Mathematics
Intermediate
42 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen
base-ten blocks

Written Addition: Multi-digit Whole Numbers

Learn to add multi-digit whole numbers using the column method, lining digits by place value and regrouping (carrying) from right to left, including cascading carries across multiple columns.

Teacher Class Feed

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    1 - Getting Started ~4 mins

    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?

    2 - Watch and Notice ~8 mins

    Illustration for Watch and Notice

    4,738 + 2,569

    Watch as we set these out one under the other and add from the units end. Look hard at the units column: 8 and 9 make 17, which is too big to fit in one column — a column can only hold a single digit. So we keep the 7 here and the spare ten moves one column to the left, because ten units are worth one ten. That is why a carry always travels left, never right: each ten is worth one in the next column up.

    9,876 + 1,234

    This time the carry keeps going. A carry lands in a column that is already full, so it tips over too and pushes another carry left. Watch how a brand-new digit appears at the very end. How many times do you count a carry happening?

    Add it up: 5,000 + 4,999

    Now nearly every column is empty on top. Lots of people guess this one lands on ten thousand. Add it up carefully — do we reach ten thousand, or stop just short? Predict your answer before we check it.

    3 - Try It Together ~10 mins

    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.

    6,847 + 3,956

    4 - Build Alongside in Your Copy ~5 mins

    COPYBOOK MOMENT

    Illustration for Build Alongside in Your CopyIn 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.

    5 - Class Challenge ~9 mins

    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:

    • 347 + 285
    • 4,738 + 2,569
    • 9,876 + 1,234
    • 5,000 + 4,999

    Add these multi-digit sums

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    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?

    7 - What's Next ~3 mins

    What we learned today

    • We line numbers up by place value, units under units, and add from the right.
    • When a column makes ten or more, we carry the ten one column to the left — because ten in a column is worth just one in the column above it, the spare ten cannot stay put.
    • Carries can cascade — one regroup can tip the next column over too, and sometimes a brand-new digit appears.

    Coming up

    Coming up

    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.

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 18 · Written Addition: Multi-digit Whole Numbers
    Download Activity Book page (PDF)
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