In the first quarter of last Friday’s netball game, Katie and Sarah scored all the points for the Gold team.

Sarah shot 1/4 of all the points. Katie shot 12 points.

How many points did the Gold team score?

In the second quarter of the game, Katie scored a fifth of the team’s 20 points while again Sarah scored the rest.

How many points did Sarah score?

Multiplication and division basic facts knowledge, enables students to work more 'fluently' with problems that involve fractions of sets. Students can solve such problems using equal addition, equal subtraction or sharing, but are disadvantaged by the lack of more intuitive number relationship knowledge.

It is therefore important to make evident to your students the multiplication and division facts that are at work as they solve problems involving fractions, and to continue to encourage their acquisition of strong basic fact knowledge.

### The Problem

In the first quarter of last Friday’s netball game, Katie and Sarah scored all the points for the Gold team. Sarah shot 1/4 of all the points. Katie shot 12 points. How many points did the Gold team score?

In the second quarter of the game, Katie scored a fifth of the team’s 20 points while again Sarah scored the rest. How many points did Sarah score?

### Lesson Sequence

- Introduce the problem by discussing netball. Ask:
*How many in the team can shoot?* - Read the problem with the class.
- Ask for ideas about how they might solve the problem.
- Let the students work on the problem in pairs. As they work ask questions that focus their thinking on the fractions.
*How do you work out a 1/4 of a set?*

If Sarah shot 2/4 how much did Katie shoot?

Convince me that your answer is correct. - Encourage the students to think about how they could convince others in the class that their answer was correct.
- Share explanations.

#### Extension Problem

What happened in the last two quarters? Get the students to finish off the story of the netball game by writing two more stories involving fractions. They can use the first two quarters as a model. Encourage them to use fractions other than quarters and fifths.

What fraction of the match total did Sarah score?

#### Other Contexts for the Problem

Other sports could be used

Shopping, where points are changed for money, and game quarters for different shops

### Solution

In the first quarter, as only 2 players shoot for the team, Katie must have scored 3/4 of the points. We know that Katie scored 12 points. If 12 points is 3/4, then 1/4 is 4 points. Therefore Sarah scored 4 points. This means that between them, Sarah and Katie scored 12 + 4 = 16 points. So the team scored 16 points in the first quarter.

In the second quarter, 20 points were scored. Katie scored a fifth of these. A fifth of 20 is 4. So Katie scored 4 points and Sarah scored 20 – 4 = 16 points.

It is likely that students will use other approaches too.

If guess and check is used, help the students to see how to improve their guesses so that their next guess is better than their first. For instance, they might guess 20 points for the first quarter answer. By dividing the 20 sticks into four groups they will see that a quarter is 5. Then three-quarters is 15. But this is more than Katie actually scored. So the original guess of 20 was too high.