Minds On

Which one doesn’t belong?

3 – 2x = 15

2x – 6 = -18

6x + 40 = 4

8x – 12 = 36

Examine the following equations and decide which one doesn’t belong.

Can you find a reason why each of the equations might not belong? What is the rule for sorting that would justify your choice?

Record your thinking using a method of your choice.

Press ‘Answer’ to reveal possible answers to the problem.

Possible answers: I think the first one doesn’t belong because there are odd numbers in the equation. The other three equations have only even numbers.

I think the fourth one doesn’t belong because the solution is x = +6, and in the other three the solution is x = -6.

I think the third one doesn’t belong because it is an addition equation, and the other three are subtraction.

I think the second one doesn’t belong because the answer is a negative number. The other three equations are all positive answers.

Action

Task 1

Consider the following problem:

Each student at school is given 7 folders on the first day of school.

The number of folders provided to students could be expressed as 7n (where n = number of students).

  • If there are 120 students in the school, then n would be 120.

The number of folders would be:

7 × 120 = 840 folders.

  • If there are 204 students in the school, then n would be 204.

The number of folders would be:

7n

7 (204) =

How many folders would there be on the first day of school?

  • If there are 455 students in the school, how many folders would they need on the first day of school? Write the expression and solve!

Press ‘Answer’ to reveal the answer to the problem.

7n

7 (455) = 3,185

There would be 3,185 folders on the first day of school.

2. A package of blank books contains 9 books.

a) Write an expression to represent the number of books found in p packages.

b) Calculate the number of books that will be found in 25 packages.

Press ‘Hint’ to reveal a hint for this problem.

Hint: p = 25

3. Eggs are sold by the dozen.

a) Write an expression to determine the number of eggs in d dozen.

b) Determine the number of eggs in 6 dozen.

Press ‘Answer’ to reveal the answer to this problem.

A) 12 d

B) 12 (6) = 72. There are 72 eggs in 6 dozen.

Task 2: Internet data plans

Game developer 1, Game developer 2, and Game developer 3, are comparing their internet data plans. They each have a different contract with the same company.

Game developer 1 agrees to pay $5 for every GB of data he uses.

Game developer 2 agrees to pay a $25 fee plus $2.50 for every GB she uses.

Game developer 3 pays a $50 fee plus $0.75 for every GB she uses.

Answer the following questions digitally, orally or in print or by creating a detailed description.

  • Create an algebraic expression for each plan.
  • Use your expressions to find what each game developer will be charged for 5GB, 10GB, 100GB of data.
  • What recommendations would you make? What is a reason someone might choose Game developer 1’s plan? Game developer 2’s plan? Game developer 3’s plan?

Press ‘Answer’ to reveal the possible solutions.

Game developer 1 = Gd1

Game developer 2 = Gd2

Game developer 3 = Gd3

Let n be the number of GB of data.

  1. G d 1 : $ 5 n
    G d 2 : $ 25 + $ 2.50 n
    G d 3 : $ 50 + $ 0.75 n
  2. 5 GB:

    Gd1 $ 5 n = 5 ( 5 ) = $ 25 Gd2 $ 25 + $ 2.50 n = $ 25 + $ 2.50 ( 5 ) = $ 25 + $ 12.50 = $ 37.50 Gd3 $ 50 + $ 0.75 ( 5 ) = $ 50 + $ 3.75 = $ 53.75

    10 GB:

    Gd1 $ 5 n = $ 5 ( 10 ) = $ 50 Gd2 $ 25 + $ 2.50 ( 10 ) = $ 25 + $ 25 = $ 50 Gd3 $ 50 + $ 0.75 n = $ 50 + $ 0.75 ( 10 ) = $ 57.50

    100 GB:

    Gd1 $ 5 n = $ 5 ( 100 ) = $ 500 Gd2 $ 25 + $ 2.50 ( 100 ) = $ 25 + $ 250 = $ 225 Gd3 $ 50 + $ 0.75 n = $ 50 + $ 0.75 ( 100 ) = $ 125
  3. I think I would recommend Game developer 1’s plan if someone didn’t need a lot of data. If someone needs a little more but not a whole lot, I would still recommend Game developer 1’s plan because it still cheaper and only equals Game developer 2’s plan at 10GB. At 10GB, I would choose either Game developer 1 or Game developer 2’s plan. Once it gets to 100GB I would definitely go with Game developer 3’s plan because the price is quite low in comparison.

Consolidation

Part-time earnings

Decorative

A florist gets paid $9 an hour on the weekend, and $7 an hour on weekdays.

Answer the following questions using a suitable method, and record your ideas digitally, orally or in print or by creating a detailed description.

  • Record an expression for their earnings.
  • If the florist works 8 hours during the week, and 12 on the weekend, how much will they earn that week? Use your equation to calculate.
  • The week later they worked 12 hours during the week, and 8 hours on the weekend. How much less did they earn?
  • Why might it be harder for the florist to work more hours on the weekend?

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel...

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.