Stage 4 - number – ratio

  • Supporting speakers of Aboriginal English.
  • Calculate a ratio; apply ratios to solve problems involving scale

Strategy

Students can:

  • calculate ratios
  • apply ratios to solve problems involving scale

Activities to support the strategy

Task outline: Students are to design a monster. Based on measurements and the use of ratios, students will produce a scale drawing of their monster.

Time Required: 1-2 lessons

Introduction

Students’ interest can be generated by drawing giant monster footsteps on the classroom floor before a lesson so that students see them when entering the room.

1. Explain to the students that an indigenous being from a faraway planet has been in the room and that it is their job to find out how big it is.

Activity 1 (whole class) – 10-15 minutes

Resources: Measuring tapes, calculator

Explain to the students how they are going to go about designing their own alien being by determining the size of the one that walked through the classroom leaving the giant footsteps behind.

  • how tall it is
  • how long its legs and arms are
  • how wide its arm span is
  • how long its torso is and
  • how fat it is

Note: The more able students may also be required to determine such things as:

  • where its elbows and knees should go
  • how big its head should be
  • how long its fingers are etc.

2. Explain that their monster is humanoid and that its body has the same proportions as a human.

Demonstrate how they can find these proportions by measuring their own body. Using two volunteer students, have one student measure the other's height, arm and leg length, arm span, torso length and waist using a measuring tape.

3. Ask one of these students to write their height and leg length on the whiteboard. Using these measurements, demonstrate how to calculate the ratio of this student's height to leg length.

4.Using the measurements, ask different students to demonstrate how to calculate the ratio of the measured student's height to arm span, arm length to leg length, and waist to torso length.

5. Demonstrate how these ratios can be used to get a picture of the monster. Choose a value for the monster's height and use the ratio to calculate the arm span of the monster. Begin to draw a monster using these measurements, explaining to students that they will have to be creative in designing their monster as they will be presenting it to the class.

Activity 2 (in pairs) – 15-20 minutes

Resources: Measuring tapes

1. Students work in pairs to complete the Human Measurements Worksheet. In pairs, they measure each other's height, arm span, arm and leg length, torso length and waist.

2. Using their measurements the students calculate the ratio of their height to arm span, arm length to leg length, and waist to torso length.

Activity 3 (individually) – 15-20 minutes

Resources: Calculators, butchers' paper, textas, coloured pencils etc.

1. Students are given the monster measurements worksheet (PDF 254KB).

2. Students then select measurements for their monster's height, arm length and torso length. Using the ratios they have discovered, they must then calculate their monster's arm span, leg length and waist.

3. Using these measurements, students must then draw their monster, being creative in their design.

Students are then to present or submit their completed monster design, along with their monster measurements worksheet.

References

Australian curriculum reference: ACMNA173

Recognise and solve problems involving simple ratios.

NSW syllabus reference: MA4-5NA

Operates with fractions, decimals and percentages.

NSW numeracy continuum reference:

  • Aspect 4: Place Value: System Place value
  • Aspect 6: Fraction Units: Fractions as Numbers.

NSW literacy continuum reference: WRIC13M6

Aspects of writing, Cluster 13, Marker 6: Creates texts with appropriate design, layout and graphics.

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