Milestones Review Unit 1 Topics Greatest Common Factor

Milestones Review

Unit 1 • Topics • • Greatest Common Factor Least Common Multiple Distributive Property Adding, Subtracting, Multiplying, and Dividing Decimals • Long Division • Dividing Fractions

Decimals The table shows the average baseball ticket price for three American cities. Location Atlanta New York Los Angeles Average Price $14. 42 $28. 59 $19. 67 http: //www. brainpop. com/math/numbersa ndoperations/decima ls/ How much more expensive is it to buy a ticket in New York than in Atlanta? $14. 17

Operations with Decimals • Dividing: If there is a decimal on the outside of the division sign, you must move it first before you can start dividing. • 575. 82 ÷ 6. 3 • 91. 4 • Multiplying: Multiply like normal and then count the decimal places in your problem and move the decimal to the right in your answer • 7. 85 3. 4 • 26. 69

Greatest Common Factor • You can use the ladder method or the rainbow method. • Remember: factors are the numbers you can multiply together to get a larger number (Ex. 1, 2, 3, 6 are the factors of 6) • What is the GCF of 24 and 16? • 8

Least Common Multiple • List all the multiples of each number until you find the first multiple they have in common • Multiple: think about the multiplication table (Ex. 5: 5, 10, 15, 20…) • What is the LCM of 8 and 10? • 40

Dividing Fractions • Keep, Change, Flip and then just multiply straight across and simplify if necessary • ⅞ ÷ ⅖ • 2 3/16 • ⅔ ÷ ½ • 1 1 /3

Distributive Property • First, find the greatest common factor of the two numbers. • 18 + 24 • GCF = 6 • 6( __ + __ ) • Second, find the number you multiply by the GCF to get the original number. • 6(3 + 4)

Unit 2 • Topics • • Ratio Unit Rate Percent of a Whole Converting Measurements

Unit Price • If three dozen cookies cost $9, what is the unit cost? • A) $0. 25 • B) $0. 50 • C) $3. 00 • D) $4. 00 Money goes on the top of your rate and the total number of cookies will go on the bottom. Then you have to divide.

Converting Fractions, Decimals, and Percentages • Fraction to decimal: Top dog goes in the house (numerator inside the division sign, denominator outside) • Decimal to percent: Move the decimal 2 times to the right • Percent to decimal: Move the decimal 2 times to the left

Ratios • Ratios can be written 3 ways: as a fraction, with a colon, or with words. Order is very important with ratios. • Amy has 5 apples and 10 oranges. What is her ratio of apples to total pieces of fruit? • Max has 3 dogs and 2 cats. What is the ratio of cats to dogs? #1 = 1: 3 #2= 2: 3

Measurements • Metric System: Remember K H D B D C M. The measurements at the base are meter, liter, and gram. • Customary System: Remember the gallon man. • • Convert 25 meters to kilometers Convert 50 deciliters to milliliters How many gallon are in 12 quarts? How many pints are in 8 cups? #1 =. 025 km #2 = 5000 m. L #3 = 3 gallons #4 = 4 cups

Percent of a Whole • Change the percent to a decimal and multiply by the whole number. • What is 30% of 50? • What is 60% of 45? #1 = 15 #2 = 27

Unit 3 • Topics • • Exponents Writing Expressions from word problems Order of Operations Parts of an expression: sum, term, product, factor, quotient, coefficient, constant • Substitution with expressions • Combining like terms • Properties

Exponents • Example: 43 = 4 4 4 = 64 • 62 • 53 • 24

Writing Expressions • Which of the expressions represents the statement, "22 more than a number squared decreased by 12"? • A) 22 + x 2 - 12 • B) 22 - x 2 - 12 • C) 22 - x 2 + 12 • D) x 2 - 22 - 12 Pick out your key words first!

Writing Expressions • Mary puts 5 dollars in her piggy bank per week, and her mom added $20 on her birthday. Mary’s birthday is this week. Write an expression to show much money Mary has saved in an unknown number of weeks. 1. Identify the key words Per = multiply and added = add 2. Choose a variable for the unknown number w= the number of weeks Mary has been saving 3. Determine the constant 20 4. Write the expression 5 w + 20

Order of Operations http: //www. youtube. com/watch? v =OWyx. Wg 2 LTY&edufilter=f. U 9 N 1 e_9 JCp 4 r. Avc 4 Pa. Vk. Q Parentheses Exponents Multiply OR Divide Add OR Subtract Ø 62 – (3 + 27 ÷ 9) • 30 Ø 2(3 + 9) – 10 • 14 Ø 5 + (10 + 3 • 4) – 6 • 21

Substitution • If x = 5 and y = 7 then 3 x + y would equal what? • Remember to place numbers in parentheses when you substitute! 3(5) + 7 = 15 + 7 = 22

Combining Like Terms • You can combine terms that have the same variable to the same exponent. • 3 x + 5 y – x + 7 y • 3 w 2 + 8 – 4 + 4 w #1 = 2 x + 12 y #2 = 3 w 2 + 4 w + 4

Properties • Identity, Associative, Commutative, Distributive • Which property matches each example? • 7 + (3 + 5) = (7 + 3) + 5 • 3+5=5+3 • 5+0=5 • 4(3 + 2) = 12 + 8 #1 = Associative #2 = Commutative #3 = Identity #4 = Distributive

Unit 4 • Topics • Write equations/inequalities from word problems • Solving equations • Solving inequalities

Inequalities • greater than >, less than <, greater than or equal to ≥, less than or equal to ≤ • To solve an inquality, you solve it exactly like an equation (WYDTOSDTTO). • 3 x ≥ 27 • x ≥ 9; any number 9 or greater • To write an inequality from a statement, you must choose the key words and pick which symbol matches the key word • The cost of the shirt will be no more than $10. • s ≤ 10

Solving Equations • Use inverse operations! • What you do to one side, do to the other! • x – 10 = 17 • x = 27 • y/ 8 =9 • y = 72 • 4 c = 24 • c=6

Equations The product of two numbers is 48, and one of the numbers is 12. Find the other number. Which equation can be used to solve this problem? A) 48 x = 12 B) 12 x = 48 C) x/12= 48 D) x/48= 12

Unit 5 • Topics • Area of square, rectangle, triangle, parallelogram, and trapezoid • Volume of rectangular prisms • Nets of 3 D figures • Surface area

Nets • James cut this shape from a piece of paper. He is going to fold the shape along the dotted lines. What solid will James create? • A) octahedron • B) tetrahedron • C) triangular prism • D) triangular pyramid http: //www. brainpop. co m/math/geometryandme asurement/polyhedrons/ preview. weml

Volume How many cubes are inside the rectangular prism? A) 21 cubes B) 28 cubes C)36 cubes D)42 cubes

6 cm. 12 m 4. 8 m ------------------------------- Area 4 cm. Area= 12 cm 2 Area= 57. 6 m 2 http: //www. brainpop. com/math/geometryandmeasurement /areaofpolygons/

Surface Area • What is the surface area of the following shape? Use the formula: SA = 2(ab) + 2(bc) + 2(ac) Choose which sides are you’re a, b, and c first. SA = 324

Unit 6 • Topics • • • Statistical questions Mean, median, mode, range Dot plots Histograms Box and whisker plots (5 Number Summary)

Mean, Median, and Mode • Use the data set to answer the following questions: 6, 5, 14, 9, 7, 12, 17 • What is the median? • What is the mean? • What is the mode? • Median: 9 • Mean: 10 • Mode: No mode

Interpret the Histogram • How many animals travel at a speed between 20 and 40 miles per hour? • How many animals travel above 60 miles per hour? #1 = 15; #2 = 2

Dot Plot What is the median, mode, and range of the data on the dot plot? Median: ¼; Mode: 1/8; Range: 7/8

How to create box and whisker plots • Step 1: Order the numbers from least to greatest Data set: 20, 15, 23, 8, 20, 15, 25, 16, 18 8, 10, 15, 16, 18, 20, 23, 25 • Step 2: Identify your minimum and maximum 5 Number Summary Min: 8 1 st Quartile: Median: 3 rd Quartile: Max: 25

How to create box and whisker plots continued… • Step 3: Find the median 8, 10, 15, 16, 18, 20, 23, 25 5 Number Summary Min: 8 1 st Quartile: Median=17 • Once you find the median, draw a fence in your data set to separate the lower and upper half. Median: 17 3 rd Quartile: Max: 25

How to create box and whisker plots continued… • Step 4: Find the first quartile (Find the median of the lower half) 8, 10, 15, 16, 18, 20, 23, 25 • Step 5: Find the third quartile (Find the median of the upper half) • 8, 10, 15, 16, 18, 20, 23, 25 5 Number Summary Min: 8 1 st Quartile: 15 Median: 17 3 rd Quartile: 20 Max: 25

Draw the box and whisker plot 5 Number Summary Min: 8 1 st Quartile: 15 Median: 17 3 rd Quartile: 20 Max: 25 5 10 15 20 25

Unit 7 • Topics • • • Absolute Value Positive and Negative integers Putting numbers on a number line Ordering rational numbers Plotting points on the coordinate plane

Absolute Value • Absolute Value is a number’s distance from zero. • Distance is always positive! • |5| • |-7| #1 = 5; #2 = 7

Comparing Integers • Compare the following integers by using an inequality symbol • -2 ____ -10 • 5 _____ -3 • -4 _____ 0 • 12 _____ 15 • -26 _____ -27 >, >, <, <, >

Think Fast! • Which point represents -7? • What integer is represented by point D? • Which 2 points represent opposites? A B -10 D E C -5 0 #1 = B; #2 = -1; #3 = C and E 5

More Practice -2 A B C -1 0 1 2 • What are the intervals of this number line? • What values do the points represent? #1 = ¼ ; #2 = A is -1 ½ B is – ¾ C is 2 ¼

Ordering Rational Numbers • Khan Academy: https: //www. khanacademy. org/math/cc-sixth-grade-math/cc-6 thnegative-number-topic/cc-6 th-comparing-negativenumbers/v/ordering-rational-numbers • To put rational numbers in order, you need to plot them on a number line! • Or you can turn your numbers into decimals because they are the easiest to compare. • Put these numbers in order from least to greatest: 0. 5, ¾, -1½, |0. 8| • Correct order: -1½, 0. 5, ¾, |0. 8|

Plot the coordinates on the coordinate plane. (-4 , 5) (-3, -2) (2, 1) (6, -3)

Polygon #1 • (3, 4) • (7, -5) Final Vertex (3, -5) Perimeter: 26 units Area: 36 units 2

Helpful Websites • https: //www. brainpop. com/math/ • Login: Username = lumpkin, password = indians • https: //www. khanacademy. org/math/cc-sixthgrade-math