## 6th Grade Formative Assessment Lessons

Some of these Formative Assessment Lessons were created by other states or Kentucky districts. They have been grouped so that the appropriate credit can be given.

*Those**created by Kentucky Department of Education Mathematics Specialists have been field tested by Kentucky teachers participating in the Mathematics Leadership Network.**These are "alpha" versions that have been through at least one revision.*If you encounter errors or would like to make suggestions for revisions, please click**here**to access the contact form.## Colorado Formative Assessment Lesson

## Bargain Shopping

This instructional task helps assess how well students:

• Find percent and fractional discounts.

• Use percent and fraction models to solve problems.

This instructional task emphasizes the following Standards for Mathematical Practice:

This instructional task also asks students to select and apply mathematical content from the Common Core State Standards: • 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

Find percent and fractional discounts.

• 6.RP.3a: Find percents of quantities as a rate per 100; solve problems involving finding the whole, given a part and the percent.

• Find percent and fractional discounts.

• Use percent and fraction models to solve problems.

This instructional task emphasizes the following Standards for Mathematical Practice:

**1. Make sense of problems and persevere in solving them; 2. Reason abstractly and quantitatively; 4. Model with mathematics**.This instructional task also asks students to select and apply mathematical content from the Common Core State Standards: • 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

Find percent and fractional discounts.

• 6.RP.3a: Find percents of quantities as a rate per 100; solve problems involving finding the whole, given a part and the percent.

## Kenton Co KY Tasks

## Kentucky Leadership Network Formative Assessment Lessons

The following FALs have not been revised.

## Orange Juice Problem - Middle School Problem Solving FAL

This lesson is intended to help you assess how well students are able to reason proportionally

in a realistic context: the recipe that will result in a stronger orange taste. In particular, this unit

aims to identify and help students who have difficulties with:

This lesson asks students to select and apply mathematical content from across the grades,

including the content standards:

in a realistic context: the recipe that will result in a stronger orange taste. In particular, this unit

aims to identify and help students who have difficulties with:

- Choosing an appropriate, often informal, strategy to solve proportions.
- Seeing how quantities vary together and are able to see how the variation in one coincides with the variation in another.
- Recognizing ratios as distinct entities representing a relationship different from the quantities they compare.

**1. Make sense of problems and persevere in solving them; 2. Reason abstractly and quantitatively; 3. Construct viable arguments and critique the reasoning of others.**This lesson asks students to select and apply mathematical content from across the grades,

including the content standards:

**6-RP: Understand ratio concepts and use ratio reasoning to solve problems.****7-RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.**

## Ratios and Proportional Relationships written by New York City Dept of Education

This 4-5 week unit focuses on developing an understanding of ratio concepts and using ratio reasoning to solve problems. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Students learn to use ratio and rate language to describe relationships; expand the scope of problems for which they can use multiplication and division; connect ratios and fractions; and solve a wide variety of problems involving ratios and rates. The Formative Assessment Lesson is embedded within the unit.

Common Core Standards addressed:

Common Core Standards addressed:

**6.RP Understand ratio concepts and use ratio reasoning to solve****problems.**This lesson involves all of the mathematical practices from the standards.## Ratio Reasoning written by New York City Dept of Education

This 2-3 week unit should follow a longer unit that introduces and develops an understanding of ratio concepts and how to use ratio and rate language to describe relationships. Specifically, students should be able to recognize and describe ratios and rates by looking for structure and using precise language. In this unit, students will build on those skills as they extend their understanding to using ratio and rate reasoning to solve real world mathematical problems.

This unit is supported by students’ prior knowledge and study of multiplication and division (and expected fluency with multi-digit division), fractions (including using fractions to solve problems, ordering fractions and finding equivalent fractions, and multiplying fractions by whole numbers), and measurement (i.e., converting measurements within a system) completed in Grades 3-5 under the Common Core standards.

Additional opportunities to deepen and apply the knowledge, skills, and understandings developed in this unit should be provided. Specifically, this unit should be followed by further study of the application of ratio reasoning to unit conversions and understanding and using percents to solve problems to ensure full alignment of the curriculum to 6.RP.3, a standard that offers opportunity for in-depth study. Additionally, this year, students will also explore the connection between ratios and proportional relationships and expressions and equations, using variables to represent two quantities in a real world problem that change in relationship to one another. Students will write an equation to express a dependent variable in terms of an independent variable using graphs and tables, and relate these to the equation (6.EE.9).

Common Core Standards addressed:

This unit is supported by students’ prior knowledge and study of multiplication and division (and expected fluency with multi-digit division), fractions (including using fractions to solve problems, ordering fractions and finding equivalent fractions, and multiplying fractions by whole numbers), and measurement (i.e., converting measurements within a system) completed in Grades 3-5 under the Common Core standards.

Additional opportunities to deepen and apply the knowledge, skills, and understandings developed in this unit should be provided. Specifically, this unit should be followed by further study of the application of ratio reasoning to unit conversions and understanding and using percents to solve problems to ensure full alignment of the curriculum to 6.RP.3, a standard that offers opportunity for in-depth study. Additionally, this year, students will also explore the connection between ratios and proportional relationships and expressions and equations, using variables to represent two quantities in a real world problem that change in relationship to one another. Students will write an equation to express a dependent variable in terms of an independent variable using graphs and tables, and relate these to the equation (6.EE.9).

Common Core Standards addressed:

**6.RP Understand ratio concepts and use ratio reasoning to solve****problems.**This lesson involves all of the mathematical practices from the standards.