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Symmetrical Patterns Exploration

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Symmetrical Patterns Exploration

Isla and Anh are making repeating signs for a wildlife sanctuary. Solve the ratio puzzles, then design a pattern that is symmetrical. A ratio compares amounts in the same order, such as 2 blue tiles to 3 green tiles.

Read the pattern plan

For one sign, Isla plans 2 blue tiles for every 3 green tiles. Anh plans a border with 1 leaf tile for every 4 plain tiles. Use these plans to answer Questions 1–4.

1.What is the ratio of blue tiles to green tiles on Isla’s sign? Write it in the order asked.

2.Isla makes 3 identical groups. How many blue tiles and how many green tiles does she need altogether?

3.Anh makes 2 identical groups of his border pattern. How many leaf tiles and plain tiles does he use?

4.Which ratio is equivalent to 2:3? Choose one.

Build balanced patterns

A pattern can repeat equal groups on both sides of a central line. Keep the tile quantities in the stated ratio while making the layout symmetrical.

5.A symmetrical badge has 4 red tiles and 6 yellow tiles. Simplify the ratio red:yellow by dividing both numbers by the same number.

6.A design uses 3 paw-print tiles for every 2 feather tiles. If it has 6 feather tiles, how many paw-print tiles should it have?

7.True or false: In a pattern with a paw-to-feather ratio of 3:2, 9 paw tiles and 6 feather tiles keep the same ratio.

TrueFalse

8.Complete the equivalent ratio: 2:5 = 6:__.

9.Anh places 2 matching tiles on the left of a vertical mirror line and 2 matching tiles on the right. What ratio of left-side tiles to right-side tiles does he make?

10.Draw a symmetrical sanctuary tile pattern using exactly 4 blue tiles and 4 green tiles. Place the vertical mirror line in the middle, and make the two sides match. Then write the ratio blue:green.

11.The sanctuary needs 12 tiles in a pattern with a blue:green ratio of 1:2. How many tiles of each colour are needed?

12.Explain one way to check that your pattern in Question 10 is symmetrical and that its ratio is correct.