Name: ___________________________________ Date: ____________________ Per: _____Expressions and ExponentsUNIT 1 PROJECTWrite your answers for each exercise in the space provided. You can use a scientific calculator, but be sure to show your work on a separate piece of paper, too. You may work together with other students, but make sure that you do your own, individual work, in your own words. Do not copy!PROJECT RUBRIC

EXERCISES POINTS EARNED(For teacher use only) POINTS POSSIBLEPART ONEExercise 1Exercise 2Exercise 3 12PART TWOExercise 4Exercise 5Exercise 6 15PART THREEExercise 7Exercise 8Exercise 9 8EXTRA CREDITCrosswordPuzzle 3TOTAL 35

Name: ___________________________________ Date: ____________________ Per: _____

Name: ___________________________________ Date: ____________________ Per: _____

PART ONE: REAL NUMBER OPERATIONS1) Compute each of the differences and answer the question. (4 pts) a. 62 – 38 = f. 38 – 62 =

b. 62 – 48 = g. 48 – 62 =c. 62 – 58 = h. 58 – 62 =d. 62 – 68 = i. 68 – 62 =e. 62 – 78 = j. 78 – 62 =k. What pattern(s) do you notice in the results of these computations?

2) For each expression below, write an equivalent expression from the box to the right. (4 pts)a. 7−2+(−3 )

b. 24÷6 •2c. 3+5 •2−(1−4 )2

MATCHING EXPRESSIONS−10+3 • 4

(25÷5−3 •(40))2

( 2552 + 2552 )4−1

1+−2 (24 )23

+10

Name: ___________________________________ Date: ____________________ Per: _____

d. (−4 )−(−11)

3) Matryoshka dolls, sometimes called Russian nesting dolls, are a set of wooden dolls made increasing in size, so that smaller dolls can fit inside larger ones. Each doll in a certain set is twice the height of the previous doll. Doll 1 in this set is 2 inches tall. Answer each question below. (4 pts)a. How tall is Doll 2?b. How tall is Doll 3?c. How tall would Doll 100 be? (You don’t need an exact answer here.)

d. A dollmaker wants to add smaller dolls to the set.How tall would Doll 0 be?

e. How tall would Doll –1 be?

f. How tall would Doll –2 be?

g. How tall would Doll –3 be?

Doll 1 Doll 2 Doll 3

Name: ___________________________________ Date: ____________________ Per: _____

h. How tall would Doll –100 be? (You don’t need an exact answer here.)

Name: ___________________________________ Date: ____________________ Per: _____

PART TWO: EXPRESSIONS4) Fill in the blanks in the steps with the information in parentheses to create your own number trick. Then, complete the table of starting and ending numbers below using the steps of your number trick. Simplify! (6 pts)STEPS:

Choose a starting number. Add __________ (your birth day number). Subtract __________ (your birth month number). Add __________ (your age). Subtract __________ (the last digit of your ID

number). The result is your ending number.

STARTING NUMBER ENDING NUMBER612−3

k

017−4

Name: ___________________________________ Date: ____________________ Per: _____

n

5) Complete the following exercises using the expression you wrote in the bolded box in exercise #4. (3 pts)a. Evaluate the expression from the bolded box for k=−3.b. How does that result relate to your answer in the box above the bolded box from exercise #4?c. Why do these results relate in this way?

6) Complete each exercise below to explore the distributive property. (6 pts)a. Show how you can use the distributive property to calculate the product 53 •101 in your head.

b. Assuming x≠0, simplify: x+2 x+3x+4 x+5xx . Then, explain why we must assume that x≠0 in this expression.

Name: ___________________________________ Date: ____________________ Per: _____

c. How does the image of the rectangle shown to the right represent using the distributive property to simplify the expression 5(x+7)?

Name: ___________________________________ Date: ____________________ Per: _____

PART THREE: POLYNOMIAL OPERATIONS AND FACTORING7) Simplify each expression, then answer the question. (4 pts)a. (x)+(2 x+5)

b. (x)+2( x+5)c. (x+2)( x+5)d. How do parentheses change the meaning of an expression?

8) Simplify: (2 x+2 )2−(2 x+1)2. (2 pts)

9) Factor out the Greatest Common Factor of the polynomial below. (2 pts)6 x3 y2−18x3 y+27 x2 y2−12 x2 y2 z

Name: ___________________________________ Date: ____________________ Per: _____

Name: ___________________________________ Date: ____________________ Per: _____

EXTRA CREDIT CROSSWORD: UNIT 1 VOCABULARY

ACROSS1. A number which can NOT be written as a fraction is said to be...3. If a polynomial contains two different variables, it is called...6. The product of two negative numbers is always...8. Terms with the same variable to the same power are said to be ___ terms.10. A type of term which does not have any variables.12. A number that is multiplied by a variable in an expressionDOWN2. The _____ of -7 is 74. The counting numbers, their opposites, and zero form the...5. A polynomial with three terms is called a...7. The word you can use to remember the Order of Operations

Name: ___________________________________ Date: ____________________ Per: _____

9. A symbol used to represent a value that can change, or an unknown11. A shortened way of saying "Greatest Common Factor"