Improper Fractions, Mixed Numbers

Name:

Date:

📚 Part 1: Build the Meaning

WALT: We are learning to recognise, represent, compare and convert improper fractions and mixed numbers.

Success criteria: I can identify the numerator and denominator; model a fraction greater than one; place a fraction on a number line; convert between improper fractions and mixed numbers; and explain my strategy clearly.

Key words: The denominator tells how many equal parts make one whole. The numerator tells how many parts we have. An improper fraction has a numerator equal to or greater than its denominator.

1. Can a fraction be greater than one? Draw a model for 5/3 using equal parts. Then write it as a mixed number.

5/3 = _________

2. Match each improper fraction to its equivalent mixed number.

A. 7/4

B. 11/5

C. 9/3

1. 2 1/5

2. 1 3/4

3. 3

A matches ____ B matches ____ C matches ____

3. Complete each comparison using <, > or =.

a) 7/3 ____ 2 b) 5/4 ____ 1 1/4 c) 9/5 ____ 2

4. Use a benchmark fraction such as 0, 1/2 or 1 to help compare 3/8 and 5/6. Which is greater? Explain briefly.

✏️ Part 2: Compare, Order and Explain

5. Order these fractions from least to greatest: 3/2, 5/4, 2, 7/4.

___________ < ___________ < ___________ < ___________

6. Place and label 3/2, 7/4 and 2 on a number line from 0 to 2.

7. Complete the conversions.

a) 13/4 = _________ b) 2 2/3 = _________/3

Show how many complete wholes you make and what fraction remains.

8. Choose the correct statement.

17/6 = 2 5/6

17/6 = 2 6/6

17/6 = 3 1/6

9. Error analysis: Hemi says, “8/3 = 8 1/3 because the numerator becomes the whole number.” What is Hemi’s mistake? Correct the conversion and explain.

10. Extension challenge: Create an improper fraction between 2 1/2 and 3. Convert it to a mixed number and explain why it fits.

11. Exit ticket: Convert 14/5 to a mixed number and place it on a number line from 0 to 3.

14/5 = __________

12. Which is greater: 9/4 or 2? Use an equivalent fraction, benchmark or number line to justify your answer.

Support and differentiation

Scaffold: Use fraction strips or a number line. Keep the benchmarks 0, 1/2 and 1 visible. Use the sentence starters: “The denominator tells me…” and “I made ___ whole(s) because…”.

Core: Show working for at least two answers and explain your strategy to a partner.

Extension: Investigate 17/6 and 23/8. Place them on a number line and create a fraction between two given mixed numbers.