Rates
A car can go 99 miles on 3 gallons of gas. What is the car's gas mileage? (hint: find the unit rate)
99 / 3 = 33 mpg (miles per gallon)
The following expression was written to describe a collection of algebra tiles.
4x² + x² + 4 + 2x + 1x + 5
Combine like terms and rewrite the expression in its simplest form.
5x² + 3x + 9
What is the method we have talked about the most in class for how to divide fractions? Describe it in words and then give an example.
The Keep Change Flip method. Keep the first fraction the same, change the division symbol to multiplication, and then flip the last fraction. (change the numerator and the denominator around)
Example: 1/4 / 1/8 = 1/4 x 8/1 = 8/4 = 2
Multiple Choice: What does the Distributive Property in math tell us? (a, b, and c are just variables standing for numbers)
A. a(b + c) = ab + ac
B. a + b = b + a
C. a - b = c
A. a(b + c) = ab + ac
Example: 3(x + 4) = 3x + 12
Write an ALGEBRAIC expression that would result from these steps.
1. Pick a number.
2. Add 4.
3. Multiply by 3.
3(x + 4)
or
3x + 12
A red car can go 200 miles on 5 gallons of gas. A blue car can go 114 miles on 3 gallons of gas. Which car has a better gas mileage? (hint: find the mpg for each car (the unit rate) and compare them) Make sure you explain how you know which car has the better gas mileage.
The red car has an mpg of 40. (200 /5 = 40)
The blue car has an mpg of 38. (114 / 3 = 38)
The red car has a better gas mileage because it goes 40 miles on a gallon of gas while the blue car only goes 38 miles on a gallon of gas.
Click the link below and look at question #1.
https://docs.google.com/document/d/11lZxJpcniXKnl4WPe0zMvqFfCD1haB5EezN1S08aV4A/edit?tab=t.0
Write an algebraic expression for the collection of the tiles. (area) Make sure to combine like terms.
4x² + 5x + 27 units²
Click the link below and look at question #2.
https://docs.google.com/document/d/11lZxJpcniXKnl4WPe0zMvqFfCD1haB5EezN1S08aV4A/edit?tab=t.0
Divide the fractions using the Keep Change Flip method. Simplify or make a mixed number if possible. This will be required on the test to get a 3!
18/20, but you need to simplify, so the correct final answer is...
9/10
Write the following expression without parentheses using the Distributive Property.
5(x + 2)
5x + 10
Write ALGEBRAIC expressions for EACH step of this magic trick.
1. Pick a number.
2. Multiply by 2.
3. Add 6.
4.Subtract 2.
5. Divide by 2.
6. Subtract original number.
1. x
2. 2x
3. 2x + 6
4. 2x + 4
5. x + 2
6. 2
Ms. Robinson can knit 4 sweaters in 176 minutes. Assuming it takes her a set amount of time to knit each sweater, how long would it take her to knit 7 sweaters?
44 x 7 = 308 minutes to knit 7 sweaters
Let's say this is an algebraic expression representing the area of a collection of algebra tiles.
4x² + 4x + 27 units²
Evaluate the expression when x = 2.
4(2)² + 4(2) + 27
(using Dorito Math step by step)
51 units²
Click the link below and look at question #3.
https://docs.google.com/document/d/11lZxJpcniXKnl4WPe0zMvqFfCD1haB5EezN1S08aV4A/edit?tab=t.0
Divide the fractions using the Keep Change Flip method. Simplify or make a mixed number if possible. This will be required on the test to get a 3!
40/12, but you can simplify this answer, so the correct final answer is...
3 and 1/3
Click the link below and look at question #6.
https://docs.google.com/document/d/11lZxJpcniXKnl4WPe0zMvqFfCD1haB5EezN1S08aV4A/edit?tab=t.0
The picture shows algebra tiles. The green tiles are x tiles and the yellow tiles are unit tiles.
Write TWO expressions for the collection of algebra tiles, one with parentheses and one without.
3(x + 1)
3x + 3
Draw the algebra tile drawings to go along with these three magic trick steps.
1. Pick a number.
2. Add 3.
3. Multiply by 4.
You should have drawn...
1. An x-tile
2. An x-tile with three unit tiles to the right of it in a row
3. Four rows total with one x-tile and three unit tiles in each row
Which is a better deal?
3 pounds of apples for $2.50
or
5 pounds of apples for $3.89?
5 pounds of apples for $3.89 because those apples only cost about 77 cents per pound while the other option costs over 80 cents per pound
Let's say this is an algebraic expression representing the area of a collection of algebra tiles.
3x² + 2x + 11 units²
Evaluate the expression when x = 3.
3(3)² + 2(3) + 11
(using Dorito Math step by step)
44 units²
Click the link below and look at question #4.
https://docs.google.com/document/d/11lZxJpcniXKnl4WPe0zMvqFfCD1haB5EezN1S08aV4A/edit?tab=t.0
Divide the fractions using the Keep Change Flip method. Simplify or make a mixed number if possible. This will be required on the test to get a 3!
50/12, but you need to simplify your answer as much as possible, so the correct final answer is...
4 and 1/6
Write the following expression WITH parentheses. You may use your factor chart to help you.
5x + 25
5(x + 5)
What is an inverse operation? Give an example.
An inverse operation is an operation that "undoes" the effect of another operation, meaning it reverses the action of the original operation. We also sometimes say this operation "cancels out" another operation.
Example: The opposite of adding 4 is subtracting 4.
2/8 / 10 = 2/8 x 1/10 = 2/80 cups of sugar in each brownie (which simplifies to 1/40)
Let's say this is an algebraic expression representing the area of a collection of algebra tiles.
3x² + x² + 2x + 10 + 3x + 1 + 1 units²
Your two tasks are...
1) Combine like terms to simplify the expression.
2) Evaluate the expression when x = 4
Expression: 4x² + 5x + 12 units²
4(4)² + 5(4) + 12
(Simplify using Dorito Math)
100 units²
Click the link below and look at question #5.
https://docs.google.com/document/d/11lZxJpcniXKnl4WPe0zMvqFfCD1haB5EezN1S08aV4A/edit?tab=t.0
Divide the fractions using the Keep Change Flip method. Simplify or make a mixed number if possible. This will be required on the test to get a 3!
18/1, but you can simplify that, so the correct final answer is...
18
Write the following expression WITH parentheses. You may use your factor chart to help you.
10r + 14
2(5r + 7)
How many unit tiles do you have to add to get from
3(x + 4)
to
3x + 20
8 unit tiles
because 3(x + 4) = 3x + 12, so 8 more unit tiles are needed to get to 20