Module 06: project option 1
instructions
sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. after collecting only three shark’s teeth, sarah decides to share the opportunity with her friend john. sarah can find shark teeth twice as fast as john, but she can earn even more money with his .

sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.

part 1: writing expressions
1. write an expression that looks like sarah’s expression: 5(2j + 3 + j). replace the coefficients so that your expression is not equivalent. you may use any number that you choose to replace the coefficients. be sure to leave the variables the same. for example, 8(3j + 7 + 3j) looks like sarah’s expression but is not equivalent.
25(10j + 18 + 5j)
2. translate the new algebraic expression you created in question 1 to a verbal expression.
skuttle offered to pay his sister izzy $25 for every four leaf clover she finds in the woods. izzy finds 18 clovers but decides to get roxy’s . izzy finds clovers twice as fast as roxy but they will over all make more money together.

the number to the left in my case the 25 is how much money they're getting paid (which will be multiplied by how many clovers they'll find). person a finds twice as much as person b (10/2 = 5). and the number in the middle of the parenthesis is how many person a found by themselves. hope this makes sense

part 2: writing equivalent expressions
3. use your knowledge of the mathematical properties to create two equivalent algebraic expressions for the algebraic expression you created in question 1. explain how you arrived at the equivalent expressions by showing all your steps and stating which properties you used.
4. use substitution to prove your algebraic expressions are equivalent. you may substitute any number for the variables you choose. show all your work for complete credit.

part 3: finish the story
5. write a few sentences to end sarah’s story. how many shark teeth did she find? how many shark teeth did john find? how much money did they earn?

Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.

Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.

Part 1: Writing Expressions

Q1.Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.

25(10j + 18 + 5j)
Your expression is good.

Q2.Translate the new algebraic expression you created in Question 1 to a verbal expression.



Skuttle offered to pay his sister Izzy $25 for every four leaf clover she finds in the woods. Izzy finds 18 clovers but decides to get Roxy’s help. Izzy finds clovers twice as fast as Roxy but they will over all make more money together.

Your verbal expression is good. It refrects your chosen equation.

Part 2: Writing Equivalent Expressions

Q3.Use your knowledge of the mathematical properties to create two equivalent algebraic expressions for the algebraic expression you created in Question 1. Explain how you arrived at the equivalent expressions by showing all your steps and stating which properties you used.

Using commutative property of addition, the expression in question 1 can be rewritten as follows:
25(10j + 18 + 5j) = 25(10j + 5j + 18)

Using distributive property of multiplication over addition, the expression in question 1 can also be rewritten as follows:
25(10j + 18 + 5j) = 250j + 450 + 125j

Q 4.Use substitution to prove your algebraic expressions are equivalent. You may substitute any number for the variables you choose. Show all your work for complete credit.

Now we can subsitute, say 7 for j.

For the first expression, we have:

25(10j + 5j + 18) = 25(10(7) + 5(7) + 18)
= 25(70 + 35 + 18) = 25(123) = 3,075.

For the second expression, we have:

250j + 450 + 125j = 250(7) + 450 + 125(7) = 1,750 + 450 + 875 = 3,075.

Thus, we can see that both expressions are equivalent.

Part 3: Finish the Story

Q5.Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did they earn?

Sarah found 3 + 7 = 10 shark teeth.

John found 10 / 2 = 5 shark teeth.

The total money they earned is $5 x 15 = $75.

A)26•2=52there are 2 sides with the same length116-52=64the other 2 side have to be half of 64 each64/2=32the width is 32b)make two sentences about these steps because your teacher knows how you write and explain things.