Grade 8 Math Exit Project

What is an Exit Project?

In March we will begin work on 8th Grade Math Exit Project. You must complete an exit project in order to graduate in June. This project is intended to assess students’ knowledge of key mathematical concepts and skills.

The project will consist of three (3) parts focusing on three of the major areas of the Grade 8 course:

v Linear Relationships, Algebra and Graphing

v Geometry

v Percentages, ratios & proportions

You must show ALL your calculations

This exit project is due on ______

Part 1: Road Trip!

You have decided to go on a road trip over summer with some friends. You have three separate trips you want to take during the 2 months of summer break.

One is to a town a distance of 90 miles to see an old friend.

Another trip is to a shopping mall 120 miles away.

And the third is to see a concert in a city 250 miles away.

Finances are tight and you need to hire a car for the trip. There are three car hire companies for you to choose from.

v Bill’s Car Hire charges a base fee of $50 and then 20c per mile

v Crazy Johns Car Hire charges a base fee of $20 and then 30c per mile

v Cheap Drive Car Hire charges 40c per mile with no base fee

Task 1

Question 1 Construct a table with the costs for each company for distances up to 500 miles. You should include at least 5 different distances but more would be helpful.

Task 2

Question 2 Write a mathematical equation to show the cost of hiring a car for each company.

Task 3

Question 3 Which car hire place would you choose for each of your trips? Explain your choice in light of your answers to Tasks 1 & 2.

(Hint: For what distances is Bill’s Car Hire the cheapest? What about Crazy John? What about Cheap Drive?)

Task 4

Question 4 At what trip distance would Bill’s Car Hire and Crazy John cost the same?

Question 5 At what trip distance would Crazy John and Cheap Drive cost the same?

Question 6 At what trip distance would Bill’s Car Hire and Cheap Drive cost the same?

Task 5

Question 7 On the same set of axes, draw a graph for each car hire company. The horizontal axis is distance and the vertical axis is cost. Make sure your graph is large and that the horizontal axis extends to at least 500 miles.

Question 8 Find the coordinates of the intersection of the lines and label them.

Question 9 Comment of the significance of these points.

Enjoy your trip!

[Using Performance Indicators 7A7, 7A8, 7A10, 8A4, 8A15, 8A19]

Part 2: Where is my phone?

I seem to have lost my phone. I know where I last saw it but it has been moved since then and I need help to locate it.

It started at the coordinates shown in the diagram.

A (14, -12); B (14, -19); C (10, -19); D (10, -14); E (13, -14); F (13, -12).

v My Mom told me she translated it 6 units to the left

v Then my little brother said he had reflected it over the Y-axis

v My friend many found it and translated it 9 units up

v Dad said he tripped over it and reflected it over the X-axis

v My sister then rotated it 900 clockwise

v Uncle Jose translated it 5 units left and 4 units down

v Cousin Michelle then said she rotated it 900 clockwise

v Finally my dog picked it up and translated it 5 units down and 10 units to the right

Where is my phone?

[Using Performance Indicators 8G7, 8G8, 8G9, 8G10]

Part 3: Unit Pricing

Sometimes foods packed in the "giant" or "family" size may seem like the best buy. You may think that buying one large container will not cost as much as two or three smaller packages. But larger containers do not always end up costing you less than smaller ones. It is important to look at the cost per unit and compare this cost. The "unit price" tells you the cost per pound, quart, or other unit of weight or volume of a food package. It is usually posted on the shelf below the food. The shelf tag shows the total price (item price) and price per unit (unit price) for the food item.

You can save money when you compare the cost of the same food in different sized containers or different brands. For example, if you want to buy frozen orange juice you may find a 6-ounce can that cost $0.64. The unit price for this small can is $3.42 per quart. A 12-ounce can of frozen orange juice in another brand may cost $0.89. The unit price for the larger container of juice is listed as $2.38 per quart. Here, the larger container is cheaper per quart.

Unit pricing can help you decide what brand to buy. Store brands and little known brands often cost less than well-known national brands. The way the lower-priced brands look may be the only difference. (Be sure to check the Nutrition Facts panel on the food label to see if the nutrients are the same.) Sometimes these foods may vary in size, color, or texture more than the national brands. If you want a perfect peach half you may want to pay the price of a national brand. If you want sliced peaches to serve your child or as a quick snack, it may not matter if each slice is the same. You can save money when you compare the unit price of each of the canned peaches before you make your decision.

Task 1: Gathering the information

You need to go to the supermarket and find out the prices of some groceries.

Part A:

For 4 products you are to find the price and the size of three different sizes of the same product. For example, you can find three different size boxes of Corn Flakes and note down the price for each box and the weight of each box.

Part B:

For 4 products you are to note the price and size of three different brands of the same product. For example, you can find the price and weight of three different brands of tinned tomatoes.

Task 2: The analysis

a) For both parts A & B you are to present your collected information in a table that clearly lists the price, size and unit price of each product. Do separate tables for each part.

b) For Part A, indicate which size is the most economical and justify your choice.

c) For Part B, indicate which product is the most economical and justify your choice.

For b) and c) present your findings in both graphical and written from.

d) What is the percentage difference between the cheapest and the most expensive product for each product in Part B?

Task 3: Other considerations

“Foods that cost less per unit are not always the better buy.”

Discus this statement and suggest reasons why this might be the case.

[Performance Indicators: 8N.3; 8N.6; 7M.5; 7M.6; 8M.1]