How Long Will You Live?

Be sure to tie it back in to the TV statistic/equation at the end

Pass out student whiteboards

Hook:

Discussion notes:

Credit: the idea for using that video clip came from the Mathalicious lesson called 22 Minutes. Here’s the Mathaliciouswebsite:
I think I’ll follow the Dan Meyer method here of asking the class what that clip makes them wonder. I should get all sorts of questions, but hopefully one of them will be, “how much does it shorten your life if you watch a certain amount of TV per day?”
Transition: guide the discussion toward writing an equation for your life expectancy based on H, the total # of hours of TV you’ve watched.
Whiteboard prompt. Let’s assume a healthy person lives to about age 80 without watching any TV. Write an equation for how long you’ll live if you watch H hours of TV. Let A = your age when you die, and let H = the number of hours of TV you’ve watched since you were 25.
Assuming a healthy person lives to about age 80, your age at death with TV factored in would be something like:
A = 80 – 22H.
But it’s more difficult than that, because 22 is in minutes, and we need it to be in years. Every hour of TV takes away how many years of your life? You could just convert it by typing into Google “22 minutes covert to years”.
Equation comes out to:
A = 80 – (4.18292e-5)H or
A = 80 – 0.00004183H
Ask several students: how many hours of TV do you watch per day? Take an average. If you watched that much TV every day for 30 years, what would your life expectancy be?
You can also ask the question backwards: If you want to live to at least age 79, how many total hours of TV can you watch? To answer this question, you have to be able to solve the equation 79 = 80 – 0.00004183H
Transition: last class, when we were learning how to model equations with algebra tiles, we never did any equations that had negative numbers or subtractions. Today we’re going to learn how to do that.
The equation we just wrote is a little complicated, because you can’t really show 0.00004183H with algebra tiles. Let’s try a simpler equation first.
Here’s a similar equation with easier numbers: 3 = 2 – 4x
Whiteboard prompt:How can we model it with algebra tiles to solve it?
[Take student suggestions. The difficult part here is modeling the subtraction. If you do this for the right side:

then you’re really modeling 2 + 4H.

Switch to powerpoint slides for the rest of this discussion and for #1-6. These slides build up to solving the equation 3 = 4 – 2x.
After the slides, I plan to hand out the algebra tiles and let everyone try#7-13.
If I think groups need my guidance when they start #7-13, I’ll have everyone start #14-21. Meanwhile, I’ll hand out algebra tiles to one small group at a time, checking their understanding of a few practice problems before letting them work independently. Groups will work on #14-21 while waiting for me to come over, but once I’ve left, they’ll work on #7-13 until they finish the algebra tiles section.

Here are some practice questions to check small groups’ readiness for #7 – 13:

a). 5x +1 = x[Solution: x = -0.25]

b). 3x + 4 = x – 2 [Solution: x = -3]

7). -3x + 2 = 8

[x = -2]

8). 5 + 2x + -1 = x + 1

[x = -3]

9). 3 – x = 3x

[x = 0.75]

10). 2(x – 1) = 4x + 8

[x = -5]

11). -1 + 3x + 5 = 6 – x

[x = 0.5]

12). 2x = 1 + x – 3x

[x = 0.25]

13). 2x – 3 = x + 1 + 3x + 4

[x = -4]

Transition notes:

If groups finish early, they’ll work on one of our next goals: scenarios whose equations have variables on both sides.
When every group is finished, I’ll discuss that we can’t finish solving our TV-and-lifespan equation (79 = 80 – 0.00004183H) until we learn how to solve equations on pencil and paper without Algebra tiles. We’ll do that next class. However, you can still figure it out without really solving an equation by doing this:
(0.00004183 years lost per hour of TV)(??? Hours of TV) = 1 year of life lost
Just divide 1/0.00004183 and you get 23906.7 hours of TV. To put that in perspective, that’s about 2 hours per day for 33 years.

Equations in Real Life, Episode #947

SCENARIO: The school soccer team is having T-shirts printed, and they’re trying to decide whether to get them from Custom Designs or National Shirts. The design has only 1 color.

14). For printing with a single color, Custom Designs charges a one-time set-up fee of $10 to prepare the design for your shirt, plus $4.00 per shirt. Fill out the table below for the cost of ordering from Custom Designs.

Ordering From Custom Designs

# of shirts / 2 / 3 / 10 / 12
Total cost ($) / 18 / 22 / 50 / 58

15). Write an equation for the cost of ordering from Custom Designs. Define your variables.

Let C = total cost and S = # of shirts. C = 4S + 10

16). Plot your points from the table on the graph below. Draw a dotted line through the points.

17). For single-color printing, National Shirts does not charge a set-up fee. Their shirts are $6.00, but the coach has a coupon for $5 off an order from them. Fill out the table below for the cost of ordering from National Shirts.

Ordering from National Shirts

# of shirts / 2 / 3 / 10 / 12
Total cost ($) / 7 / 13 / 55 / 67

18). Write an equation for the cost of ordering from National Shirts. Define your variables.

Let C = total cost and S = # of shirts. C = 6S – 5

19). Please go back to the graph in #16 and plot the data for the cost from National Shirts. Draw a solid line through these points.

See graph

20). Is it cheaper to buy from Custom Designs or from National Shirts, or does the answer depend on the situation? Be as specific as you can, and explain your reasoning.

If you’re buying 7 shirts or less, it’s cheaper to get them from National Shirts. You can see this on the graph because the solid line is lower than the dotted line when you’re at 7 shirts or less.

If you’re buying 8 shirts or more, it’s cheaper to get them from Custom Designs. You can see this on the graph because the dotted line is lower when you’re at 8 shirts or less.

21). How many shirts would you have to buy for the cost to be the same from both companies? How can you tell?

Discussion notes:

On the graph, you can see that the lines intersect between 7 shirts and 8 shirts, but it’s hard to tell exactly where.
Graphing can be a little inaccurate, especially if you’re estimating where to put the points on the graph because they fall between the grid lines.
In addition, graphing takes a fair amount of time.
There’s a faster way to find the intersection point by solving an equation. [Guide class through coming up with and solving the equation 4x + 10 = 6x – 5. If you have a document camera, you can show it on the blackline master for #21.

Licensing:

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Author:

Kevin Hall