This problem solving activity has a number (multiplication and division) focus.
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.
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?
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?
In the first quarter, as only 2 players shoot for the team, Katie must have scored 3/4 of the points (4/4 - 1/4 = 3/4). 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 (e.g. guess and check, drawing a diagram, repeated addition, skip counting). Value these approaches, and support students to see how they could use basic facts knowledge to check their calculations, with a view of eventually using this multiplication knowledge to solve similar problems.
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.
In the first quarter, Sarah scored 1/4 of all points. In the second quarter, she scored 4/5 of all points. To calculate the total fraction of all points Sarah scored, we must add these two fractions together (4/5 + 1/4). However, these fractions have different denominators, which we need to change into like denominators, to calculate the total fraction.
To change these denominators into like denominators, we need to change them both using the lowest common multiple (in this case, 20). To change our denominators to 20, we need to consider what factor is multiplied with each of the pre-existing denominators to create 20 (i.e. 4 x 5 = 20, and 5 x 4 = 20). Once we have changed our denominators into 20, we need to apply the same multiplication to the numerators (i.e. x 5 and x 4).
The expression 4/5 + 1/4 then becomes 16/20 + 5/20. Together these fractions result in 21/20 or 1 and 1/20.
This fraction work would be quite advanced for a Level 2 student. You could ask your students to identify that Sarah scored 1/4 and 4/5 of the total points.
Printed from https://nzmaths.co.nz/resource/netball-goals at 3:44am on the 30th March 2024