Exponents
True or false: In 7^2, 7 is the exponent and 2 is the base.
False -- other way around!
Evaluate: 24 - 12 ÷ 6
22
Is 64 a perfect square?
Yes! (8 * 8)
Give an example for each.
Addition and multiplication
What is the value of the 5 in 2,153,927?
ten thousands / five ten thousands / fifty thousand
Write the product in exponential form: 5 * 5 * 5 * 5
5^4
Evaluate: 28 ÷ 7 * 8
32
70 is between ___^2 and ___^2
8^2 and 9^2
Which two operations are associative?
Give an example for each.
Addition and multiplication
Round 845,699 to the nearest ten thousand.
850,000
1296
Evaluate: (72 ÷ 3^2 + 2)^3 - 1
999
If a square has a side length of m units, what is the area of the square?
m^2 units
The distributive property applies when... _______
A sum is being multiplied by a number, e.g. (3 + 4) * 2
Name three perfect cubes.
1, 8, 27, 64, 125, etc.
Read this aloud: 4^10 * x^2 * y^3 * z^1
four to the tenth power, times x squared, times y cubed, times z to the first power
Evaluate: ((8 - 2) * 4^2) / (2 + 5 * 2)
8
Why is taking a number to the power of 3 called cubing?
3 represents the three dimensions of a cube being multiplied together to find its volume
Which property justifies this?
3 * (2 + 1) = 3 * (1 + 2)
Commutative property of addition
What's the distinction between 4 * 3 and 4^3?
4 * 3 means 4 groups of 3 or 12; 4^3 means 4 multiplied by itself 3 times, or 4 * 4 * 4 = 64
Evaluate x^3 * y^2 if x = 3 and y = 2
108
Evaluate: (16^2 - 7 * 8) / ((3 + 3^3)/3)
20
List all the perfect squares less than or equal to 50.
1, 4, 9, 16, 25, 36, 49
Which property or properties justify this?
2 * (9 + 1) = (2 * 1) + (2 * 9)
Distributive property (since the multiplier of 2 was distributed to the terms of the sum)
Commutative property of addition (since the order of the terms switched)
I have two secret numbers. Both are greater than 2.
Which result do you think will be bigger: the product of my two numbers, or one number taken to the power of the other number?
Explain your reasoning.
Certainly, one number taken to the power of the other number will be bigger!
[Desmos demonstration]