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

First topic!

Chapters 9 and 10 Data Analysis : Graphs, line plots, double bar graphs Mean, median, mode, and range

Know the difference between numerical data and categorical data.

X X X X X X X X X X _X X X X X X X X X_ th Grade Math Test Scores X X X X X X X X X X _X X X X X X X X X_ th Grade Math Test Scores 1.) What type of data is represented here? 2.) Find the Range, Mean, Mode and Median for the set of data shown on the line plot below.

1.) Numerical Data 2.) Range: 29 Mean: Mode: 75 Median: 80

Create a Stem and Leaf Graph for the following set of data. 2. Find the Range, Mean, Mode and Median.

STEM LEAF STEM LEAF Range: 17 Mean: Mode: 18 Median: 20

1.) What is the total number of students who chose Soccer as their favorite sport? 2.) Did more boys or more girls participate in this survey? 3.) What is the total number of students included in this survey? 4.) What is the girls’ favorite sport? The boys’ favorite sport? 5.) How many more students preferred soccer over basketball?

1.) What is the total number of students who chose Soccer 9 as their favorite sport? 2.) Did more boys or more girls participate in this survey? Boys 3.) What is the total number of students included in this survey? 22 4.) Girls’ favorite sport? Soccer Boys’ favorite sport? Basketball 5.) How many more students preferred soccer over basketball? 3

Types of Graphs Bar Graph Double Bar Graph Line Graph Double Line Graph Circle Graph Histogram Line Plot Pictograph Stem and Leaf Plot

Next chapter….

Chapter 11 Whole Numbers: Divisibility rules, prime factorization (factor trees, prime numbers, and exponent form)

Tell whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, and ,360

Tell whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, and , 3, 4, 6, 8, 12 3,360 2, 3, 4, 5, 6, 8, 10 and 12

Tell whether the following numbers are Prime (P), Composite (C), or Neither (N)

Tell whether the following numbers are Prime (P), Composite (C), or Neither (N). 82 C 109P 51C 136C 117C 313P 225C

Write the Prime Factorization of the number as a product of prime factors AND in exponent form. (Hint: Use Factor Trees to help you.)

Write the Prime Factorization of the number as a product of prime factors AND in exponent form. (Hint: Use Factor Trees to help you.) 1082 x 2 x 3 x 3 x 3 2² x 3³ 2253 x 3 x 5 x 5 3² x 5²

Find the Greatest Common Factor (GCF) of the following set of numbers:

Find the Greatest Common Factor (GCF) of the following set of numbers:

Find the Least Common Multiple (LCM) of the following set of numbers:

Find the Least Common Multiple (LCM) of the following set of numbers:

Write the exponent form for the following: 2 x 2 x 3 x 3 x 3

Write the exponent form for the following: 2 x 2 x 3 x 3 x 3 2² x 3³

Write the exponent form for the following: 10,000

Write the exponent form for the following: 10,

Write the standard numeral for the following: 3³

Write the standard numeral for the following: 3³ 27 (3 x 3 x 3)

Write the standard numeral for the following: 2³ x 3²

Write the standard numeral for the following: 2³ x 3² 72 2 x 2 x 2 3 x 3 8 x 9

Compare. Write >,, <, or = 6² 4³

Compare. Write >,, <, or = 6² < 4³ 6 x 6 = 36 4 x 4 x 4 = 64

Next topic….

Chapters : Fractions

Comparing fractions Problem Solve: Several fifth-graders have decided to join the HP track team. During yesterday’s practice, Ben ran 3/4 of a mile, Sam ran 5/8 of a mile, and Ryan ran 5/6 of a mile and Jack ran 1 ¼ miles. Order the students according to how far they ran, from shortest to longest distance (least to greatest). Problem Solve: Several fifth-graders have decided to join the HP track team. During yesterday’s practice, Ben ran 3/4 of a mile, Sam ran 5/8 of a mile, and Ryan ran 5/6 of a mile and Jack ran 1 ¼ miles. Order the students according to how far they ran, from shortest to longest distance (least to greatest). Who ran the farthest? Who ran the farthest?

Comparing fractions Answer (from least to greatest): Answer (from least to greatest): Sam, 5/8 of a mile Sam, 5/8 of a mile Ben, 3/4 of a mile Ben, 3/4 of a mile Ryan, 5/6 of a mile Ryan, 5/6 of a mile Jack, 1 ¼ miles. Jack, 1 ¼ miles. Who ran the farthest? Jack Who ran the farthest? Jack

Problem Solve: Last weekend, Tom, Sam, Trish and Maria rode their bicycles around the park. Tom rode 2 5/12 miles, Sam rode 2 ¾ miles, Trish rode 2 5/6 miles and Maria rode 2 1/3 miles. Order the students according to how far they rode, from shortest to longest distance (least to greatest). Who rode the farthest? Comparing fractions

 Problem Solve: Maria rode 2 1/3 miles Tom rode 2 5/12 miles Sam rode 2 ¾ miles Trish rode 2 5/6 miles Who rode the farthest? Trish Comparing fractions

Addition and Subtraction of Fractions & Mixed Numbers

Plot each fraction on the number line. ½ 1¼ ⅞ 1⅝ ___________________________ 0 1 2

Plot each fraction on the number line. ½ 1¼ ⅞ 1⅝ ½ ⅞ 1¼ 1⅝ ___________________________ 0 1 2

Estimate the sum or difference

Estimate the sum or difference ½ + 1 = 1½

Estimate the sum or difference. 8⅝ - 3½

Estimate the sum or difference. 8⅝ - 3½ 8½ - 3½ = 5

Find the actual sum or difference Find the actual sum or difference

Find the actual sum or difference /14

Find the actual sum or difference. 8 ¼ - 2 ⅞ Find the actual sum or difference. 8 ¼ - 2 ⅞

Find the actual sum or difference. 8 ¼ - 2 ⅞ 5⅜

Find the actual sum or difference. ¼ + 2 ⅞ + 1 ½ =

Find the actual sum or difference. ¼ + 2 ⅞ + 1 ½ = 4⅝

For word problem practice, review textbook pages 355, 378 and 379.

Multiplication & Division of Fractions

Find the product or quotient. ¾ x ⅝ Find the product or quotient. ¾ x ⅝

Find the product or quotient. ¾ x ⅝ 15 32

Find the product or quotient. 5 x ¼ Find the product or quotient. 5 x ¼

Find the product or quotient. 5 x ¼ 5 = 1 ¼ 4

Find the product or quotient. 2¾ x 3½ Find the product or quotient. 2¾ x 3½

Find the product or quotient. 2¾ x 3½ 9 ⅝ Find the product or quotient. 2¾ x 3½ 9 ⅝

Find the product or quotient. 7 ÷ Find the product or quotient. 7 ÷ 1 8 4

Find the product or quotient. 7 ÷ = 3½ 2

Find the product or quotient. 6 ÷ ¾ Find the product or quotient. 6 ÷ ¾

Find the product or quotient. 6 ÷ ¾ 8

Find the product or quotient. 7 ½ ÷ 1¼ Find the product or quotient. 7 ½ ÷ 1¼

Find the product or quotient. 7 ½ ÷ 1¼ 6

Vera bought 5¼ pounds of wood chips for her guinea pig’s cage. She will use 2/3 of the wood chips. How many pounds of wood chips will Vera use?

5¼ x 2/3 = 3½

Next topic…

Chapter 16: Fractions, Decimals, Percents Ratios, rates, unit rates, maps & scales, solving proportions

Complete the chart. Write all fractions in simplest form. FractionsDecimalsPercents.22 7% ⅛

Complete the chart. Write all fractions in simplest form. FractionsDecimalsPercents 22 = % % ⅛ %

Write the decimal, fraction (in simplest form) and percent that represent the shaded part.

= %

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 22: 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 chapter…

Chapter 23: 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!