Mathematics 4: Fractions and Decimals

Day 1: Fractions

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Why Use Fractions?

In your day-to-day life, you use whole numbers (1, 2, 3, 4, 5, and so on) for most of your counting needs. You might count people, boxes, coins, toys, books, cookies, hours, or centimetres as you go through a typical day.

However, there will be times when you wish to count parts of an object. For example, you may need to cut a cake into eight pieces, or you may wish to divide two pizzas equally among five people. You may wish to save one half of your allowance.

How do you count these parts that are less than one whole thing? Whole numbers will not work. You must find another way to refer to these parts of a whole object.

Suppose you and three friends are growing carrots in a shared garden space. You want to divide the carrot crop equally. The four of you have grown three sacks of carrots. How many sacks of carrots will each person get?

In the space below, try to work out how much the equal shares are. Use words, numbers, pictures, or all of these things to show your ideas.












It’s not important if you didn’t get the exact answer for the carrot problem. The important thing to realize is that each person gets less than one full sack of carrots. You must use numbers to show amounts that are less than 1. Such numbers are called fractions.

What Do Fractions Look Like?

Fractions are equal parts of a whole figure or a whole set. The parts must all be the same size in order to be called fractions.

For example, to divide a circle into two equal fractions, each fraction or part must be the same size.

Tell which of the following figures are divided into equal parts or fractions. Answer Yes or No.

1. 

   __________

2. 

   __________

3. 

   __________

4. 

   __________

5. 

   __________

1. Divide this triangle into two equal parts.

   

2. Show three different ways of dividing a rectangle into four equal parts.

   

Draw a rectangle that is divided into ten equal parts.

Fractions of Sets of Objects

Sets of objects can be divided into equal fractions. Each part of the set must have the same number of objects.

This set of hearts is split into two equal parts or fractions.

Each part has the same number of hearts in it.

This set of hearts is not divided into two equal fractions. The parts are different sizes.

One part has two hearts and the other part has four hearts.

The parts are not equal in size.

This set is split into four equal parts or fractions. Each part of the set contains two triangles.

This set shows three equal parts or fractions. Each part of the set contains three circles.

Each part or fraction of the set must be the same.

Look at this set. One part of the set of squares is much larger than the other parts. This set does not show five equal parts or fractions.

Here are two other examples showing unequal parts of a set.

Tell which of the following sets are divided into equal parts or fractions. Answer Yes or No.
1. 

   __________

2. 

   __________

In each of the following sets, tell whether the number of shaded parts equals the number of unshaded parts. Answer Yes or No.
1. 

   __________

2. 

   __________

Divide this set into four equal parts or fractions. Draw circles around the objects to show the equal parts.

Basic Number Facts Practice

Before you do your Assignment Booklet activities for Day 1, it is time to review your addition number facts.

Turn to the Number Facts Progress Chart for Module 3 in the Appendix. Remove the chart from the Appendix and hang it in your study area. You will use this chart to record your scores for the number facts drills in Module 3.

Ask your home instructor to time you as you complete the following exercise. Your goal is to complete all 25 questions in 2 minutes. At the end of 2 minutes, count up how many questions you were able to complete. Write this number in the chart below. Then use the answer key in the Appendix to mark the exercise, and record your score in the space provided. Before you move on, go back and complete any questions you did not finish during the 2 minutes. Mark these questions using the answer key as well.

Basic Number Facts Practice

Addition Number Facts

Number Completed in 2 Minutes __________

Number Correct in 2 Minutes __________

Record your score on the Number Facts Progress Chart.

Addition Number Facts

Timed Exercise: 2 minutes

Suggested Answers

Module 3: Day 1

Four gardeners need to share the carrots, so each sack will be divided into four equal parts. Share one sack at a time. Each gardener will get one part of each sack. Since there are three sacks, each gardener will get three parts of a sack in total, or (three fourths) of a sack altogether.

1. Yes
2. No
3. Yes
4. Yes
5. No

1. The triangle can be divided into two equal parts in three different ways.

   

2. The rectangle can be divided into four equal parts in the following ways.

   

Figures will vary. Be sure there are ten equal parts.

1. No
2. Yes

1. No
2. Yes

Addition Number Facts

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