Here are four digit cards: 3, 7, 0 and 5. You may use each card once. What is the biggest four-digit number you could make from them? And where do you think the 7 should go?
Hands up when you have an idea. Think first about which card should sit at the very front.
Show the four cards 3, 7, 0, 5 on the IWB as pupils settle. Take three hands-up answers, not open call-outs. Give five seconds of quiet think-time before any hands go up. Don't confirm an answer yet — the reasoning is unpacked in the next step.
The interactive shows the biggest and smallest numbers made from the cards 7, 5, 3 and 0, and that smallest number rounded to the nearest 100, on the place-value mat. Look at where each digit sits and why. See if you can spot the rule for the biggest number, the smallest, and what rounding does.
7,530 the biggest: largest card in the highest-value column, 7 in thousands, then 5, 3, 0. Ask why not the 7 in units.
3,057 the smallest: make-or-break idea. Ask could we put the 0 in front, let them reason a leading zero drops it to three digits. So 3 leads, then 0, 5, 7 in units.
Rounding 3,057 to the nearest 100: point at the tens digit, 5, as the decider, so it rounds up to 3,100.
Today we work through a fresh set of cards together: 1, 9, 4, 6. First we build the biggest number on the mat, then rebuild the same cards to make the smallest. Talk each arrangement through as we place the cards.
Build the biggest number first, then rebuild to make the smallest. Notice how the same cards swap ends between the two numbers.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Load the cards 1, 9, 4, 6. Ask a pupil to place the 9 first and explain why. Rearrange the cards live on the mat to show the smallest number, and let the class say where each card should land before a pupil moves it. Watch for pupils reversing the order — check that biggest starts with the largest card and smallest starts with the smallest non-zero card. There is no leading-zero trap in this set, so it is a clean warm-up before the challenge.
In your maths copy, use these four digits: 2, 5, 8, 0. Write the biggest four-digit number you can make, then write the smallest four-digit number. Remember the 0 cannot go in front. Then round each of your two numbers to the nearest 100 and write the rounded answer beside it.
Walk the room glancing for the leading-zero slip on the smallest number (it should start with 2, not 0) and for the tens digit being used to round. No individual marking — this is whole-class copybook practice, not assessment.
Today we investigate one set of digits: 2, 4, 6, 8, using each digit once. We will work these in order: (a) make the biggest possible number; (b) make the smallest possible number; (c) make the smallest number you can between 4,000 and 5,000; (d) make a number that rounds to 8,600 to the nearest 100, with 2 in the tens place — and explain which arrangement works.
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.
Run the four targets in order on the mat. For (c) the number must start with a 4, and asking for the smallest pins one answer: 4,268 (if a pupil builds another valid arrangement like 4,628, praise the reasoning aloud, then ask for the smallest). For (d) rounding to the nearest 100 uses the tens digit: 8,624 has a tens digit of 2, which is less than 5, so it rounds down to 8,600 (8,642 also rounds to 8,600 — the "2 in the tens place" condition is what pins 8,624). Ask pupils to justify each arrangement aloud before pressing Check.
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