UNIT 3: Investagating rate, ratio, and proportional reasoning
Unit Description:
In this unit, students use computational skills (focusing on fractions) to solve problems in context. Students make connections to the classroom beyond the school day when they explore unit rate, ratios, and calculate percentages using proportional reasoning.
In this unit, students use computational skills (focusing on fractions) to solve problems in context. Students make connections to the classroom beyond the school day when they explore unit rate, ratios, and calculate percentages using proportional reasoning.
IN THIS UNIT, STUDENTS WILL:
● understand the concept of a ratio and how to represent ratios using appropriate language to describe relationships ● make tables of equivalent ratios, use such tables to compare ratios, and find missing values in the tables ● solve proportion problems ● describe rates, including unit rates, in the context of ratio relationships ● solve unit rate problems (e.g., unit price, constant speed, words per minute…) ● understand percent as a rate of per 100 and solve real-world percent problems ● use ratios to convert within measurement systems to solve authentic problems |
Khan Academy Resources
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Learning Objectives
6.NR.4.1 Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.
6.NR.4.2 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.NR.4.3 Solve problems involving proportions using a variety of student-selected strategies.
6.NR.4.4 Describe the concept of rates and unit rate in the context of a ratio relationship.
6.NR.4.5 Solve unit rate problems including those involving unit pricing and constant speed.
6.NR.4.6 Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.
6.NR.4.7 Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life.
6.NR.4.1 Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.
6.NR.4.2 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.NR.4.3 Solve problems involving proportions using a variety of student-selected strategies.
6.NR.4.4 Describe the concept of rates and unit rate in the context of a ratio relationship.
6.NR.4.5 Solve unit rate problems including those involving unit pricing and constant speed.
6.NR.4.6 Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.
6.NR.4.7 Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life.
I Can Statements:
- I can explain the concept of a ratio, such as using part-to-part or part-to-whole.
- I can fluently use ratio language to describe a ratio relationship between two quantities.
- I can find the missing values in a table of equivalent ratios.
- I can create a table of values displaying the ratio relationships.
- I can plot pairs of values that represent equivalent ratios on the coordinate plane.
- I can determine the independent and dependent relationship of rate with mathematical situations.
- I can write an equation to represent the relationship between the independent and dependent variable.
- I can write equations to represent the relationship between distance and time where the unit rate is the simple multiplicative relationship.
- I can analyze the relationship between a ratio a:b and a unit rate a/b where b ≠ 0.
- I can convert fractions to decimals when the denominators are 2,4,5 and 10.
- I can find the missing part, whole, or percent when given the other two parts of the percent.
- I can solve real-world and mathematical problems involving percent.
- I can convert measurement units when given a conversion factor within one system of measurement and between two systems of measurement (customary and metric) using proportional reasoning.
Textbook Connections
Module 1 – Lesson 1 Understand Ratios
Students will understand the concept of a ratio
Module 1 – Lesson 2 Tables of Equivalent Ratios
Students will use tables to find equivalent ratios.
Module 1 – Lesson 3 Graphs of Equivalent Rations
Students will use graphs to represent ratio relationships.
Module 1 – Lesson 4 Compare Ratio Relationships
Students will use graphs and tables to compare ratio relationships.
Module 1 – Lesson 5 Solve Ratio Problems
Students will solve real-world problems involving ratios.
Module 1 – Lesson 6 Convert Customary Measurement Units
Students will use ratio reasoning to convert between customary units of measurement.
Module 1 – Lesson 7 Understand Rates and Unit Rates
Students will compare quantities by using unit rates.
Module 1 – Lesson 8 Solve Rate Problems
Students will solve real-world problems involving rates.
Module 2 – Lesson 1 Understand Percents
Students will use 10 × 10 grids and bar diagrams to model percents.
Module 2 – Lesson 2 Percents Greater Than 100% and Less Than 1%
Students will use 10 × 10 grids to model percents that are greater than 100% and less than 1%.
Module 2 – Lesson 3 Relate Fractions, Decimals, and Percents
Students will relate fractions, decimals, and percents.
Module 2 – Lesson 4 Find the Percent of a Number
Students will use bar diagrams, equivalent ratios, double number lines, and ratio tables to find the percent of a number.
Module 2 – Lesson 5 Estimate the Percent of a Number
Students will estimate the percent of a number.
Module 2 – Lesson 6 Find the Whole
Students will find the whole given the percent and the part.
Module 1 – Lesson 1 Understand Ratios
Students will understand the concept of a ratio
Module 1 – Lesson 2 Tables of Equivalent Ratios
Students will use tables to find equivalent ratios.
Module 1 – Lesson 3 Graphs of Equivalent Rations
Students will use graphs to represent ratio relationships.
Module 1 – Lesson 4 Compare Ratio Relationships
Students will use graphs and tables to compare ratio relationships.
Module 1 – Lesson 5 Solve Ratio Problems
Students will solve real-world problems involving ratios.
Module 1 – Lesson 6 Convert Customary Measurement Units
Students will use ratio reasoning to convert between customary units of measurement.
Module 1 – Lesson 7 Understand Rates and Unit Rates
Students will compare quantities by using unit rates.
Module 1 – Lesson 8 Solve Rate Problems
Students will solve real-world problems involving rates.
Module 2 – Lesson 1 Understand Percents
Students will use 10 × 10 grids and bar diagrams to model percents.
Module 2 – Lesson 2 Percents Greater Than 100% and Less Than 1%
Students will use 10 × 10 grids to model percents that are greater than 100% and less than 1%.
Module 2 – Lesson 3 Relate Fractions, Decimals, and Percents
Students will relate fractions, decimals, and percents.
Module 2 – Lesson 4 Find the Percent of a Number
Students will use bar diagrams, equivalent ratios, double number lines, and ratio tables to find the percent of a number.
Module 2 – Lesson 5 Estimate the Percent of a Number
Students will estimate the percent of a number.
Module 2 – Lesson 6 Find the Whole
Students will find the whole given the percent and the part.
IXL Modules with Short Cut Codes
6.NR.4.1
Write a Ratio - 83K
Write a Ratio: Word Problems - SBQ
Which Model Represents the Ratio? - 66V
6.NR.4.2
Identify Equivalent Ratios - 2LM
Write an Equivalent Ratio - NEA
Equivalent Ratio: Word Problems - RLZ
Ratio Tables - PPF
Ratios and Rates: Complete a Table and Make a Graph - 6ZD
6.NR.4.3
Use Tape Diagrams to Solve Ratio Word Problems - YMD
Do Ratios form a Proportion? - LVW
Solve the Proportion - 7H5
6.NR.4.4
Unit Rates - JSZ
6.NR.4.5
Compare Rates: Word Problems - NAF
Ratio and Rates: Word Problems - ZB9
Unit Prices - UKD
6.NR.4.6
What Percentage is Illustrated? - RHG
Convert Between Percent, Fractions and Decimals - ZAV
Percent of Number and Money Amounts - 8N4
Percent of Number: Word Problems - BBY
Percent of Numbers: Fraction and Decimal Percent - CD5
Find What Percent one Number is of Another - PE7
Find What Percent one Number is of Another: Word Problems - 49B
Find the Total Given a Part and a Percent - D6L
Solve Percent Problems - ELY
Solve Percent Word Problems - YWB
6.NR.4.7
Convert and Compare Customary Units - 9TJ
Convert and Compare Metric Units - FDH
Convert Between Customary and Metric Systems - 5CF