This is a level (2+ to 3+) mathematics in science contexts activity from the Figure It Out series.

A PDF of the student activity is included.

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Students will:

- make a scale drawing of an eco-kennel to suit a given volume
- scale up the drawing by specifi ed percentages.

Students should discover that:

- volume is length by width by height
- increasing dimensions by 50% or less can double the volume of a cuboid.

a computer design program (optional)

access to relevant books and/or the Internet (optional)

FIO, Sustainability, Levels 2+-3+, An Eco-kennel, page 24

**Preparation and points to note**

Some students may need the help of materials when working with volumes. Help them to fi nd the volume for rectangular prisms such as different-sized cereal boxes or shoe boxes. Check that your students’ understanding of percentages is suffi cient for them to be able to increase dimensions by 20 and 50 percent.

This activity uses terms such as volume, percent, and the symbol %. Students take time to build up

understanding of the abstract concepts embodied in these terms, and they need multiple opportunities to do so. A suitable key competency focus is *using language, symbols, and texts*.

**Points of entry: Mathematics**

In this activity, volume is described as length by height by width. It might just as easily be described as length by width by height, as it is in the previous activity. You could use this to discuss with the students why the order doesn’t matter (as long as it’s used consistently in the same context): the volume is the same, regardless of whether it is 45 x 30 x 20, 45 x 20 x 30, or 30 x 20 x 45.

Have the students visualise how big Perry is so that they can get a feel for appropriate measurements. For example, ask them to make a pile of books equal in size to Perry. Note that a 45 x 30 x 20 cm kennel will be too small because Perry needs to be able to move around inside it. The students may fi nd it useful to mark out dimensions in chalk or use tape on the floor. Encourage them to test for reasonableness. Ask *How big should the door be?*

Your students may be tempted to introduce circular or diagonal elements into their design. Give them

freedom to be creative, but suggest that they calculate the volume of a rectangular box that encloses their kennel instead of working out the exact volume of a diffi cult design. As a practical consideration, construction materials tend to come in rectangular pieces.

Question **3** requires the students to increase the dimensions of their kennel by 20 and 50 percent. They can think of these either as increases of 1/5 and 1/2 or as an increase of 1/10 doubled and an increase of 1/10 multiplied by 5. They should learn that an increase of 20% is represented as 120% and that 120% = 1.2.

The calculation in question **4** may require use of a calculator. Regardless of the dimensions chosen, Tosh’s kennel will have a volume that is 216% of Perry’s. In other words, the bigger kennel will have 2.16 times the volume of the smaller kennel. You could invite discussion on what is meant by “twice the size”; students may interpret this in different ways (for example, as twice the height). You could also discuss whether it is correct to say that Tosh’s kennel is “twice the size” of Perry’s when, technically, it will be 2.16 times the size.

[**Note for teachers**. The extent of the increase can be found by the multiplication 1.5 x 1.2 x 1.2 = 2.16. However, you don’t need to tell your students this as it involves unnecessary abstraction at a time when most students are still trying to work out how to apply percentages in simple, practical contexts.]

As an extension, the students might try to work out how much of each material they would need to buy (bearing in mind that they would be using recycled materials, if available), fi nd out prices, and then work out the cost of their kennels.

**Points of entry: Science**

Consider introducing this activity by picking up on the speech bubble “conversation” in the students’ book. The prefi x “eco-” is often tacked onto things (including houses) as a marketing ploy. Have your students discuss in groups what “eco” might mean in this context and then share their ideas with the wider class.

This activity could be made into a challenge by restricting the type and amount of materials. Encourage the students to draw on expertise and understanding gained from previous activities in making their decisions. They will need to discuss and identify the needs of the dog before making any decisions; this investigation could form part of the design brief and/or the basis for a set of criteria against which to check their design. (Similar processes are followed in technology.)

In question **1**, the students brainstorm requirements for an eco-kennel (it should protect the dog from the elements, be relatively inexpensive to make, use sustainable materials, and so on). Encourage them to research eco-houses, what materials are best suited to their construction, and how they compare in cost with more conventional materials.

Discuss with the students the fact that good scientists make sure that their decisions are informed by evidence. Ask the students probing questions so that they justify their decisions about their eco-kennels. For example, “I chose recycled plastic for the roof because it needs to keep the rain off, and I chose a straw-fi lled cotton mattress for the fl oor because it’s cheap, organic, and comfortable.”

**Answers**

1. Your ideas about suitable materials will vary, but they should be fi t for the purpose and be

sustainable. For example, you might decide on recycled corrugated iron for the roof. Make sure

that you have a good reason for each choice of material.

2. a. Designs will vary. Perry is 45 cm long, 30 cm high, and 20 cm wide, so he will occupy a space 45 x 30 x 20 = 27 000 cm3. The kennel must have a door that he can fit through (a bit bigger than 30 cm x 20 cm) and be large enough for him to lie down in. A possible kennel might be a box shape

measuring 60 x 40 x 30 cm. Your design should indicate the materials for each part of the kennel.

b. The volume of his kennel is the product of the 3 measurements. If his kennel is 60 x 40 x 30 cm, the volume is 60 x 40 x 30 = 72 000 cm3.

3. Answers will vary, depending on the size of the kennel you have designed for Perry. If Perry’s kennel is 60 x 40 x 30 cm as in the example for **2b**, the dimensions for Tosh’s kennel will be:

length: 60 x 150% = 60 x 1.5 = 90 cm

height: 40 x 120% = 40 x 1.2 = 48 cm

width: 30 x 120% = 30 x 1.2 = 36 cm.

4. Yes: Tosh’s kennel will be twice the volume of Perry’s (a bit more than twice, actually). This

will be true whatever the size of the kennel that you planned for Perry. You can show this by

multiplying the dimensions for Tosh’s kennel and comparing the result with the volume of Perry’s

kennel. (Using the example from question **3**, Tosh’s kennel would have a volume of 90 x 48 x 36 = 155 520 cm3. This is more than double 72 000 cm3, which is the volume of Perry’s kennel.)