real question. Would you ever reach for a pencil to work that out, or is there a faster way in your head? What did you do to it to make it easy?

The number line shows three ways to add and subtract big numbers: compensation, round-and-adjust, and partition. Look at the jumps on each number line and notice which numbers are chosen to make each one tidy.

First we work this one out together on the empty number line on screen: 5,996 + 247. We will say the clever first jump aloud before we draw it. Then, on the board beside it, we will trace two more by hand: 7,003 − 1,996 and 2,560 + 3,470, naming the strategy for each before we start.

First we solve one full calculation together and name the strategy: 6,998 + 457. We plan the jumps, draw them, and check we land on the right total. Then we work through these on the line, one at a time: reach 10,000 from each starting number using only the jump sizes shown, in as few jumps as you can. Plan your route first, which tidy number do we bridge to before we land on 10,000? After each one, name the strategy your jumps show (partition, compensation or round-and-adjust).

Today we

• added and subtracted in our heads using partition, compensation and round-and-adjust
• drew our thinking as jumps on an empty number line
• decided when a mental strategy beats the column method