Mathematics 7

# Web Quests

## DESIGNING A BUTTERFLY GARDEN

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

7m28 demonstrate a verbal and written understanding of, and ability to apply, accurate measurement strategies that relate to their environment

7m30 solve problems related to the calculation [and comparison] of the perimeter and the area of irregular two-dimensional shapes

7m33 describe measurement concepts using appropriate measurement vocabulary

7m36 understand that irregular two-dimensional shapes can be decomposed into simple two-dimensional shapes to find the area and perimeter

7m37 [estimate and] calculate the perimeter and area of an irregular two-dimensional shape

7m39 [estimate and] calculate the area of a trapezoid, using a formula

7m41 develop the formulas for finding the area of a parallelogram and the area of a triangle

### MATERIALS

grid paper

a ruler

a calculator (optional)

a geoboard (optional)

pattern blocks (optional)

### INSTRUCTIONAL PROCESS

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 TEACHER:

Divide students in pairs.
As a class, 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 to use the worm castings as fertilizer; 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 nice place to spend time.

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 that students are clear on what is expected of them. The number and type of shapes to be included in the garden design can be adapted to meet specific students’ or classroom needs.

For extra support, have students model the shapes they plan to include in their design on a geoboard or with pattern blocks. Have students make a rough draft of their garden design to allow them to explore possible designs and shapes more freely.

For extra challenge, have students calculate how many bags of fertilizer they will need for their flowerbeds if one bag of fertilizer will cover 50 cm² with a one-centimetre layer of fertilizer. (They can find the number of cm 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

POSSIBLE QUESTIONS:

Question 1

Ask students questions related to the information found on this web site to assess their comprehension and retention of information found in the text.

“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.

Vaux le Vicomte in pictures

Garden Design uk

Question 2

While students are working, observe and/or interview them to see how they are carrying and interpreting the task. Encourage students to be creative when incorporating shapes into their designs. Some elements could include: birdhouses, feeders, birdbaths, flags, benches, sculpture, sundials, poles and paths.

The first site has several examples of unusual gardens to spark students’ imaginations. The second site shows a garden that is a good example of geometric shapes being used in garden layout. The third site provides students with a couple examples of garden design drawings, which may help them in creating their 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

Students could also use a drawing program to create their garden design. Verify that students who need extra support have 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

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

“How can you organize the data so it is clear?

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

Question 5

“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.

“What is the formula for calculating the area of a triangle/parallelogram/trapezoid or complex shape?”

• Refer students to the chart on p.173 of the Student book for an example of how to approach this question.

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:

Students should be able to explain clearly how they calculated the perimeter of their garden and that the perimeter of their garden, measured in metres, equals the quantity of logs needed in metres. For students who finish early, have them calculate the number of logs they would need if each logs was __ cm long.

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.

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:

For extra support, have students model this question.

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

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.

### ASSESSMENT

 Level 1 Level 2 Level 3 Level 4 Understanding of Concepts . garden design (description, inclusion of shapes and calculation of their areas and perimeters) shows student has an insufficient understanding of 2-D measurement . garden design (description, inclusion of shapes and calculation of their areas and perimeters) shows student has a growing, but still incomplete understanding of 2-D measurement . garden design (description, inclusion of shapes and calculation of their areas and perimeters) shows student has a grade-appropriate understanding of 2-D measurement . garden design (description, inclusion of shapes and calculation of their areas and perimeters) shows student has an in-depth understanding of 2-D measurement Application of Procedures . selects an inappropriate procedure for calculating the area and perimeter of parallelograms, triangles trapezoids and irregular shapes . makes major errors and/or omissions when making calculations . selects a simple or partially correct procedure for calculating the area and perimeter of parallelograms, triangles, trapezoids and irregular shapes . makes several errors and/or omissions when making calculations . selects an appropriate procedure for calculating the area and perimeter of parallelograms, triangles, trapezoids and irregular shapes . makes only a few minor errors and/or omissions when making calculations . explores more than one strategy before selecting an appropriate procedure for calculating the area and perimeter of parallelograms, triangles, trapezoids and irregular shapes . makes almost no errors when making calculations Communication . few conventions (e.g., symbols, units, labels) are used correctly . provides incomplete explanations for determining how to calculate the area of complex shapes and when explaining thinking . organization is minimal and seriously impedes communication . some conventions (e.g., symbols, units, labels) are used correctly . provides partial explanations for determining how to calculate the area of complex shapes and when explaining thinking . organization is limited, but does not seriously impede communication . most conventions (e.g., symbols, units, labels) are used correctly . provides complete, clear, and logical explanations for determining how to calculate the area of complex shapes and when explaining thinking . organization is sufficient to support communication . almost all conventions (e.g., symbols units, labels) are used correctly . provides clear, thorough, and insightful explanations for determining how to calculate the area of complex shapes and when explaining thinking . organization is effective and aids communication