1. Complete the following in your groups. Name the property being used: a). (5 + 2) + n = 7 + n b). For any numbers a, b, and c, if a = b and b = c, then a = c. c). For any number a, a + 0 = a. d). For any numbers a and b, a + b = b + a and ab = ba. e). If 3 + 2 = 5, then 5 = 3 + 2. f). x = x g). 2 + 6 = 2 + 6 h). y(0) = 0 i). 9(1) = 9

2. Properties continued: a). Name two properties used to evaluate b). Evaluate. Name the property used in each step.

3. Graph the set of numbers a). {-2, -1, 0, 4} b). {all integers greater than 2}

4. Translate the expression into a verbal or algebraic expression. a). b). c). Three times the cube of a number. d). Eight to the fourth power increased by six

5. Perform the indicated operations: a). 12 + - 4 b). – 10 – 3 c). 13 - - 2 d). – 32 ÷ - 4 e). f).

6. Answer the following questions and translate into a numeric expression : a). The chefs added 6 hot cubes to the cauldron and then removed 2 hot cubes. How many hot cubes were left in the cauldron? What was the temperature? b). The chefs added 10 hot cubes in the cauldron and then removed 20 cold cubes. How many hot cubes were left in the cauldron? What was the temperature?

7. Tell a Story to represent each equation a). Create a situation. b). Ask a question so that your reader knows what he/she is solving for. c). Define a variable and explain what the variable represents. d). SOLVE! Write your solution as an answer to the question. a). x + 10 = 27 b). c). 3m – 3 = 9

8. Using the Mystery Bags model, complete both a visual and an algebraic or verbal representation of the following situations. Then, you need to help the king find the amount of gold in each mystery bag. a). There are five mystery bags and fourteen ounces of lead weights on one side of the pan balance, and twelve mystery bags on the other side of the pan balance. b). There are six mystery bags and two ounces of lead weights on one side of the pan balance, and six mystery bags and two ounces of lead weights on the other side of the pan balance.

9. Using the Mystery Bags model, complete both a visual and an algebraic or verbal representation of the following situations. Then, you need to help the king find the amount of gold in each mystery bag. a). There was one mystery bag and 3 ounces of lead weight on one side of the pan balance and 14 ounces of lead weight on the other side. b). There were 5 mystery bags on one side of the pan balance and 65 ounces of lead weight on the other side of the pan balance.

10. Using the Mystery Bags model, complete both a visual and an algebraic or verbal representation of the following situations. Then, you need to help the king find the amount of gold in each mystery bag. a). 4M = 16 b). 2M + 13 = 15

11. Simplify the following: a). d). b). e). c).

12. a). Evaluate the following expression if a = 12, b = 5, and c = 4 : b). Evaluate the following expression if x = 12, y = 8, and z = 6 :