Introduction to Ratio in Pattern

Hello, Year 6! Today, we are going to explore something called “ratio in patterns.” This concept helps us understand how different parts of a group relate to each other. Let’s break it down step by step!

What is a Ratio?

A ratio is a way to compare two or more quantities. It tells us how much of one thing there is compared to another. For example, if we have 2 apples and 3 oranges, we can say the ratio of apples to oranges is 2:3. This means for every 2 apples, there are 3 oranges.

Understanding Ratio in Patterns

When we talk about a ratio in a pattern, we look at how different parts of the pattern relate to each other. Let’s see how this works!

Example 1: Coloured Blocks

Imagine you have a pattern made from blocks:

  • Red, Red, Blue, Red, Red, Blue.

In this pattern:

  • Red blocks: 4
  • Blue blocks: 2

The ratio of red to blue blocks is 4:2. We can simplify this to 2:1 by dividing both numbers by 2. This tells us there are 2 red blocks for every 1 blue block.

Key Rules for Ratios

  1. Keep It Simple: Always try to simplify the ratio if you can.
  2. Order Matters: The order of items in a ratio is important. In our example, red comes first, so we compare red to blue.
  3. Same Units: Make sure you’re comparing the same type of things (like blocks, fruits, etc.).

Tips and Tricks

  • Use Visuals: Drawing the pattern can help you see the ratios clearly.
  • Count Carefully: Always double-check your counts to ensure accuracy.

Examples in Patterns

Let’s look at more examples:

Example 2: Beads on a Necklace

If you have a necklace with 6 blue beads and 3 green beads, the ratio of blue to green is 6:3, which simplifies to 2:1.

Example 3: Shapes in a Picture

In a picture with 5 circles and 10 squares, the ratio of circles to squares is 5:10, which simplifies to 1:2.

Questions for Practice

Now, let’s test your understanding with some questions!

Easy Level Questions

  1. What is the ratio of 2 apples to 4 oranges?
  2. In the pattern (Star, Star, Circle), what is the ratio of stars to circles?
  3. If there are 3 red cars and 6 blue cars, what’s the ratio of red to blue?
  4. In a fruit bowl with 5 bananas and 5 apples, what’s the ratio of bananas to apples?
  5. How would you write the ratio for 8 cats and 2 dogs?
  6. If a pattern has 2 triangles and 4 squares, what is the ratio of triangles to squares?
  7. What is the ratio of 10 pencils to 5 erasers?
  8. If there are 3 green marbles and 6 red marbles, what’s the ratio of green to red?
  9. In a class of 10 boys and 5 girls, what is the ratio of boys to girls?
  10. If you see a pattern of (Circle, Circle, Square), what’s the ratio of circles to squares?

Medium Level Questions

  1. In a pattern of (Blue, Blue, Green, Blue), what is the ratio of blue to green?
  2. If there are 4 dogs and 2 cats, what is the ratio of dogs to cats?
  3. A fruit basket has 3 apples, 7 bananas, and 2 pears. What is the ratio of apples to bananas?
  4. In a group of 12 students, if 4 are wearing glasses, what is the ratio of students with glasses to those without?
  5. If there are 5 red blocks and 10 blue blocks, what’s the ratio in simplest form?
  6. A cake is divided into 8 pieces, with 3 having chocolate and 5 having vanilla. What is the ratio of chocolate to vanilla?
  7. In a zoo, there are 6 lions and 4 tigers. What is the ratio of lions to tigers?
  8. A box contains 15 chocolates and 5 lollipops. What is the ratio of chocolates to lollipops?
  9. If a pattern is (Triangle, Circle, Triangle, Circle), what’s the ratio of triangles to circles?
  10. In a classroom, there are 10 chairs and 5 tables. What is the ratio of chairs to tables?

Hard Level Questions

  1. In a pattern (Red, Green, Blue, Red, Green, Blue), what is the ratio of red to green?
  2. A fruit basket has 12 oranges, 8 apples, and 4 bananas. What is the ratio of oranges to total fruits?
  3. If there are 20 students in a class and 10 are girls, what is the ratio of boys to girls in simplest form?
  4. A garden has 5 roses, 10 tulips, and 15 daisies. What is the ratio of roses to daisies?
  5. In a game, there are 9 players wearing red shirts and 3 wearing blue shirts. What is the ratio of red to blue shirts?
  6. A library has 30 fiction books and 15 non-fiction books. What is the ratio of fiction to non-fiction in simplest form?
  7. If there are 6 red balls, 3 green balls, and 9 blue balls, what is the ratio of red to blue?
  8. In a pattern (Circle, Triangle, Circle, Circle, Triangle), what is the ratio of circles to triangles?
  9. A class has 12 boys and 8 girls. What is the ratio of girls to boys in simplest form?
  10. If 50% of the students in a class have pets and there are 20 students, how many do not have pets? What’s the ratio of students with pets to those without?

Answers

Easy Level Answers

  1. 1:2
  2. 2:1
  3. 2:1
  4. 1:1
  5. 4:1
  6. 1:2
  7. 2:1
  8. 1:3
  9. 2:1
  10. 2:1

Medium Level Answers

  1. 3:1
  2. 2:1
  3. 3:7
  4. 1:2
  5. 1:2
  6. 3:5
  7. 3:2
  8. 3:1
  9. 2:1
  10. 2:1

Hard Level Answers

  1. 2:2 or 1:1
  2. 12:24 or 1:2
  3. 10:10 or 1:1
  4. 1:3
  5. 3:1
  6. 2:1
  7. 2:3
  8. 3:2
  9. 2:3
  10. 10 students; ratio is 1:1.

I hope this helps you understand ratios in patterns! Keep practicing, and you’ll become a pro in no time!