2024 Key Stage 1 Mathematics Paper 2: Reasoning

💡 What are we looking for?

We need to find the value of the digit in the “tens” column of the number 38.

💡 What are we looking for?

We need to find the number 26 on the calendar grid.

💡 How many equal parts are there?

The circle is divided into 4 equal parts.

💡 What does this tell us?

If 1 out of 4 parts is shaded, the fraction is one quarter.

💡 What does “how much further” mean?

It means we need to find the difference between the two distances. We subtract the smaller number from the larger number.

💡 Strategy:

We need to pick three numbers that add up to 12. Let’s try starting with the even numbers.

💡 What does a cylinder look like?

Think of a tin of beans or a glue stick. It has a curved surface and two flat faces at the ends.

💡 What shape are the flat faces?

The top and bottom of a cylinder are circles.

Therefore, if Kemi draws around the face, she will draw a circle.

💡 What do we need to draw?

• black: 2 horses
• brown: 0 horses
• grey: 4 horses

💡 Tips for accuracy:

• For black, draw a bar up to the line numbered 2.
• For brown, the number is 0. This means we draw nothing! Be careful not to colour anything in this column.
• For grey, draw a bar up to the line numbered 4.

💡 What does “fly away” mean?

When ducks fly away, the number gets smaller. We need to subtract.

💡 Look at the numbers we have:

We see 73, 74 at the end.

To get from 73 to 74, we add 1.

So the pattern is counting in ones.

Let’s check by counting forwards:

69, 70, 71, 72, 73, 74. Does it sound right? Yes.

💡 Say the pattern out loud:

• Box 1: Top-Left is shaded.
• Box 2: Bottom-Right is shaded.
• Box 3: Top-Left is shaded.
• Box 4: Bottom-Right is shaded.

The pattern is alternating: Top-Left, Bottom-Right, Top-Left, Bottom-Right…

💡 Why subtraction?

Sam “gives” marbles away. This means the number he has gets smaller. We need to subtract.

💡 Simplification:

Instead of counting 90 dots, think in tens.

9 tens – 5 tens = ?

💡 Coins: £1, 1p, 10p.

£1 is equal to 100p.

100p is greater than 10p and 1p.

Action: Tick the £1 coin.

💡 Coins: 50p, £2, 20p.

£2 is equal to 200p.

200p is much bigger than 50p or 20p.

Action: Tick the £2 coin.

💡 What do we need?

We need three numbers that add up to 14.

\( \bigcirc + \bigcirc + \bigcirc = 14 \)

Other correct answers:

• 5, 5, 4
• 6, 4, 4
• 7, 7, 0
• 8, 4, 2

Any three numbers that sum to 14 are accepted.

💡 Goal: Find two purses with the same amount.

We actually found three purses with 12p! Any pair of these is correct, but usually, we look for different combinations that equal the same amount.

Recommendation: Tick the Right purse (10p, 2p) and the Bottom Left purse (5p, 5p, 2p).

💡 How many bags are there?

There are 6 bags in the picture.

Each bag has 10 marbles.

💡 Don’t forget the loose ones!

There are 8 marbles left over.

💡 The rule:

We need to multiply 5 by a number to get 5.

If we multiply by 0, we get 0.

If we multiply by 1, the number stays the same.

💡 What are we calculating?

We know the start (18) and the end (24). We need to find the gap between them.

You can count up from 18 to 24.

💡 What’s wrong with 3 – 20?

If you start with 3, you cannot take away 20 (unless you go into negative numbers, which isn’t 17).

This is the incorrect one.

💡 What numbers do we have?

• Number of cars (groups) = 8
• Number of seats per car (items in group) = 5

💡 Problem: \( 9 + \text{?} = 20 \)

We can count on from 9 to 20, or do \( 20 – 9 \).

💡 Problem: \( 12 + \text{?} = 20 \)

💡 Look at the units digit:

7, 17, 27, 37…

Every number ends in a 7.

When we count in 10s from a number ending in 7, the units digit never changes.

💡 Grouping:

We have 30 stickers in total.

We need to put them into groups of 5.

This is division: \( 30 \div 5 \).

💡 Buying badges:

Each badge costs 10p.

We need to see how many 10ps we can get out of 45p.

Amy has 45p. She spends 40p on 4 badges.

She has 5p left over. This is not enough for another badge.

💡 Look at the lines:

There is a line for 100 ml and a line for 200 ml.

There are smaller tick marks in between.

The tick mark halfway between 0 and 100 represents 50 ml.

💡 What is a line of symmetry?

If you fold the shape along the line, both halves must match exactly.

• Trapezium (1st shape): Yes, it is isosceles. You can fold it vertically.
• Triangle (2nd shape): Yes, it is isosceles. You can fold it vertically.
• Quadrilateral (3rd shape): No, it is irregular.
• House/Pentagon (4th shape): Yes, you can fold it vertically.
• Side Triangle (5th shape): No, all sides are different lengths.

• Top Left: A square split down the middle. One side is shaded. This is half.
• Top Right (Bars): A square split into 4 strips. 2 are shaded. \( \frac{2}{4} = \frac{1}{2} \). This is half.
• Bottom Right (Diagonal): A square split diagonally. One triangle is shaded. This is half.

• Bottom Left (X): Split into 4 triangles. Only 1 is shaded. \( \frac{1}{4} \). This is not half.
• Middle Left: Be careful! The question asks for “squares”. This shape looks slightly taller than it is wide (a rectangle), or the line might not be perfectly in the middle. We do not tick this one.

💡 What equals a half?

If you have 4 parts, half of them would be 2 parts.

So, \( \frac{2}{4} \) is the same as \( \frac{1}{2} \).

💡 We know:

1 quarter of 8 is 2.

We need to find 3 quarters.

💡 Working in the same unit:

£1 is the same as 100p.

💡 “Half of the animals are cows”

We need to find half of 30.

Now we add the cows and the sheep together to find out how many animals are NOT horses.

Subtract the cows and sheep from the total number of animals.

💡 What does the balance tell us?

The scales are level.

This means the mass on the left is equal to the mass on the right.

3 cylinders = 15 kg

💡 How much money did she hand over?

She used four 20p coins.

💡 Finding the difference:

She paid 80p. The drink cost 65p.

We subtract the cost from the amount paid.