Math 6 Boot Camp Review

6.4 Multiplying and Dividing Fractions using Models•Multiplication: One fraction is your rows,

the second your columns. The numerator (top) is how many are shaded, the denominator (bottom) is how many total rows/columns. Answer = the number of boxes double shaded over the total number of boxes

•Ex: ¼ x ½•Ex: 3 x ½

Don’t Forget…• Division: Remember that in division you are

seeing how many parts it takes to make the first part. Model the first fraction. Draw a box to match exactly underneath it. Cut the bottom box into the denominator of the second fraction. Shade the bottom to match the top. The numerator of the second fraction tells you how many make a group. Answer = the number of groups.

• Ex: ¾ ÷ • Ex: 3 ÷ ¾

6.8 Order of Operations

•Please (Parentheses)•Excuse (Exponents)•My (Multiplication)•Dear (Division)•Aunt (Addition)•Sally (Subtraction)

•Ex: (15 ÷ 5)³ - 9 + 1•Ex:

*Remember: Multiplication and Division you do in the order you see them.

*Remember: Addition and Subtraction you do in the order you see them.

6.9 Metrics1. 1 inch is about 2.5 centimeters2. 1 foot is about 30 centimeters3. 1 meter is a little longer than a yard (40 inches)4. 1 mile is slightly farther than 1.5 kilometers5. 1 kilometer is slightly farther than ½ a mile6. 1 ounce is about 28 grams7. 1 pound is 16 ounces8. 1 nickel has the mass of about 5 grams9. 1 kilogram is a little more than 2 pounds.10. 1 quart is a little less than a liter11. 1 liter is a little more than a quart12. Water freezes at 0 degrees Celcius and 32 degree F13. Water boils at 100 degrees Celcius and 212 F14. Normal Body temperature is about 37 degrees C and 98

degrees F15. Room temperature is about 20 degrees celcius and 70 degrees

F

6.9 Metric Examples

•Ex: What number of meters equals 24 yards?

•Ex: How many liters is equivalent to 3 gallons?

•Ex: If a pencil is 8 inches long, how many centimeters is that?

•Ex: If Tom runs 10 kilometers, how many miles did he run?

•On the moon April weighs 60 kilometers, how much does she weigh on earth in pounds?

6.18 Equations

•Write your equation down and draw the line through the equals sign

•Goal: to get the variable by itself•Perform the inverse (opposite) operation to

get rid of the number attached to the variable

•What you do to one side, you must do to the other side.

•Ex: y – 1 ¾ = 3•Ex:

6.18 Equations Vocabulary

•Equation – has an = sign•Expression – has NO = sign•Coefficient – the number in front of the

variable 3x•Variable – the letter in the equation or the

expression 3x•Term – each section of an equation or an

expression separated by a +, -, or =.•Ex: 3 + 2x = 9

6.18 Models

6.7 Computation of Decimals• When working with word

problems you have to read the problem carefully.

• Determine what the question is asking.

• Eliminate the given information that you don’t need.

• Determine what operation is needed to solve the problem.

6.7 Decimal Examples• Ex: Jill bought items costing $3.45, $1.99, $6.59, and $12.98.

She used a coupon worth $2.50. If Jill had $50.00 when she went into the store, how much did she have when she left?

• Ex: Samuel bought 4 rolls of tape to seal boxes. Each roll contains 32.9 meters of tape. He uses 1.2 meters of this tape to seal each box. What is the total number of boxes Samuel can seal with these 4 rolls of tape?

• Ex: Alisha wants to buy a camera that cost $228, including tax. She has saved $4.75 each week for the past 8 weeks. How much more money does Alisha need to purchase the camera?

• Ex: The regular price of a meal is $6.75. On Tuesday, the meal is on sale for $2.00 off the regular price. Sarah bought 4 of these meals on Tuesday. What is the total cost of these 4 meals before tax?

6.15 Measure of Central Tendency• Mean – when the data set

has no very high or low numbers and all numbers are close in value

• Median – when the data set has some high or low numbers and most of the data in the middle are close in value

• Mode – when the data set has many identical numbers (you can only have one mode for it to be the best measure, usually the number repeats at least 3 times)

• Ex: Which situation would require finding the median as an appropriate center of measure?a) The temperatures recorded were

either 20 degrees or 25 degreesb) All of the temperatures recorded

were all between 80 degrees and 90 degrees

c) A few of the temperatures recorded were very low or very high

d) All of the temperatures recorded were 55 degrees

• Ex: Find the mean, median, and mode(s) of the data. Choose the measure that best represents the data. 48, 12, 11, 45, 48, 48, 43, 32

• Ex: Which measure best describe the cost of the CDs? $12, $14, $18, $10, $14, $12, $12, $12

6.15 Mean as a Balance Point• The balance point is just

the mean, plotted on a number line, where the data is equally distributed.

• The sum of the number of bunny hops from each x on the right of the balance point has to be the same as the sum of the number of bunny hops from each x on the left of the balance point.

6.15 Mean as a Balance Point

6.3 Absolute Value/Integers• The distance or bunny hops

from zero, distance is ALWAYS POSITIVE.

• Left and down means negative

• Up and right means positive• When ordering and

comparing integers think of money. Which ever one you would rather have is the bigger number.

• Remember the bigger the negative the smaller the number.

• Integers cannot be a fraction or a decimal

• Order for least to greatest: -5, 27 , 8, - 32, 0, 15

• Order for greatest to least: -7, 3, 2, 1, -10, -4

• Compare: -7 to -8, -20 to -14, 10 to 8, -13 to -11

• Absolute Value of: -4, 2, 0, 1, -3

6.2 Fractions, Decimals, and Percents

•Dr. Pepper:•Decimal to Percent -> to the right two

times•Percent to Decimal <- to the left two

times•Decimal to Fraction: place value•Fraction to decimal: timber and divide•Fraction to percent: timber and divide,

then Dr. Pepper•Percent to fraction: drop %, and put over,

then simplify

6.2 Fraction, Decimal, and Percent Examples Fraction Decimal Percent

½ 0.5 50%

¼ 0.25 25%

¾ 0.75 75%

1/3 0.33 33%

2/3 0.66 67%

1/5 0.2 20%

2/5 0.4 40%

3/5 0.6 60%

4/5 0.8 80%

• Ex: Order from greatest to least: 0.5%, 3/5, 0.22

• Ex: Compare ¾ to 80%, 0.87 to 7/10, 0.25% to 0.25

• Ex: Which one belong between 2/3 and 87%?

A) 6/10B) ¾C) 92/10D) 55/100

6.13 Quadrilaterals All angles add up to be 360°

6.13 Quadrilaterals Examples• Ex: Which shapes are not

parallelograms?• Ex: Which statement is

false?A) all squares are rectanglesB) all squares are parallelogramsC) all rhombuses are squaresD) all rhombuses are parallelograms

6.17 Sequences• Arithmetic: common

difference, adding and subtracting

• Geometric: common ratio, multiplying and dividing

• Ex: If the arithmetic pattern shown continues, what will be the 8th number:

54, 48, 42, 36, …A) 34B) 30C) 12D) 6

• Ex: Which statement is true about the pattern shown?

5, 20, 80, 320, …A) the common ratio is 4B) the common ratio is 15C) the common difference is 4D) the common difference is 15