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Pool Border Problem

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In this Desmos-ified treatment of a classic math problem, students will first construct expressions with numbers to determine the number of tiles that border a pool. Then they'll use those numerical expressions to help them write an expression with VARIABLES. Then they'll put the algebraic expression to the test and see if it helps them find the tiles for lots of pools very quickly. Translated by the Desmos localization team into: Spanish: https://teacher.desmos.com/activitybuilder/custom/5efa5eb945f50e629123f938 Translated by volunteers into: French: https://teacher.desmos.com/activitybuilder/custom/5a942a30d9f103093fb076e8

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Your job is to buy the right number of tiles for the border of different swimming pools. Continue to the next screen when you're ready.
1What is your job?
Without counting them one-by-one, how many orange tiles should you buy for the border of the Nguyens' 3 x 3 swimming pool? How do you know? Use the sketch tool if it helps illustrate your thinking.
2Here's a 3 x 3 swimming pool.
Without counting them one-by-one, how many orange tiles should you buy for the border of the Kelly's 5 x 5 swimming pool? How do you know? Use the sketch tool if it helps illustrate your thinking.
3Here's a 5 x 5 swimming pool.
How many orange tiles should you buy for the border of the Reyes' 10 x 10 swimming pool? Note that you can type expressions like $$2+2 in the space below. Press "Submit" to check your answer!
4Here's a 10 x 10 swimming pool.
How many orange tiles should you buy for the border of the Mason's 13 x 13 swimming pool? Note that you can type expressions like $$2+2 in the space below. Press "Submit" to check your answer!
5Here's a 13 x 13 swimming pool.
How many orange tiles should you buy for the border of the Coleman's 16 x 16 swimming pool? Note that you can type expressions like $$2+2 in the space below. Press "Submit" to check your answer
6Here's a 16 x 16 swimming pool.
The dimensions of this pool are $$n x $$n. We don't know the value of $$n though. How many orange tiles should you buy for a pool with a side length of $$n tiles?
7Here's an n x n swimming pool.
You have to buy tiles for 10 pools for 10 different families. We'll use the expression you entered on the previous screen to buy them quickly and automatically. Press "Buy Tiles" until you have seen the perfect number of tiles on all 10 pools.
8Let's test your expression.
A shopping list for tiles for five families' swimming pools. The Cruz family has 226 tiles. The Patel family has 256 tiles. The Anderson family has 100 tiles. The Cummings family has 484 tiles. The Kim family has 600 tiles.
Here is Sam's shopping list for tiles for five families' swimming pools. One of them is incorrect. Which one is incorrect?
9Fix the Error
In this activity you've seen expressions with NUMBERS like $$2·15+2·13 or $$56. You've also seen expressions with VARIABLES like $$4n+1. When is each kind of expression more valuable than the other?
10What makes numbers and variables valuable?
Measure
Measure
Summary | 1 Annotation
Let's
2020/11/21 22:30