Year 8 Maths • AC9M8M07 • Authored homework
Ratio and rate modelling
Practise Ratio and rate modelling through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.
Part A
Short-answer questions
Simplify the ratio 18:24.
Share $84 in the ratio 2:5.
A map scale is 1:50 000. Find the real distance for 6 cm on the map.
A student adds the ratio parts incorrectly when sharing. Correct the method.
Write the rule or formula most useful for Ratio and rate modelling.
Show how to check one answer using estimation, substitution or inverse operations.
Write one common mistake students make in Ratio and rate modelling 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 Ratio and rate modelling and solve it.
Part B
Long-answer questions
A recipe uses flour and sugar in the ratio 5:2. Scale it to use 350 g of flour.
Model a road trip using distance, time and fuel rate, then decide whether the plan is realistic.
Solve a multi-step problem involving Ratio and rate modelling and explain every step clearly.
Create a realistic word problem for Ratio and rate modelling, solve it and interpret the answer.
Compare two methods for a problem in Ratio and rate modelling 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 Ratio and rate modelling.
Explain how this topic connects to a previous Year 7 or Year 8 maths skill.
Write a full-mark response to a challenging Ratio and rate modelling question, including reasoning and final answer.
Part C
Research and understanding task
Research a scale, recipe, map or speed context. Build a ratio/rate model and solve it.