Unit 2: Ratios & Proportions
Unit 2: Ratios & ProportionsIn this unit students will explore ratios and rates. Students will apply their knowledge of multiplication and division to write and simplify ratios as well as determine equivalent rates. Students will calculate unit rate utilizing different strategies. Students will also learn how manipulate percentages. They will determine an amount from a given percentage, and then find a missing percentage from a given set of whole numbers. Students will have to apply these concepts to real world situations including, but not limited to, determining the best deal, finding a quicker pace, determine sale prices from a percent discount and determine a total whole number amount from a percentage.
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Learning Target |
NYS Standard |
Engage NY |
Textbook Resources |
1: I can write and simplify a ratio. |
6.RP.1 |
Module 1, Topic A, Lesson 1 Module 1, Topic A, Lesson 2 Module 1, Topic A, Lesson 3 Module 1, Topic A, Lesson 4 Module 1, Topic A, Lesson 5 Module 1, Topic A, Lesson 6 Module 1, Topic A, Lesson 7 Module 1, Topic A, Lesson 8 Module 1, Topic B, Lesson 9 Module 1, Topic B, Lesson 10 Module 1, Topic B, Lesson 13 |
CMP3 Comparing Bits & Pieces Go Math 6.1 |
2: I can calculate and apply a unit rate. |
6.RP.2 6.RP.3a 6.RP.3b |
CMP3 Comparing Bits & Pieces Go Math 6.2 |
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3: I can apply ratio reasoning to manipulate units to solve real world problems. |
6.RP.3a 6.RP.3d |
CMP3 Prime Time Go Math 6.3 Go Math Module 7 |
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4: I can calculate the percent of a given quantity. |
6.RP.3c |
Go Math 8.1 Go Math 8.3 |
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5: I can determine the percent give the part and the total quantity. |
6.RP.3c |
Go Math 8.1 Go Math 8.3 |
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6: I can calculate the total quantity given a percent and part of the total. |
6.RP.3c |
Go Math 8.1 Go Math 8.3 |
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7: I can convert between fractions, decimals and percentages. |
6.NS.2 6.NS.3 6.NS.6 |
CMP3 Let's Be Rational Go Math 8.2 |
Learning Target 1: I can write and simplify a ratio.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.1.A: I can explain what a ratio is. |
(1) Students may fail to differentiate between part:part and part:whole relationship. |
(1) What is a ratio?; Virtual Nerd Video (2) Part-to-Part Ratios; Learn Zillion Video (3) Part-to-Total Ratios; Learn Zillion Video |
(1) |
2.1.B: I can write a ratio from a given situation. |
(1) Students may fail to write numerical values in proper order according to situation, therefore not representing correct comparison |
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2.1.C: I can write and simplify a ratio from a given situation. |
(1) Students may fail to simplify ratio completely; only using a common factor rather than the GCF. |
(1) Writing & Simplifying Ratios; Virtual Nerd Video |
(1) Simplifying Ratios; Cube activity |
2.1.D: I can explain what a ratio means based on a given situation. |
Value |
Value |
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2.1.E: I can calculate a missing value in a proportional situation given a ratio. |
When setting up a proportion, students must place values with corresponding categories in order to determine missing value and display understanding of relationship between values |
(1) What are equivalent ratios?; Virtual Nerd Video (2) What is a proportion?; Virtual Nerd Video (3) Means-Extremes Property of Proportions; Virtual Nerd Video (4) Solving a Proportion Using Cross Products; Virtual Nerd Video (5) Using a proportion to determine equivalent ratios/find a missing value; Skill practice (6) Solving a proportion; Skill practice |
(1) Ratio Rows; Card game - students must identify equivalent ratios |
2.1: I can write and simplify a ratio. |
Learning Target 2: I can calculate and apply a unit rate.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.2.A: I can distinguish between rates and ratios. |
Students must recognize a ratio as a comparison between two numbers and a rate as relating one quantity per one unit of another. |
(1) |
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2.2.B: I can calculate equivalent ratios/rates. |
(1) Students may neglect to multiply/divide both values in ratio by the same number in order to form ratio with equivalent value. Students must recognize equivalent ratios as ratios that are written in the same simplest form. Equivalent ratios can be determined by multiplying or dividing the ratio by a form of 1 whole. |
(1) Ratio Stadium; online game; up to 4 players (2) Determining if two ratios are equal using cross products; Video (3) Cross multiplying to determine equivalence; Practice Sheet (4) Finding a missing value in a proportion; Practice Sheet (5) Writing equivalent ratios; Practice Sheet |
Value |
2.2.C: I can calculate a unit rate using division or a proportion. |
(1) Students may incorrectly determine which value is being used as "per one of something" and therefore incorrectly swap values to be used as divisor and dividend. Students must recognize the value category being used as the unit should be the divisor. |
(1) Relating Rates and Unit Rates; Virtual Nerd Video (2) Relating Rates & Unit Rates; Video (3) Unit rate using division or a proportion; Word Problems (4) Notes sheet with practice problems; PDF form |
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2.2.D: I can apply unit rate to real world situations. |
(1) Students may make errors based on reading comprehension. |
(1) Applying unit rate to real world situations; Video (2) Real-life unit rate ; Video (3) Real Life Unit Rates; Video |
(1) Comparison Shopping; Problem Set (2) Finding the Best Buy; M; division through the hundredth place (3) Shopping Activity; M and Shopping Activity; L; only whole numbers (4) Apply unit rate to real world situations (various scenarios); Problem Set |
2.2: I can calculate and apply a unit rate. |
Learning Target 3: I can apply ratio reasoning to manipulate units to solve real world problems.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.3.A: I can convert between given units. |
Value |
(1) |
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2.3: I can apply ratio reasoning to manipulate units to solve real world problems. |
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Value |
Unit 2 Mastery Quiz 1: see assessment tabs
Learning Target 4: I can calculate the percent of a quantity.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.4.A: I can create and solve a percent proportion to calculate the percent of a given quantity. |
(1) Students may place values incorrectly when setting up proportion. Students must recognize percentages are out of 100 and the part is a portion of the whole or total, therefore the proportion used should be percentage/100 = part/whole |
(1) |
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2.4.B: I can solve real world problems involving finding the percent of a given quantity. |
(1) Students may make errors based on reading comprehension. |
(1) Solve real world problems involving finding the percent of a given quantity; Video (2) Solve real world problems involving finding the percent; Video (3) Finding the percent of a total; Problem Set |
Value |
2.4: I can calculate the percent of a given quantity. |
(1) |
Learning Target 5: I can determine a percentage given the part and the total quantity.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.5.A: I can create and solve a percent proportion to calculate a percentage. |
(1) Students may place values incorrectly when setting up proportion. Students must recognize percentages are out of 100 and the part is a portion of the whole or total, therefore the proportion used should be percentage/100 = part/whole |
(1) Calculating a percent from a given part and total; Notes sheet with examples (2) Calculating a percent from a given part and total; Notes sheet with examples |
(1) |
2.5.B: I can solve real world problems involving finding a missing percentage. |
(1) Students may make errors based on reading comprehension. |
(1) |
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2.5: I can determine a percentage given the part and the total quantity. |
(1) |
(1) |
Unit 2 Mastery Quiz 2: see assessment tab
Learning Target 6: I can find the total quantity given a percent and a part of the total.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.6.A: I can create and solve a percent proportion to find a missing total amount given the part and the percentage. |
(1) Students may place values incorrectly when setting up proportion. Students must recognize percentages are out of 100 and the part is a portion of the whole or total, therefore the proportion used should be percentage/100 = part/whole |
(1) Calculating the missing total; Notes sheet (2) Proportion Method for LT 5, 6 & 7 (3) Find the whole given the part and percent; Video |
(1) |
2.6.B: I can solve real world problems involving finding a missing total quantity. |
(1) Students may make errors based on reading comprehension. |
(1) Calculating a missing total; Notes sheet with examples (2) Solve percent problems by finding the total using a tape diagram; video |
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2.6: I can find a missing total given the percentage and a part of a total. |
(1) |
Learning Target 7: I can convert between fractions, decimals and percentages.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
2.7.A: I can convert a decimal to a percent, and a percent to a decimal. |
Students must recognize decimal place values being on base ten system and therefore can be easily converted to percentages since percent is out of 100. When converting to percent, this is multiplying by 100 and will move the decimal point two places to the right. Students must recognize percentage as being value out of 100. When converting to decimal, this is dividing by 100 and will move the decimal point two places to the left. |
(1) Convert a decimal to a percent, and a percent to a decimal; Video (2) Converting between fractions, decimals and percentages; Practice Sheet (3) Converting between fractions, decimals and percentages; Practice Sheet- includes whole numbers & repeating decimals (4) Converting between fractions, decimals and percentages; Practice Sheet |
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2.7.B: I can solve real world problems involving fractions, decimals and percentages. |
(1) Students may make errors based on reading comprehension. |
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2.7: I can convert between fractions, decimals and percentages. |
(1) |
Unit 2 Mastery Quiz 3: see assessment tab
Department Assessments |
Teacher Made Assessments |
Culminating Projects |
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Unit 2 Post Test Multiple Choice |
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