Rational vs. Irrational Numbers

Name:

Date:

📚 Part 1: Multiple Choice

WALT (We Are Learning To): recognise and classify rational and irrational numbers and locate them approximately on a number line.

Success criteria: I can classify numbers as rational or irrational and justify my choices with a mathematical reason.

1. Is 0.75 rational or irrational?

Rational

Irrational

2. Is √9 (square root of 9) rational or irrational?

Rational

Irrational

3. Is √2 rational or irrational?

Rational

Irrational

4. Is π (pi) rational or irrational?

Rational

Irrational

✏️ Part 2: Short Answers & Application

5. Classify and give a one-sentence reason: −3/4. Is it rational or irrational?

6. On the number line from 0 to 2, which is closest to √2 (about 1.414)? Tick one.

1.3

1.41

1.5

7. Check all numbers that are irrational:

22/7

√16

0.121212... (repeating)

8. Exit ticket — For each number classify as Rational or Irrational and explain briefly: π ; 22/7 ; √8.

Differentiation: Support — work with simpler fractions and use calculators to test decimal patterns. Challenge — estimate and justify irrational placements using square root bounds (e.g. √8 between 2 and 3) and explore why 22/7 is an approximation of π.

Extension: Choose a real-world example (e.g. circumference of a circle, diagonal length of a square) and write 1–2 sentences describing how an irrational number appears and its effect on measurement accuracy.