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Level Five > Number and Algebra

# Hot Shots

Keywords:
Achievement Objectives:

Achievement Objective: Use rates and ratios.

Specific Learning Outcomes:

Solve problems involving ratios.

Description of mathematics:

Number Framework Stage 8

Required Resource Materials:
Percentage Strips (Material Master 7-4)
Calculators
Paper clips
Activity:

### Using Materials

Discuss a situation where the students have encountered percentages in their daily

life. They will often suggest sports (for example, shooting for goal), shopping (such

as discounts or GST), and, in country areas, calving or lambing percentages. Tell the

students that the % sign comes from the “out of” symbol, /, and the two zeros from

100. It means, “out of 100”.

Problem: “In a game of netball, Irene gets in 43 out of her 50 shots. Sharelle takes 20

shots and gets in 17. Who is the better shot?”

Tell the students that percentages are used to compare fractions. In Irene’s case, the

fraction is 43/50 . Doubling 43 calculates the shooting percentage because 43/50 is equivalent

to 86/100  (86 out of 100). Represent this on a double number line.

Ask the students to work out what Sharelle’s shooting percentage was for the same

game. Represent this on a double number line to show that fi nding a percentage is

like mapping a proportion onto a base of 100.

Pose the students a percentage problem that can be modelled with the percentage strips.

For example: “Tony got in 18 out of his 24 shots. What percentage did he shoot?”

Mapping 18 out of 24 onto a base of 100 gives 75%.

Pose similar problems that the students can solve by aligning differently based

strips with the 100-base strip. Examples might be:

16 out of 32 (50%) 9 out of 36 (25%) 10 out of 25 (40%)

12 out of 16 (75%) 12 out of 40 (30%) 4 out of 20 (20%)

### Using Imaging

Show the students the base strip, but have the percentage strip aligned to it and

turned over so they can’t see the beads. Give the students “out of” problems and

have them estimate the percentage by visualising.

For example, pose six out of 16. Mark six with a paper clip. The students should

estimate the percentage as just below 40% or greater than 33.3% (one-third). A

calculator can be used to work out the exact percentage by keying in 6 ÷ 16%. The

percentage strip can then be turned over to check the estimate. Ask how else they

could have estimated the percentage if there had been no strips.

Look for ideas like “Six out of 16 is the same as three out of eight, and that is half of

three out of four” or “There are over six sixteens in 100. Six times six is 36, so it will

be more than 36 percent.”

Pose similar imaging problems like:

8 out of 20 (40%) 15 out of 25 (60%) 4 out of 16 (25%)

32 out of 40 (80%) 20 out of 32 (62.5%) 14 out of 36 (39%)

Focus on strategies based on the numbers involved that could have been used to

estimate the percentages.

The students can play the game of Percents (see Material Master 7–5) to consolidate

their visualisation.

### Using Number Properties

Give the students percentage problems to solve. Pose these problems in contexts

of sports scores, shopping discounts or mark-ups, or lambing percentages. Pose

some problems where duplication of the base onto 100 is not easy. For example, 25

is easily mapped onto 100 through multiplying by four, whereas 40 is not so easily

mapped (although students should be encouraged to recognise that 2.5 _ 40 = 100).

Examples that involve percentages greater than 100 should also be used.

Some examples might be:

18/24 =  ? %? (75%)

25/40 = ? %? (62.5%)

18/27 = ? %? (66.6%)

8/32 = ? %? (25%)

24/16 = ? %? (150%)

55/20 = ? %? (275%)

Get the students to record their thinking using double number lines or ratio tables,

e.g., 27/36  = 75%.

Independent Activity

Use brochures from local retailers. Tell the students that one shop has a “25% off”

sale, another has a “40% off” sale, and a third has a “one-third off” sale. Give the

students an arbitrary budget to spend at the three shops.

## Tree-mendous Measuring

Solve problems involving ratios.

## Extending Mixing Colours

Solve problems involving ratios.

## Extending Hotshots

Solve problems involving ratios.

## Combining Proportions

Solve problems involving ratios.

## Sharing in Ratios

Solve problems involving ratios.