Grade 6

Unit 1: Area and Surface Area
18 Topics
Tiling the Plane.
Finding Area by Decomposing & Rearranging
Reasoning to Find Area
Parallelograms
Bases and Heights of Parallelograms
Area of Parallelograms
From Parallelograms to Triangles
Area of Triangles
Formula for the Area of a Triangle
Bases and Heights of Triangles
Polygons
What is Surface Area?
Polyhedra
Nets and Surface Area
More Nets, More Surface Area
Distinguishing Between Surface Area and Volume
Squares and Cubes
Surface Area of a Cube
Unit 2: Introducing Ratios
16 Topics
Introducing Ratios and Ratio Language
Representing Ratios with Diagrams
Recipes
Color Mixtures
Defining Equivalent Ratios
Introducing Double Number Line Diagrams
Creating Double Number Line Diagrams
How Much for One? (Working with Ratios)
Constant Speed
Comparing Situations by Examining Ratios
Representing Ratios with Tables
Navigating a Table of Equivalent Ratios
Tables and Double Number Line Diagrams
Solving Equivalent Ratio Problems
Part-Part-Whole Ratios
Solving More Ratio Problems
Unit 3: Unit Rates And Percentages
15 Topics
Anchoring Units of Measurement
Measuring with Different-Sized Units
Converting Units
Comparing Speeds and Prices
Interpreting Rates
Equivalent Ratios Have the Same Unit Rates
More about Constant Speed
Solving Rate Problems
What Are Percentages?
Percentages and Double Number Lines
Percentages and Tape Diagrams
Benchmark Percentages
Solving Percentage Problems
Finding This Percent of That
Finding the Percentage
Unit 4: Dividing Fractions
16 Topics
Size of Divisor and Size of Quotient
Meaning of Division
Interpreting Division Situations
How Many Groups? (Part 1)
How Many Groups? (Part 2)
Using Diagrams to Find the Number of Groups
What Fraction of a Group?
How Much in Each Group? (Part 1)
How Much in Each Group? (Part 2)
Dividing by Unit and Non-Unit Fractions
Using an Algorithm to Divide Fractions
Fractional Lengths
Rectangles with Fractional Side Lengths
Fractional Lengths in Triangles and Prisms
Volume of Prisms with Fractional Length
Solving Problems Involving Fractions
Unit 5: Arithmetic in Base Ten
14 Topics
Using Decimals in a Shopping Context
Using Diagrams to Represent Addition and Subtraction
Adding and Subtracting Decimals with Few Non-Zero Digits
Adding and Subtracting Decimals with Many Non-Zero Digits
Decimal Points in Products
Methods for Multiplying Decimals
Using Diagrams to Represent Multiplication
Calculating Products of Decimals
Using the Partial Quotients Method
Using Long Division
Dividing Numbers that Result in Decimals
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Using Operations on Decimals to Solve Problems
Unit 6: Expressions And Equations
18 Topics
Tape Diagrams and Equations
Truth and Equations
Staying in Balance
Practice Solving Equations and Representing Situations with Equations
Write Expressions Where Letters Stand for Numbers
Revisit Percentages
Equal and Equivalent
The Distributive Property, Part 1
The Distributive Property, Part 2
The Distributive Property, Part 3
Meaning of Exponents
Expressions with Exponents
Evaluating Expressions with Exponents
Equivalent Exponential Expressions
Two Related Quantities, Part 1
Two Related Quantities, Part 2
More Relationships
Tables, Equations, and Graphs
Unit 7: Rational Numbers
19 Topics
Positive and Negative Numbers
Points on the Number Line
Comparing Positive and Negative Numbers
Ordering Rational Numbers
Using Negative Numbers to Make Sense of Contexts
Absolute Values of Numbers
Comparing Numbers and Distance from Zero
Writing and Graphing Inequalities
Solutions of Inequalities
Interpreting Inequalities
Points on the Coordinate Plane
Constructing the Coordinate Plane
Interpreting Points on a Coordinate Plane
Distances on a Coordinate Plane
Shapes on the Coordinate Plane
Common Factors
Common Multiples
Using Common Multiples and Common Factors
Drawing on the Coordinate Plane
Unit 8: Data Sets and Distribution
18 Topics
Got Data?
Statistical Questions
Representing Data Graphically
Dot Plots
Using Dot Plots to Answer Statistical Questions
Interpreting Histograms
Using Histograms to Answer Statistical Questions
Describing Distributions on Histograms
Mean
Finding and Interpreting the Mean as the Balance Point
Variability and MAD
Using Mean and MAD to Make Comparisons
Median
Comparing Mean and Median
Quartiles and Interquartile Range
Box Plots
Using Box Plots
Using Data to Solve Problems
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Fractional Lengths in Triangles and Prisms

Grade 6 Unit 4: Dividing Fractions Fractional Lengths in Triangles and Prisms

Warmup

Activity #1

Find Area of a Triangle with Fractional Lengths & Missing Side Lengths.

  • Study the diagrams below and answer the questions that follow.

Find the area of Triangle A in square centimeters. Show your reasoning.

The area of Triangle B is 8 square units. Find the length of b. Show your reasoning.

The area of Triangle C is 54/5 square units. What is the length of h? Show your reasoning.

Activity #2

Finding Missing Sides Lengths of Similar Triangles with Decimal Lengths.

  • Use cubes or the applet below to help you answer the following questions.​

(1.) How many cubes with edge lengths of  inch are needed to fill the cube below?

(2.) What is the volume in cubic inches, of a cube with edge lengths of   inch? Explain or show your reasoning.

Activity #3

Find Volume of a Prism by Counting Cubes.

  • Use cubes or the applet to help you answer the following questions.​

(1.) Four cubes are piled in a single stack to make a prism. Each cube has an edge length of ½ inch. Sketch the prism, and find its volume in cubic inches.

(2.) For each prism, record in the table how many -inch cubes can be packed into the prism.

Challenge #1

The area of Triangle B is 8 square units. Find the length of b. Show your reasoning.

Challenge #2

Challenge #3

Which expression can be used to find how many cubes with edge length of 13 unit fit in a prism that is 5 units by 5 units by 8 units?

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