Learning Fractions: Parts of a Whole

Level: Special education, 5th grade (age 13)

Assumption: “Factions” means fractions.

Materials

• Paper or index cards
• Pencil and colored pencils or crayons
• Scissors
• 8 small objects, such as counters, coins, or cereal pieces
• A paper plate or a circle drawn on paper
• Fraction cards made from the examples below

Goal

The student will identify the numerator and denominator and represent simple fractions such as 1/2, 1/3, 2/4, 3/4, and 4/8 using pictures and objects.

Lesson: 50 minutes

1. Hook: Sharing Fairly — 5 minutes

Place 8 objects on the table. Say:

“You and one friend are sharing these 8 pieces fairly. How many pieces should each person get? What fraction of the pieces does each person get?”

Let the student share the objects. Guide them to see that each person gets 4 out of 8 pieces: 4/8. Explain that a fraction shows part of a whole group or object.

2. Show It: The Parts of a Fraction — 10 minutes

Write 3/4 in large numbers.

• The top number is the numerator. It tells how many parts we have or are talking about.
• The bottom number is the denominator. It tells how many equal parts make the whole.

Draw a circle divided into 4 equal sections. Shade 3 sections.

Say:

“The circle is divided into 4 equal parts, so the denominator is 4. Three parts are shaded, so the numerator is 3. This picture shows 3/4.”

Repeat with these examples:

3. Do It Together: Fold, Shade, and Name — 15 minutes

Give the student four paper circles or squares. Help the student fold or draw lines to make equal parts.

1. Fold one shape into 2 equal parts. Shade 1 part. Ask, “What fraction is shaded?” Answer: 1/2.
2. Divide one shape into 3 equal parts. Shade 2 parts. Ask, “What fraction is shaded?” Answer: 2/3.
3. Divide one shape into 4 equal parts. Shade 1 part. Ask, “What fraction is shaded?” Answer: 1/4.
4. Divide one shape into 4 equal parts. Shade 3 parts. Ask, “What fraction is shaded?” Answer: 3/4.

Use the same sentence frame each time:

“The whole is divided into ___ equal parts. ___ parts are shaded. The fraction is ___/___.”

If drawing is difficult, let the student use the 8 objects. Ask them to show:

• 1/2 of 8: 4 objects
• 1/4 of 8: 2 objects
• 3/4 of 8: 6 objects

4. Learner Practices Alone — 12 minutes

Give the student these tasks. Read the directions aloud if needed.

Part A: Name the Parts

1. In 2/5, which number is the numerator?
2. In 2/5, which number is the denominator?
3. In 3/4, how many equal parts are in the whole?
4. In 3/4, how many parts are being described?

Part B: Draw and Shade

The student should draw a shape divided into equal parts and shade the requested number.

5. Draw and shade 1/2.
6. Draw and shade 2/3.
7. Draw and shade 3/4.

Part C: Choose the Fraction

8. A shape has 4 equal parts. 1 part is shaded. Is it 1/4 or 3/4?
9. A group has 8 objects. 6 are red. Is the fraction red 6/8 or 2/8?

Offer a short movement or sensory break after question 4 if the student needs one. Return to the same task without penalty.

5. Brief Recap — 5 minutes

Ask the student to complete these sentences:

• “The bottom number tells me how many __________ parts make the whole.”
• “The top number tells me how many parts we __________.”
• “In 3/5, the numerator is __________ and the denominator is __________.”

End by saying:

“A fraction names equal parts of a whole. The denominator tells the total number of equal parts, and the numerator tells how many parts we have.”

Quick Check

Ask the student to complete this independently:

1. Draw a rectangle divided into 4 equal parts.
2. Shade 2 parts.
3. Write the fraction represented.
4. Circle the numerator and underline the denominator.

Answer Key

1. Numerator: 2
2. Denominator: 5
3. There are 4 equal parts.
4. 3 parts are being described.
5. Student should show 1 of 2 equal parts shaded: 1/2.
6. Student should show 2 of 3 equal parts shaded: 2/3.
7. Student should show 3 of 4 equal parts shaded: 3/4.
8. 1/4
9. 6/8
10. Quick check answer: 2/4; numerator 2, denominator 4.

Make it easier: Use only halves and fourths, provide pre-drawn shapes, and let the student answer by pointing, choosing between two options, or using objects.

Make it harder: Ask the student to explain why 2/4 and 1/2 show the same amount, using a picture or folded paper.