SATs 2023 Key Stage 1 Mathematics Paper 2: Reasoning

What does the dice show?

We count the black spots on the square dice.

There are 5 spots.

Why do we subtract?

The question asks for “2 less”. This means we need to take away 2.

What numbers do we have?

We have the digits: 6, 2, 8, 3.

How do we make the number as big as possible?

For a two-digit number to be the largest, the first number (the Tens) must be the biggest digit available.

The biggest digit is 8. So, 8 goes in the first box.

What comes next?

After using 8, we look for the next biggest digit to put in the Ones place.

The remaining digits are 6, 2, and 3. The biggest is 6.

What does a 20p coin look like?

A 20 pence coin is:

• Silver in colour
• Small but not the smallest
• Heptagonal (it has 7 sides, not round)

Which coin matches?

We look for the small 7-sided coin. The large 7-sided coin is 50p. The small round one is 5p.

The correct coin is the small 7-sided one on the top right.

How much fruit do we see?

We have 4 bananas and 3 pears.

How many are left?

The total number of fruit is 12.

We know 7 are NOT oranges. The rest are oranges.

What does “multiplied by ten” mean?

We need to calculate \( 6 \times 10 \).

When we multiply a whole number by 10, the digit moves one place to the left, and we add a zero to the end.

We can count in tens six times: 10, 20, 30, 40, 50, 60.

• ninety-nine: This means 9 tens and 9 ones -> 99.
• sixteen: This means 1 ten and 6 ones -> 16.
• forty-three: This means 4 tens and 3 ones -> 43.

We connect the word box to the matching number box.

The question tells us: “There are 4 ducks in the pond.”

We need to find the row for Ducks (the bottom row).

We count 4 blocks in the Duck row starting from number 1.

We shade blocks 1, 2, 3, and 4.

• Rectangle (Top Left): 4 sides
• Hexagon (Top Right): 6 sides
• Triangle (Middle Left): 3 sides
• Circle (Middle Right): 1 curved side
• Pentagon (Bottom Left): 5 sides
• Triangle (Bottom Right): 3 sides

We are looking for two shapes with the same number of sides.

We found two shapes with 3 sides.

• Playing Cards: Rectangular faces, box shape. This is a Cuboid.
• Tube (Crisps): Circular top and bottom, straight sides. This is a Cylinder.
• Cereal Box: Rectangular faces, box shape. This is a Cuboid.
• Party Hat: Circular base, point at the top. This is a Cone.

We place a tick in the correct column for each row.

• Row 2 (Cards) → Cuboid column
• Row 3 (Tube) → Cylinder column
• Row 4 (Cereal) → Cuboid column
• Row 5 (Hat) → Cone column

In a race, the person who runs the fastest has the smallest time.

Let’s order the times from smallest (fastest) to largest (slowest):

1. 10 minutes (1st place)
2. 11 minutes (2nd place) – Done for you
3. 13 minutes (3rd place)
4. 15 minutes (4th place)

We need to draw lines connecting:

• 10 minutes → 1st
• 13 minutes → 3rd
• 15 minutes → 4th

• \( < \) means less than (smaller)
• \( > \) means greater than (bigger)
• \( = \) means equal to (the same)

Tip: The crocodile mouth always eats the bigger number!

21 and 12: Look at the tens. 2 tens is bigger than 1 ten. So 21 is greater.

48 and 64: Look at the tens. 4 tens is smaller than 6 tens. So 48 is smaller.

55 and 55: These are exactly the same.

Look at the numbers we have: 50, 60, 70.

We are counting in tens.

The numbers are getting bigger as we go down the line.

We need to count backwards (up) from 50.

50 take away 10 is 40.

40 take away 10 is 30.

The top box is 2 steps above 50, so it is 30.

We need to count forwards (down) from 70.

70 add 10 is 80.

80 add 10 is 90.

90 add 10 is 100.

The bottom box is 3 steps below 70, so it is 100.

Goal: 15 blocks

Have: 9 blocks

We need to find the difference between 15 and 9.

We can count up from 9 to 15.

9… 10, 11, 12, 13, 14, 15.

That is 6 fingers.

Or we can subtract:

We want two numbers that add up to 20.

Example: \( 5 + 15 = 20 \). (This is drawn for us)

We have 7.

\( 20 – 7 = 13 \).

So, we match 7 to 13.

We have 4.

\( 20 – 4 = 16 \).

So, we match 4 to 16.

We have 9.

\( 20 – 9 = 11 \).

So, we match 9 to 11.

Look at the tally marks for the blue tit.

We see a group of 5 (four lines crossed through) plus 1 more line.

\( 5 + 1 = 6 \).

Write 6 in the number box.

The number of sparrows is 10.

We need to draw 10 tally marks.

10 is two groups of 5.

Draw: Two “gates” (four vertical lines with a diagonal line through them).

We have 6 teams.

There are 5 children in each team.

To find the total, we multiply: \( 6 \times 5 \).

Count in fives 6 times:

5, 10, 15, 20, 25, 30.

We start with 5 tens (which is 50).

The question says add 2 more tens.

\( 5 \text{ tens} + 2 \text{ tens} = 7 \text{ tens} \).

7 tens is 70.

The ones (6) stay the same.

7 tens and 6 ones make 76.

We need to find the total of 26 and 32.

\( 26 + 32 \)

Add the tens: 2 tens + 3 tens = 5 tens (50).

Add the ones: 6 ones + 2 ones = 8 ones.

50 + 8 = 58.

  26
+ 32
----
  58

Let’s try the signs:

• \( 8 + 2 = 10 \) (No)
• \( 8 – 2 = 6 \) (No)
• \( 8 \times 2 = 16 \) (Yes)

30 is getting smaller, so it must be \( – \) or \( \div \).

• \( 30 – 10 = 20 \) (No)
• \( 30 \div 10 = 3 \) (Yes)

13 is bigger than 7, so it must be \( + \) or \( \times \).

• \( 7 \times 6 = 42 \) (Too big)
• \( 7 + 6 = 13 \) (Yes)

Look at the first numbers:

7, 17, … , … , 47

These numbers are going up by 10 each time.

7 -> 17 -> 27 -> 37 -> 47.

The line ends with “= 30”.

So the calculation is \( \mathbf{27} + 3 = 30 \).

The next number in the pattern is 37.

We need to add 3.

\( 37 + 3 = \mathbf{40} \).

We see 3 groups (boxes).

Inside each group, there are 4 marbles.

Addition: We are adding 4 marbles three times.

\( 4 + 4 + 4 \)

Multiplication: We have 3 groups of 4.

\( 3 \times 4 \)

We are told that one quarter (\( \frac{1}{4} \)) of 8 is 2.

\( \frac{2}{4} \) is two of these parts.

\( 2 + 2 = 4 \).

\( \frac{3}{4} \) is three of these parts.

\( 2 + 2 + 2 = 6 \).

Ben has: 50p + 20p + 5p.

50 + 20 = 70.

70 + 5 = 75p.

Sita has: 50p + 10p + 2p + 2p + 1p.

50 + 10 = 60.

60 + 2 = 62.

62 + 2 = 64.

64 + 1 = 65p.

“How much more” means we need to find the difference.

Ben has 75p. Sita has 65p.

\( 75 – 65 = 10 \).

We can see 5 cars in the picture.

The question says this is half (\( \frac{1}{2} \)) of his cars.

To find the total (the whole), we need two halves.

We need to double the number we see.

Look at the first sum: Star + Star = 20.

The stars are the same, so we need two equal numbers that add to 20.

\( 10 + 10 = 20 \).

So, Star = 10.

The second sum is: Star \( \times \) Star = ?

We know Star = 10.

So we calculate \( 10 \times 10 \).

Counting in tens ten times gives 100.

Sam has four £5 notes.

We can count in fives: 5, 10, 15, 20.

Sam has £20.

The book costs £17.

To find the change, we subtract the cost from the money he has.

Count up from 17 to 20: 18, 19, 20. That is 3.

9 children eat 2 sandwiches each.

We calculate \( 9 \times 2 \).

Double 9 is 18.

Amy started with 24 sandwiches.

18 were eaten.

We subtract 18 from 24.

Count up from 18 to 24: 19, 20, 21, 22, 23, 24. That is 6.

The arrow starts pointing UP.

Anti-clockwise means turning the opposite way to a clock hands (turning left).

A \( \frac{1}{4} \) turn is a quarter of a circle (90 degrees).

Imagine the arrow moving from 12 o’clock backwards to 9 o’clock.

The arrow should point to the Left.

Add the weight of the card (32g) and the gift (47g).

\( 32 + 47 \)

\( 30 + 40 = 70 \)

\( 2 + 7 = 9 \)

Total = 79g.

  32
+ 47
----
  79

The total weight for all three items is 100g.

We know the first two weigh 79g.

We need to find the difference: \( 100 – 79 \).

Count up from 79 to 100.

79 to 80 is 1.

80 to 100 is 20.

Total difference is 21.

We have: something + 2 = 0 (ending in 0).

The only way to get a 0 at the end when adding 2 is if the sum is 10.

So, \( 8 + 2 = 10 \).

The digit in the first box must be 8.

So the first number is 38.

If the first number is 38, we need to add something ending in 2 to get 50.

\( 50 – 38 = 12 \).

So the second number is 12.

Let’s check: \( 38 + 12 \).

• \( 8 + 2 = 10 \)
• \( 30 + 10 + 10 (\text{carried}) = 50 \)

It works!

The calculation is a subtraction: \( 16 – 4 = 12 \).

To check a subtraction, we can use the inverse (opposite), which is addition.

We add the parts together to see if they make the whole.

The parts are 12 and 4. The whole is 16.

We need to add 12 and 4.

\( 12 + 4 = 16 \) or \( 4 + 12 = 16 \).

The pattern adds 5 each time.

Let’s find the next few numbers after 22:

• \( 22 + 5 = 27 \)
• \( 27 + 5 = 32 \)
• \( 32 + 5 = 37 \)

We need the next even number.

27 is an odd number (ends in 7).

32 is an even number (ends in 2).