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Purpose

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
A PDF of the student activity is included.

Achievement Objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Student Activity

  

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Specific Learning Outcomes

find percentages of whole numbers

Description of Mathematics

Number Framework Links
Use this activity to:
• develop confidence in students who are beginning to use advanced proportional strategies (stage 8)
• help students to consolidate and apply their knowledge of percentages (stage 8).
 

Required Resource Materials
FIO, Level 3-4+, Proportional Reasoning, Book Two, Laser Blazer, pages 12-13
Activity

This activity provides an interesting context in which students find fractions and percentages and practise expressing fractions as percentages. The score printout is an excellent example of a double number line.
Use question 1 to introduce the context and to check students’ understanding of percentages. Have the students use the think, pair, share technique to discuss possible strategies. A strategy might go like this: “Since 3 people can enter for the price of 2, it will cost $30 for 3, which is $10 per person.” Or this: “If they all paid $15, it would be 15 x 6 = $90, but take off $30 for the two who don’t have to pay and the total is $60. $60 ÷ 6 = $10 per person.”
The total discount was $30 off the normal price of $90; the per-person discount was $5 off the normal price of $15. This means the discount was 30/90 = 5/15 = 1/3. As a percentage (fraction of 100), this is 33 %.
Students who do not understand how to write fractions as percentages could use 100 beads on a string as an open number line. The string is labelled from 0 at one end to 1 at the other, and the 100 beads represent one whole or 100%. Students can find 1/3 of the string and see that it is 33 %.
Another useful aid is Percentage Strips (Material Master 7–4) which shows a drawing of the 100-bead number line. Both these models can help students image a percentage as the answer to the question “This would be equivalent to how much of 100?”
Have the students explain how the score printout shows not only the number of hits but the relative success of the player (their accuracy). They should generalise this in a hits/shots statement, showing the hits as a fraction of total shots.
The students should try to express their statement as an equation or formula. They can use letters to stand for the two variables, hits and shots: accuracy = h/s. Then they should try to adapt their formula so that it expresses accuracy as a percentage: accuracy = h/s x 100. They can use their formula five times to solve question 2 for each of the friends.
As a percentage, Luke’s accuracy = 30/50 x 100. This is equivalent to of 100. 1/5 of 100 is 20, so 3/5 x 100 = 20 x 3 = 60. This means that 60% of Luke’s shots are hits.
Students who need the support of materials could use the 100-bead string or material master 7–4 to help them solve the parts of question 2.
Question 3 switches the focus from the hits to shots ratio to the remaining hits to shots ratio needed to meet the 75% benchmark. This is not an easy idea for students to get their heads around, but the introductory diagram clearly shows them where to look for the data, and the thought bubble models the required thinking. For each printout, they need to work out:
• how many more hits the person needs to get to reach 53
• how many shots they have left (out of their total of 70).
Note that, in this case, students are asked to express their answers as fractions rather than percentages. The question has been constructed so that each answer, when simplified, is an everyday fraction. Once your students have the fractions, you could ask them to go a step further and express them also as percentages.
Question 3b requires students to reflect on the meaning of their answers.

Answers to Activities

1. a. $10. (They paid for 4, and 2 got in free. 4 x 15 = $60. 60 ÷ 6 = $10.)
b. 33 1/3 %. (Without the discount, they would have paid 6 x 15 = $90, so they saved $30. 30 ÷ 90 = 1/3 or 33 1/3%.)
2. Luke 30/50 = 60%
Tangihaere 30/40 = 75%
Matt 42/56 = 75%
Alex 44/66 = 66 2/3%
Ese 36/60 = 60%
3. a. Luke 12/20 = 3/5
Tangihaere 21/24 = 7/8
Matt 30/40 = 3/4
Alex 11/22 = 1/2
Ese 17/17 (all)
b. Ese. To gain marksman rating, he will have to score hits with all of his remaining
17 shots.

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Level Five