Quantitative Reasoning with Addition and Subtraction for Primary 1

Whole Numbers (Quantitative aptitude on Addition and Subtraction)

Performance Objectives

By the end of the lesson, students should be able to:

1. solve quantitative aptitude tasks on addition and subtraction of whole numbers

What is Quantitative Reasoning?

Quantitative reasoning is like solving a number puzzle. It means looking at a group of numbers and finding the rule or pattern that connects them. Once you find the rule, you can use it to find the missing number in the puzzle.

In Primary 1, we will use addition and subtraction to find these missing numbers. We look to see if the numbers are getting bigger (addition) or smaller (subtraction) and by how much.

Quantitative Reasoning with Addition

When numbers in a pattern are getting bigger, it usually means we are adding a number each time. To find the missing number, we need to find out what number is being added repeatedly.

Finding Missing Numbers by Adding

Let us look at some examples of quantitative reasoning problems that use addition.

Example 1: Find the missing number in the pattern:

$2, 4, 6, \_\_$

Solution:

1. Look at the first two numbers: 2 and 4.
2. To get from 2 to 4, we add 2 ($2 + 2 = 4$).
3. Look at the next two numbers: 4 and 6.
4. To get from 4 to 6, we add 2 ($4 + 2 = 6$).
5. The rule is to add 2 each time.
6. So, to find the missing number, we add 2 to the last number: $6 + 2 = 8$.

The missing number is 8.

The complete pattern is: $2, 4, 6, 8$.

Example 2: Find the missing number in the pattern:

$5, 10, 15, \_\_$

Solution:

1. Look at the first two numbers: 5 and 10.
2. To get from 5 to 10, we add 5 ($5 + 5 = 10$).
3. Look at the next two numbers: 10 and 15.
4. To get from 10 to 15, we add 5 ($10 + 5 = 15$).
5. The rule is to add 5 each time.
6. So, to find the missing number, we add 5 to the last number: $15 + 5 = 20$.

The missing number is 20.

The complete pattern is: $5, 10, 15, 20$.

Example 3: Find the missing number in the pattern:

$3, 6, 9, \_\_$

Solution:

1. Look at the first two numbers: 3 and 6.
2. To get from 3 to 6, we add 3 ($3 + 3 = 6$).
3. Look at the next two numbers: 6 and 9.
4. To get from 6 to 9, we add 3 ($6 + 3 = 9$).
5. The rule is to add 3 each time.
6. So, to find the missing number, we add 3 to the last number: $9 + 3 = 12$.

The missing number is 12.

The complete pattern is: $3, 6, 9, 12$.

Quantitative Reasoning with Subtraction

When numbers in a pattern are getting smaller, it usually means we are subtracting a number each time. To find the missing number, we need to find out what number is being subtracted repeatedly.

Finding Missing Numbers by Subtracting

Let us look at some examples of quantitative reasoning problems that use subtraction.

Example 1: Find the missing number in the pattern:

$10, 8, 6, \_\_$

Solution:

1. Look at the first two numbers: 10 and 8.
2. To get from 10 to 8, we subtract 2 ($10 – 2 = 8$).
3. Look at the next two numbers: 8 and 6.
4. To get from 8 to 6, we subtract 2 ($8 – 2 = 6$).
5. The rule is to subtract 2 each time.
6. So, to find the missing number, we subtract 2 from the last number: $6 – 2 = 4$.

The missing number is 4.

The complete pattern is: $10, 8, 6, 4$.

Example 2: Find the missing number in the pattern:

$20, 15, 10, \_\_$

Solution:

1. Look at the first two numbers: 20 and 15.
2. To get from 20 to 15, we subtract 5 ($20 – 5 = 15$).
3. Look at the next two numbers: 15 and 10.
4. To get from 15 to 10, we subtract 5 ($15 – 5 = 10$).
5. The rule is to subtract 5 each time.
6. So, to find the missing number, we subtract 5 from the last number: $10 – 5 = 5$.

The missing number is 5.

The complete pattern is: $20, 15, 10, 5$.

Example 3: Find the missing number in the pattern:

$12, 9, 6, \_\_$

Solution:

1. Look at the first two numbers: 12 and 9.
2. To get from 12 to 9, we subtract 3 ($12 – 3 = 9$).
3. Look at the next two numbers: 9 and 6.
4. To get from 9 to 6, we subtract 3 ($9 – 3 = 6$).
5. The rule is to subtract 3 each time.
6. So, to find the missing number, we subtract 3 from the last number: $6 – 3 = 3$.

The missing number is 3.

The complete pattern is: $12, 9, 6, 3$.

Solving Mixed Quantitative Reasoning Problems

Sometimes, you need to decide if the pattern uses addition or subtraction before you can find the missing number. Always check if the numbers are getting bigger or smaller.

Identifying the Pattern

Let us look at more examples.

Example 1: Find the missing number in the pattern:

$1, 3, 5, \_\_$

Solution:

1. The numbers are getting bigger, so we are adding.
2. From 1 to 3, we add 2 ($1 + 2 = 3$).
3. From 3 to 5, we add 2 ($3 + 2 = 5$).
4. The rule is to add 2.
5. So, $5 + 2 = 7$.

The missing number is 7.

The complete pattern is: $1, 3, 5, 7$.

Example 2: Find the missing number in the pattern:

$15, 12, 9, \_\_$

Solution:

1. The numbers are getting smaller, so we are subtracting.
2. From 15 to 12, we subtract 3 ($15 – 3 = 12$).
3. From 12 to 9, we subtract 3 ($12 – 3 = 9$).
4. The rule is to subtract 3.
5. So, $9 – 3 = 6$.

The missing number is 6.

The complete pattern is: $15, 12, 9, 6$.

Example 3: Find the missing number in the pattern:

$4, 8, 12, \_\_$

Solution:

1. The numbers are getting bigger, so we are adding.
2. From 4 to 8, we add 4 ($4 + 4 = 8$).
3. From 8 to 12, we add 4 ($8 + 4 = 12$).
4. The rule is to add 4.
5. So, $12 + 4 = 16$.

The missing number is 16.

The complete pattern is: $4, 8, 12, 16$.

Example 4: Find the missing number in the pattern:

$18, 16, 14, \_\_$

Solution:

1. The numbers are getting smaller, so we are subtracting.
2. From 18 to 16, we subtract 2 ($18 – 2 = 16$).
3. From 16 to 14, we subtract 2 ($16 – 2 = 14$).
4. The rule is to subtract 2.
5. So, $14 – 2 = 12$.

The missing number is 12.

The complete pattern is: $18, 16, 14, 12$.

Practice Problems

Find the missing number in each pattern:

1. $1, 2, 3, \_\_$
2. $10, 9, 8, \_\_$
3. $2, 5, 8, \_\_$
4. $16, 14, 12, \_\_$
5. $7, 9, 11, \_\_$
6. $25, 20, 15, \_\_$
7. $6, 10, 14, \_\_$
8. $11, 8, 5, \_\_$
9. $10, 12, 14, \_\_$
10. $19, 17, 15, \_\_$