50 POINTS FOR THE FIRST ONE TO ANSWER Module Six 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 help.
Sarah can use the expression 5(2j + 3 + j) to represent the amount of money she can earn.
Part 1: Writing Expressions
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.
Translate the algebraic expression you created in Question 1 to a verbal expression.
Part 2: Writing Equivalent Expressions
You will now use mathematical properties to create two expressions that are equivalent to the expression you created in Question 1. Make sure you show all steps in your work.

Use either the commutative property or combine like terms to create an equivalent expression.
Use the distributive property to create an equivalent expression.
Pick a number from 1 to 10. Use that number to verify your three expressions (the original, the one from 3a, and the one from 3b) are equivalent by substituting it into each expression. Show all your work for complete credit.
Part 3: Finish the Story
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 Sarah earn?
Choose a method to present your assignment. You may submit your work in a Word Document or you may choose to develop a PowerPoint presentation or video recording of yourself. Use your creativity! Make sure to include the information from all three parts in your Word Document or presentation.
What to Submit
Name the assignment 06_07_EquivalentExpressions _Your Name.
In the Assessment Area, submit your work to 06.07 Equivalent Expressions.
Rubric
Look over the grading rubric to see how you will be evaluated.

Perfect!
Almost there!
Not quite yet!
Keep going!
Part 1: Writing Expressions
10 points
Both the expression and verbal translation are correct and clearly explained.
9−7 points
Most of the expression and verbal translation are correct and clearly explained.
6−3 points
Some of the expression and verbal translation are correct and clearly explained.
2−0 points
Few or none of the expression and verbal translation are correct and clearly explained.
Part 2: Writing Equivalent Expressions
15 points
All the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.
14−11 points
Most of the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.
10−7 points
Some of the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.

6−0 points
Few or none of the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.
Part 3: Finishing the story
5 points
Ending of story matches equivalent expressions, and presentation has all the required information.
4 points
Ending of story matches most of the equivalent expressions, and presentation has most of the required information.
3 points
Ending of story matches some of the equivalent expressions, and presentation has some of the required information.
2−0 points
Ending of the story has almost none to no match to the equivalent expressions, and presentation has few to none of the required information.
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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 help.

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

Part 1: Writing Expressions

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.

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

Part 2: Writing Equivalent Expressions

You will now use mathematical properties to create two expressions that are equivalent to the expression you created in Question 1. Make sure you show all steps in your work.

Use either the commutative property or combine like terms to create an equivalent expression.

Use the distributive property to create an equivalent expression.

Pick a number from 1 to 10. Use that number to verify your three expressions (the original, the one from 3a, and the one from 3b) are equivalent by substituting it into each expression. Show all your work for complete credit.

Part 3: Finish the Story

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 Sarah earn?

Choose a method to present your assignment. You may submit your work in a Word Document or you may choose to develop a PowerPoint presentation or video recording of yourself. Use your creativity! Make sure to include the information from all three parts in your Word Document or presentation.

What to Submit

Name the assignment 06_07_EquivalentExpressions _Your Name.

In the Assessment Area, submit your work to 06.07 Equivalent Expressions.

Rubric

Look over the grading rubric to see how you will be evaluated.

Perfect!

Almost there!

Not quite yet!

Keep going!

Part 1: Writing Expressions

10 points

Both the expression and verbal translation are correct and clearly explained.

9−7 points

Most of the expression and verbal translation are correct and clearly explained.

6−3 points

Some of the expression and verbal translation are correct and clearly explained.

2−0 points

Few or none of the expression and verbal translation are correct and clearly explained.

Part 2: Writing Equivalent Expressions

15 points

All the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.

14−11 points

Most of the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.

10−7 points

Some of the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.

6−0 points

Few or none of the mathematical properties and substitution steps are used correctly to prove two expressions are equivalent.

Part 3: Finishing the story

5 points

Ending of story matches equivalent expressions, and presentation has all the required information.

4 points

Ending of story matches most of the equivalent expressions, and presentation has most of the required information.

3 points

Ending of story matches some of the equivalent expressions, and presentation has some of the required information.

2−0 points

Ending of the story has almost none to no match to the equivalent expressions, and presentation has few to none of the required information.

Save | Print

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step-by-step explanation:

because mean value defines that total sum value over total number of set

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)