Student Outcomes
Students understand that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students understand that a ratio is often used instead of describing the first number as a multiple of the second.
Students use the precise language and notation of ratios (e.g.,3:2, 3 to 2). Students understand that the order of the pair of numbers in a ratio matters and that the description of the ratio relationship determines the correct order of the numbers. Students conceive of real-world contextual situations to match a given ratio.
Watch this video to help you understand ratios:
http://www.youtube.com/watch?v=evfNoVHUb9s&noredirect=1
Lesson 2: Ratios
Student Outcomes
Students reinforce their understanding that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students continue to learn and use the precise language and notation of ratios (e.g., 3:2, 3 to 2). Students demonstrate their understanding that the order of the pair of numbers in a ratio matters.
Students create multiple ratios from a context in which more than two quantities are given. Students conceive of real-world contextual situations to match a given ratio.
Watch this video to help you understand ratios:
http://www.youtube.com/watch?v=hs71ev4FRCY&list=PLnIkFmW0ticPlYQmBXjAsVtSf4Gccgecr
Lesson 3: Equivalent Ratios
Student Outcomes
Students develop an intuitive understanding of equivalent ratios by using tape diagrams to explore possible
quantities of each part when given the part-to-part ratio. Students use tape diagrams to solve problems when
the part-to-part ratio is given and the value of one of the quantities is given.
Students formalize a definition of equivalent ratios: Two ratios,𝐴:𝐵 and 𝐶:𝐷, are equivalent ratios if there is
a positive number, 𝑐, such that 𝐶 = 𝑐𝐴 and 𝐷 = 𝑐𝐵.
http://www.youtube.com/watch?v=RutvGWKc4oc&list=PL0573514AC020D58D&index=2
Lesson 4: Equivalent Ratios
Student Outcomes
Given a ratio, students identify equivalent ratios. Students use tape diagrams and the description of
equivalent ratios to determine if two ratios are equivalent.
Students relate the positive number, 𝑐, in the description of equivalent ratios to the tape diagrams they have
been using to find equivalent ratios.
This video will help:
http://www.youtube.com/watch?v=dFJX3E98dwM (ratio table is like the tape diagram)
http://www.youtube.com/watch?v=eTRDw2UaQo4&list=PL0573514AC020D58D
Lesson 5: Solving Problems by Finding Equivalent Ratios
Student Outcomes
Students use tape diagrams to find an equivalent ratio when given the part-to-part ratio and the total of those
two quantities. Students use tape diagrams to find an equivalent ratio when given the part-to-part ratio and
the difference between those two quantities.
Students make the connection between the constant, 𝑐, in the definition of equivalent ratios and the value of
the unit in the tape diagram used to solve ratio problems.
Watch this video if you need help!
http://www.youtube.com/watch?v=Nlf2cDFD0tw&list=PL0573514AC020D58D
Lesson 6: Solving Problems by Finding Equivalent Ratios
Student Outcomes
Students use tape diagrams to solve problems when given a ratio between two quantities and a change to those quantities that changes the ratio.
http://www.youtube.com/watch?v=1iNgR_4IhvI&list=PLnIkFmW0ticOoXdgAuD-ieIxde563xh-s&index=4
http://learnzillion.com/lessons/2851-solve-multiplicative-comparison-word-problems-by-using-bar-models-to-represent-division
Students use tape diagrams to solve problems when given a ratio between two quantities and a change to those quantities that changes the ratio.
http://www.youtube.com/watch?v=1iNgR_4IhvI&list=PLnIkFmW0ticOoXdgAuD-ieIxde563xh-s&index=4
Lesson 7: Associated Ratios and the Value of Ratios
Student Outcomes
Student Outcomes
Students understand the relationship between ratios and fractions. Students describe the fraction
associated with the ratio 𝐴: 𝐵 as the value of the ratio 𝐴 to 𝐵.
Students understand that when given a ratio 𝐴: 𝐵, different ratios can be formed from the numbers 𝐴 and 𝐵.
For example, 𝐵: 𝐴, 𝐴: (𝐴 + 𝐵), and 𝐵: (𝐴 + 𝐵) are associated with the same ratio relationship.
Watch this video to help you with this concept:
Watch this video to help you with this concept:
Lesson 8: Equivalent Ratios Defined Through the Value of a Ratio
Student Outcomes
Students understand the value of a ratio 𝐴: 𝐵 is 𝐴/𝐵. They understand that if two ratios are equivalent, the ratios have the same value. Students use the value of a ratio to solve ratio problems in a real-world context.
Student Outcomes
Students understand the value of a ratio 𝐴: 𝐵 is 𝐴/𝐵. They understand that if two ratios are equivalent, the ratios have the same value. Students use the value of a ratio to solve ratio problems in a real-world context.
Students use the value of a ratio in determining whether two ratios are equivalent.
View this video is you are in need of help with this lesson:
http://learnzillion.com/lessons/316-determine-whether-two-ratios-are-equivalent
http://learnzillion.com/lessons/608-solve-missing-values-in-ratio-problems-using-a-table
http://learnzillion.com/lessons/2851-solve-multiplicative-comparison-word-problems-by-using-bar-models-to-represent-division
http://learnzillion.com/lessons/586-solve-ratio-problems-using-tables-and-addition
http://learnzillion.com/lessons/587-solve-ratio-problems-using-tables-and-multiplication
Lesson 11: Comparing Ratios Using Ratio Tables
http://learnzillion.com/lessons/316-determine-whether-two-ratios-are-equivalent
Lesson 9: Tables of Equivalent Ratios
Student Outcomes
Students understand that a ratio is often used to describe the relationship between the amount of one quantity and the amount of another quantity as in the cases of mixtures or constant rates.
Students understand that a ratio table is a table of equivalent ratios. Students use ratio tables to solve problems.
Here is a video to help you with ratio tables:
Student Outcomes
Students understand that a ratio is often used to describe the relationship between the amount of one quantity and the amount of another quantity as in the cases of mixtures or constant rates.
Students understand that a ratio table is a table of equivalent ratios. Students use ratio tables to solve problems.
Here is a video to help you with ratio tables:
http://learnzillion.com/lessons/2851-solve-multiplicative-comparison-word-problems-by-using-bar-models-to-represent-division
Lesson 10: The Structure of Ratio Tables—Additive and
Multiplicative
Student Outcomes
Students identify both the additive and multiplicative structure of a ratio table and use the structure to make additional entries in the table.
Students use ratio tables to solve problems.
Watch these videos to help you with this lesson.
Multiplicative
Student Outcomes
Students identify both the additive and multiplicative structure of a ratio table and use the structure to make additional entries in the table.
Students use ratio tables to solve problems.
Watch these videos to help you with this lesson.
http://learnzillion.com/lessons/587-solve-ratio-problems-using-tables-and-multiplication
Lesson 11: Comparing Ratios Using Ratio Tables
Student Outcomes
Students solve problems by comparing different ratios using two or more ratio tables.
Watch this video to help you with this lesson:
http://youtu.be/565tHsq1ksM
Lesson 12: From Ratio Tables to Double Number Line Diagrams
Students solve problems by comparing different ratios using two or more ratio tables.
Watch this video to help you with this lesson:
http://youtu.be/565tHsq1ksM
Lesson 12: From Ratio Tables to Double Number Line Diagrams
Student Outcomes
Students create equivalent ratios using a ratio table and represent these ratios on a double number line diagram.
Students extend and use a double number line diagram to solve ratio problems related to the real world.
Watch this video to help you with this lesson:
http://www.mentormob.com/mobile/i/solving-ratio-problems-using-tables-and-the-coordinate-plane-1/solve-ratio-problems-using-double-number-lines
Lesson 13: From Ratio Tables to Equations Using the Value of a Ratio
Student Outcomes*Students restate a ratio in terms of its value; e.g., if the ratio of length 𝐴to length 𝐵is 3:5 (in the same units), students state that "length 𝐴is 35 of length 𝐵", "length 𝐵is 53 of length 𝐴", " length 𝐴is 38 of the total length", and "length 𝐵is 58 of the total length".
*Students use the value of the ratio to problem-solve by writing and solving equations.
This video should help you with this lesson:
http://learnzillion.com/lessons/608-solve-missing-values-in-ratio-problems-using-a-table
Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
Student Outcomes
Students associate with each ratio 𝐴:𝐵the ordered pair (𝐴, 𝐵) and plot it in the 𝑥-𝑦coordinate plane.
Students represent ratios in ratio tables, equations, and double number line diagrams and then represent those ratios in the coordinate plane.
A video to help with this lesson:
http://learnzillion.com/lessons/588-solve-ratio-problems-using-double-number-lines
http://youtu.be/UNCxIkO2vZ4
Lesson 15: A Synthesis of Representations of Equivalent Ratio Collections
Student Outcomes
Students associate with each ratio 𝐴:𝐵the ordered pair (𝐴, 𝐵) and plot it in the 𝑥-𝑦coordinate plane.
Given a ratio table, students plot the ratios in the plane and observe that they lie on a line through the origin. Students conclude that the coordinates in the line satisfy 𝑦=𝑘𝑥where 𝑘is the value of an associated ratio.
A video to watch to help with this lesson:
http://learnzillion.com/lessons/590-solve-ratio-problems-by-graphing-on-a-coordinate-plane
Lesson 16: From Ratios to Rates
Student Outcomes
Students recognize that they can associate a ratio of two quantities, such as the ratio of miles per hour is 5:2, to another quantity called the rate.
Given a ratio, students precisely identify the associated rate. They identify the unit rate and the rate unit.
A video to help with this lesson:
Students create equivalent ratios using a ratio table and represent these ratios on a double number line diagram.
Students extend and use a double number line diagram to solve ratio problems related to the real world.
Watch this video to help you with this lesson:
http://www.mentormob.com/mobile/i/solving-ratio-problems-using-tables-and-the-coordinate-plane-1/solve-ratio-problems-using-double-number-lines
Lesson 13: From Ratio Tables to Equations Using the Value of a Ratio
Student Outcomes*Students restate a ratio in terms of its value; e.g., if the ratio of length 𝐴to length 𝐵is 3:5 (in the same units), students state that "length 𝐴is 35 of length 𝐵", "length 𝐵is 53 of length 𝐴", " length 𝐴is 38 of the total length", and "length 𝐵is 58 of the total length".
*Students use the value of the ratio to problem-solve by writing and solving equations.
This video should help you with this lesson:
http://learnzillion.com/lessons/608-solve-missing-values-in-ratio-problems-using-a-table
Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
Student Outcomes
Students associate with each ratio 𝐴:𝐵the ordered pair (𝐴, 𝐵) and plot it in the 𝑥-𝑦coordinate plane.
Students represent ratios in ratio tables, equations, and double number line diagrams and then represent those ratios in the coordinate plane.
A video to help with this lesson:
http://learnzillion.com/lessons/588-solve-ratio-problems-using-double-number-lines
http://youtu.be/UNCxIkO2vZ4
Lesson 15: A Synthesis of Representations of Equivalent Ratio Collections
Student Outcomes
Students associate with each ratio 𝐴:𝐵the ordered pair (𝐴, 𝐵) and plot it in the 𝑥-𝑦coordinate plane.
Given a ratio table, students plot the ratios in the plane and observe that they lie on a line through the origin. Students conclude that the coordinates in the line satisfy 𝑦=𝑘𝑥where 𝑘is the value of an associated ratio.
A video to watch to help with this lesson:
http://learnzillion.com/lessons/590-solve-ratio-problems-by-graphing-on-a-coordinate-plane
Lesson 16: From Ratios to Rates
Student Outcomes
Students recognize that they can associate a ratio of two quantities, such as the ratio of miles per hour is 5:2, to another quantity called the rate.
Given a ratio, students precisely identify the associated rate. They identify the unit rate and the rate unit.
A video to help with this lesson:
http://learnzillion.com/lessons/839-understand-rates-as-a-type-of-ratio
Lesson 17: From Rates to Ratios
Student Outcomes
Given a rate, students find ratios associated with the rate, including a ratio where the second term is one and a ratio where both terms are whole numbers.
Students recognize that all ratios associated to a given rate are equivalent because they have the same value.
A video to help with this lesson:
Lesson 18: Finding a Rate by Dividing Two Quantities Student OutcomesWhile there is no physical way to divide two different quantities like (5 miles)/(2 hours), students make use of the structure of division and ratios to model (5 miles)/(2 hours) as a quantity 2.5 mph. Interpreting a rate as a division of two quantities, or better yet a fraction, is the first step towards converting measurement units using rates later in the module, and dimensional analysis in high school. They use this interpretation of a rate in word problems when multiplying a rate by a quantity, as in: 5𝑔𝑎𝑙𝑚𝑖𝑛∙(10 𝑚𝑖𝑛)= 5 𝑔𝑎𝑙1 𝑚𝑖𝑛∙10 𝑚𝑖𝑛=50 𝑔𝑎𝑙.
A video to watch about this lesson:
Lesson 19: Comparison Shopping—Unit Price and Related Measurement Conversions Student Outcomes Students solve problems by analyzing different unit rates given in tables, equations, and graphs.
Lesson 20: Comparison Shopping—Unit Price and Related Measurement Conversions Student Outcomes Students solve problems by analyzing different unit rates given in words, tables, equations, and graphs.
Lesson 21: Getting the Job Done—Speed, Work, and Measurement Units Student Outcomes Students use rates between measurements to convert measurement in one unit to measurement in another unit. They manipulate and transform units appropriately when multiplying or dividing quantities.
Lesson 22: Getting the Job Done—Speed, Work, and Measurement Units Student Outcomes Students decontextualize a given speed situation, representing symbolically the quantities involved with the formula 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒=𝑟𝑎𝑡𝑒∙𝑡𝑖𝑚𝑒.
Lesson 23: Problem Solving Using Rates, Unit Rates, and Conversions Student Outcomes Students solve constant rate work problems by calculating and comparing unit rates.
Lesson 24: Percent and Rates per 100 Student Outcomes Students understand that percents are related to part-to-whole ratios and rates where the whole is 100.
Students model percents and write a percent as a fraction over 100 or a decimal to the hundredths place.
Lesson 17: From Rates to Ratios
Student Outcomes
Given a rate, students find ratios associated with the rate, including a ratio where the second term is one and a ratio where both terms are whole numbers.
Students recognize that all ratios associated to a given rate are equivalent because they have the same value.
A video to help with this lesson:
Lesson 18: Finding a Rate by Dividing Two Quantities Student OutcomesWhile there is no physical way to divide two different quantities like (5 miles)/(2 hours), students make use of the structure of division and ratios to model (5 miles)/(2 hours) as a quantity 2.5 mph. Interpreting a rate as a division of two quantities, or better yet a fraction, is the first step towards converting measurement units using rates later in the module, and dimensional analysis in high school. They use this interpretation of a rate in word problems when multiplying a rate by a quantity, as in: 5𝑔𝑎𝑙𝑚𝑖𝑛∙(10 𝑚𝑖𝑛)= 5 𝑔𝑎𝑙1 𝑚𝑖𝑛∙10 𝑚𝑖𝑛=50 𝑔𝑎𝑙.
A video to watch about this lesson:
Lesson 19: Comparison Shopping—Unit Price and Related Measurement Conversions Student Outcomes Students solve problems by analyzing different unit rates given in tables, equations, and graphs.
Lesson 20: Comparison Shopping—Unit Price and Related Measurement Conversions Student Outcomes Students solve problems by analyzing different unit rates given in words, tables, equations, and graphs.
Lesson 22: Getting the Job Done—Speed, Work, and Measurement Units Student Outcomes Students decontextualize a given speed situation, representing symbolically the quantities involved with the formula 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒=𝑟𝑎𝑡𝑒∙𝑡𝑖𝑚𝑒.
Lesson 23: Problem Solving Using Rates, Unit Rates, and Conversions Student Outcomes Students solve constant rate work problems by calculating and comparing unit rates.
Lesson 24: Percent and Rates per 100 Student Outcomes Students understand that percents are related to part-to-whole ratios and rates where the whole is 100.
Students model percents and write a percent as a fraction over 100 or a decimal to the hundredths place.
