# Grade 8 Math

##### by dave james 06/04/2014

## Grade 8 Math

by dave james## 1. Percent, Rate and Ratio

### 1.1. Fractions = Decimals

1.1.1. Decimals = Fractions

1.1.1.1. Game: http://www.mathplayground.com/Decention/Decention.html

### 1.2. Decimals = Fractions

1.2.1. Fractions = Decimals

1.2.1.1. Vid: http://www.youtube.com/watch?v=NBzqxRIa9BY

### 1.3. Percents = decimals

1.3.1. Vid: http://www.youtube.com/watch?v=66934Q4VjkU

### 1.4. How to calculate a percent

1.4.1. Vid: http://www.youtube.com/watch?v=IRmiUD2nflA

### 1.5. How to calculate a fraction

1.5.1. take the number available as the numerator (the number on top) and take the total number possible as the denominator (the number on the bottom)...remember to record in lowest terms.

### 1.6. How to calculate a decimal

1.6.1. Divide the number given by the total number possible to calculate a decimal

### 1.7. How to Calculate sales tax

1.7.1. percent alone

1.7.1.1. take the regular price of an item and multiply it by the decimal form of the sales tax EX. $2.00 x 0.05 = $0.10

1.7.2. Price including tax

1.7.2.1. Multiply the original price by 1 and the decimal form of the sales tax. EX $2.00 x 1.05 = $2.10

1.7.3. http://www.youtube.com/watch?v=9Gzw9hM6-hU

### 1.8. How to calculate discounts

1.8.1. Discount alone

1.8.1.1. Multiply the original price by the decimal equivalent of the percent the item is reduced by. EX: a $2 item is sold for 25% 0ff : 2 x 0.25 = 0.50

1.8.2. price including discount

1.8.2.1. Multiply the original price by the decimal value of the percent not deduced: Ex if the sale on a $2 item is 25%, the percent NOT deducted is 75% or 0.75 : 075 x 2.00 = $1.50

### 1.9. Ratio

1.9.1. A RATIO is the comparison of two or more numbers, quantities, or measures

1.9.1.1. Video: https://www.youtube.com/watch?v=UxWsY59NVgc

1.9.1.2. part to part compares the quantities within various groups ex; blue smarties to red smarties

1.9.1.3. part to whole compares the quantities of individuals within groups to the grand total of individuals ex Blue smarties to all smarties

1.9.1.4. How do you represent (write ) a ratio A:B or A:B:C:D: ...

1.9.2. Equivalent Ratios

1.9.2.1. Similar to equivalent fractions, equvilant ratios are ratios that have the same proportional value with different numbers

1.9.2.1.1. in the example 3:5 you multiply the first and second term by the same number. 3:5 multiplied by 2 is 6;10 (Like 3/5 = 6/10)

1.9.3. Video https://www.youtube.com/watch?v=OkphNNHRKmE

1.9.3.1. Game: http://www.mathplayground.com/ASB_RatioBlaster.html

### 1.10. Comparing ratios

1.10.1. Method 1: First term- Make the first term of the ratios that are being compared identical.

1.10.2. Method 2: Second term- Make the second term of the ratios that are being compared identical.

1.10.2.1. ex: 4:6 and 3:5 can be converted to a ratio with a second term of 30 by multiplying the 1st ratio by 5 and the second ratio by 6.

1.10.2.1.1. What are some real life examples of times we may want to compare 4:6 and 3:5?

1.10.2.2. 4:6 and 3:5 = 20:30 and 18:30

1.10.3. Method 3: proportion to 1- make the second term equal 1

1.10.4. Further instruction: http://www.mathvillage.info/node/90

1.10.5. Problem: if Seth can do 200 back flips in 30 minutes and Dawson can do 375 back flips in 50 minutes, who can do the most back flips in a given time?

1.10.5.1. method 1) 200:30 x 15 = 3000:450 and 375:50 x 8 =3000:400

1.10.5.2. Method 2) 200 :30 x 5=1000:150 and 375 : 50 x 3= 1125:150

1.10.5.3. Method 3) 200/30 = 6.666 flips per min -and- 375/50 = 7.5 flips per min

## 2. Fractions

### 2.1. How to add & subtract fractions

2.1.1. Vid: http://www.youtube.com/watch?v=52ZlXsFJULI

### 2.2. How to multiply fractions

2.2.1. Game: http://www.mathplayground.com/ASB_SnowSprint.html

### 2.3. Equivilant fractions

2.3.1. Equivalent fractions are fractions are different fractions with the same value. both the denominator and the numerator of one fraction can be either multiplied or divided by one specific number to change them to a different fractionwiththe same value.

2.3.1.1. Example: 5/10 divided by 5 equals 1/5, so 1/5 and 5/10 are equivalent fractions.

2.3.2. Game: http://www.mathplayground.com/Triplets/Triplets.html

2.3.3. vid:: http://www.youtube.com/watch?v=Su4DKLbK8mA

## 3. Linear Equations and Graphing

### 3.1. What is a Linear Equation?

3.1.1. https://www.youtube.com/watch?v=tdiNDwKOBvw

3.1.2. An equations that between 2 variables that creates a straight line when plotted on a graph

3.1.3. Linear Equations games http://www.elkriver.k12.mn.us/elkriver_highschool.cfm?subpage=26155

3.1.4. Ex:

3.1.5. Game:Save the Zlogs http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.html

### 3.2. a) What is "distributive property"? b) What is a "linear relation"? c) What is an "ordered pair"? d) What is "discrete data"?

3.2.1. Linear relation:

3.2.1.1. A relationship that occurs when variable quantities are directly proportional to one another. A linear relationship can be represented on a graph as a STRAIGHT LINE. Linear relationships always follow the formula: y=mx+b where y is the value of the y-coordinate, where my is the slope of the line, where x is the value of the x-coordinate, and b is the y-intercept

3.2.1.1.1. https://ca.answers.yahoo.com/question/index?qid=20071201142939AAhqYby

3.2.2. Distributive property

3.2.2.1. Distributive Property The Distributive Law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately http://www.mathsisfun.com/definitions/distributive-law.html

3.2.2.2. a(b +c) = ab +ac

3.2.2.2.1. 5(3 + 4) = 15 + 20 = 35

3.2.2.3. distributive property

3.2.2.4. Cute lil video explaining dist. prop. https://www.youtube.com/watch?v=QzwvSp-ZtBY

3.2.3. Ordered Pair

3.2.3.1. Two numbers written in a certain order. Usually written in parentheses like this: (4,5) Can be used to show the position on a graph, where the "x" (horizontal) value is first, and the "y" (vertical) value is second.

3.2.3.1.1. http://www.mathsisfun.com/definitions/ordered-pair.html

3.2.4. Discrete Data

3.2.4.1. Data that can only take certain values. For example: the number of students in a class (you can't have half a student).

3.2.4.1.1. http://www.mathsisfun.com/definitions/discrete-data.html

### 3.3. Expressing and solving linear equations with tiles https://www.youtube.com/watch?v=iTXrUQ2VadA

3.3.1. 5 rules for solving liniear equations with algebra tiles (based on video)

3.3.1.1. 1-When we have a positive and a negetive tile on the same side of an equation, they cancel each other out

3.3.1.2. 2-Tiles that are the same color and size on OPPOSITE sides of an equation, they cancel each other out

3.3.1.3. 3) We can eliminate tiles by creating equal groups

3.3.1.4. 4) We can move from one side to another , by flipping the tile

3.3.1.5. 5) When solving an equation with tiles you shoudl always move all the x tiles onto the right side of the equation

3.3.2. http://www.quia.com/rr/42586.html

### 3.4. Solving linear equations with fractions https://www.youtube.com/watch?v=10TJfOy3H-w

3.4.1. Step 1- WE DON'T NEED NO STINKING FRACTIONS!!!...So lets get rid of them

3.4.1.1. Step 2: Find the LCM of the fractions

3.4.1.1.1. Step 3"Multiply each operation by the LCM

### 3.5. Solving a linear equation with a t-chart

3.5.1. a. Write original question at the top b. After each change to the equation rewrite the equation with new values c. Circle the final answer d. Check response

### 3.6. Table of values

3.6.1. a table of values is a chart consisting of rows and columns used to express incoming and outgoing measurements or values

3.6.2. The points on a table of values can be represented on a graph

3.6.3. Key terms: Table of Values Input Output Linear relation Ordered pair

### 3.7. Graphing and equation

3.7.1. y=mx + b (y-intercept formula)

3.7.2. Example: y= 3x + 4

3.7.3. b is the point along the y axis that intercepts the plotted line, the line would cross the y axis at +4

3.7.4. m is the slope (rise over run. Since the example shows whole numbers, the rise is +3 and the run is +1 (3 up and 1 to the right)

3.7.5. x- is our input variuble, and this will determine the value of y for any given input

3.7.6. Game: http://hotmath.com/hotmath_help/games/kp/kp_hotmath_sound.swf

3.7.7. Instructional vid: https://www.youtube.com/watch?v=miG-JhttnZo