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Proportional Reasoning Art Project

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Proportional Reasoning Art Project

A supermarket is planning a geometric mural for its community noticeboard. Help the design team keep every shape and colour mix in proportion. Show your working and include units where needed.

Ratios and scaling

Use equivalent ratios and scale factors to solve each design problem.

1.Arjun sketches a rectangle with side lengths in the ratio 2:3. Its shorter side is 8 cm. What is its longer side?

2.A motif is 4 cm wide on the draft and 14 cm wide on the mural plan. What scale factor changes the draft width into the plan width?

3.The supermarket noticeboard is 28 cm by 35 cm. A design is enlarged by a scale factor of 2. If a shape is 6 cm wide in the original design, what is its new width?

4.A blue-to-white paint mix uses a ratio of 3:2. If the team uses 90 mL of blue paint, how much white paint is needed?

Colour and proportion puzzles

Check whether a relationship stays proportional, then use the information to plan the mural.

5.Ngaio mixes orange paint using 2 parts red to 5 parts yellow. How many total parts are in the mix, and what fraction of the mixture is red?

6.The design team triples every length in a motif. What happens to the area of the motif?

It is tripled
It is multiplied by 6
It is multiplied by 9
It stays the same

7.A supermarket sells ribbon at a constant rate of $4.80 per metre. Is the total cost proportional to the length bought? Explain briefly.

8.A designer changes a rectangle's width from 5 cm to 10 cm but leaves its height at 4 cm. Is this an enlargement by one scale factor? Explain why or why not.

Create a proportional motif

Plan a mini geometric artwork using a ratio you can scale accurately.

9.Choose a rectangle-and-triangle motif. Write a simple ratio for two of its dimensions, such as rectangle width to triangle height. Then sketch the motif in the box.

10.Use a scale factor of 2.5 for your motif. If one original side is 4 cm, calculate its enlarged length. Write the multiplication you used.

11.A final motif must fit inside a 28 cm by 35 cm board. Your sketch is 8 cm by 10 cm. What is the largest scale factor that lets it fit without turning it?

12.In one or two sentences, explain why using the same scale factor for every length matters when enlarging artwork.