Know and apply the properties of exponents to generate equivalent numerical expressions.
Use square root and cube root symbols to represent solutions to equations.Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
Solve linear equations in one variable.
Writing and Solving one and two-step equations using one variable.
MATH VOCABULARY
100
Write the following with exponents: 31 x 31 x 53 x 53 x 53 x 53 21 x 21 x 45 x 45 x 45 x 82 x 82
31^2 x 53^4 21^2 x 45^3 x 82^2
100
Which of the following is a perfect square? How do you know? a. 20 b. 9 c. 8 d. 18
B – 9 is a perfect square. I know this because if I make a square out of it, there are 3 on each side – which makes it a perfect square.
100
Write an equation to show the cost of apples at David’s Orchard, where p = pounds. Cost =
David’s Cost = $2(10) + $1p
100
A large pizza pie with 15 slices is shared among p students so that each student's share is 3 slices.
3p = 15 Students show work: 15 = 3P 3p (÷3) = 15 (÷3) p = 5
100
What is an operation? And give three examples.
Operation is an math sign or function of an equation example: subtraction, multiplication, division, addition
200
Evaluate 43. Explain how you solved the problem
48 Student explains that 43 is the same as 4 x 4 x 4. 4 x 4 = 16. Then 16 x 4 = 48, so the answer is 48.
200
Which of the following is a perfect cube? How do you know a. 16 b. 25 c. 100 d. 125
125 is the perfect cube. I know this because I tried a few numbers and 5s worked out.
200
Write an equation to show the cost of apples at Pam’s Orchard, where p = pounds. Cost =
Pam’s Cost = 10 + $1.50(10) + $0.75p
200
Fatimah has 40 quarts of ice cream to distribute amongst the four grades at her school. Write an equation to represent the number of quarts each grade will receive.
4i= 46 Students show work: i = 46 4i (÷4) = 40 (÷4) i = 10
200
What is a variable?
The unknown! The variable is represented with a letter in the equation and it is what we are trying to find out.
300
Faced with the problem of multiplying 56 times 53, Brook is having trouble deciding which of these four answers is correct. Which of these is correct and explain how you know: a) 5^18 b) 5^9 c) 25^18 d) 25^9
B) 5^9 when you have two like numbers with being multiplied by one another you add the exponents creating 59.
300
8. Find the length of one square whose area is 64.
8X8= 64 STUDENTS DRAW AN 8 BY 8 SQUARE!
300
How much does this cost at David’s Orchard?
$50.00 $2(10) + 1(30) (I put 30 there because it’s 40 pounds – 10 pounds of the first) 20 + 30 = 50
300
Stacey delivers newspapers. She earns $15 each week plus $2 for each customer on her route. Write an equation that can be used to find c, the number of customers she needs to earn exactly $25 each week? Show your work and solve for
15 + 2c = 25 Students show work: 15 +2c = 25 15 (-15) +2c = 25 (-15) 2c (÷2) = 10 (÷2) C = 5
300
What is a rational and irrational number give two examples of both.
rational: whole number, repeated decimals, 1/4 and 89.02020202 irational: pi and 67.787889028938 square root of 2
400
Which of the following expressions is not equivalent to 1/25: Explain your answer. 53 x 5-5 5-1 x 5-1 5-3 x 5 5-2 x 54
D: 5-2 x 54 Student explains that a) is equivalent to 5-2, b) is also equivalent to 5-2, and c is also equivalent to 5-2, which all create the fraction 1/25. The only one that does not do this is D. 5-2 x 54 = 25.
400
Kendall is trying to plan his 16th birthday at the movie theater. The more people he brings the less it costs per person. The formula he can use to figure out how much it is going to cost is c = √p + 10, with c = cost and p = people.
P, People 4 16 25 36 49 C, Cost 12 14 15 16 17
400
How much does it cost at Pam’s Orchard
30 = 2(10) + 1p 30 (-20)= 20 + p (-20) 10 = p 10+10 = 20 pounds total (I added 10 pounds to the total because of the original 10 lbs)
400
One set of furniture set contains one table and four chairs. A single table costs 80 dollars and the whole furniture set costs 200 dollars. How much is one chair in this case?
4c+80= 200 c=30
400
What is a cube root and square root? Give an example. for both.
Cubed root: a special value that when cubed gives the original number 25 is a cube root foor>>>> 125 A square root of a number is a number that, when multiplied by itself, equals the given number. (Every number has a positive and negative square root.) 4 is a square root for >>16
500
Write the following integer exponent in fraction form: 32 x 3-5. Show your work.
32 x 3-5 = 3-3 ; 3-3 = 1/3 x 1/3 x 1/3 1/3 x 1/3 = 1/9 ; 1/9 x 1/3 = 1/27
500
Sarah has 56 square tiles. She wants to make a perfect square out of those tiles. Which of the following must she do – explain how you know. a. Subtract 6 from the 56 tiles she has b. Add 6 to the 56 tiles she has c. Subtract 7 from the 56 tiles she has d. Add 7 to the 56 tiles she has.
Sara needs to subtract 7 from the 56. She needs to do this because when she subtracts 56 – 7, she gets 47. I know that 49 is a perfect square.
500
Chris has $30 to spend. If Chris goes to Pam’s Orchard, how many pounds will he get? Show and explain how you figured it out.
30 = 10 + 1.50 (10) + 0.75p 30 (-25) = 10 +15 + 0.75p (-25) 5 (÷0.75) = 0.75p (÷0.75) a. = p +10 pounds = 16.33 pounds total (added 10 pounds because of the original 10 lbs)
500
Last week Julia ran 30 miles more than Pranav. Julia ran 47 miles. How many did Pranav run?
47=p+30 p=17
500
What is a perfect square and perfect root? Give an example for both.
A perfect square is a number made by squaring a whole number. i.e. 16 is a perfect square because 42=16; 25 is also perfect because 52 =25 Perfect cube: a whole number that is cubed 125 >>>5
M
e
n
u