Year 4 Exam>Year 4 Notes>Mathematics for Year 4>Making a whole
Understanding Fractions
- Introduction to Fractions: When we talk about fractions, we are essentially talking about parts of a whole. Imagine a shape like a circle or a square. If we divide these shapes into different parts, each part represents a fraction of the whole shape. The sum of these parts always equals one whole shape.
- Example 1 - Dividing Shapes: Consider a circle divided into quarters. If we take three quarters and add one quarter to it, we have a total of four quarters, which equals one whole circle.
- Example 2 - Understanding Tenths: Let's think about dividing a shape into tenths. If we take seven tenths and combine them with three tenths, we end up with ten tenths, which is the same as one whole shape.
Visual Representation
- Importance of Visuals: Visual aids like images can help us grasp fractions better. They provide a clear representation of how parts come together to form a whole.
- Example Images:
Understanding Fractions Using Number Lines
- Representation of Wholes on a Number Line
Let's explore how number lines can help us visualize wholes:
- One Unit as a Whole
We can represent one whole unit on a number line.
We can divide this line to show fractions of the whole where each part represents a fraction, adding up to one whole.
- Understanding Fractions
For example, on a number line, 5/8 + 3/8 equals 8/8, which is one whole.
- One Unit as a Whole
- Exploring More Fractions
Let's delve deeper into fractions using another number line:
- Fractions in Action
When we add 5/10, 2/10, and 3/10 on the number line, they sum up to 10/10, which equals one whole.
- Fractions in Action
Understanding Wholes Using Hundred Squares
In a hundred square, fractions and decimals can help us understand wholes and their equivalents.
When we combine eighty-seven hundredths and thirteen hundredths, we get one hundred hundredths, which equals one whole.
This relationship can be visualized on a number line where 0.87 and 0.13 combine to make 1.
Examples and Explanation
Visual Representation
In the provided hundred square, imagine shading in eighty-seven out of one hundred squares and then adding thirteen more to make the whole square.
Decimal Equivalents
On the number line, the colored bar representing 0.87 and the bar representing 0.13 visually show how they combine to make 1.
0.87 + 0.13 = 1
Understanding Number Partitioning
Definition of Number Partitioning
Number partitioning involves breaking down a number into smaller parts or components.
Examples of Number Partitioning
Here are some examples illustrating different ways a number can be divided into two or more parts:
Using Part-Whole Models
Another method to represent number partitioning is through part-whole models, which visually display how a whole number can be divided into various parts:
Illustrating with Examples
Part-whole models are effective in demonstrating how a whole can be broken into parts, ensuring that the sum of these parts equals the whole:
Activity
Quiz
Test your knowledge about making wholes by taking this quiz and assessing your skills.
More on Fractions
Delve deeper into the world of fractions by exploring the following topics:
- Equivalent Decimals of Halves and Quarters (13 out of 26)
- Finding a Quarter (14 out of 26)
- Finding a Third (15 out of 26)
- Recognize and Find a Half (16 out of 26)
Understand how fractions like halves and quarters translate into decimals.
Learn to identify and locate one-fourth of a whole.
Discover how to pinpoint one-third of a total.
Learn to identify and calculate half of a whole.
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