Number
Exploring Equal Groups, Halves, and Quarters
Grade 1 · Grade 2 · Grade 3
- ✓By the end of this lesson students will be able to identify and create equal groups of objects.
- ✓By the end of this lesson students will be able to use repeated addition to find the total number of items in equal groups.
- ✓By the end of this lesson students will be able to identify and create halves of whole objects or sets.
- ✓By the end of this lesson students will be able to identify and create quarters (or fourths) of whole objects or sets.
- ✓By the end of this lesson students will be able to use appropriate math language to describe equal groups, halves, and quarters.
Key concepts
When you have groups of things, and each group has the exact same number of items, we call them 'equal groups'. This is a very important idea for understanding multiplication. For example, if you have 3 plates and each plate has 2 cookies, you have 3 equal groups of 2 cookies.
When you divide a whole object or a whole set of things into two parts that are exactly the same size, each part is called a 'half'. For example, if you cut an apple into two equal pieces, each piece is a half of the apple. Two halves make one whole.
When you divide a whole object or a whole set of things into four parts that are exactly the same size, each part is called a 'quarter' or a 'fourth'. For example, if you cut a sandwich into four equal pieces, each piece is a quarter of the sandwich. Four quarters make one whole.
Key facts to remember
- 1Equal groups mean that every group has the same number of items.
- 2You can find the total for equal groups by adding the number in each group over and over (repeated addition).
- 3When a whole is divided into two parts that are exactly the same size, each part is called a half.
- 4Two halves always make one whole.
- 5When a whole is divided into four parts that are exactly the same size, each part is called a quarter or a fourth.
- 6Four quarters always make one whole.
- 7For something to be a half or a quarter, the parts must always be equal in size.
Worked examples
Example 1
There are 4 baskets. Each basket has 3 toy cars. How many toy cars are there in total?
Answer
There are 12 toy cars in total.
This shows 4 equal groups of 3.
Example 2
Draw a square cake and show how to cut it into halves. Then, show how to cut one of those halves into two equal pieces.
Answer
The drawing should show a square with a vertical line down the middle. One of the halves should then have a horizontal line across it, making two smaller rectangles.
Remember, the parts must be equal in size!
Example 3
You have 6 cookies. You want to share them equally among 2 friends. How many cookies does each friend get? What fraction of the cookies does each friend get?
Answer
Each friend gets 3 cookies. Each friend gets one half of the cookies.
Sharing equally among 2 means finding halves.
Common mistakes
- ✗Not making groups truly equal when counting or drawing.
- ✗Dividing a shape or set into parts that are not equal in size and still calling them halves or quarters.
- ✗Confusing halves with quarters (e.g., thinking 2 parts are quarters).
- ✗Counting the number of groups instead of the total number of items when working with equal groups.
Exam tips
- ★Always draw pictures or use objects to help you understand and solve problems about equal groups, halves, and quarters.
- ★When asked to show halves or quarters, always double-check that your parts are exactly the same size.
- ★Read the question carefully to know if you need to find equal groups, halves, or quarters.
- ★Use your fingers or a pencil to count carefully when finding totals in equal groups.
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