Irrational numbers in applied contexts

Estimate √45 to one decimal place and explain how you know it is between 6 and 7.

Use π to write the exact circumference of a circle with diameter 12 cm, then approximate it.

Explain why √36 is rational but √37 is irrational.

A student says π = 3.14 exactly. Correct the statement.

Write the rule or formula most useful for Irrational numbers in applied contexts.

Show how to check one answer using estimation, substitution or inverse operations.

Write one common mistake students make in Irrational numbers in applied contexts and correct it.

Create a small table, diagram or equation that represents this topic.

State where units, exact form or rounding matter in this topic.

Write one exam-style short question on Irrational numbers in applied contexts and solve it.

A circular garden has radius 2.8 m. Find its exact area in terms of π and an approximate area to one decimal place.

A square has area 50 cm². Estimate its side length and explain why the exact answer is irrational.

Solve a multi-step problem involving Irrational numbers in applied contexts and explain every step clearly.

Create a realistic word problem for Irrational numbers in applied contexts, solve it and interpret the answer.

Compare two methods for a problem in Irrational numbers in applied contexts and explain which is more efficient.

Write a worked solution that includes a check for reasonableness.

Create a problem with a deliberate trap, then solve it correctly and explain the trap.

Use a diagram, table, graph or equation to model a situation involving Irrational numbers in applied contexts.

Explain how this topic connects to a previous Year 7 or Year 8 maths skill.

Write a full-mark response to a challenging Irrational numbers in applied contexts question, including reasoning and final answer.