Final Exam Review: Part II (Chapters 9+) 5 th Grade Advanced Math

First topic!

Chapter 9 Integers

Definition Positive integer – a number greater than zero. Positive integer – a number greater than zero

Definition Negative number – a number less than zero. Negative number – a number less than zero

Place the following integers in order from least to greatest:

Place the following integers in order from least to greatest:

Definition Absolute Value – The distance a number is from zero on the number line Absolute Value – The distance a number is from zero on the number line The absolute value of 9 or of –9 is 9.

Hint If you don’t see a negative or positive sign in front of a number, it is ALWAYS positive. If you don’t see a negative or positive sign in front of a number, it is ALWAYS positive. 9 +

Integer Addition Rules Rule #1 – When adding two integers with the same sign, ADD the numbers and keep the sign. Rule #1 – When adding two integers with the same sign, ADD the numbers and keep the sign = = -14

Solve the Following Problems: = = = = (+3) + (+4) = (+3) + (+4) = = = = = = =

Check Your Answers : = = = = (+3) + (+4) = (+3) + (+4) = = = = = = =

Solve the following: = 2. – = = 4. – =

Check Your Answers = – = = – = -49

Integer Addition Rules Rule #2 – When adding two integers with different signs, find the difference (SUBTRACT) and take the sign of the larger number. Rule #2 – When adding two integers with different signs, find the difference (SUBTRACT) and take the sign of the larger number = = 4 Larger absolute value: Answer = - 4

Solve These Problems = = = = (+3) + (-4) = (+3) + (-4) = = = = = = = -2 5 – 3 = – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

Solve the following: 1. – = 2. – = (-7) = 4. – =

Check Your Answers 1. – = – = (-7) = – = -55

Integer Subtraction Rule Subtracting a negative number is the same as adding a positive one. Change the sign and add. “Keep, change, change.” 2 – (-7) is the same as 2 + (+7) = 9

Here are some more examples. 12 – (-8) 12 + (+8) = – (-11) -3 + (+11) = 8

Solve the following: 1. 8 – (-12) = – (-30) = 3. – 17 – (-3) = 4. –52 – 5 =

Check Your Answers 1. 8 – (-12) = = – (-30) = = – 17 – (-3) = = –52 – 5 = (-5) = -57

Integer Multiplication Rules Rule #1 When multiplying two integers with the same sign, Rule #1 When multiplying two integers with the same sign, the product is always positive. Rule #2When multiplying two integers with different signs, the product is always negative. Rule #2When multiplying two integers with different signs, the product is always negative. Rule #3If the number of negative signs is even, Rule #3If the number of negative signs is even, the product is always positive. Rule #4If the number of negative signs is odd, Rule #4If the number of negative signs is odd, the product is always negative.

Solve the following: x (-12) = x +30 = 3. – 17 x (-3) = x +5 =

Check Your Answers: x (-12) = x +30 = – 17 x (-3) = x +5 = +250

Integer Division Rules Rule #1 When dividing two integers with the same sign, Rule #1 When dividing two integers with the same sign, the quotient is always positive. Rule #2When dividing two integers with different signs, the quotient is always negative. Rule #2When dividing two integers with different signs, the quotient is always negative.

Solve the following: 1. (-36) ÷ 4 = ÷ -5 = 3. – 18 ÷ (-9) = ÷ +5 =

Check Your Work: 1. (-36) ÷ 4 = ÷ -5 = – 18 ÷ (-9) = ÷ +5 = +10

Evaluate the following: ² (9 – 4) = ÷ 5² + (3 - 6) =

Check Your Work: = -5 3² (9 – 4) = ÷ 5² + (3 - 7) = -6

Evaluate the following if n = -2 : (2n – 2)² n - 6

Check Your Work: (2n – 2)² n - 6

Next chapter…

Chapter 11 Expressions & Equations

Write an algebraic expression for the following. Tell what the variable represents. Ben has 12 pencils. He lost 3 and bought some more.

Write an algebraic expression for the following. Tell what the variable represents. Ben has 12 pencils. He lost 3 and bought some more. 12 – 3 + p (p = pencils that Ben bought)

Write each algebraic expression in words s - 47

Write each algebraic expression in words s less than some number

Write each algebraic equation in words ½ n = 16

Write each algebraic equation in words ½ n = 16 one half of some number is 16

Evaluate the following algebraic expressions for the given value of the variable: (n = 11) (n + 25) 9

Evaluate the following algebraic expressions for the given value of the variable: (n = 11) (n + 25) 9 4

Simplify the following expressions (combine like terms). Then evaluate the expression for the given value of the variable: (if a = 3) 3a a

Simplify the following expressions (combine like terms). Then evaluate the expression for the given value of the variable: (if a = 3) 3a a 2a (3)

Write an algebraic equation for the following and evaluate. Tell what the variable represents. Sam had fish in his fish tank. 6 of them died. There were 12 left swimming in the tank. How many fish did Sam have originally?

Sam had fish in his fish tank. 6 of them died. There were 12 left swimming in the tank. How many fish did Sam have originally? f – 6 = 12 f = 18 f is the number of fish Sam had originally in his tank.

Evaluate the following algebraic equations. Show your work. 30 = 5y ¼n = 7 8 = x ÷ 9 3 = 18 + s t - 12 = 23 y ÷ 6 = 7

Evaluate the following algebraic equations. Show your work. 30 = 5y 6 ¼n = = x ÷ = 18 + s -15 t - 12 = y ÷ 6 = 7 42 Evaluate the following algebraic equations. Show your work. 30 = 5y 6 ¼n = = x ÷ = 18 + s -15 t - 12 = y ÷ 6 = 7 42

For word problem practice, review textbook pages 331, 340 and 341.

Next topic…

Chapter 12: Patterns

Guess What’s Next

A. What is the Rule? B. What are the next 3 numbers in the sequence? _______ _______ _______

A. What is the Rule? B. What are the next 3 numbers in the sequence? Rule is: Subtract 8 Rule is: Multiply by

A. What equation shows the function? B. Find the missing term. xy

xy Equation: x³ = y Missing Term: 64

A. What equation shows the function? B. Find the missing terms. w t6710

A. What equation shows the function? B. Find the missing terms. A. What equation shows the function? B. Find the missing terms. Equation: w ÷ 5 = t Missing Term: 8, 9 w t6710

Draw the seventh possible figure in the pattern. How many squares will it have?

Draw the seventh possible figure in the pattern. How many squares will it have? 7 x 7 49 small squares

Find the 9 th term in the sequence. 20, 40, 60, 80………… What is the rule? Write the rule as an algebraic expression.

Find the 9 th term in the sequence: , 40, 60, 80………… What is the rule? Multiply the position of the term by 20. Write the rule as an algebraic expression: 20n

Next chapter…

Chapter 13 Graph Relationships

Inequalities Inequality: is an algebraic sentence that contains the symbol: Inequality: is an algebraic sentence that contains the symbol: > (greater than) > (greater than) < (less than) ≥ (greater than or equal to) ≤ (less than or equal to) ≠ (not equal to) ***Inequalities can be graphed on a number line*** ***Inequalities can be graphed on a number line***

Graphing Inequalities on a Number Line

Graphing Functions Function: a relationship between two numbers or variables. One quantity depends uniquely on the other Function: a relationship between two numbers or variables. One quantity depends uniquely on the other

Remember your Quadrants!

Plotting Coordinates (x,y) (x,y) Find the point on the x-axis first Find the point on the x-axis first (horizontal / left to right) (horizontal / left to right) Then find the point on the y-axis and graph (vertical / up and down) Then find the point on the y-axis and graph (vertical / up and down)

Linear Equations When graphing a function, some functions form a straight line When graphing a function, some functions form a straight line Equations that Equations that are straight lines are straight lines when graphed are when graphed are called linear called linearequations

Next topic…

Chapter 22: Ratio and Proportion Ratios, rates, unit rates, maps & scales, solving proportions

Use the picture to write the ratios. Tell whether the ratio compares part to part, part to whole, or whole to part. All shapes to triangles. Rectangles to ovals. Ovals to all shapes.

Use the picture to write the ratios. Tell whether the ratio compares part to part, part to whole, or whole to part. All shapes to triangles. 18 : 9 whole to part Rectangles to ovals. 3 : 6part to part Ovals to all shapes. 6 : 18part to whole

Which of the following shows two equivalent ratios? a. 7 : 9 and 14 : 16 b. 7 : 9 and 14 : 18

Which of the following shows two equivalent ratios? b. 7 : 9 and 14 : 18 7 =

Write two equivalent ratios for each of the following. a. 12 : 15 b. 1 3

Write two equivalent ratios for each of the following. a. 12 : 1524 : 304 : 5 b *Note: There is more than 1 right answer.

Tell whether the ratios form a proportion. Write yes or no. 4 and 2624 and

Tell whether the ratios form a proportion. Write yes or no. 4 and 2624 and YesNo

Solve the following proportions using Cross Products. Show your work!! 8=x9= x20

Solve the following proportions using Cross Products. Show your work!! 8=x9= x20 36x = 8(54) 12x = 9(20) 36x = x = x = 12 x = 15

Find the % of the number. 75% of 120

Find the % of the number. 75% of x 120 = 90

Find the % of the number. 30% of 50

Find the % of the number. 30% of x 50 = 15

Find the % of the number. 6% of 300 Find the % of the number. 6% of 300

Find the % of the number. 6% of x 300 = 18

What is the unit rate ? Show your work!! a. Earn $56 for an 8 hour day b. Score 120 points in 15 games

What is the unit rate ? Show your work!! a. $$ $56 = x hours 8 1 x = $7 per hour b. points 120 = x games 15 1 x = 8 points per game

If the map scale is 1 in. = 15 miles, what is the map distance if the actual distance is 60 miles?

If the map scale is 1 in. = 15 miles, what is the map distance if the actual distance is 60 miles? Inch 1 = x Miles x = 1(60) 15x = x = 4 inches

It takes Kenny 25 minutes to inflate the tires of 50 bicycles. How long will it take him to inflate the tires of 120 bicycles?

It takes Kenny 25 minutes to inflate the tires of 50 bicycles. How long will it take him to inflate the tires of 120 bicycles? minutes 25 = x bicycles x = 25 (120) 50x = 3, x = 60 minutes

How many pizzas do you need for a party of 135 people if at the last party, 90 people ate 52 pizzas?

How many pizzas do you need for a party of 135 people if at the last party, 90 people ate 52 pizzas? pizzas 52 = x people x = 52 (135) 90x = 7, x = 78 pizzas

Next chapter….

Chapter 18: Measurement Customary measurement of length, mass and volume Metric measurement of length, mass and volume

Customary Measurements A system of measurement used in the United States used to describe how long, how heavy, or how big something is A system of measurement used in the United States used to describe how long, how heavy, or how big something is Examples: inches, feet, yards, miles Examples: inches, feet, yards, miles

Customary Measurement of length 12 inches = 1 foot 3 feet = 1 yard 36 inches = 1 yard 5,280 feet = 1 mile

Customary Measurements of weight/mass 16 ounces (0z) = 1 pound (lb) 2000 pounds (lbs) = 1 ton (T)

Customary Measurement of Capacity/ Volume Capacity/volume: how much a container can hold Capacity/volume: how much a container can hold 8 fl oz = 1 cup 2 cups = 1 pint 2 pints = 1 quart 2 quarts = 1/2 gallon 4 quarts = 1 gallon

Metric Measurements A system of measurement used in most other countries to measure how long, how heavy, or how big something is A system of measurement used in most other countries to measure how long, how heavy, or how big something is

Metric Measurements of Length 10 millimeters (mm) = 1 centimeter (cm) 100 centimeters = 1 meter (m) 1,000 meters = 1 kilometer (km)

Metric Measurements of Weight/Mass 1,000 milligrams (mg) = 1 gram (g) 1,000 grams = 1 kilogram (kg)

Metric Measurements of Capacity/ Volume The milliliter (mL) is a metric unit used to measure the capacities of small containers. Example= a dropper The milliliter (mL) is a metric unit used to measure the capacities of small containers. Example= a dropper The liter (L) is equal to 1,000 mL, so it is used to measure the capacities of larger containers. Example= a bottle of soda The liter (L) is equal to 1,000 mL, so it is used to measure the capacities of larger containers. Example= a bottle of soda

Remember… K ing H enry’s D affy Uncle D rinks C hoc M ilk *This can help you with conversions………

Next topic…

Geometry Quadrilaterals, Plotting coordinates on a grid Perimeter and Area Volume of rectangular prisms

Quadrilaterals Quadrilaterals are any four-sided shapes. They must have straight lines and be two-dimensional. Quadrilaterals are any four-sided shapes. They must have straight lines and be two-dimensional. Examples: squares, rectangles, rhombuses, parallelograms, trapezoids, kites Examples: squares, rectangles, rhombuses, parallelograms, trapezoids, kites

More about quadrilaterals

The Square The square has four equal sides. The square has four equal sides. All angles of a square equal 90 degrees. All angles of a square equal 90 degrees.

The Rectangle The Rectangle has four right angles and two sets of parallel lines. The Rectangle has four right angles and two sets of parallel lines. Not all sides are equal to each other. Not all sides are equal to each other.

The Rhombus A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. A rhombus is sometimes called a diamond.

The Parallelogram A parallelogram has opposite sides parallel and equal in length.parallelogram Also opposite angles are equal.

Plotting Coordinates

Plotting Coordinates (continued) (x,y) (x,y) Find the point on the x-axis first Find the point on the x-axis first (horizontal / left to right) (horizontal / left to right) Then find the point on the y-axis and graph (vertical / up and down) Then find the point on the y-axis and graph (vertical / up and down)

Finding the Perimeter To find the perimeter of most To find the perimeter of most two-dimensional shapes, two-dimensional shapes, just add up the sides just add up the sides

Area Area is the measurement of a shape’s surface. Area is the measurement of a shape’s surface. Remember that units are squared for area!! Remember that units are squared for area!!

Finding the Area of a Square To find the area of a square, To find the area of a square, multiply the length times the width multiply the length times the width A= (l)(w) A= (l)(w) A = 2 x 2 A = 2 x 2 A = 4 cm² A = 4 cm²

Finding the area of rectangles To find the area of a rectangle, just multiply the length and the width. To find the area of a rectangle, just multiply the length and the width. A= (l)(w) A= (l)(w)

Volume Volume is Volume is the amount of space that a substance or object occupies, or that is enclosed within a container Remember that the units of volume are cubed (example: inches^3) because it measures the capacity of a 3-dimensional figure!

Finding the Volume of Rectangular Prisms To find the volume of a rectangular prism, multiply the length by the width and by the height of the figure To find the volume of a rectangular prism, multiply the length by the width and by the height of the figure V = (l)(w)(h) V = (l)(w)(h) V = 6 x 3 x 4 V = 6 x 3 x 4 V = 72 cm³ V = 72 cm³

Practice,Practice,Practice!