Mathematics
Intermediate
40 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen
decimal column-grid sheet

Addition and Subtraction of Decimals to Thousandths

Learn to add and subtract decimals to thousandths by lining up decimal points, filling gaps with zeros, and working column by column, including carrying and borrowing across decimal places.

Teacher Class Feed

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    1 - Getting Started ~4 mins

    Here is a sum to look at: 3.4 + 0.275. Quick question for you: if we just lined up the very last digits of each number and added straight down, what would go wrong? Is it right to put the 4 above the 5?

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    3.4 + 0.275 = 3.675

    Watch how we line up the decimal points first, then fill 3.4 out to 3.400 so every column has a digit. Now we add column by column from the right.

    12.06 + 5.349 = 17.409

    Watch this one carefully — when we add the hundredths, six and four make ten, so we write the zero and carry one across into the tenths. See how that little carry sits right above the next column.

    8.53.726 = 4.774

    This is a take-away. We fill 8.5 out to 8.500, then borrow across the tenths and hundredths so we have enough to subtract the thousandths.

    10.04.085 = 5.915

    Here the borrow has to travel all the way through the zeros before we can subtract.

    3 - Try It Together ~9 mins

    Let's work this one through together on the board: 5.6 + 2.34. We line up the points first, fill the gap with a zero so 5.6 becomes 5.60, then add one column at a time from the right.

    Line up, fill, add

    4 - Line Them up in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, rewrite each of these calculations with the decimal points lined up one under the other and the gaps filled with zeros. Then work each one out column by column and underline your final answer.

    • 4.7 + 0.265
    • 6.08 + 3.5
    • 9.24.137

    5 - Class Challenge ~10 mins

    Today we tackle these subtractions together at the board: 7.23.485, then 15.06.074, then a thinking one — find a decimal that subtracts from 9.5 to leave exactly 3.275.

    Subtract the decimals

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    Think back to the very first sum. Why does forgetting the trailing zeros change the answer? What goes wrong if you line up the last digits instead of the decimal points?

    7 - What's Next ~2 mins

    What we learned today

    • Line up the decimal points before you add or subtract decimals.
    • Fill the empty columns with zeros so every column has a digit.
    • Carry and borrow across the decimal places exactly as you do across whole numbers.

    Coming up

    Next we move on to multiplying multi-digit whole numbers, breaking each factor into place-value parts and using the area model to see every partial product.

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 14 · Addition and Subtraction of Decimals to Thousandths
    Download Activity Book page (PDF)
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