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2023 Key Stage 1 Mathematics Paper 1: Arithmetic
Mark Scheme Legend
- (M1): Method mark – for a correct method
- (A1): Accuracy mark – for a correct answer based on method
- (1m): 1 Mark awarded
Table of Contents
- Question 1 (Addition)
- Question 2 (Addition)
- Question 3 (Subtraction)
- Question 4 (Multiplication)
- Question 5 (Addition)
- Question 6 (Addition)
- Question 7 (Multiplication)
- Question 8 (Addition)
- Question 9 (Subtraction)
- Question 10 (Addition)
- Question 11 (Multiplication)
- Question 12 (Division)
- Question 13 (Division)
- Question 14 (Addition)
- Question 15 (Fractions)
- Question 16 (Subtraction)
- Question 17 (Subtraction)
- Question 18 (Addition)
- Question 19 (Algebra)
- Question 20 (Algebra)
- Question 21 (Fractions)
- Question 22 (Fractions)
- Question 23 (Subtraction)
- Question 24 (Subtraction)
- Question 25 (Subtraction)
Question 1 (1 mark)
\( 3 + 6 = \)
Worked Solution
Step 1: Understanding the Question
What are we doing? We are adding two small numbers together.
We can start with the larger number (6) and count on 3 more.
Step 2: Counting On
Start at 6.
Count on 3: 7, 8, 9.
\[ 3 + 6 = 9 \]
Check: We can also count 6 onto 3. Start at 3: 4, 5, 6, 7, 8, 9.
Final Answer:
9
✓ (1 mark)
Question 2 (1 mark)
\( 12 + 2 + 2 = \)
Worked Solution
Step 1: Strategy
Why do we do this? We have three numbers to add. It is easier to add the small numbers first.
Let’s add the two 2s together first.
Step 2: Adding the small numbers
\[ 2 + 2 = 4 \]
Now our sum is: \( 12 + 4 \)
Step 3: Finishing the addition
Start at 12 and count on 4.
13, 14, 15, 16.
\[ 12 + 4 = 16 \]
Check: You could also do \( 12 + 2 = 14 \), then \( 14 + 2 = 16 \).
Final Answer:
16
✓ (1 mark)
Question 3 (1 mark)
\( 13 – 7 = \)
Worked Solution
Step 1: Strategy
Why do we do this? Subtracting 7 from 13 crosses the number 10. It is often easier to take away enough to get to 10 first.
Step 2: Bridging through 10
To get from 13 down to 10, we take away 3.
\( 13 – 3 = 10 \)
We need to take away 7 in total. We have taken away 3. How many more do we need to take away?
\( 7 – 3 = 4 \)
So we take away 4 more from 10.
\( 10 – 4 = 6 \)
Check: \( 6 + 7 = 13 \). Yes, it is correct.
Final Answer:
6
✓ (1 mark)
Question 4 (1 mark)
\( 10 \times 4 = \)
Worked Solution
Step 1: Understanding Multiplication
What does this mean? This means 4 groups of 10.
We can count in tens 4 times.
Step 2: Counting in Tens
10, 20, 30, 40.
\[ 10 \times 4 = 40 \]
Final Answer:
40
✓ (1 mark)
Question 5 (1 mark)
\( 35 + 5 + 5 = \)
Worked Solution
Step 1: Grouping Numbers
Strategy: Look for number bonds to 10. We know that \( 5 + 5 = 10 \). This makes adding easier.
Step 2: Adding
First, add the 5s:
\( 5 + 5 = 10 \)
Now add this to 35:
\( 35 + 10 = 45 \)
Check: You can also count in 5s. 35… 40… 45.
Final Answer:
45
✓ (1 mark)
Question 6 (1 mark)
\( 22 + 20 = \)
Worked Solution
Step 1: Understanding Place Value
What are we adding? We are adding 20 to 22.
20 is exactly 2 tens. So the units (ones) will stay the same, but the tens will change.
Step 2: Adding Tens
22 has 2 tens and 2 ones.
Add 2 more tens to the 2 tens:
\( 2 \text{ tens} + 2 \text{ tens} = 4 \text{ tens} \)
The ones stay as 2.
So we have 42.
Final Answer:
42
✓ (1 mark)
Question 7 (1 mark)
\( 3 \times 5 = \)
Worked Solution
Step 1: Understanding Multiplication
What does this mean? This means 3 groups of 5.
We can count in 5s three times.
Step 2: Counting
5, 10, 15.
\[ 3 \times 5 = 15 \]
Final Answer:
15
✓ (1 mark)
Question 8 (1 mark)
\( 10 + 60 + 20 = \)
Worked Solution
Step 1: Adding Tens
Strategy: These are all multiples of 10. We can just add the tens digits.
\( 1 \text{ ten} + 6 \text{ tens} + 2 \text{ tens} \)
Step 2: Calculation
\( 1 + 6 = 7 \)
\( 7 + 2 = 9 \)
So we have 9 tens.
9 tens is 90.
Final Answer:
90
✓ (1 mark)
Question 9 (1 mark)
\( 79 – 6 = \)
Worked Solution
Step 1: Strategy
What are we subtracting? We are taking away 6 ones.
We only need to look at the ones digit in 79.
Step 2: Calculation
79 has 9 ones.
\( 9 – 6 = 3 \)
The tens (70) stay the same.
So the answer is 73.
Final Answer:
73
✓ (1 mark)
Question 10 (1 mark)
\( 9 + 32 = \)
Worked Solution
Step 1: Strategy
How to solve: It is easier to put the bigger number first.
\( 32 + 9 \)
We can bridge through the next ten (40).
Step 2: Bridging to 40
32 needs 8 more to get to 40.
Split 9 into 8 and 1.
\( 32 + 8 = 40 \)
Now add the remaining 1.
\( 40 + 1 = 41 \)
Final Answer:
41
✓ (1 mark)
Question 11 (1 mark)
\( 11 \times 2 = \)
Worked Solution
Step 1: Understanding Multiplication
What does this mean? This means 11 groups of 2, or 2 groups of 11.
Multiplying by 2 is the same as doubling.
Step 2: Doubling
Double 10 is 20.
Double 1 is 2.
\( 20 + 2 = 22 \)
Final Answer:
22
✓ (1 mark)
Question 12 (1 mark)
\( 6 \div 2 = \)
Worked Solution
Step 1: Understanding Division
What does this mean? We are sharing 6 into 2 equal groups.
This is the same as finding half of 6.
Step 2: Calculation
Half of 6 is 3.
\( 3 + 3 = 6 \)
So \( 6 \div 2 = 3 \)
Final Answer:
3
✓ (1 mark)
Question 13 (1 mark)
\( 24 \div 2 = \)
Worked Solution
Step 1: Strategy
What are we doing? Dividing by 2 means halving.
We can partition (split) 24 into tens and ones to make it easier.
Step 2: Partitioning and Halving
Split 24 into 20 and 4.
Half of 20 is 10.
Half of 4 is 2.
\( 10 + 2 = 12 \)
Final Answer:
12
✓ (1 mark)
Question 14 (1 mark)
\( 32 + 46 = \)
Worked Solution
Step 1: Strategy
How to solve: We can add the ones and then add the tens.
Step 2: Adding Column by Column
3 2 + 4 6 ----- 7 8
Ones: \( 2 + 6 = 8 \)
Tens: \( 30 + 40 = 70 \) (or \( 3 + 4 = 7 \) tens)
Total: 78
Final Answer:
78
✓ (1 mark)
Question 15 (1 mark)
\( \frac{1}{2} \text{ of } 60 = \)
Worked Solution
Step 1: Understanding Fractions
What does \( \frac{1}{2} \) mean? It means we need to find half.
Finding half is the same as dividing by 2.
Step 2: Halving
60 is 6 tens.
Half of 6 is 3.
So, half of 6 tens is 3 tens.
3 tens is 30.
Final Answer:
30
✓ (1 mark)
Question 16 (1 mark)
\( 45 – 13 = \)
Worked Solution
Step 1: Strategy
How to solve: We subtract the ones first, then subtract the tens.
Step 2: Subtraction
4 5 - 1 3 ----- 3 2
Ones: \( 5 – 3 = 2 \)
Tens: \( 4 – 1 = 3 \)
Answer: 32
Final Answer:
32
✓ (1 mark)
Question 17 (1 mark)
\( 94 – 40 = \)
Worked Solution
Step 1: Understanding Place Value
What are we subtracting? We are taking away 40, which is exactly 4 tens.
The ones digit (4) will stay the same. We just need to change the tens digit.
Step 2: Calculation
94 has 9 tens.
\( 9 \text{ tens} – 4 \text{ tens} = 5 \text{ tens} \)
So we have 5 tens and 4 ones.
Answer: 54
Final Answer:
54
✓ (1 mark)
Question 18 (1 mark)
\( 14 + 77 = \)
Worked Solution
Step 1: Setting up
Strategy: Use column addition. Be careful because the ones might add up to more than 9.
Step 2: Adding Ones
\( 4 + 7 = 11 \)
Write down the 1 and carry the 10 (1 ten) to the tens column.
Step 3: Adding Tens
1 4 + 7 7 ----- 9 1 1
\( 1 + 7 = 8 \)
Add the carried 1: \( 8 + 1 = 9 \)
Total: 91
Final Answer:
91
✓ (1 mark)
Question 19 (1 mark)
\( \Box – 5 = 3 \)
Worked Solution
Step 1: Inverse Operations
What is the question asking? Some number, take away 5, equals 3.
To find the missing number, we can work backwards. The opposite of taking away 5 is adding 5.
Step 2: Calculation
\( 3 + 5 = 8 \)
Let’s check: \( 8 – 5 = 3 \). This is correct.
Final Answer:
8
✓ (1 mark)
Question 20 (1 mark)
\( 11 + \Box = 77 \)
Worked Solution
Step 1: Inverse Operations
What is the question asking? We start at 11 and need to add something to get to 77.
To find the missing part, we can do a subtraction: \( \text{Whole} – \text{Part} = \text{Missing Part} \).
Step 2: Subtraction
\( 77 – 11 = ? \)
Subtract ones: \( 7 – 1 = 6 \)
Subtract tens: \( 7 – 1 = 6 \)
Answer: 66
Let’s check: \( 11 + 66 = 77 \). Correct.
Final Answer:
66
✓ (1 mark)
Question 21 (1 mark)
\( \frac{1}{2} \text{ of } 42 = \)
Worked Solution
Step 1: Understanding Halving
Strategy: We need to halve 42. We can split it into tens and ones first.
Step 2: Partitioning and Halving
42 is 40 and 2.
Half of 40 is 20.
Half of 2 is 1.
Put them back together: \( 20 + 1 = 21 \).
Final Answer:
21
✓ (1 mark)
Question 22 (1 mark)
\( \frac{1}{4} \text{ of } 28 = \)
Worked Solution
Step 1: Understanding Quarters
What is \( \frac{1}{4} \)? Finding a quarter is the same as halving and then halving again.
Step 2: Halving twice
Half of 28 is 14.
Now find half of 14.
Half of 14 is 7.
Final Answer:
7
✓ (1 mark)
Question 23 (1 mark)
\( 41 – 15 = \)
Worked Solution
Step 1: Setting up
Strategy: Use column subtraction. Look at the ones: \( 1 – 5 \). We cannot do this, so we need to exchange a ten.
Step 2: Exchanging
34 11
- 1 5
-------
2 6
Take 1 ten from 40, leaving 30.
Give that ten to the 1, making 11.
Now subtract: \( 11 – 5 = 6 \)
Subtract tens: \( 3 – 1 = 2 \)
Final Answer:
26
✓ (1 mark)
Question 24 (1 mark)
\( 67 – 58 = \)
Worked Solution
Step 1: Strategy
Method 1: Column subtraction.
Method 2: Counting on. 58 is very close to 67.
Step 2: Method 2 (Counting Up)
Start at 58.
Count up to 60: that’s 2.
Count from 60 to 67: that’s 7.
\( 2 + 7 = 9 \)
Check with column subtraction: \( 7 – 8 \) needs exchange. \( 17 – 8 = 9 \). \( 50 – 50 = 0 \).
Final Answer:
9
✓ (1 mark)
Question 25 (1 mark)
\( 82 – 63 = \)
Worked Solution
Step 1: Setting up
Strategy: Use column subtraction. \( 2 – 3 \) is not possible without exchanging.
Step 2: Exchanging
78 12
- 6 3
-------
1 9
Take 1 ten from 80, leaving 70.
Give that ten to the 2, making 12.
Now subtract: \( 12 – 3 = 9 \)
Subtract tens: \( 7 – 6 = 1 \)
Final Answer:
19
✓ (1 mark)