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Grades 2–4
4 sections · 4 questions

Nearly right

Four questions a child will almost get right in their head — and the last small step is the entire point of the page.

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What's on this test

Section 1 covers a digit in each half of an addition, and the ones column gives one of them away — but that column overflows, so the tens column is not the sum of what you can see. A child who reads it straight is ten out. Section 2 gives a total and a difference. Halving the total is the right first move and the wrong answer; the two numbers are half the difference either side of it. Section 3 is a division that is finished before the question starts — the same 38 and 12 give four different answers depending on whether you are hiring buses, buying stickers, counting what is left, or filling the last box. Section 4 divides a fence by a gap and asks for the posts, which is one more, or one fewer, or exactly the same, depending on where the ends are.

How the paper is put together

None of the four is hard arithmetic. That is deliberate: a child of eight can do every calculation on the page, so nothing here is acceleration — what is being asked for is the reading, and the reading is where the marks go. A child who answers all four quickly and gets two wrong has learned more from this page than from twenty problems.

Nearly right

Name: Date:

1. Challenge puzzlesTwo digits are covered in each sum. Work out what they were, and show how.1 question

1This sum was photocopied badly and two digits came out blank: 2■ + ■9 = 40.What were the two numbers?Why

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2. Challenge puzzlesFind the two numbers. Show how you worked them out.1 question

2Two baskets hold 12 apples altogether. One basket has 2 more apples than the other.How many apples are in each basket?Why

3. Challenge puzzlesDo the division, then read the question again before you answer.1 question

325 cards are dealt out equally to 3 players.How many cards are left undealt?Why

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4. Challenge puzzlesDecide whether you want the things or the gaps. Show your working.1 question

4A path is 45 meters long. A tree is planted every 9 meters, with one at each end.How many trees are there?Why

Think about it

Every question here had a first answer that was close and wrong. Pick one and say what made the wrong answer so easy to reach.

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Answer key

Challenge puzzles

If they are stuck: One of the two columns can be settled on its own. Which, and what does settling it change?

1. Start with the ones: something and 9 has to end in 0, and 1 + 9 = 10 — so the covered digit is 1, and a ten goes across to the next column. The tens column has that ten in it: 2 + 1 = 3, and 3 + 1 = 4, so the other covered digit is 1. The numbers are 21 and 19. Read the tens column on its own and it asks for 2 instead, giving 29 — and 21 + 29 = 50, ten too many.

Challenge puzzles

If they are stuck: What would the two numbers be if they were the SAME? Start there, then ask what has to change.

2. Half of 12 is 6, so 6 and 6 would add up right — but they are the same, and these two differ by 2. Move half the difference, 1, from one to the other: 6 + 1 = 7 and 6 − 1 = 5. More than one way works here. The other is to add the two facts: 12 + 2 = 14, and half of that is the bigger number, 7 — then 12 − 7 = 5. Same answer, one step fewer, and it is the road algebra takes later.

Challenge puzzles

If they are stuck: Do the division first, then read the question again before writing anything down.

3. 3 × 8 = 24, and 25 − 24 = 1. So 1 cards are left over. The question never asked how many each player got, which is the number the division hands you first.

Challenge puzzles

If they are stuck: Draw four of them in a row and count the gaps. Is the answer the things or the spaces?

4. 45 ÷ 9 = 5, but that counts the GAPS between the trees. There is a tree at both ends, so there is always one more tree than gap: 5 + 1 = 6 trees.

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