Here are two big numbers I want to add together: 4,738 + 2,569. We could try it in our heads, but these numbers are awkward. Where would you start if you had to add them on paper? Hands up: would you start with the big thousands or the little units?
Take three hands-up answers, not open call-outs. Don't resolve the start question yet — let the disagreement sit. The 'start from the units' rule is the key one of the next step, so resist confirming it here.
Look at these worked examples. Each pair is added one column at a time, starting from the units on the right. Keep an eye on the little carry digits: notice which way they travel and when a brand-new digit appears. Count the carries in the second one, and predict the last one before we check.
4,738 + 2,569 = 7,307. Units: 8 and 9 make 17 — write 7, carry 1. Only one digit fits in a column, so the spare ten moves left because ten units are worth one ten. Three regroups here; get pupils to name each one.
Show why it moves left: lay out 17 unit cubes, trade ten for one ten-rod, slide it into the tens column — the carry-1 is that trade written down. No blocks: draw ten dots, ring them, move the ring one column left.
Between examples one and two, turn-and-name: one pupil says where the carry went and why, then revoice it for the whole room.
9,876 + 1,234 = 11,110. The real cascade — a carry lands in a full column and tips over, pushing another carry left, until a new ten-thousands digit appears. Ask how many carries they counted before revealing.
5,000 + 4,999 = 9,999. The near-miss, not a cascade — no carries, stays at four digits. The common slip is guessing ten thousand. Pause on the prediction before checking.
Drive home: a carry always moves one column left, never right, because ten in a column is worth one in the column above.
Today we work through this one together on the board: 6,847 + 3,956. We will set it out, then add one column at a time from the right. Before each carry lands, call out where it has to go.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Step the algorithm column by column. As you reach each column, ask the class to predict the digit and the carry before it lands. Have individual pupils come up to set each column. Watch for the common slip of writing the full two-digit sum in a column instead of carrying — say the carry out loud every time: '13 — write the 3, carry the 1'. The answer is 10,803, so this one grows a fifth digit; flag that as it happens.
In your maths copy, set up the lesson's first sum, 4,738 + 2,569, one number under the other with the units lined up. Work each column with the class, and mark every regroup with a small carry-1 above the next column to the left.
Walk the room glancing at column alignment and the small carry-1 marks — this is whole-class copybook practice, not marking. The most common slip is poor lining-up, so catch a crooked layout early.
Today we work through these sums together, each one a little bigger than the last. We will set each one out, add from the units, and check the answer as a class before we move on:
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.
The first sum is a quick win so every pupil enters. The next three need real working time: 9,876 + 1,234 is the cascade into a new digit, and 5,000 + 4,999 is the near-miss — let pupils predict whether it reaches ten thousand before checking. Use the on-screen Check (✓) as part of the narration: 'yes — that's it'. Fast finishers watch the board and mouth the next carry rather than working ahead.
Why does a carry in addition always move LEFT, never right? And here is a quick check: if you add two numbers and your answer is smaller than one of them, what must have gone wrong?
Listen for pupils explaining the carry in their own words — that each column can only hold one digit, so the spare ten belongs in the next column up. Revoice a strong answer: so the ten can't stay where it is — it's worth a whole new column to the left. The second question heads off the common slip of dropping a carry: a sum smaller than an addend is impossible, so a missed regroup must be the cause.
Next we take the same line-up-the-columns idea and use it on decimals, where the decimal point becomes the anchor we line everything up against.
Keep this brief. The cascade idea (one carry triggering another) is the piece worth restating, as it is the part pupils most often forget on paper.
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