MEL4E
Unit 6: Mathematics and Design
Activity 3: Budgeting for a Home Improvement Project
Watch Mr. Blandings Builds His Dream House;
Home improvement projects can be exciting. Dreams about creating your perfect bathroom can be exciting! BUT -- home improvements have to be carefully planned and executed, or disaster may happen.
Read this story, from Gwenna in Ontario:
When we moved into our new house, we knew that we wanted to renovate the bathroom. The tile was too dark and the appliances were in rough shape. Thinking we could do this on our tight budget, we got started. That was when everything went downhill. When we started removing the tub surround we found tile behind it. "What a pain," we thought but just a small delay. But behind the tile, we were confronted with more than we bargained for. We could see the inside of the shingles on the side of the house. The entire wall, including the insulation had rotted away!
One discovery after another, and we were eventually forced to gut the entire bathroom right down to the studs. Triple the cost later, we have a functional bathroom.
Gwenna’s story is not at all unusual. Disasters happen more often than you might think. Even small home improvements need planning.
When you bought that big screen TV, did you measure the size of the wall you wanted to put it on? Did you check if the wall could support it?
Before you started putting in a new counter top, did you check if the corners of the wall were still 90° (right) angles?
Garden Improvement Project - A Beautiful Patio
In Activity 2 of this unit, you looked at some garden improvements -- an outdoor fireplace and a water feature. In this activity, you will complete the garden improvement by designing the patio.
Getting Ready! Stage 1
Things you need to know:
The garden is 70 feet wide (across) by 36 feet deep.
The patio:
- The patio is in the middle of the garden (across).
- It begins against the house (depth).
- It has a rectangular shape.
The fireplace:
- The fireplace is 4 feet wide and 2 feet deep.
- The fireplace will be on the patio, in the middle (across), as far from the house as possible.
The water feature:
- The water feature will also be on the patio.
- It is circular in shape, and it is 1 m in diameter.
- It is in the middle of a grey square platform made of stone.
- The platform is 2 m wide.
The scale diagram represents the whole garden.
The scale diagram has 35 squares across and 18 squares deep.
Use the information above to answer the following questions:
Questions
What ratio can you set up to create a scale for the scale drawing? Select the two correct answers.
a. 18 squares : 35 squares
b. 18 squares : 36 feet
c. 35 squares : 70 feet
d. 36 feet : 70 feet
Answer
In the scale diagram, each square will represent some number of feet, so, to set a scale, we need a ratio that tells us:
number of squares : number of feet
So b. and c. are correct.
What will be the scale for the scale drawing? Select the correct answer.
1 square = 0.5 feet
1 foot = 2 squares
1 square = 2 feet
Answer
1 square = 2 feet
From question 1, you can create the ratio table:
First thing first - Things you need to do:
You need to indicate where the patio, fireplace, and water feature and its stone platform should be on the scale diagram. To do this, you need to deal with a problem.
The water feature and platform dimensions are in metres, but the scale drawing uses feet.
You can type "2 m in feet" into a Google search to convert measurements between the metric system (that uses metres) and the Imperial system (that uses feet). Conversion software uses proportional reasoning and a scaling factor to perform the conversion.
Use the information above to answer the following questions:
Questions
Convert the dimensions of the water feature and platform from metres to feet. Find out what 1 m and 2 m are in feet. Use 1 decimal place of accuracy.
a. 1 metre = 0.3 feet, so 2 metres = 0.6 feet
b. 1 metre = 3.2 feet, so 2 metres = 6.4 feet
c. 1 metre = 3.3 feet, so 2 metres = 6.6 feet
Answer
c. is correct.
If you chose a then ask yourself, did you input 1 meter or 1 foot?
If you chose b then ask yourself, did you check your rounding rules?
Do you agree that you need about 3 1/3 squares to represent the platform on the scale drawing?
Answer
One way to do this question is to set up a ratio table:
It would be really difficult to count 3.3 squares on the scale drawing. The estimate 3 1/3 square will be fine.
Before you move to the next section, you need to figure out how many squares you will need for the diameter of the water feature. Hint: If you need 3 1/3 squares to represent the platform (that is 2 m), then I need just over 1.5 squares to represent the diameter of the water feature.
Assignment Patio Design - Stage 1
In this assignment you are going to actually design your patio! You are to decide on the size and shape of the patio, as well as the locations for your fireplace and water feature.
There are a number of ways you can do this:
- You can find some grid paper and design the patio using pencil and paper.
- You can print out the following grid and design the patio using pencil and paper.
- You can use the interactive that is located below. This interactive includes draggable lines to represent the perimeter of your patio, and it includes a number of different sized fireplaces and water features. It is your job to select the correct sizes for both the fireplace and the water feature and to include them somewhere on the patio. You can then generate a screen capture in order to save your final patio design.
This interactive allows shapes to be dragged on to a grid. The shapes represent the perimeter of the patio, the fireplace and the water feature.
Once you have decided on your method, your task is to:
- Indicate the location of the patio on the scale diagram.
Things to think about! - Remember to check "Things you need to know."
- The size of the patio is up to you, but remember that the fireplace and the water feature must fit on the patio.
- Design the patio in a way that there will be a nice place to sit and relax.
- Later, you will be deciding what other features, such as flower pots and furniture are wanted, so keep that in mind as you make your design.
- Remember to check the dimensions and the scale.
- Place the fireplace on your scale drawing. Remember to check the dimensions and the scale. If you are using the interactive, notice how there are several possible scale drawings for the fireplace? Select the one that shows the correct proportions given the scale. Place the fireplace on your scale drawing.
- Place the water feature on your scale drawing. Remember to check the dimensions and the scale. If you are using the interactive, notice how there are several possible scale drawings of the water feature. Select the one that shows the correct proportions given the scale. Place the water feature on your scale drawing.
Checkpoint (Self-Check):
- Did I place the patio against the house?
- Did I place the patio so that it is in the middle of the garden (horizontally, or across)? How do I know?
- Did I make the patio large enough to accommodate the fireplace and the water feature while still leaving space for furniture and other items that are to come?
- Did I place the fireplace at the back of the patio?
- Did I figure out how many squares I need to represent the fireplace width and depth on the scale drawing?
- Did I place both the water feature and the grey stone platform on the patio?
When you are satisfied with your design and scale drawing, answer the following questions:
- What are the (real) dimensions of your physical patio?
- What is the area of your patio?
Adding Flower Bed - Stage 2
There is to be a flower garden around the perimeter of the patio. It will be in the garden (not on the patio). It will be 3 feet wide, so that some tall bushes and small cedar trees can be planted among the flowers (for some extra privacy).
1. Add the flower bed to your scale drawing design.
2. The flower bed is going to have a decorative fence, like this one, as a trim around the flower bed.
3. The trim will separate the flower bed from the rest of the garden. It will be on three sides of the flower bed. (It will not need to be on the patio side of the flower bed.)
4. The trim comes in panels that are 4 feet long. Each panel of trim costs $3.50.
It is recommended that a flower bed have 12 inches (which is 1 foot) of soil. Soil costs $40.50 per cubic yard.
The next step will be to compute the expenses of adding the flower bed. The following examples will help you do your own calculations.
Ty made this scale drawing of his design.
Ty had designed a patio to be 46 feet wide by 20 feet deep.
Trim:
To calculate the amount of trim he would need, he reasoned that the flower bed is 3 feet deeper and 6 feet wider than the patio. The flower bed is 52 feet wide and 23 feet deep.
To trim the 52 foot width, he would need to buy 13 4-foot panels (exactly 52 feet). To get the two sides, he would need 23 feet of trim on each side. He would have to buy 6 panels for each side, or 12 panels.
In total, Ty would have to buy 25 panels.
Since each panel costs $3.50, the trim would cost $87.50.
Soil:
Ty reasoned that the flower bed was 52 feet wide by 23 feet deep, but only a small part of this rectangle was used for the flower bed.
Ty decided to break up the flower bed into 3 rectangles.
He found the volume of each of the three rectangular prisms.
A: 20 feet deep by 3 feet wide by 1 foot deep. Volume = 60 cubic feet (cu. ft.)
C: Same as A. Volume = 60 cu. ft.
B: 3 feet deep by 52 feet wide by 1 foot deep. Volume = 156 cu. ft.
Total volume of soil required: 276 cu. ft.
Ty found an online calculator that tells you how much soil you need. He used this one to check his calculations.
Now he needed the cost. His volume was in cubic feet, but soil was sold in cubic yards!
Ty searched "convert cubic yards to cubic feet" and found that 1 cubic yard is 27 cubic feet.
Next step? Proportional reasoning!
One more step:
Ty concluded that the expenses for the flower bed would be $87.50 for the trim and $414.00 for the soil.
Adding Flower Bed - Stage 2
It is now time to add a flower bed to your own patio.
- If you completed your patio using grid paper, then you can add the flower bed directly onto your design;
- If you completed your patio using the interactive, then you can quickly rebuild your patio in the interactive below and then add the outline for your patio.
This interactive allows shapes to be dragged on to a grid. The shapes represent the perimeter of the patio, the fireplace, the water feature and the flower bed.
After adding your flower bed, answer the following questions:
Questions
What is the area of your flower bed?
Hint 1 - Hint 2 - Hint 3
Hint 1: Area is connected to covering a surface.
Hint 2: In a scale drawing, area can be estimated by counting whole squares and then scaling back up to the true size.
Hint 3: Area is measured in square units. What will be the square units in this application?
How many feet of fencing will you need to buy?
Hint 1 - Hint 2 - Hint 3 - Hint 4
Hint 1: Fencing is related to perimeter.
Hint 2: The flower bed is shaped like a rectangle, but it only has three sides.
Hint 3: Which sides of the flower bed do you need to measure - the inside (against the patio), or the outside (against the garden)?
Hint 4: Which sides of the flower bed do you need to measure - the inside (against the patio), or the outside (against the garden)?
How many 4 foot panels will you need to buy?
Hint 1 - Hint 2
Hint 1: Did you take into account that you have to buy pieces that are 4 feet long?
Hint 2: Did you decide what to do if you could not use an exact number of 4 foot lengths for any of the sides of the flower bed?
How much will the trim cost?
Hint 1 - Hint 2
Hint 1: This is a proportional reasoning question.
Hint 2: How many panels will you need?
The flower beds will require 1 foot (depth) of soil. About how much soil will you need to order?
Hint 1 - Hint 2 - Hint 3
Hint 1: This is a volume calculation.
Hint 2: You can buy soil by the cubic yard.
Hint 3: The flower bed can be thought of as several rectangular prisms.
The Furniture
No patio would be complete without a nice table and chairs.
Consider the following questions:
Questions
The table has a diameter of 4 feet. The backs of the chairs need to be able to push 2 feet away from the table in order for people to sit down. About how much of the patio will the table and chairs use?
a. 28 - 36 sq. ft.
b. 36 - 50 sq. ft.
c. 50 - 64. sq. ft.
Answer
The correct answer is c.
You could draw a circular area around the table, and the space around the table and chairs would be about 50 square feet. But you could also draw a square around the table and chairs, and then the area would be 64 square feet.
The area of the purple circle around the table is about 50 sq. ft. The area of the square around the table is 64 sq. ft.
What is the total cost of the table and 4 chairs if the table costs $629 and each chair is $129?
a. $758
b. $1145
c. $2645
d. $3032
Answer
The correct answer is b.
Four chairs cost $516. The table costs $629. The total cost is $1145.
Select the correct scale drawing for the table and chairs from the two choices below.
The correct answer is b.
The scale shows that 1 square represents 2 feet, and the table is 4 feet in diameter so it uses 2 squares.
In answer a, the table would be 8 feet across.
Go back to your scale drawing and add the furniture. Make any adjustments you feel you need to make to create a wonderful new backyard living space.
If you completed your patio using grid paper, then you can add the furniture directly onto your design. If you completed your patio using the interactive, then you can quickly rebuild your patio in the interactive below and then add the furniture. Be sure to take a scerenshot of your finished patio.
This interactive allows shapes to be dragged on to a grid. The shapes represent the perimeter of the patio, the fireplace, the water feature, the flower bed and the patio furniture.
Introduction
Learning Goals and Success Criteria
Learning Skills and Work Habits
Rubric 1