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 Units: Unit 1:  Operations and Reasoning about RatiosUnit 2:  Expressions and 3-D Geometry

Unit Title

## Unit 1: Operations and Reasoning about Ratios

Timeframe

40 days

Unit Summary

In this unit students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success, apply appropriate academic and technical skills to working with whole numbers, fractions, decimals, and rates and ratios (CRP11).  Students will be able to compute quotients of fractions.  Students will be able to construct visual fraction models to represent quotients of fractions and use the relationship between multiplication and division to explain division of fractions.  They will solve real-world problems involving quotients of fractions and interpret the solutions in the context given (CRP2).  Student will fluently divide multi-digit numbers using the standard algorithms, as well as fluently add, subtract, multiply and divide multi-digit decimals. (9.2.8.B.3 )Students will collaborate at school to help ready them for future careers (CRP12).  This will enable them to act as a responsible and contributing citizen and employee (CRP1).  Students will use ratio and rate language to explain the relationship between two quantities, in addition to describing a unit rate.  Students will solve real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.  Students will use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities (CRP4).  Students will find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two numbers less than or equal to 12.

Topic 1: Use positive and rational numbers.

Topic 5: Understand and use ratio and rate.

Topic 6: Understand and use percent

Learning Targets

Essential Questions

Topic 1 - How do operations with integers relate to the same operations with rational numbers?  How can you determine the correct operation to use to solve problems?

Enduring Understandings

Students will understand:

• #### Compute fluently with multi-digit numbers and find common factors and multiples

• Understand ratio concepts and use ratio reasoning to solve problems

Know

By the end of this unit, students will know:

•  A ratio shows relative sizes or values of two quantities.

Do

By the end of this unit, students will be able to:

•  Divide a fraction by a fraction.
•  Represent division of fractions using visual models.
•  Interpret quotients of fractions in the context of the problem.
•  Compute quotients of fractions in order to solve word problems.
•  Write equations to solve word problems involving division of fraction by a fraction.
•  Use the relationship between multiplication and division to explain division of fractions.
•  Use the standard algorithm to divide multi-digit numbers with speed and accuracy.
•  Describe a ratio relationship between two quantities using ratio language.
•  A rate is a ratio comparing two different types of quantities.
•  Determine the unit rate given a ratio relationship
•  Describe a unit rate relationship between two quantities using rate language.
•  Use ratio and rate reasoning to create tables of equivalent ratios relating quantities with whole number measurements, find

missing values in tables and plot pairs of values.

•  Compare ratios using tables of equivalent ratios.
•  Solve real world and mathematical problems involving unit rate (including unit price and constant speed).
•  Calculate a percent of a quantity and solve problems by finding the whole when given the part and the percent.
•  Convert measurement units using ratio reasoning.
•  Transform units appropriately when multiplying and dividing quantities.
•  Add and subtract multi-digit decimals with accuracy and efficiency.
•  Multiply and divide multi-digit decimals with accuracy and efficiency.
•  Create lists of factors for two whole numbers less than or equal to 100; find the largest factor common to both lists.
•  Create lists of multiples for two whole numbers less than or equal to 12; find the smallest multiple common to both lists.

Evidence of Learning

Formative

Summative/ Benchmark

• Topic Assessment
• MAP - Math Assessment

Alternative Assessments

• ## ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Compute quotients of fractions.
• Construct visual fraction models to represent quotients of fractions and use the relationship between multiplication and division to explain division of fractions.
• Solve real-world problems involving quotients of fractions and interpret the solutions in the context given.
• Fluently divide multi-digit numbers using the standard algorithms.
• Explain the relationship of two quantities in given ratio using ratio language.
• Use rate language, in the context of the ratio relationship, to describe a unit rate.
• Create and complete tables of equivalent ratios to sole real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.
• Use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.
• Fluently add, subtract, multiply and divide multi-digit decimals.
• Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two numbers less than or equal to 12.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.NS.A.1 Traffic Jam

6.RP.A.1 Games at Recess

6.RP.A.2 Price per pound and pounds per dollar

6.RP.A.3 Voting for Three, Variation 1

6.RP.A.3c Shirt Sale

6.NS.B.3 Reasoning about Multiplication and Division and Place Value, Part 1

6.NS.B.4 Factors and Common Factors

6.NS.B.4 Multiples and Common Multiples

 Modifications/Accommodations (IEPs, ELLs, 504s, G/T & BASIC SKILLS) Quick CheckIntervention Activity Center Games Math and Science ActivityVisual Learning Math ToolsMath Games Higher Order Thinking QuestionsLeveled Homework and PracticeListen and Look for Lesson VideoVirtual Nerd VideosAdaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System ELL Toolkit

Unit Title

## Unit 2: Expressions and 3-D Geometry

Timeframe

40 days

Unit Summary

In this unit students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success and apply appropriate academic and technical skills to working with algebraic and geometric concepts.  Students will use mathematical language to write and evaluate numerical and algebraic expressions involving whole number exponents (including evaluating formulas).

Students will apply properties of operations (factor, distribute, and combine like terms) to generate equivalent expressions and to identify when two expressions are equivalent.  Students will find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes and show that the volume is the same as it would be if found by multiplying the edge lengths; apply volume formulas to right rectangular prisms with fractional edge lengths.  Students will represent three dimensional figures objects with nets made of rectangles and triangles, and use the nets to find the surface area of the figures in order to solve real world and mathematical problems. (CRP2) (CRP8). Students will utilize critical thinking to make sense of problems and persevere in solving them. Students will understand how geometric concepts apply to the 16 Career Clusters and can lead to career success (9.2.8.B.1) (CRP3).

Topic 3: Numeric and Algebraic Expressions.

Topic 4: Represent and solve equations and inequalities.

Topic 7: Solve area, surface area and volume problems.

Learning Targets

Essential Questions

Enduring Understandings

Students will understand:

• #### Solve real-world and mathematical problems involving area, surface area, and volume

Know

By the end of this unit, students will know:

• #### A variable can represent an unknown number or any number in a set of numbers.

Do

By the end of this unit, students will be able to:

• #### Folve real world and mathematical problems involving surface area using nets.

Evidence of Learning

Formative

Summative/ Benchmark

• Topic Assessment
• MAP - Math Assessment

Alternative Assessments

• ## ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Write and evaluate numerical expressions involving whole number exponents.
• Use mathematical language to identify parts of an expression.
• Write and evaluate algebraic expressions involving exponents (include evaluating formulas).
• Apply properties of operations (factor, distribute, and combine like terms) to generate equivalent expressions and to identify when two expressions are equivalent.
• Use variables to represent numbers and write expressions when solving real world or mathematical problems.
• Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes and show that the volume is the same as it would be if found by multiplying the edge lengths; apply volume formulas to right rectangular prisms with fractional edge lengths.
• Represent three dimensional figures objects with nets made of rectangles and triangles, and use the nets to find the surface area of the figures in order to solve real world and mathematical problems.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.EE.A.1 The Djinni's Offer

6.EE.A.2 Rectangle Perimeter 1

6.EE.A.4 Rectangle Perimeter 2

6.EE.A.4 Equivalent Expressions

6.G.A.2 Volumes with Fractional Edge Lengths

6.G.A.4 Nets for Pyramids and Prisms

 Modifications/Accommodations (IEPs, ELLs, 504s, G/T & BASIC SKILLS) Quick CheckIntervention Activity Center Games Math and Science ActivityVisual Learning Math ToolsMath Games Higher Order Thinking QuestionsLeveled Homework and PracticeListen and Look for Lesson VideoVirtual Nerd VideosAdaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System ELL Toolkit

Unit Title

## and 2-D  Geometry

Timeframe

40 days

Unit Summary

In this unit students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success and apply appropriate academic and technical skills to working with equations, the rational number system and 2-D geometry.

Students will use substitution to determine whether a given number makes an equation or inequality true (CRP3).  Students will solve real world problems by writing and solving equations of the form x + p = q and px = q (p, q, and x are non-negative rational numbers). (CRP8)  Use positive and negative numbers to represent quantities in real-world situations, explaining the meaning of zero in the context of the real-world situation. Locate rational numbers and their opposites on horizontal and vertical number line; explain their relation of the opposites to zero.  Plot pairs of positive and negative rational numbers in the coordinate plane; describe two ordered pairs that differ only by signs as reflections across one or both axes. Use statements of inequality to determine relative positions of two rational numbers on a number line; write and explain statements of order for rational numbers in real-world contexts.  Explain the meaning of absolute value of a rational number as distance from zero on the number line and as magnitude for a positive or negative quantity in a real-world situation.(CRP4) Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem and represent them on a number line.  Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinate.  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes to solve real world or mathematical problems.

Topic 2: Integers and rational numbers.

Topic 4: Represent and solve equations and inequalities.

Topic 7: Solve area, surface area and volume problems.

Learning Targets

Essential Questions

Topic 2- What are integers and rational numbers?  How are points graphed on a coordinate plane?

Enduring Understandings

Students will understand:

• #### Solve real-world and mathematical problems involving area, surface area, and volume

Know

By the end of this unit, students will know:

• #### Infinity (x > c and x < c have an infinite number of solutions).

Do

By the end of this unit, students will be able to:

• #### Dompose rectangles and decompose into triangles in order to solve real-world problems.

Evidence of Learning

Formative

Summative/ Benchmark

• Topic Assessment
• MAP - Math Assessment

Alternative Assessments

• ## ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Use substitution to determine whether a given number makes an equation or inequality true.
• Solve real world problems by writing and solving equations of the form x + p = q and px = q (p, q, and x are non-negative rational numbers).
• Use positive and negative numbers to represent quantities in real-world situations, explaining the meaning of zero in the context of the real-world situation.
• Locate rational numbers and their opposites on horizontal and vertical number line; explain their relation of the opposites to zero.
• Plot pairs of positive and negative rational numbers in the coordinate plane; describe two ordered pairs that differ only by signs as reflections across one or both axes.
• Use statements of inequality to determine relative positions of two rational numbers on a number line; write and explain statements of order for rational numbers in real-world contexts.
• Explain the meaning of absolute value of a rational number as distance from zero on the number line and as magnitude for a positive or negative quantity in a real-world situation.
• Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem and represent them on a number line.
• Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinate.
• Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes to solve real world or mathematical problems.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.EE.B.5 Make Use of Structure

6.EE.B.7 Morning Walk

6.NS.C.5 Warmer in Miami

6.NS.C.6 Mile High

6.NS.C.7 Jumping Flea

6.NS.C.7a Fractions on the Number Line

6.NS.C.7b Comparing Temperatures

6.G.A.1, 6.G.A.3 Polygons in the Coordinate Plane

 Modifications/Accommodations (IEPs, ELLs, 504s, G/T & BASIC SKILLS) Quick CheckIntervention Activity Center Games Math and Science ActivityVisual Learning Math ToolsMath Games Higher Order Thinking QuestionsLeveled Homework and PracticeListen and Look for Lesson VideoVirtual Nerd VideosAdaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System ELL Toolkit

Unit Title

## between Quantities

Timeframe

40 days

Unit Summary

In this unit, students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success and apply appropriate academic and technical skills to working with statistical variability, rates, and ratios.  Students will write an equation using two variables to represent two quantities that change in relationship to in another in a real world problem(CRP8).  Students will analyze the relationship between the dependent and independent variables and relate the equation to a given graph and to its table of values.  They will distinguish questions that are statistical from those that are not.  Students will display numerical data in plots on the number line and summarize in relation to their context.  Students will summarize numerical data in relation to their context by identifying the number of observations and describing how the data was measured.  They will calculate, and interpret measures of center and variability; report measures of center and variability appropriate to the shape of the distribution and context.  Students will create and complete tables of equivalent ratios to solve real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100(CRP5).  They will use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.  Students will solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane(CRP2); use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinates.

Topic 2: Integers and rational numbers.

Topic 5: Understand and use ratio and rate.

Topic 6: Understand and use percent.

Topic 8: Develop and understand statistics and probability.

Learning Targets

Essential Questions

Topic 2- What are integers and rational numbers?  How are points graphed on a coordinate plane?

Enduring Understandings

Students will understand:

• #### Apply and extend previous understandings of numbers to the system of rational numbers

Know

By the end of this unit, students will know:

• #### A measure of variation describes, with a single number, how the values of a data set vary.

Do

By the end of this unit, students will be able to:

• #### Use coordinates to solve real-world distance, perimeter, and area problems.

Evidence of Learning

Formative

Summative/ Benchmark

• Topic Assessment
• MAP - Math Assessment

Alternative Assessments

• ## ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Write an equation using two variables (independent and dependent) to represent two quantities that change in relationship to one another in a real world problem.
• Analyze the relationship between the dependent and independent variables and relate the equation to a given graph and to its table of values.
• Distinguish questions that are statistical (anticipate variability in data) from those that are not.
• Display numerical data in plots on the number line (including dot plots, histograms, and box plots) and summarize in relation to their context.
• Summarize numerical data in relation to their context by identifying the number of observations and describing how the data was measured.
• Calculate, and interpret measures of center (mean and median) and variability (interquartile range and mean absolute deviation); report measures of center and variability appropriate to the shape of the distribution and context.
• Create and complete tables of equivalent ratios to sole real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.
• Use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.
• Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane; use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinate.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.EE.C.9 Families of Triangles

6.SP.A.1 Identifying Statistical Questions

6.SP.A.2, 6.SP.B.4 Puppy Weights

6.SP.A.3 Is It Center or Is It Variability?

6.SP.B.5c Number of Siblings

6.SP.B.5d Mean or Median?