Slide 1 / 130. Ratios, Rates & Proportions

Size: px
Start display at page:

Download "Slide 1 / 130. Ratios, Rates & Proportions"

Transcription

1 Slide 1 / 130 Ratios, Rates & Proportions

2 Slide 2 / 130 Table of Contents Click on the topic to go to that section Writing Ratios Equivalent Ratios Rates Writing an Equivalent Rate Proportions Application problems Sampling Scale Drawings Similar Figures

3 Slide 3 / 130 Writing Ratios Return to Table of Contents

4 Slide 4 / 130 Ratios What do you know about ratios? When have you seen or used ratios? Ratio - A comparison of two numbers by division Find the ratio of boys to girls in this class

5 Slide 5 / 130 Ratios can be written three different ways: a to b a : b a b Each is read, "the ratio of a to b." Each ratio should be in simplest form.

6 Slide 6 / 130 There are 48 animals in the field. Twenty are cows and the rest are horses. Write the ratio in three ways: a. The number of cows to the number of horses b. The number of horses to the number of animals in the field Remember to write your ratios in simplest form!

7 Slide 7 / There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of vanilla cupcakes to strawberry cupcakes? A 7 : 9 B 7 27 C 7 11 D 1 : 3

8 Slide 8 / There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of chocolate & strawberry cupcakes to vanilla & chocolate cupcakes? A B 11 7 C 5 4 D 16 20

9 Slide 9 / There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of chocolate cupcakes to total cupcakes? A 7 9 B 7 27 C 9 27 D 1 3

10 Slide 10 / There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of total cupcakes to vanilla cupcakes? A 27 to 9 B 7 to 27 C 27 to 7 D 11 to 27

11 Slide 11 / 130 Equivalent Ratios Return to Table of Contents

12 Slide 12 / 130 Equivalent ratios have the same value 3 : 2 is equivalent to 6: 4 1 to 3 is equivalent to 9 to is equivalent to 42

13 x 3 Slide 13 / 130 There are two ways to determine if ratios are equivalent x 3 2. Cross Products Since the numerator and denominator were multiplied by the same value, the ratios are equivalent Since the cross products are equal, the ratios are equivalent. 4 x 15 = 5 x = 60

14 Slide 14 / is equivalent to True False

15 Slide 15 / is equivalent to True False

16 Slide 16 / :12 is equivalent to 9, which is equivalent to True False

17 Slide 17 / is equivalent to 10, which is equivalent to True False

18 Slide 18 / :7 is equivalent to 10, which is equivalent to 5 to True False

19 Slide 19 / 130 Rates Return to Table of Contents

20 Slide 20 / 130 Rate: a ratio of two quantities measured in different units Examples of rates: 4 participants/2 teams 5 gallons/3 rooms 8 burgers/2 tomatoes Unit rate: Rate with a denominator of one Often expressed with the word "per" Examples of unit rates: 34 miles/gallon 2 cookies per person 62 words/minute

21 Slide 21 / 130 Finding a Unit Rate Six friends have pizza together. The bill is $63. What is the cost per person? Hint: Since the question asks for cost per person, the cost should be first, or in the numerator. $63 6 people Since unit rates always have a denominator of one, rewrite the rate so that the denominator is one. $ people 6 $ person The cost of pizza is $10.50 per person

22 Slide 22 / Sixty cupcakes are at a party for twenty children. How many cupcakes per person?

23 Slide 23 / John's car can travel 94.5 miles on 3 gallons of gas. How many miles per gallon can the car travel?

24 Slide 24 / The snake can slither 24 feet in half a day. How many feet can the snake move in an hour?

25 Slide 25 / There are six chaperones at the dance of 100 students. How many students per chaperone are there?

26 Slide 26 / The recipe calls for 6 cups of flour for every four eggs. How many cups of flour are needed for one egg?

27 Slide 27 / 130 Population Density Population Density: A unit rate of people per square mile This data is compiled by the US Census Bureau every 10 years and is used when determining the number of Representatives each state gets in the House of Representatives. Look at the following Population Densities from New Jersey: 1,184 people per square mile Montana: 7 people per square mile California: 237 people per square mile

28 Slide 28 / The population of Newark, NJ is 278,980 people in square miles. What is its population density?

29 Slide 29 / The population of Moorestown, NJ is 19,509 people in 15 square miles. What is its population density?

30 Slide 30 / The population of Waco, TX is 124,009 people in 75.8 square miles. What is its population density?

31 Slide 31 / 130 Writing an Equivalent Rate Return to Table of Contents

32 Slide 32 / 130 To write equivalent rates, conversion factors must be used. Conversion factors are used to convert from one unit to another. Conversion factors must be equal to 1. Some examples of conversion factors: 1 pound or 16 ounces 16 ounces 1 pound 12 inches or 1 foot 1 foot 12 inches 3 feet or 1 yard 1 yard 3 feet 1 day or 24 hours 24 hours 1 day Create 5 conversion factors of your own!

33 Slide 33 / 130 Identify the conversion factor that results in the desired unit. Find a conversion factor that converts minutes to seconds. minutes seconds PULL 60 seconds 1 minute or 1 minute 60 seconds Hint: You want the rate of minute to cancel, so that you are left with the rate of seconds

34 Slide 34 / 130 Identify the conversion factor that results in the desired unit. Find a conversion factor that converts 12 feet to yards. 12 feet? yards PULL 3 feet 1 yard or 1 yard 3 feet PULL Hint: You want the rate of feet to cancel, so that you are left with the rate of yards.

35 Slide 35 / 130 Identify the conversion factor that results in the desired unit. Find a conversion factor that converts miles to feet. 5 miles? feet PULL 5280 feet 1 mile or 1 mile 5280 feet Hint: You want the rate of miles to cancel, so that you are left with the rate of feet PULL

36 Slide 36 / 130 To write equivalent rates, conversion factors must be used. Example 1: 2 inches? inches 1 hour 1 day 2 inches 24 hours 48 inches 1 hour 1 day 1 day Example 2: 5 feet? feet 1 sec 1 hour 5 feet 60 sec 300 feet 1 sec 1 hour 1 hour

37 Slide 37 / Write the equivalent rate. 40 mi? mi 1 min 1 h

38 Slide 38 / Write the equivalent rate. 54 inches? inches 1 year 1 month

39 Slide 39 / Write the equivalent rate. 1 day 1week $75? dollars

40 Slide 40 / Write the equivalent rate. 30 sec 1min 425 mi? miles

41 Slide 41 / Write the equivalent rate. 40 feet inches 3 hrs hr Hint: Find the equivalent rate and then determine the unit rate

42 Slide 42 / Write the equivalent rate. 20,000 feet? feet 4 seconds minute Hint: Find the equivalent rate and then determine the unit rate

43 Slide 43 / Write the equivalent rate people? people 6 days hr Hint: Find the equivalent rate and then determine the unit rate

44 Slide 44 / 130 Proportions Return to Table of Contents

45 Slide 45 / 130 A proportion is an equation that states that two ratios are equivalent. Example:

46 Slide 46 / 130 If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example 1: x x x Hint: To find the value of x, multiply 3 by 3 also x 3

47 Slide 47 / 130 If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example: x x Hint: To find the value of x, divide 32 by 4 also

48 Slide 48 / Solve the proportion using equivalent ratios x

49 Slide 49 / Solve the proportion using equivalent ratios 4 x 9 36

50 Slide 50 / Solve the proportion using equivalent ratios x

51 Slide 51 / Solve the proportion using equivalent ratios x

52 Slide 52 / Solve the proportion using equivalent ratios 3 21 x 28

53 Slide 53 / 130 In a proportion, the cross products are equal

54 Slide 54 / 130 Proportions can also be solved using cross products x Cross multiply 4x = x = 60 x = 15 Solve for x Example 2 7 x 8 48 Cross multiply 8x = x = 336 x = 42 Solve for x

55 Slide 55 / Use cross products to solve the proportion 9 = x 51 17

56 Slide 56 / Use cross products to solve the proportion x =

57 Slide 57 / Use cross products to solve the proportion 45 = _x 18 6

58 Slide 58 / Use cross products to solve the proportion 2 = _x 15 60

59 Slide 59 / Use cross products to solve the proportion 7 = _3 x 21

60 Slide 60 / 130 Application problems Return to Table of Contents

61 Slide 61 / 130 Chocolates at the candy store cost $5.99 per dozen. How much does one candy cost? Round your answer to the nearest cent. Solution: $ dozen 1 dozen 12 (Use equivalent rates) $ $0.50 per candy

62 Slide 62 / 130 Example 2: There are 3 books per student. There are 570 students. How many books are there? Set up the proportion: Books Students 3 Where does the 570 go? 1 3 x x x 1,710 books

63 Slide 63 / 130 Example 3: The ratio of boys to girls is 4 to 5. There are 125 people on a team. How many are girls? Set up the proportion: Girls People How did we determine this ratio? 5 Where does the 125 go? = 9 5 = x x = x = 625 x = girls

64 Slide 64 / Cereal costs $3.99 for a one pound box. What is the price per ounce? Round your answer to the nearest penny.

65 Slide 65 / Which is the better buy? Brand A: $2.19 for 12 ounces Brand B: $2.49 for 16 ounces A B Brand A Brand B

66 Slide 66 / There are 4 girls for every 10 boys at the party. There are 56 girls at the party. How many boys are there?

67 Slide 67 / The farmer has cows and chickens. He owns 5 chickens for every cow. He has a total of 96 animals. How many cows does he own?

68 Slide 68 / The auditorium can hold 1 person for every 5 square feet. It is 1210 square feet. How many people can the auditorium hold?

69 Slide 69 / The recipe for one serving calls for 4 oz of beef and 2 oz of bread crumbs. 50 people will be attending the dinner. How many lbs. of bread crumbs should be purchased?

70 Slide 70 / Mary received 4 votes for every vote that Jane received people voted. How many votes did Jane receive?

71 Slide 71 / To make the desired shade of pink paint, Brandy uses 3 oz. of red paint for each oz. of white paint. She needs one quart of pink paint. How many oz. of red paint will she need?

72 Slide 72 / In a sample of 50 randomly selected students at a school, 38 students eat breakfast every morning. There are 652 students in the school. Using these results, predict the number of students that eat breakfast. A 76 B 123 C 247 D 496 Question from ADP Algebra I End-of-Course Practice Test

73 Slide 73 / 130 Sampling Return to Table of Contents

74 Slide 74 / 130 Your task is to count the number of whales in the ocean or the number of squirrels in a park. How could you do this? What problems might you face?

75 Slide 75 / 130 How would you estimate the size of a crowd? What methods would you use? Could you use the same methods to estimate the number of wolves on a mountain?

76 Slide 76 / 130 One way to estimate the number of wolves on a mountain is to use the CAPTURE - RECAPTURE METHOD.

77 Slide 77 / 130 Suppose this represents all the wolves on the mountain.

78 Slide 78 / 130 Wildlife biologists first find some wolves and tag them.

79 Slide 79 / 130 Then they release them back onto the mountain.

80 Slide 80 / 130 They wait until all the wolves have mixed together. Then they find a second group of wolves and count how many are tagged.

81 Slide 81 / 130 Biologists use a proportion to estimate the total number of wolves on the mountain: tagged wolves on mountain total wolves on mountain = tagged wolves in second group total wolves in second group For accuracy, they will often conduct more than one recapture. 8 2 = w 9 2w = 72 w = 36 There are 36 wolves on the mountain

82 Slide 82 / 130 Try This: Biologists are trying to determine how many fish are in the Rancocas Creek. They capture 27 fish, tag them and release them back into the Creek. 3 weeks later, they catch 45 fish. 7 of them are tagged. How many fish are in the creek? 27 7 = f 45 27(45) = 7f 1215 = 7f = f There are 174 fish in the river

83 Slide 83 / 130 A whole group is called a POPULATION. A part of a group is called a SAMPLE. When biologists study a group of wolves, they are choosing a sample. The population is all the wolves on the mountain. Population Sample

84 Slide 84 / 130 Example: 860 out of 4,000 people surveyed watched Grey's Anatomy. How many people in the US watched if there are 93.1 million people? 860 = x ,100, (93,100,000) = 4000x 80,066,000,000 = 4000x 20,016,500 = x 20,016,500 people watched

85 Slide 85 / 130 Try This: 315 out of 600 people surveyed voted for Candidate A. How many votes can Candidate A expect in a town with a population of 1500?

86 Slide 86 / 130 Margin of Error The results of sampling are estimates, which always contain some error. The margin of error estimates the interval that is most likely to include the exact result for the population. Margin of error is given as a percent in the problem. To find the interval using margin of error: Find the percent of the population Add/Subtract that amount from the answer to create an interval.

87 Slide 87 / 130

88 Slide 88 / 130

89 Slide 89 / You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000.

90 Slide 90 / You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000. Use a 2% margin of error. What is the amount you are going to + by?

91 Slide 91 / You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000. Use a 2% margin of error. What is the lower number in your interval?

92 Slide 92 / You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000. Use a 2% margin of error. What is the upper number in your interval?

93 Slide 93 / You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect?

94 Slide 94 / You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect? Find an interval using a 3% margin of error. What is the amount you are going to + by?

95 Slide 95 / You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect? Find an interval using a 3% margin of error. What is the lower number in your interval?

96 Slide 96 / You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect? Find an interval using a 3% margin of error. What is the upper number in your interval?

97 Slide 97 / 130 Scale Drawings Return to Table of Contents

98 Slide 98 / 130 Scale drawings are used to represent objects that are either too large or too small for a life size drawing to be useful. Examples: A life size drawing of an ant or an atom would be too small to be useful. A life size drawing of the state of New Jersey or the Solar System would be too large to be useful.

99 Slide 99 / 130 A scale is always provided with a scale drawing. The scale is the ratio: drawing real life (actual) When solving a problem involving scale drawings you should: Write the scale as a ratio Write the second ratio by putting the provided information in the correct location (drawing on top & real life on the bottom) Solve the proportion

100 Slide 100 / 130 Example: This drawing has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.

101 Slide 101 / 130 Example: The distance between Philadelphia and San Francisco is 2,950 miles. You look on a map and see the scale is 1 inch : 100 miles. What is the distance between the two cities on the map? Write the scale as a ratio 1 x 100 = x = 2950 x = inches on the map

102 Slide 102 / 130 Try This: On a map, the distance between your town and Washington DC is 3.6 inches. The scale is 1 inch : 55 miles. What is the distance between the two cities?

103 Slide 103 / The distance between Moorestown, NJ and Duck, NC is 910 miles. What is the distance on a map with a scale of 1 inch to 110 miles?

104 Slide 104 / The distance between Philadelphia and Las Vegas is 8.5 inches on a map with a scale 1.5 in : 500 miles. What is the distance in miles?

105 Slide 105 / You are building a room that is 4.6 m long and 3.3 m wide. The scale on the architect's drawing is 1 cm : 2.5 m. What is the length of the room on the drawing?

106 Slide 106 / You are building a room that is 4.6 m long and 3.3 m wide. The scale on the architect's drawing is 1 cm : 2.5 m. What is the width of the room on the drawing?

107 Slide 107 / Find the length of a 72 inch wide door on a scale drawing with a scale 1 inch : 2 feet.

108 Slide 108 / You recently purchased a scale model of a car. The scale is 1cm : 24m. What is the length of the model car if the real car is 4m?

109 Slide 109 / You recently purchased a scale model of a car. The scale is 1cm : 24m. The length of the model's steering wheel is 2.25 cm. What is the actual length of the steering wheel?

110 Slide 110 / The figure is a scale of the east side of a house. In the drawing, the side of each square represents 4 feet. Find the width and height of the door. A B C D 4 ft by 9 ft 4 ft by 12 ft 4 ft by 8 ft 4 ft by 10 ft

111 Slide 111 / On a map, the scale is 1/2 inch= 300 miles. Find the actual distance between two stores that are 5 1/2 inches apart on the map. A B C D 3000 miles 2,727 miles 3,300 miles 1,650 miles

112 Slide 112 / On a map with a scale of 1 inch =100 miles, the distance between two cities is 7.5 inches. If a car travels 55 miles per hour, about how long will it take to get from one city to the other. A B C D 13 hrs 45 min. 14 hrs 30 min. 12 hrs 12 hrs 45 min.

113 Slide 113 / 130 Similar Figures Return to Table of Contents

114 Slide 114 / 130 Two objects are similar if they are the same shape but different sizes. In similar objects: corresponding angles are congruent corresponding sides are proportional

115 Slide 115 / 130 To check for similarity: Check to see that corresponding angles are congruent Check to see that corresponding sides are proportional (Cross products are equal)

116 Slide 116 / 130 Example: Is the pair of polygons similar? Explain your answer. 4 yd 3 yd 6 yd 4.5 yd 4 3 = (4.5) = 6(3) 18 = 18 YES

117 Slide 117 / 130 Example: Is the pair of polygons similar? Explain your answer. 8 m 5 m 10 m 13 m 5 8 = (13) = 10(8) 65 = 80 NO

118 Slide 118 / 130 Example: Find the value of x in the pair of similar polygons. 15 cm x 6 cm 10 cm 8 cm 15 6 = x 10 15(10) = 6x 150 = 6x 25 cm = x

119 Slide 119 / 130 Try This: Find the value of y in the pair of similar polygons. 15 in y 7.5 in 5 in

120 Slide 120 / Are the polygons similar? You must be able to justify your answer. Yes No 15 ft 9 ft 21 ft 12 ft

121 Slide 121 / Are the polygons similar? You must be able to justify your answer. Yes No 10 m 8 m 2.5 m 2 m

122 Slide 122 / Are the polygons similar? You must be able to justify your answer. Yes No 15 yd 37.5 yd 15 yd 6 yd

123 Slide 123 / Find the measure of the missing value in the pair of similar polygons y

124 Slide 124 / Find the measure of the missing value in the pair of similar polygons ft 25 ft 25 ft w 18 ft

125 Slide 125 / Find the measure of the missing value in the pair of similar polygons. x 17 m 4 m 4.25 m

126 Slide 126 / Find the measure of the missing value in the pair of similar polygons. 6 mm y 11 mm 38.5 mm

127 Slide 127 / Find the measure of the missing value in the pair of similar polygons. 63 m 13 m 7 m? 119 m

128 Slide 128 / Find the measure of the missing value in the pair of similar polygons. 7 m 63 m? 13 m 9 m 119 m

129 Slide 129 / Find the measure of the missing value in the pair of similar polygons. 2 mm 5 mm 27.5 mm x

130 Slide 130 / 130

Ratios, Rates & Proportions

Ratios, Rates & Proportions Slide 1 / 130 Ratios, Rates & Proportions Table of Contents Click on the topic to go to that section Slide 2 / 130 Writing Ratios Equivalent Ratios Rates Writing an Equivalent Rate Proportions Application

More information

Factor. 7th Grade Math. Ratios & Proportions. Writing Ratios. 3 Examples/ Counterexamples. Vocab Word. Slide 2 / 184. Slide 1 / 184.

Factor. 7th Grade Math. Ratios & Proportions. Writing Ratios. 3 Examples/ Counterexamples. Vocab Word. Slide 2 / 184. Slide 1 / 184. Slide / Slide / New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

More information

7th Grade. Slide 1 / 206. Slide 2 / 206. Slide 3 / 206. Ratios and Proportions. Table of Contents

7th Grade. Slide 1 / 206. Slide 2 / 206. Slide 3 / 206. Ratios and Proportions. Table of Contents Slide 1 / 206 Slide 2 / 206 7th Grade Ratios and Proportions 2015-11-18 www.njctl.org Table of Contents Slide 3 / 206 Writing Ratios Equivalent Ratios Rates Proportions Direct & Indirect Relationships

More information

7th Grade Ratios and Proportions

7th Grade Ratios and Proportions Slide 1 / 206 Slide 2 / 206 7th Grade Ratios and Proportions 2015-11-18 www.njctl.org Slide 3 / 206 Table of Contents Writing Ratios Equivalent Ratios Rates Proportions Direct & Indirect Relationships

More information

Essential Mathematics. Study Guide #1

Essential Mathematics. Study Guide #1 Math 54CM Essential Mathematics Name Date Study Guide # Exam # is closed book and closed notes. NO CALCULATORS. Please clearly show any work necessary to get partial credit. Be sure to show your answer

More information

Adding & Subtracting Decimals. Multiplying Decimals. Dividing Decimals

Adding & Subtracting Decimals. Multiplying Decimals. Dividing Decimals 1. Write the problem vertically, lining up the decimal points. 2. Add additional zeroes at the end, if necessary, to make the numbers have the same number of decimal places. 3. Add/subtract as if the numbers

More information

LESSON F3.1 RATIO AND PROPORTION

LESSON F3.1 RATIO AND PROPORTION LESSON F. RATIO AND PROPORTION LESSON F. RATIO AND PROPORTION 7 8 TOPIC F PROPORTIONAL REASONING II Overview You have already studied fractions. Now you will use fractions as you study ratio and proportion.

More information

PMI 6th Grade Ratios & Proportions

PMI 6th Grade Ratios & Proportions Unite Rate Packet.notebook December 02, 2016 www.njctl.org PMI 6th Grade Ratios & Proportions 2016 09 19 www.njctl.org www.njctl.org Table of Contents Click on the topic to go to that section Writing Ratios

More information

Ms. Campos - Math 7 Unit 5 Ratios and Rates

Ms. Campos - Math 7 Unit 5 Ratios and Rates Ms. Campos - Math 7 Unit 5 Ratios and Rates 2017-2018 Date Lesson Topic Homework W 6 11/22 1 Intro to Ratios and Unit Rates Lesson 1 Page 4 T 11/23 Happy Thanksgiving! F 11/24 No School! M 1 11/27 2 Unit

More information

WS Stilwell Practice 6-1

WS Stilwell Practice 6-1 Name Date Pd WS Stilwell Practice 6-1 Write each ratio in three different ways. Write your answer in simplest form. 1) 2) triangles to total circles to triangles 3) 4) all figures to circle triangles to

More information

Incoming Advanced Grade 7

Incoming Advanced Grade 7 Name Date Incoming Advanced Grade 7 Tell whether the two fractions form a proportion. 1. 3 16, 4 20 2. 5 30, 7 42 3. 4 6, 18 27 4. Use the ratio table to find the unit rate in dollars per ounce. Order

More information

6. four inches less than Kimi 7. the quotient of a number and nine, minus three

6. four inches less than Kimi 7. the quotient of a number and nine, minus three Semester Exam Practice Test Short Answer 1. The bus station sends buses out on regular intervals to a neighboring city. The first four departure times are shown below. Use the four-step plan to find the

More information

12 inches 4 feet = 48 inches

12 inches 4 feet = 48 inches Free Pre-Algebra Lesson 9! page Lesson 9 Converting Between Units How many minutes in a year? How many feet in sixteen and one-quarter miles? The need to convert between units arises so frequently that

More information

Measurement and Data Core Guide Grade 4

Measurement and Data Core Guide Grade 4 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (Standards 4.MD.1 2) Standard 4.MD.1 Know relative sizes of measurement units within each system

More information

Minute Simplify: 12( ) = 3. Circle all of the following equal to : % Cross out the three-dimensional shape.

Minute Simplify: 12( ) = 3. Circle all of the following equal to : % Cross out the three-dimensional shape. Minute 1 1. Simplify: 1( + 7 + 1) =. 7 = 10 10. Circle all of the following equal to : 0. 0% 5 100. 10 = 5 5. Cross out the three-dimensional shape. 6. Each side of the regular pentagon is 5 centimeters.

More information

Core Connections, Course 2 Checkpoint Materials

Core Connections, Course 2 Checkpoint Materials Core Connections, Course Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn exactly the same way at the same time. At

More information

UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet

UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet Name Period Date UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet 20.1 Solving Proportions 1 Add, subtract, multiply, and divide rational numbers. Use rates and proportions to solve problems.

More information

Section 1.4 Fractions LAWS & PROCESSES. Addition of Fractions DEFINITIONS & BASICS. 1. Common Denominator 2. Add numerators 3. Carry by denominator

Section 1.4 Fractions LAWS & PROCESSES. Addition of Fractions DEFINITIONS & BASICS. 1. Common Denominator 2. Add numerators 3. Carry by denominator 34 Fractions DEFINITIONS & BASICS 1) Numerator the top of a fraction 2) Denominator the bottom of the fraction 3) Simplify Fractions are simplified when the numerator and have no factors in common. 4)

More information

RATIOS AND PROPORTIONS

RATIOS AND PROPORTIONS UNIT 6 RATIOS AND PROPORTIONS NAME: GRADE: TEACHER: Ms. Schmidt Equal Ratios and Proportions Classwork Day 1 Vocabulary: 1. Ratio: A comparison of two quantities by division. Can be written as b a, a :

More information

a. $ b. $ c. $

a. $ b. $ c. $ LESSON 51 Rounding Decimal Name To round decimal numbers: Numbers (page 268) 1. Underline the place value you are rounding to. 2. Circle the digit to its right. 3. If the circled number is 5 or more, add

More information

+ 4 ~ You divided 24 by 6 which equals x = 41. 5th Grade Math Notes. **Hint: Zero can NEVER be a denominator.**

+ 4 ~ You divided 24 by 6 which equals x = 41. 5th Grade Math Notes. **Hint: Zero can NEVER be a denominator.** Basic Fraction numerator - (the # of pieces shaded or unshaded) denominator - (the total number of pieces) 5th Grade Math Notes Mixed Numbers and Improper Fractions When converting a mixed number into

More information

Math 7 Notes - Part A: Ratio and Proportional Relationships

Math 7 Notes - Part A: Ratio and Proportional Relationships Math 7 Notes - Part A: Ratio and Proportional Relationships CCSS 7.RP.A.: Recognize and represent proportional relationships between quantities. RATIO & PROPORTION Beginning middle school students typically

More information

4-5 Convert Measurement Units. Complete ft = yd SOLUTION: Since 1 yard = 3 feet, multiply by lb = oz SOLUTION:

4-5 Convert Measurement Units. Complete ft = yd SOLUTION: Since 1 yard = 3 feet, multiply by lb = oz SOLUTION: Complete. 1. 18 ft = yd Since 1 yard = 3 feet, multiply by. 2. 2 lb = oz Since 16 ounces = 1 pound, multiply by. 3. 6.5 c = fl oz Since 8 fluid ounces = 1 cup, multiply by. 4. 2 mi = ft Since 5,280 feet

More information

Dimensional Analysis

Dimensional Analysis Dimensional Analysis How does dimensional analysis work? It will involve some easy math (Multiplication & Division) In order to perform any conversion, you need a conversion factor. Conversion factors

More information

2 Scale Drawings Def: a special ratio that gives the. 3 Measurements

2 Scale Drawings Def: a special ratio that gives the. 3 Measurements 1 Percents Def: a special ratio in which the denominator is 100 Formula pppppppp (iiii) = % wwwwwwwwww (oooo) 111111 What percent of $10 is $4? 2 Scale Drawings Def: a special ratio that gives the relationship

More information

3.NBT NBT.2

3.NBT NBT.2 Saxon Math 3 Class Description: Saxon mathematics is based on the principle of developing math skills incrementally and reviewing past skills daily. It also incorporates regular and cumulative assessments.

More information

L_sson 9 Subtracting across zeros

L_sson 9 Subtracting across zeros L_sson 9 Subtracting across zeros A. Here are the steps for subtracting 3-digit numbers across zeros. Complete the example. 7 10 12 8 0 2 2 3 8 9 1. Subtract the ones column. 2 8 requires regrouping. 2.

More information

Warm Up. Solve each equation. Check your answer. 1. 6x = m = y =18.4

Warm Up. Solve each equation. Check your answer. 1. 6x = m = y =18.4 Warm Up Solve each equation. Check your answer. 1. 6x = 36 6 2. 3. 5m = 18 4. 48 3.6 63 5. 8y =18.4 2.3 Write and use ratios, rates, and unit rates. Write and solve proportions. Objectives Key Concepts

More information

Squares Multiplication Facts: Square Numbers

Squares Multiplication Facts: Square Numbers LESSON 61 page 328 Squares Multiplication Facts: Square Numbers Name Teacher Notes: Introduce Hint #21 Multiplication/ Division Fact Families. Review Multiplication Table on page 5 and Quadrilaterals on

More information

Lesson 12: Ratios of Fractions and Their Unit Rates

Lesson 12: Ratios of Fractions and Their Unit Rates Student Outcomes Students use ratio tables and ratio reasoning to compute unit rates associated with ratios of fractions in the context of measured quantities, e.g., recipes, lengths, areas, and speed.

More information

A Plan for Problem Solving (pages 6 9)

A Plan for Problem Solving (pages 6 9) A A Plan for Problem Solving (pages 6 9) You can use a four-step plan to solve a problem. Explore Plan Solve Examine Read the problem carefully. Ask yourself questions like, What facts do I know? See how

More information

4 rows of 6 4 x 6 = rows of 4 6 x 4 = 24

4 rows of 6 4 x 6 = rows of 4 6 x 4 = 24 Arrays 8/8/16 Array a rectangular arrangement of equal rows 4 4 rows of 6 4 x 6 = 24 6 6 6 rows of 4 6 x 4 = 24 4 Dimension the number of rows and columns in an array Multiplication the operation of repeated

More information

Begin Practice Round

Begin Practice Round Indiana Academic M.A.T.H. Bowl Invitational February 2012 Begin Practice Round 1 2012 MATH Invitational Practice Round 30 seconds 16 + 12 =? a. 18 b. 14 c. 4 d. 28 2012 MATH Invitational Practice Round

More information

Indiana Academic M.A.T.H. Bowl. Invitational February 2012

Indiana Academic M.A.T.H. Bowl. Invitational February 2012 Indiana Academic M.A.T.H. Bowl Invitational February 2012 Begin Practice Round 2012 MATH Invitational Practice Round 30 seconds a. 18 b. 14 c. 4 d. 28 16 + 12 =? 2012 MATH Invitational Practice Round 16

More information

Converting Within Measurement Systems. ESSENTIAL QUESTION How do you convert units within a measurement system? 6.RP.1.3d

Converting Within Measurement Systems. ESSENTIAL QUESTION How do you convert units within a measurement system? 6.RP.1.3d ? L E S S O N 7.3 Converting Within Measurement Systems ESSENTIAL QUESTION How do you convert units within a measurement system? Use ratio reasoning to convert measurement units; manipulate and transform

More information

Converting Within Measurement Systems. ESSENTIAL QUESTION How do you convert units within a measurement system? 6.RP.1.3d

Converting Within Measurement Systems. ESSENTIAL QUESTION How do you convert units within a measurement system? 6.RP.1.3d L E S S O N 7.3 Converting Within Measurement Systems Use ratio reasoning to convert measurment units; manipulate and transform units appropriately when multiplying or dividing quantities. Also 6.RP.1.3

More information

Number Line: Comparing and Ordering Integers (page 6)

Number Line: Comparing and Ordering Integers (page 6) LESSON Name 1 Number Line: Comparing and Ordering Integers (page 6) A number line shows numbers in order from least to greatest. The number line has zero at the center. Numbers to the right of zero are

More information

Perimeter, Circumference, Area and Ratio Long-Term Memory Review Grade 6 Review 1

Perimeter, Circumference, Area and Ratio Long-Term Memory Review Grade 6 Review 1 Review 1 1. Which procedure is used to find the perimeter of any polygon? A) Add all the lengths B) Multiply length times width (l w) C) Add only one length and one width D) Multiply all of the lengths.

More information

5 th Grade Summer Mathematics Review #1. Name: 1. Find the median. 2. Compare using <, >, or =. 5, 12, 18, 7, 24, 16. a) b)

5 th Grade Summer Mathematics Review #1. Name: 1. Find the median. 2. Compare using <, >, or =. 5, 12, 18, 7, 24, 16. a) b) 1. Find the median. 5 th Grade Summer Mathematics Review #1 2. Compare using , or =. 5, 12, 18, 7, 24, 16 a) 0.432 0.4310 b) 0.199 0.2 3. Create a word problem for this open statement. 4. Solve. 72

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all the factors of the number. ) 30,, 3,, 6, 0,, 30 B),, 3,, 6, 0, 0, 30 C), 6, 0, 30 D),, 6,

More information

2-6 Rates, Ratios, and Proportions. Warm Up. Solve each equation. Check your answer. 1. 6x = m = y =18.4 Multiply

2-6 Rates, Ratios, and Proportions. Warm Up. Solve each equation. Check your answer. 1. 6x = m = y =18.4 Multiply Warm Up Solve each equation. Check your answer. 1. 6x = 36 2. 3. 5m = 18 4. 5. 8y =18.4 Multiply. 6. 7. Learning Goals 1. Students will identify important information from an application problem and use

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all the factors of the number.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all the factors of the number. Test Bank for Basic College Mathematics through Applications 5th Edition by Akst and Bragg Link download full: Test Bank for Basic College Mathematics through Applications 5th Edition by Akst and Bragg

More information

Ratio and Proportions Unit 6

Ratio and Proportions Unit 6 Ratio and Proportions Unit 6 The ratio of circles to triangles is 3:2 Name Date Period 1 Lesson 1: Equal Ratios and Proportions Vocabulary: 1. Ratio: A comparison of two quantities by division. Can be

More information

Accuplacer Math Packet

Accuplacer Math Packet College Level Math Accuplacer Math Packet 1. 23 0 2. 5 8 5-6 a. 0 b. 23 c. 1 d. None of the above. a. 5-48 b. 5 48 c. 5 14 d. 5 2 3. (6x -3 y 5 )(-7x 2 y -9 ) a. 42x -6 y -45 b. -42x -6 y -45 c. -42x -1

More information

For Preview Only GEO5 STUDENT PAGES. GEOMETRY AND MEASUREMENT Student Pages for Packet 5: Measurement. Name Period Date

For Preview Only GEO5 STUDENT PAGES. GEOMETRY AND MEASUREMENT Student Pages for Packet 5: Measurement. Name Period Date Name Period Date GEO5 STUDENT PAGES GEOMETRY AND MEASUREMENT Student Pages for Packet 5: GEO5.1 Conversions Compare measurements within and between measurement systems. Convert measurements within and

More information

DECIMAL COMPUTATION. 6th Grade Unit 2. Long Division Review. 6th Grade Unit 2 Decimal Computation.notebook. Name: Decimal Computation Unit Topics

DECIMAL COMPUTATION. 6th Grade Unit 2. Long Division Review. 6th Grade Unit 2 Decimal Computation.notebook. Name: Decimal Computation Unit Topics Name: 6th Grade Unit 2 DECIMAL COMPUTATION 2012 07 09 www.njctl.org 1 Decimal Computation Unit Topics Click on the topic to go to that section Long Division Review Adding Decimals Subtracting Decimals

More information

6th Grade. Slide 1 / 215. Slide 2 / 215. Slide 3 / 215. Fraction & Decimal Computation. Fraction and Decimal Computation

6th Grade. Slide 1 / 215. Slide 2 / 215. Slide 3 / 215. Fraction & Decimal Computation. Fraction and Decimal Computation Slide 1 / 215 Slide 2 / 215 6th Grade Fraction & Decimal Computation 2015-10-20 www.njctl.org Fraction and Decimal Computation Slide 3 / 215 Fraction Division Long Division Review Adding Decimals Subtracting

More information

CUCC; You may use a calculator.

CUCC; You may use a calculator. 7th Grade Final Exam Name Date Closed Book; 90 minutes to complete CUCC; You may use a calculator. 1. Convert to decimals, fractions or mixed numbers in simplest form: decimal.64 2.45 fraction or mixed

More information

MATH NEWS. 5 th Grade Math. Focus Area Topic A. Grade 5, Module 2, Topic A. Words to know. Things to Remember:

MATH NEWS. 5 th Grade Math. Focus Area Topic A. Grade 5, Module 2, Topic A. Words to know. Things to Remember: MATH NEWS Grade 5, Module 2, Topic A 5 th Grade Math Focus Area Topic A Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka

More information

Math 2 nd Grade GRADE LEVEL STANDARDS/DOK INDICATORS

Math 2 nd Grade GRADE LEVEL STANDARDS/DOK INDICATORS Number Properties and Operations Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop

More information

Word. Problems. Focused Practice to Master Word Problems. Download the free Carson-Dellosa PEEK app and bring this product to life!

Word. Problems. Focused Practice to Master Word Problems. Download the free Carson-Dellosa PEEK app and bring this product to life! Word GRADE 8 Problems Focused Practice to Master Word Problems Real world applications Multi-step word problems Whole numbers, decimals, and fractions Ratio and proportion Percents and interest Metric

More information

Chapter 4 YOUR VOCABULARY

Chapter 4 YOUR VOCABULARY C H A P T E R 4 YOUR VOCABULARY This is an alphabetical list of new vocabulary terms you will learn in Chapter 4. As you complete the study notes for the chapter, you will see Build Your Vocabulary reminders

More information

Go MATH! Aligned! Get ready for. 4th grade. Refine, Review, & Learn something New. Summer themed math packet aligned to get you ready for 4th grade

Go MATH! Aligned! Get ready for. 4th grade. Refine, Review, & Learn something New. Summer themed math packet aligned to get you ready for 4th grade Go MATH! Aligned! Get ready for 4th grade Refine, Review, & Learn something New Summer themed math packet aligned to get you ready for 4th grade Ordering & writing numbers to the thousands Use the following

More information

6th Grade Fraction & Decimal Computation

6th Grade Fraction & Decimal Computation Slide 1 / 215 Slide 2 / 215 6th Grade Fraction & Decimal Computation 2015-10-20 www.njctl.org Slide 3 / 215 Fraction and Decimal Computation Fraction Division Long Division Review Adding Decimals Subtracting

More information

3 x 5 is greater than 5. x 8 is greater than 8. 1 x 10 is less than 10 x 7 is less than 7. x 21 is less than 21. x 4 is greater than 4 3 = = =

3 x 5 is greater than 5. x 8 is greater than 8. 1 x 10 is less than 10 x 7 is less than 7. x 21 is less than 21. x 4 is greater than 4 3 = = = 6 6 5 6 7 8 9 0 6 6 x 8 is greater than 8 5 x 5 is greater than 5 x 0 is less than 0 x 7 is less than 7 7 8 x is less than x is greater than 5 6 = x = x5 x5 7 8 x6 = = x6 8 x x 9 0 . Edward had 0 baseball

More information

6th Grade. Slide 1 / 216. Slide 2 / 216. Slide 3 / 216. Fraction & Decimal Computation. Fraction and Decimal Computation

6th Grade. Slide 1 / 216. Slide 2 / 216. Slide 3 / 216. Fraction & Decimal Computation. Fraction and Decimal Computation Slide / 6 Slide / 6 6th Grade Fraction & Decimal Computation 05-09-4 www.njctl.org Fraction and Decimal Computation Slide 3 / 6 Fraction Division Long Division Review Adding Decimals Subtracting Decimals

More information

Name Period Date. are equivalent because they both simplify to 43. Two fractions are equivalent when they simplify to the same value.

Name Period Date. are equivalent because they both simplify to 43. Two fractions are equivalent when they simplify to the same value. Lesson C ~ Ratios 3 6 Two fractions are equivalent when they simplify to the same value. For example, 4 and 8 are equivalent because they both simplify to 43. This means the ratios 3 : 4 and 6: 8 are equivalent

More information

Unit 9 Notes: Proportions. A proportion is an equation stating that two ratios (fractions) are equal.

Unit 9 Notes: Proportions. A proportion is an equation stating that two ratios (fractions) are equal. Name: Block: Date: MATH 6/7 NOTES & PRACTICE Unit 9 Notes: Proportions A proportion is an equation stating that two ratios (fractions) are equal. If the cross products are equivalent, the two ratios form

More information

Saxon Math Manipulatives in Motion Primary. Correlations

Saxon Math Manipulatives in Motion Primary. Correlations Saxon Math Manipulatives in Motion Primary Correlations Saxon Math Program Page Math K 2 Math 1 8 Math 2 14 California Math K 21 California Math 1 27 California Math 2 33 1 Saxon Math Manipulatives in

More information

MATH-4 Kaechele_Ott_Measurement and Time Exam not valid for Paper Pencil Test Sessions

MATH-4 Kaechele_Ott_Measurement and Time Exam not valid for Paper Pencil Test Sessions MATH-4 Kaechele_Ott_Measurement and Time Exam not valid for Paper Pencil Test Sessions [Exam ID:YBW Landon needed to measure the mass of a pencil using the metric system. Which unit would be best for him

More information

Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 5

Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 5 Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 5 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may use calculators

More information

The Nathan's Hot Dog Eating Contest is an annual American competitive-eating competition that is held each July 4 at Nathan's Famous New York

The Nathan's Hot Dog Eating Contest is an annual American competitive-eating competition that is held each July 4 at Nathan's Famous New York The Nathan's Hot Dog Eating Contest is an annual American competitive-eating competition that is held each July 4 at Nathan's Famous New York restaurant. In 2011 over 40,000 spectators attended the event,

More information

1) Combine like terms: 4x 52y 31z + 64y 16z 23

1) Combine like terms: 4x 52y 31z + 64y 16z 23 Upcoming 8 th Grade Summer Math Review All problems taken from FSA Assessment Readiness Practice and Digital Lessons.com 7 th grade Warm-ups. If students are struggling with one area, you can do a google

More information

Module 1 Study Guide

Module 1 Study Guide 1. John is filling a bathtub that is 18 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take ten more minutes for the water to reach the

More information

Essentials. Week by. Week

Essentials. Week by. Week Week by Week MATHEMATICS Essentials Grade 5 WEEK Math Trivia The ancient Greeks believed that if you studied numbers you had to be a peson who did not need to work because you would probably be a person

More information

Foundations of Math 11: Unit 2 Proportions. The scale factor can be written as a ratio, fraction, decimal, or percentage

Foundations of Math 11: Unit 2 Proportions. The scale factor can be written as a ratio, fraction, decimal, or percentage Lesson 2.3 Scale Name: Definitions 1) Scale: 2) Scale Factor: The scale factor can be written as a ratio, fraction, decimal, or percentage Formula: Formula: Example #1: A small electronic part measures

More information

General Math Unit 2. Proportional Reasoning. Solving equations arising from a context

General Math Unit 2. Proportional Reasoning. Solving equations arising from a context General Math Unit 2 Proportional Reasoning Solving equations arising from a context Day 1 U2D1 I can explain what a ratio is I can use ratio tables to solve problems involving ratios Math Notes Ratios

More information

Summer Math Calendar

Summer Math Calendar Going into Third Grade Directions: Follow the daily activities to practice different math concepts. Feel free to extend any of the activities listed. When the work is completed, have a parent initial the

More information

Northern York County School District Curriculum

Northern York County School District Curriculum Northern York County School District Curriculum Course Name Grade Level Mathematics Fourth grade Unit 1 Number and Operations Base Ten Time Frame 4-5 Weeks PA Common Core Standard (Descriptor) (Grades

More information

Third Grade Mathematics

Third Grade Mathematics Standard 1: Number & Operation 3.M.1.1.1 Read, write, compare, and order whole numbers to 10,000. (287.01.a) and use numbers 38-40% and use numbers Content Limit: When comparing numbers between 1,000 and

More information

a. The probability of getting a yellow marble or P(yellow) is 2/3. What is P(blue or green)?

a. The probability of getting a yellow marble or P(yellow) is 2/3. What is P(blue or green)? Chapter 1 Practice Exam Name: A bag of marbles contains only the colors blue, yellow and green. a. The probability of getting a yellow marble or P(yellow) is 2/3. What is P(blue or green)? b. P(green)

More information

xcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopa Grade 2 Math Crook County School District # 1 Curriculum Guide

xcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopa Grade 2 Math Crook County School District # 1 Curriculum Guide qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjkl zxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiop asdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmq wertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklz Crook County School District

More information

7 Mathematics Curriculum

7 Mathematics Curriculum New York State Common Core 7 Mathematics Curriculum GRADE Table of Contents 1 Percent and Proportional Relationships GRADE 7 MODULE 4... 3 Topic A: Finding the Whole (7.RP.A.1, 7.RP.A.2c, 7.RP.A.3)...

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify the fraction as proper or improper. 1) 5 7 2) 39 8 A) proper B) improper A) improper B) proper

More information

NAME DATE PERIOD. Study Guide and Intervention

NAME DATE PERIOD. Study Guide and Intervention 1-1 A Plan for Problem Solving Four-Step Problem-Solving Plan When solving problems, it is helpful to have an organized plan to solve the problem. The following four steps can be used to solve any math

More information

Smarter Design Test Prep FOUR WEEKS TO GO TO SHOW WHAT I KNOW! TH FINAL 20 DAY MATH SPIRALED REVIEW TEST PREP CRUNCH TIME

Smarter Design Test Prep FOUR WEEKS TO GO TO SHOW WHAT I KNOW! TH FINAL 20 DAY MATH SPIRALED REVIEW TEST PREP CRUNCH TIME FOUR WEEKS TO O TO SHOW WHAT I KNOW! TH TEST PREP CRUNCH TIME Smarter Design Test Prep FINAL 20 MATH SPIRALED REVIEW 5 th rade Test Prep CRUNCH TIME Kelley has 3 piles of 4 rocks. Joel gives her 6 more.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a fraction to represent the shaded part of the object. 1) A) 1 3 3 1 C) 3 4 2) D) 1 4 A) 1 6

More information

Name: Period: !"#$. "%&'&()*

Name: Period: !#$. %&'&()* Name: Period: Today you will extend your study of ratios by looking at enlargements and reductions of geometric figures. Think of a copy machine and what it does to a picture when the enlargement button

More information

Math 6. Colonial School District. Summer Math Packet

Math 6. Colonial School District. Summer Math Packet Math 6 Colonial School District Summer Math Packet The concepts included in this packet will help reinforce key skills your child has encountered in math this year. Please encourage them to complete as

More information

Math Mammoth Grade 6 End of the Year Test Notes

Math Mammoth Grade 6 End of the Year Test Notes Math Mammoth Grade 6 End of the Year Test Notes This test is very long, because it contains questions on all major topics covered in Math Mammoth Grade 6 Complete Curriculum. Its main purpose is to be

More information

Oregon Focus on Ratios, Rates & Percents Lesson 1 Answers

Oregon Focus on Ratios, Rates & Percents Lesson 1 Answers Lesson 1 Answers 1. 1 2 2. 1 4 3. 3 1 or 3 4. 1 3. 1 1 or 1 6. 3 2 7. 2 3 8. 1 2 9. 4 1, 2 : 3, 2 to 3, 1 : 2, 1 to 2, 4 : 1, 4 to 1. 2 3, 2 : 3, 2 to 3 11. 1 1 12. 1 13. a. 7 8 or 1; 1 : 1; 1 to 1 b.

More information

Number and Operations Fractions

Number and Operations Fractions Number and Operations Fractions Standards Entry Points Access Skills 3 Page 59 Pages 60 61 Pages 60 62 4 Pages 63 64 Page 65 67 5 Pages 68 69 Page 70 72 MATHEMATICS 58 CONTENT AREA Mathematics DOMAIN Number

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify the fraction as proper or improper. ) 3 5 ) A) proper B) improper 2) 47 6 A) improper B)

More information

GRADE 4. M : Solve division problems without remainders. M : Recall basic addition, subtraction, and multiplication facts.

GRADE 4. M : Solve division problems without remainders. M : Recall basic addition, subtraction, and multiplication facts. GRADE 4 Students will: Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as

More information

MATH EOG Practice Test

MATH EOG Practice Test Copyright 2016 Edmentum All rights reserved. MATH EOG Practice Test Question #1 Round to the nearest tenth: 9.646 A. 9 9.6 C. 9.5 D. 9.64 Question #2 Evaluate the following. 10 3 A. 30 100 C. 1,000 D.

More information

Thank you for Downloading

Thank you for Downloading Thank you for Downloading Get More FREE resources at You ve Got This Math YOU MAY Print as many copies as you would like for your OWN personal use Save this file on YOUR computer Share on a blog, facebook

More information

Summer Solutions Common Core Mathematics 4. Common Core. Mathematics. Help Pages

Summer Solutions Common Core Mathematics 4. Common Core. Mathematics. Help Pages 4 Common Core Mathematics 63 Vocabulary Acute angle an angle measuring less than 90 Area the amount of space within a polygon; area is always measured in square units (feet 2, meters 2, ) Congruent figures

More information

Lesson 1: Understanding Proportional. Relationships

Lesson 1: Understanding Proportional. Relationships Unit 3, Lesson 1: Understanding Proportional Relationships 1. Priya jogs at a constant speed. The relationship between her distance and time is shown on the graph. Diego bikes at a constant speed twice

More information

Lesson 6 ~ Write and Solve Proportions

Lesson 6 ~ Write and Solve Proportions Lesson 6 ~ Write and Solve Proportions Solve each proportion. 3 x 1. = 2. 4 20 5 25 8 a = 3. = 7 y 28 7 4. x 32 = 3 16 5. 6 12 = y 48 6. 3 5 = 15 b 7. 11 14 = x 28 8. 26 30 = x 15 9. 5 = 20 4 y Determine

More information

Summer Math Learning Packet

Summer Math Learning Packet Summer Math Learning Packet Sixth grade math was a blast, The year just went by so fast! Let s keep everything fresh in your mind, So you can rely on it in a bind. Just complete two problems a day, And

More information

Place Value and Patterns

Place Value and Patterns Lesson 1.1 Reteach Place Value and Patterns You can use a place-value chart and patterns to write numbers that are times as much as or 1 of any given number. Each place to the right is 1 of the value of

More information

Lesson 1C ~ Measurement

Lesson 1C ~ Measurement Lesson 1C ~ Measurement Determine the best unit of measurement you would use in each situation. 1. distance from your home to the nearest airport. best customary unit: best metric unit: 2. mass of a marble.

More information

Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 6

Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 6 Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 6 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may use calculators

More information

ShillerMath Book 4 Test Answers

ShillerMath Book 4 Test Answers ShillerMath Book 4 Test Answers LESSON 4-44 REVIEW TEST #4-1 ANSWERS HOW KIDS LEARN MATH Grading instructions: compare the answers here to the student s answers. For each correct answer, add the appropriate

More information

!!!!!!!!!!!!!!! Rising 6 th Grade Summer Interactive Math Practice

!!!!!!!!!!!!!!! Rising 6 th Grade Summer Interactive Math Practice Rising 6 th Grade Summer Interactive Math Practice Rising Sixth Grade Summer Math Packet I. Place Value Write each number in word form, in expanded form, expanded notation, name the place of the underlined

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Underline the digit that occupies the given place. 1) 926 Tens place 1) A) 926 B) 926 C)

More information

Lesson 20T ~ Parts of Circles

Lesson 20T ~ Parts of Circles Lesson 20T ~ Parts of Circles Name Period Date 1. Draw a diameter. 2. Draw a chord. 3. Draw a central angle. 4. Draw a radius. 5. Give two names for the line drawn in the circle. Given the radius, find

More information

Name Period Date MATHLINKS: GRADE 6 STUDENT PACKET 16 APPLICATIONS OF PROPORTIONAL REASONING

Name Period Date MATHLINKS: GRADE 6 STUDENT PACKET 16 APPLICATIONS OF PROPORTIONAL REASONING Name Period Date 6-16 STUDENT PACKET MATHLINKS: GRADE 6 STUDENT PACKET 16 APPLICATIONS OF PROPORTIONAL REASONING 16.1 Saving for a Purchase Set up equations to model real-world problems involving saving

More information

6 th Grade Middle School Math Contest 2017 Page 1 of 9

6 th Grade Middle School Math Contest 2017 Page 1 of 9 1. In 2013, Mia s salary was a certain amount. In 2014, she received a 10% raise from 2013. In 2015, she received a 10% decrease in salary from 2014. How did her 2015 salary compare to her 2013 salary?

More information

Essentials. Week by. Week. Fraction Action Bill, Rasheed, and Juan own a hobby shop. Probability Pizzazz

Essentials. Week by. Week. Fraction Action Bill, Rasheed, and Juan own a hobby shop. Probability Pizzazz Week by Week MATHEMATICS Essentials Bill, Rasheed, and Juan own a hobby shop. Juan owns of the shop. Rasheed owns twice as much as Bill. What fraction of the shop does Bill own? Andy and Fran are playing

More information