Today's problem: 4.5 − 1.75. You already know how to line up the decimal points when adding. Does subtracting need anything different, or does the same rule still work?
Thumbs up if you think the same rule still works; thumbs sideways if you think we need a new rule. Then three hands up for the reasoning.
Run the thumbs read first so every pupil commits to a position before any voice goes up. Then take three hands-up answers, not open call-outs. Listen for pupils who say 'you can't take 75 from 5' — that's the live misconception that the lesson resolves. Don't reveal the answer; this question is the hook into the model step.
Watch as we work four decimal subtractions on the column-subtraction tool. Notice how the same line-up-the-points rule you already know from adding decimals still holds, but instead of carrying we now decompose — we break a unit down into ten of the smaller place value next to it.
The 4.5 becomes 4.50 so the hundredths column has something to subtract from. Then we regroup one tenth into ten hundredths to take 5 away.
A lonely tenth on top. The trailing zero on 0.60 makes the hundredths column visible — then we regroup just like before.
The whole one breaks down in a chain. It splits into ten tenths, one of which then splits into ten hundredths.
Thousandths now. The same chain reaches one column further to the right — every column needs to regroup.
Walk each example aloud one at a time, in order. Pause on the regroup mark in each one.
Pacing lever between examples 2 and 3: pause and ask the class, 'will the same trick work when the top number is a whole number with nothing after the point?' Take a quick thumbs read (up = same trick, sideways = something new), then run example 3 so pupils watch with a prediction in their heads.
Now let's work the same kind of subtraction together. Today we try: 3.2 − 1.45. We enter the top number and the bottom number on the column-subtraction tool, then we step through each column from the right — the smallest place first, regrouping when the top digit is too small.
Three pupils take turns at the board. The rest of us watch each column land and think what the next digit will be before it appears.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Set up 3.2 − 1.45 on the board. Have one pupil add the trailing zero to make 3.20, then a second pupil work the hundredths column (it needs a regroup), then a third pupil work the tenths and units. Pause after each column and ask the class what the next digit will be before it lands.
If time allows, run a second example with the class — try 0.7 − 0.34 using the same step-by-step rhythm. Listen for the misconception 'you can't take 4 from 0' — revoice it as 'right, that's our cue to regroup from the tenths column.'
In your maths copy, set up each of these decimal subtractions vertically with the decimal points lined up in a single column. Work each column from the right, regrouping when the top digit is too small. Circle every regroup mark so you can see where the decomposition happened.
This is whole-class copybook practice, not marking. The four problems above are the same ones we just modelled, so pupils should be replicating what they saw, not improvising. With 8 minutes you can walk the room twice — first time round glance at decimal-point alignment on problem 1 before pupils commit further; second time round catch unmarked regroups on the cascade problem (1.0 − 0.85) and the thousandths problem (5.005 − 0.999). If a pupil is stuck on lining up 5.005 with 0.999, point them back at the on-screen model rather than re-teaching from scratch.
Today's bank: five decimal subtractions of escalating trickiness. Pupils take turns at the board to solve each one on the column-subtraction tool.
The rest of the class watches each column and works out the next digit before it lands on the board.
This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. The same five-problem bank reruns at home as tonight's homework, so keep the board work brisk rather than over-explaining.
Engagement protocol: the pupil at the board taps a digit; before each next digit lands, ask the class what it will be and take a quick answer. This keeps every watching pupil tracking each column.
Watch for the chain in problem 3 (1.0 − 0.73) — the regroup runs from units → tenths → hundredths and is the make-or-break moment. Problem 4 (5.005 − 0.988) extends the same chain one column further to thousandths; let pupils articulate 'same trick, one more column' before they tap.
If pacing allows after the bank of five, pull one extension problem from the extension bank for a final stretch question to round off the lesson.
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