Counting in Twos and Recognising Number Patterns for JSS 1

Counting in twos

Performance Objectives

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

1. count in group of twos.

The Concept of Counting in Twos

Counting in twos is a mathematical method of skip-counting or grouping objects in pairs where each step increases or decreases by a value of two.

This method is highly efficient for counting large quantities of items quickly. Instead of counting objects one by one, objects are grouped into pairs and counted as two, four, six, eight, and so on.

Grouping Objects in Twos

Grouping in twos involves taking a collection of items and arranging them into pairs. A pair consists of exactly two items. This process helps to determine the total number of items quickly and introduces the concept of multiplication and division by two.

For example, if a student has a collection of 20 bottle tops, the student can arrange them into distinct groups of two. Counting these groups sequentially gives the total count.

Observe the diagram below showing 20 bottle tops arranged in groups of twos.

Number Patterns in Twos

Counting in twos creates a distinct mathematical pattern. Starting from zero and adding two repeatedly generates the sequence of even numbers.

The sequence of counting forward in twos starting from 2 is represented as:

$$2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, \dots$$

Each number in this sequence is called an even number. An even number is any integer that can be divided exactly by 2 without leaving a remainder.

Counting can also be performed backward in twos. For example, counting backward from 20 in twos gives:

$$20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0$$

A number line can be used to visualize skip-counting in twos. Each jump on the number line represents an addition of 2.

Observe the number line diagram below.

Worked Examples

Example 1

A student has 20 bottle tops. How many groups of twos can be formed from these bottle tops? Show the counting sequence.

Solution:

To find the number of groups, divide the total number of bottle tops by 2:

$$\text{Number of groups} = \frac{20}{2} = 10\text{ groups}$$

The student forms 10 groups of two. The counting sequence for the 10 groups is:

$$2, 4, 6, 8, 10, 12, 14, 16, 18, 20$$

Therefore, 10 groups of twos are formed, making a total of 20 bottle tops.

Example 2

A teacher provides 30 pieces of matchsticks to a class. If the learners are asked to form bundles of two-two objects, how many bundles will they get? Write down the counting pattern.

Solution:

To find the number of bundles of two-two objects, divide the total number of matchsticks by 2:

$$\text{Number of bundles} = \frac{30}{2} = 15\text{ bundles}$$

The learners will get 15 bundles. The counting pattern in twos up to 30 is:

$$2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30$$

Therefore, 15 bundles of twos are formed from 30 pieces.

Example 3

Identify the missing numbers in the counting pattern below:

$$12, 14, \square, 18, \square, 22, 24, \square$$

Solution:

The pattern shows counting forward in twos. To find each missing number, add 2 to the preceding number.

The first missing number after 14 is:

$$14 + 2 = 16$$

The second missing number after 18 is:

$$18 + 2 = 20$$

The third missing number after 24 is:

$$24 + 2 = 26$$

The complete sequence is:

$$12, 14, 16, 18, 20, 22, 24, 26$$

Practical Activity: Grouping and Counting Objects in Twos

This activity provides a practical method for grouping and counting physical objects in twos using counters or bottle tops.

The required materials are:

1. 30 pieces of bottle tops or plastic counters
2. Rubber bands or small containers for bundling
3. A flat table or desk surface

The procedure involves the following steps:

1. Place all 30 bottle tops in a single pile on the flat surface.
2. Take 2 bottle tops from the pile and place them together to form the first pair.
3. Take another 2 bottle tops from the pile and place them next to the first pair.
4. Repeat this process of taking 2 bottle tops at a time until 10 pairs (20 bottle tops) have been separated from the main pile.
5. Count the separated bottle tops aloud in twos: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. Note that there are exactly 10 groups.
6. Continue grouping the remaining bottle tops from the main pile in pairs of two until the pile is empty. Use rubber bands to secure each pair into a bundle if using sticks or counters.
7. Count all the formed bundles aloud in twos from the first to the last: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30.
8. Record the total number of bundles formed, which should be exactly 15 bundles.

Study Questions

Solve the following exercises to practice counting in twos:

1. Obtain 20 pieces of bottle tops. Arrange them in groups of twos and write down the step-by-step counting sequence.
2. Form bundles of two-two objects from a total collection of 30 counters. How many bundles are formed in total?
3. Count backward in twos starting from 30 down to 10. Write out the complete sequence.
4. A farmer has 16 eggs. If the farmer packs them in crates that hold 2 eggs each, how many crates will be filled completely?
5. Complete the following number pattern: $32, 34, \square, 38, \square, 42, 44, \square$.