Maths in basketball: free throws

Quick answer

When you play basketball, you can use maths to work out how many free throws you've made compared to how many you've tried. This is done using fractions, like 3 out of 5 or 7 out of 10.

Learning outcome

By the end of this page, you will understand how to use fractions to show how many free throws you've made in basketball, and you will be able to compare your scores with friends or family.

• You can write a fraction showing how many free throws you made out of how many you tried.
• You can compare your fraction with another player's fraction to see who did better.
• You can draw a picture or use objects to show your fraction.
• You can use the words "numerator" and "denominator" to describe your fraction.

Why this matters

Maths helps us understand how good we are at basketball. When you play basketball and take free throws, you can count how many you make and how many you try. Then, you can use fractions to show your success. This is useful for improving your game, comparing your progress, and even for fun!

Whether you're playing with friends or watching your favourite team, knowing how to use fractions helps you understand the scores and how well players are doing. It’s also a great way to see how much you’ve improved over time.

How it works

Let’s imagine you are playing basketball and you take 5 free throws. You make 3 of them. To show this using a fraction:

1. Count how many you made – that’s the top number of the fraction (the numerator).
2. Count how many you tried – that’s the bottom number of the fraction (the denominator).
3. Write it as a fraction – for example, 3 out of 5 is written as 3/5.

You can also use words like “three-fifths” or “three out of five” to say the fraction.

Examples you can see

Let’s look at some real examples of basketball free throws:

Emma made 7 out of 10 free throws. James made 5 out of 8. Lily made 4 out of 6. You can see that Emma did the best because 7/10 is more than 5/8 and 4/6.

Try drawing a picture to show this:

• Draw 10 circles for Emma’s 10 free throws.
• Colour in 7 of them to show how many she made.
• Write the fraction 7/10.

Try it as a mini adventure

Imagine you are on a basketball adventure! You and your friend are playing a game where you each take 10 free throws. You take turns, and you want to see who is better.

Here’s your adventure:

1. First turn: You take 10 free throws and make 6. Your friend takes 10 and makes 8.
2. Second turn: You take 5 free throws and make 3. Your friend takes 5 and makes 4.
3. Third turn: You take 8 free throws and make 5. Your friend takes 8 and makes 7.
4. Final turn: You take 6 free throws and make 4. Your friend takes 6 and makes 5.

Now, let’s work out your total scores using fractions:

• You made 6 + 3 + 5 + 4 = 18 out of 10 + 5 + 8 + 6 = 29 free throws.
• Your friend made 8 + 4 + 7 + 5 = 24 out of 29 free throws.
• So your fraction is 18/29 and your friend’s is 24/29.

Who did better? Your friend made more free throws, so 24/29 is better than 18/29.

Common mistakes

• Mistake: Writing the fraction the wrong way around. For example, saying you made 10 out of 6 free throws.
  Why it happens: Confusing which number is the part and which is the whole.
  Fix: Remember: the number of free throws you made goes on top, and the total number of tries goes on the bottom.
• Mistake: Thinking that 3/5 is the same as 5/3.
  Why it happens: Not understanding that the numerator and denominator have different roles.
  Fix: Remember: 3/5 means 3 parts out of 5 total parts.
• Mistake: Using a fraction like 7/5 when you only tried 5 free throws.
  Why it happens: Not checking if the numerator is smaller than the denominator.
  Fix: The numerator (top number) must be less than or equal to the denominator (bottom number).

Parent and carer guide

Helping your child with basketball fractions is a fun way to build their maths skills. Here’s how:

1. Play the game together: Take turns shooting free throws and write down the fractions for each round.
2. Use real objects: Use counters or coins to represent made and attempted free throws.
3. Draw it out: Ask your child to draw circles or stars to show how many they made.
4. Ask questions: “Who made more?” or “What fraction shows the best score?”
5. Keep it light: Don’t make it feel like a test. Keep it playful and encouraging.

Don’t worry if your child makes mistakes. It’s part of learning. Use mistakes as a chance to explain again with a new example or drawing.

Practice questions

1. Tom tried 8 free throws and made 5. What fraction shows how many he made?
2. Lily tried 12 free throws and made 9. What is her fraction?
3. Ben tried 6 free throws and made 4. What fraction is this?
4. If you made 10 out of 15 free throws, what is your fraction?
5. Which fraction is bigger: 4/6 or 3/5?

Answers:

1. 5/8
2. 9/12
3. 4/6
4. 10/15
5. 4/6 is bigger (because 4/6 = 0.67 and 3/5 = 0.6)

FAQ

What is a fraction in basketball?

A fraction shows how many free throws you made compared to how many you tried. For example, if you made 3 out of 5, it's written as 3/5.

How can I use fractions to improve at basketball?

Fractions help you track your progress. If you start with 2/5 and improve to 4/5, you know you’re getting better!

Can I use fractions with other sports?

Yes! You can use fractions in football (goals scored), cricket (runs made), or even in games like darts (how many you hit the bullseye).

Why do we need to know about fractions in basketball?

Fractions help us compare how good players are, track our own progress, and make games more fun and meaningful.

How do I explain fractions to a 4-year-old?

You can say, “If you had 5 cookies and ate 2, you ate 2 out of 5 cookies.” This helps them understand the idea of parts and totals.