The five ideas

💡This is a sharing question where everybody must get one. That changes what you do with the ones left over.🔊

1Work out 34 ÷ 8 before you look at the options.🔊

234 ÷ 8 = 4 packs, and 2 children still have nothing. Those two need a pack of their own.🔊

💡Never read a scale off its label. Work out what one space is worth first.🔊

1The top mark is 800 mL and there are 4 equal spaces. Divide.🔊

2Work out how much one space is worth, then count how many spaces the water fills.🔊

💡Two small steps, not one: how many people, then how many things each person brings.🔊

1Add the children together first: 9 + 8.🔊

2That is 17 children, and each brings 3 + 4 = 7 things. Now multiply 17 by 7.🔊

💡A shape’s name comes from the number of sides, and the start of the word is the clue.🔊

1Line the prefixes up: penta 5, hexa 6, hepta 7, octa 8.🔊

2You want the one that means seven.🔊

💡The caterpillar does not change length. Find how far it moved, then move the head the same amount.🔊

1The tail went from the 8 mm mark to the 15 mm mark. How far is that?🔊

2It moved 7 mm. The head started on 25 mm and moves the same 7 mm.🔊

💡A balance compares one thing only. Work out which one before you read the options.🔊

1A see-saw tips when one side is heavier. So what is it actually testing?🔊

2Balancing proves the two masses are equal. It says nothing about size, shape or how much is inside — a small heavy bag balances a big light one.🔊

💡Area means how many squares fit inside, so you need both side lengths in squares.🔊

1Count along the bottom, then count down the side.🔊

2Multiply those two counts. Do not count the squares one at a time — you will lose your place.🔊

💡Nine of something is ten of them, with one taken away.🔊

1Rewrite 68 × 9 as 68 × (10 − 1).🔊

2That is 68 × 10, minus one whole 68. Notice it is 68 you take off, not 9.🔊

💡Take away the parts that were not shared out before you divide anything.🔊

1She kept 5 and had 2 left over. Take both off the 40 first.🔊

240 − 5 − 2 = 33 stickers were actually shared, 3 to each friend. Now divide.🔊

💡On a number line the bottom of the fraction is how many spaces — not how many marks you can see.🔊

1The line is cut into 10 equal spaces, so each space is one tenth.🔊

2The mark sits 3 spaces along from 0. Count in tenths.🔊

💡Compare how much of the circle each colour covers, not how many pieces there are.🔊

1Add up all the black parts together — they do not have to be touching.🔊

2You want the spinner where black covers more than half.🔊

💡Two steps: work out one day first, then the week.🔊

1From 4:40 to 5:15 — count up to 5:00, then carry on.🔊

220 min + 15 min = 35 minutes a day. Now do 35 × 7 minutes and turn the answer into hours.🔊

💡You do not need the two missing sides on their own. Sides going the same way add up to the same total.🔊

1Add the sides that go across, and the sides that go down, separately.🔊

2The unmarked sides fill the gaps exactly, so each direction totals the same as the side opposite it. Push the step flat and the shape becomes a rectangle.🔊

💡‘Must use all of them’ is a rule, not decoration. The most rides means as many cheap ones as possible — but the total has to land exactly.🔊

1Try to make 30 out of 4s and 7s. Start with as many 4s as you can and see what is left.🔊

2Six 4s is 24 and leaves 6 — no good. Two 7s is 14, and the 16 left is exactly four 4s. Count the rides.🔊

💡Fill the gaps using the totals you already have, then add.🔊

1Find a row or a column with only one number missing. That is the one you can work out.🔊

2Work out each missing number the same way, then add every cell once.🔊

💡Ask whether the two pieces would sit exactly on top of each other.🔊

1A cut from one corner to the opposite corner gives you two triangles. Are they the same?🔊

2Turn one of them round and it lands exactly on the other — the same three sides.🔊

💡‘Twice as many as he already had’ is an extra amount. It is not the new total.🔊

1He had 18, and is given 2 × 18 more. Add those together.🔊

218 + 36 = 54 stamps. He then gives away 7 × 4 = 28. Take that off.🔊

💡The same shape as the juice boxes: everybody has to get on, so you round up.🔊

1Work out 50 ÷ 12 first.🔊

2Four buses carry 48 people, and 2 are still standing. They need a bus of their own.🔊

💡Work out what one space is worth before you even look at the arrow.🔊

1The scale runs 0 to 60 in 6 equal spaces. Divide.🔊

2One space is 10. Now count how many spaces along the arrow sits.🔊

💡Area is rows times columns. Adding the two numbers gives you something else entirely.🔊

1There are 5 rows, with 3 squares in each row.🔊

2Multiply 3 by 5. (Adding them gives 8, which is not an area at all.)🔊

💡Ask which single thing was actually tested here.🔊

1The water moved across and filled the cup exactly, with none left. What does that compare?🔊

2It proves they hold the same amount. Nothing was weighed, and a tall thin jug can hold exactly as much as a short wide cup.🔊

💡The pencil does not change length. Find its length first.🔊

1From the 3 cm mark to the 14 cm mark — how long is that?🔊

2It is 11 cm long. One end is now on 7 cm, so the other end is 11 cm further along.🔊

💡Count the spaces, not the marks.🔊

1Count how many equal spaces the whole line has been cut into.🔊

2That number goes on the bottom of the fraction. Then count the spaces up to the red mark.🔊

💡Count the sides. Do not judge it by how it looks.🔊

1A hexagon has six straight sides. They do not have to be the same length, and the shape may even be dented inwards — six straight sides is the whole test.🔊

2Put your finger on one corner and count all the way round, back to where you started.🔊

💡Two steps: how many children, then how many pieces of fruit each.🔊

1Add the children first: 12 + 13.🔊

225 children, each bringing 5 + 5 = 10 pieces. Now multiply.🔊

💡Do not work out 214 × 5. Change one thing at a time instead.🔊

1214 × 5 is 214 × 4 with one more 214 added on.🔊

2So the whole thing is 214 × 4 + 214 − 210, and 214 − 210 is small enough to do in your head.🔊

💡Take off everything that was not shared out before you divide.🔊

14 were thrown away and 2 were left over. Take both off the 50.🔊

250 − 4 − 2 = 44 pens were shared, 4 to each student. Now divide.🔊

💡One day first, then the week. Never try to do both at once.🔊

1From 7:35 to 8:05 — count up to 8:00, then carry on.🔊

225 + 5 = 30 minutes a day. Now do 30 × 7 minutes and turn it into hours.🔊

💡Most likely simply means the colour with the most counters.🔊

1Compare the three counts in the question — which colour has more than the other two?🔊

2Line the three counts up side by side and pick the biggest number — that is your answer. You do not need to work out a single fraction here.🔊

💡Use the totals to fill the gaps first — the table is telling you more than it looks.🔊

1Find the row or column with only one number missing.🔊

2Work out each missing number that way, then add every counter once. Do not add the totals in as well.🔊

💡‘Three times as many as she already had’ is an extra bag. It is not the new total.🔊

1She had 30, and is given 3 × 30 more.🔊

230 + 90 = 120 beads. She then gives away 12 × 5 = 60. Take that off.🔊

💡Think before you calculate. Cutting a square out of a corner does not change the distance round the outside at all.🔊

1The two new cut edges are exactly as long as the two bits you took away — they have just moved inwards.🔊

2So the L-shape has the same perimeter as the rectangle you started with: 2 × (9 + 6).🔊

💡The most rides means as many cheap ones as possible — but the total has to land exactly on 19.🔊

119 is odd, and 2s can only ever make even numbers. So how many 5s must you use?🔊

2An odd number of 5s. One 5 leaves 14, which is exactly seven 2s. (Three 5s leaves only 4, which is two 2s — far fewer rides.)🔊

💡Two pieces make a square only if the edges that meet are the same length and the corners are right angles.🔊

1Look at the edge where the two pieces would join. Do they match exactly?🔊

2Two right-angled triangles whose short sides are equal make a square when you put their long slanted edges together.🔊