UNIT 3: Investigating rate, ratio, and proportional reasoning
IN THIS UNIT, STUDENTS WILL BE EXPECTED TO:
- 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.
- 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.
LEARNING OBJECTIVES:
6.NR.4 Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning.
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 rates 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 Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning.
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 rates 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.
LEARNING TARGETS (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 solve real-world problems using proportional reasoning.
- 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 variables.
- 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 percents.
- 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.
- 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 solve real-world problems using proportional reasoning.
- 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 variables.
- 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 percents.
- 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:
(Use Georgia Reveal Math - Course 1 - 6th Grade)
Module 1 – Ratios and Rates
Use ratio and rate reasoning to solve real-world and mathematical problems.
Lesson 1-1 Understand Ratios
Students will understand the concept of a ratio.
Lesson 1-2 Tables of Equivalent Ratios
Students will use tables to find equivalent ratios.
Lesson 1-3 Graphs of Equivalent Ratios
Students will use graphs to represent ratio relationships.
Lesson 1-4 Compare Ratio Relationships
Students will use graphs and tables to compare ratio relationships.
Lesson 1-5 Solve Ratio Problems
Students will solve real-world problems involving ratios.
Lesson 1-6 Convert Customary Measurement Units
Students will use ratio reasoning to convert between customary units of measurement.
Lesson 1-7 Understand Rates and Unit Rates
Students will compare quantities by using unit rates.
Lesson 1-8 Solve Rate Problems
Students will solve real-world problems involving rates.
Module 2 – Fractions, Decimals, and Percents
Learn about the relationship between fractions, decimals, and percents, and apply that relationship to finding the percent of a number.
Lesson 2-1 Understand Percents
Students will use 10 x 10 grids and bar diagrams to model percents.
Lesson 2-2 Percents Greater Than 100% and Less Than 1%
Students will use 10 x 10 grids to model percents that are greater than 100% and less than 1%.
Lesson 2-3 Relate Fractions, Decimals, and Percents
Students will relate fractions, decimals, and percents.
Lesson 2-4 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.
Lesson 2-5 Estimate the Percent of a Number
Students will estimate the percent of a number.
Lesson 2-6 Find the Whole
Students will find the whole given the percent and the part.
(Use Georgia Reveal Math - Course 1 - 6th Grade)
Module 1 – Ratios and Rates
Use ratio and rate reasoning to solve real-world and mathematical problems.
Lesson 1-1 Understand Ratios
Students will understand the concept of a ratio.
Lesson 1-2 Tables of Equivalent Ratios
Students will use tables to find equivalent ratios.
Lesson 1-3 Graphs of Equivalent Ratios
Students will use graphs to represent ratio relationships.
Lesson 1-4 Compare Ratio Relationships
Students will use graphs and tables to compare ratio relationships.
Lesson 1-5 Solve Ratio Problems
Students will solve real-world problems involving ratios.
Lesson 1-6 Convert Customary Measurement Units
Students will use ratio reasoning to convert between customary units of measurement.
Lesson 1-7 Understand Rates and Unit Rates
Students will compare quantities by using unit rates.
Lesson 1-8 Solve Rate Problems
Students will solve real-world problems involving rates.
Module 2 – Fractions, Decimals, and Percents
Learn about the relationship between fractions, decimals, and percents, and apply that relationship to finding the percent of a number.
Lesson 2-1 Understand Percents
Students will use 10 x 10 grids and bar diagrams to model percents.
Lesson 2-2 Percents Greater Than 100% and Less Than 1%
Students will use 10 x 10 grids to model percents that are greater than 100% and less than 1%.
Lesson 2-3 Relate Fractions, Decimals, and Percents
Students will relate fractions, decimals, and percents.
Lesson 2-4 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.
Lesson 2-5 Estimate the Percent of a Number
Students will estimate the percent of a number.
Lesson 2-6 Find the Whole
Students will find the whole given the percent and the part.
IXL SKILLS: