Mathematics 7

# Web Quests

## CHAPTER 5

### TASK CONTEXT

For this Web Quest, as for the Chapter 5 Chapter Task, students will use their growing knowledge of 2-D measurement to create and describe a design. Building on the Chapter 4 Web Quest topic of vermicomposting, student will work in pairs to create a design for a butterfly garden, which will incorporate shapes worked with in Chapter 5 Nelson Mathematics 7 . Students will be responsible for calculating the area and perimeter of these shapes.

### GOALS

• solve problems related to the calculation of area and perimeter

• describe orally and in writing, strategies for solving problems

• apply formulas to calculate the area of a trapezoid, parallelogram, triangle and complex polygons

• create an accurately scaled and labeled garden design which incorporates required shapes into design

• recognize the importance of accurate 2-D measurement in the design of a garden

### MATERIALS

grid paper

a ruler

a calculator (optional) a geoboard (optional)

pattern blocks (optional)

### VOCABULARY

Your child should be familiar with the following vocabulary:

parallelogram - a quadrilateral with equal and parallel opposite sides

trapezoid - a quadrilateral with only one pair of parallel sides

area - the number of square units needed to cover a surface

formula - a rule represented by symbols, numbers, or letters, often in the form of an equation

base - the line segment that is perpendicular to the height

isosceles trapezoid - a trapezoid where the non-parallel sides have equal lengths

### HELPING YOUR CHILD THROUGH THE TASK

FROM STUDENT PAGE

INTRODUCTION

Now that your school has started up a vermicomposting program, your principal has been thinking about what you can do with all the fertilizer (castings) the worms are producing. One idea is to create a school butterfly/wildflower garden, which could be funded by the sales of bags of the worm castings. What would be some of the benefits of this type of project?

NOTES FOR PARENTS:

This Web Quest was designed to be done in pairs. While it can be completed individually, your child would benefit from having you collaborate with him or her on the design and 2-D measurement of shapes.

Whith your child, read the Introduction.  Brainstorm possible advantages of having a butterfly garden on school property. Possible advantages could include: creation of habitat for butterflies and other insects/animals; a way to put use the worm castings; opportunity to learn about a) butterflies and other insects and wildlife that might be attracted to the garden, b) native plants, and c) growing cycles first hand; it would be aesthetically pleasing and a nice place to spend time.

TASK

Your principal has asked Grade 7 students to submit butterfly garden designs. With a partner, design a garden. Your design must include the following shapes:

three triangles

two parallelograms

two trapezoids

three complex shapes

Together, read the Task section of the Student Page. Ensure your child is clear on what is expected of him or her. The number and type of shapes to be included in the garden design can be adapted to meet your child's specific needs.

For extra support, have your child model the shapes he or she plans to include in his or her design on a geoboard or with pattern blocks. Have your child make a rough draft of their garden design to allow him  or her to explore possible designs and shapes more freely.

For extra challenge, have your child calculate how many bags of fertilizer he or she will need for his or her flowerbeds if one bag of fertilizer will cover 50 cm² with a one-centimetre layer of fertilizer. (He or she can find the number of centimetres the layer should be (3 cm) by clicking on the link to the FRW web site).

Find out:

a) the recommended size for your garden

b) the spacing of wild aggressive and non-aggressive wild plants

c) the minimum number of plants of one species that should be planted together

Question 1:

Ask your child questions related to the information found on this web site to assess his or her comprehension and retention of information found in the text.
Possible Questions:
“What can you tell me about butterfly/wildflower gardens?”
“Where do they recommend you place your garden?”

• No closer than 5 m away from a parking lot or road

• Away from play areas

• Where the garden will receive a minimum of five hours or sunlight a day

“Is there a specific shape your garden should be”

• No.

“Why should you put logs or rocks around the perimeter of your garden?”

• To prevent soil erosion

How often and when should you fertilize your garden?”

• Twice. Once in late spring and once in early summer.

2. Discuss with your partner some of the elements you would like to include in your garden. Visit some of the following web sites for inspiration.

BBC - Gardening - Design - Design Inspiration

Vaux le Vicomte in pictures

Garden Design uk

Question 2:

Encourage your child to be creative when incorporating shapes into his or her design. Some elements could include: birdhouses, feeders, birdbaths, flags, benches, sundails, sculpture, poles and paths.

The first site has several examples of unusual gardens to spark your child's imagination. The second site shows a garden that is a good example of geometric shapes being used in garden layout. The third site provides your child with a couple examples of garden design drawings, which may help him or her in creating his or her own.

3. On a piece of grid paper, draw a scale diagram of your garden. Remember, your garden can be any shape, so think creatively.

Question 3:

If you have suitable software, have your child create his or her garden design using  your computer. Verify that your child has chosen an appropriate scale for their design.

4. Create a table to display the area and perimeter of the shapes you included in your design.

Question 4:

Sample Questions to ask your child while he or she is working:

"What information are you going to include in your table?"

"How can you orgainze the data so it is clear?"

5. Explain how you calculated the area of the complex shapes you included in your design.

Question 5:

If your child is struggling, refer to the chart on p.173 of the Student book for an example of how to appraoch this question.

Sample questions to ask your child while he or she is working

“How do we determine which side is the base and which side is the height in a shape?”

• The height is perpendicular to the base. This means that it forms a right angle at the base.

• There is a right angle at the bottom of the height line and the base line.

“How can you determine the area of a parallelogram?”

• I can use a rectangle.

• I can rearrange the parts of the parallelogram to create a rectangle.

"How can you determine the area of a triangle?"

• I multiply the base by the height and divide by 2.

6. Friends of the Rouge Valley suggest putting logs around the perimeter of your garden to keep the sand in your garden from blowing away. How many metres of logs would you need? Explain your thinking.

Question 6:
Your child should be able to explain clearly how he or she calculated the perimeter of the garden and that the perimeter of the garden, measured in metres, equals the quantity of logs needed in metres.

7. What would be the minimum area, measured in metres, of a square flowerbed planted with aggressive wildflowers and a square flowerbed planted with less aggressive wildflowers if you followed the plant spacing advice given at the FRW web site? Explain your thinking.

Question 7:

Less aggressive plants should be planted 15 cm apart, whereas more aggressive plants should be planted 25 cm apart. Plants should be planted in a minimum group of nine.

For extra support, have your child model this question.

For extra challenge, have your child answer the following question. “Do you think the shape of a flowerbed could make the plant spacing easier or more difficult?”

Sample Answer:
I know that:

• A minimum of 9 flowers should be planted together.

• Less aggressive plants should be planted 15 cm apart.

• More aggressive plants should be planted 25 cm apart.

If the flowerbed had 9 plants in it, one way to arrange the plants would be in three rows of three, which would form a square. For aggressive plants, they must be 25 cm apart. This means the width of the flowerbed would be 75 cm. I multiplied the number of plants to be planted widthwise in the flowerbed by the space needed between each plant to get my answer. I repeated this to find the length of the flowerbed, which is also 75 cm. I know that Area = length x width so, if I multiply . 75 x .75 we get the area of the flowerbed in metres. The area of a flowerbed planted with 9 aggressive plants would be .5625 m².

8. In writing, describe your design.