Listed below, in the section for each unit, are links to learnzillion.com. These are links to short video lessons on the mathematical content stated.

# Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

## learnzillion.com

# Unit 1 Rates, Ratios, and Proportions

Unit 1 Research and Background Information (pdf)

## Big Idea 1: Multiplication and Rates (RP.2-3)

Understand rates as a type of ratio (RP.2)

Graph ratios using a table (RP.3)

Compare ratios using tables and percents (RP.3)

Find missing values in ratio problems using a table (RP.3)

Solve ratio problems using double number lines (RP.3)

Find the total when the percent and part are known (RP.3)

## Big Idea 2: Special rate Situations and Graphing (RP.2-3, EE.6, EE.9)

See Big Idea 1

Understand how variables are used (EE.6)

Identify independent and dependent variables (EE.9)

Relate independent and dependent variables using a function table (EE.9)

## Big Idea 3: Solve Problems with Ratio and Proportion (RP.1-3)

Visualize part-to-part ratios using pictures (RP.1)

Visualize part-to-total ratios using pictures (RP.1)

Understand the difference between fractions and ratios (RP.1)

## Big Idea 4: Identify, Solve, and Write Proportion Situations (RP.1-3, NS.4)

See Big Ideas 1-3

# Unit 2 Area of Polygons

Unit 2 Research and Background Information (pdf)

## Big Idea 1: Derive Area Formulas and Solve Problems -- Parallelograms and Triangles (G.1, EE.2)

Find the area of a right triangle (G.1)

Find the area of a parallelogram by decomposing (G.1)

Find the area of a trapezoid by decomposing a parallelogram (G.1)

Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids (G.1)

Simplify addition and subtraction expressions: combining like terms (EE.2)

Read and write an algebraic expression containing a variable (EE.2)

Write word problems as algebraic expressions (EE.2)

Read and write algebraic expressions using parentheses (EE.2)

Evaluate one-step equations by combining like terms (EE.2)

## Big Idea 2: Derive Area Formulas and Solve Problems -- Trapezoids and other Polygons (G.1, G.3, EE.2, EE.3, EE.6)

Draw polygons using given coordinates as vertices (G.3)

Find perimeter and area by finding lengths of sides using coordinates (G.3)

Simplify algebraic expressions by combining like terms (EE.3)

Write equivalent expressions using the Distributive Property of Multiplication over Addition (EE.3)

Understand how variables are used (EE.6)

# Unit 3 Operations with Whole numbers, Fractions, and Decimals

Unit 3 Research and Background Information (pdf)

## Big Idea 1: Multiplication and Division of Whole Numbers and Decimals (NS.2-3)

Divide with two-digit divisors using base ten blocks (NS.2)

Divide 4-digit numbers by 2-digit numbers using long division (no remainder) (NS.2)

Add decimals (NS.3)

Multiply decimals (NS.3)

Multiply multi-digit decimals using the standard algorithm (NS.3)

Divide decimals (NS.3)

## Big Idea 2: Relating, Composing, and Decomposing Decimals and Fractions (NS.3-4)

Find the greatest common factor of two numbers (NS.4)

Find the GCF of two numbers using the distributive property (NS.4)

Find the least common multiple of two numbers (NS.4)

Find the GCF and LCM using prime factorization (NS.4)

## Big Idea 3: Multiplying Fractions and Dividing with Fractions and Whole Numbers (NS.1, NS.3-4)

Multiply fractions by fractions using an algorithm (NS.1)

Multiply fractions by fractions using area models (NS.1)

Simplify fraction multiplication problems using common factors (NS.1)

Divide a fraction by a whole number (NS.1)

Use visual models for division of whole numbers by unit fractions (NS.1)

Use models for division of fractions by fractions (NS.1)

Divide mixed numbers by fractions: using models (NS.1)

Divide fractions by fractions: dividing across (NS.1)

## Big Idea 4: Dividing a Fraction by a Fraction (NS.1, NS.3)

See Big Idea 1-3

# Unit 4 Surface Area of Prisms and Pyramids

Unit 4 Research and Background Information (pdf)

## Big Idea 1: Nets and Surface Area of Prisms (G.1, G.4, EE.2)

Find the area of a right triangle (G.1)

Find the area of a parallelogram by decomposing (G.1)

Find the area of a trapezoid by decomposing a parallelogram (G.1)

Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids (G.1)

Identify the parts of three-dimensional solids (G.4)

Represent three-dimensional figures with nets (G.4)

Find surface area of a rectangular prism (G.4)

Find the surface area of a triangular prism (G.4)

Simplify addition and subtraction expressions: combining like terms (EE.2)

Read and write an algebraic expression containing a variable (EE.2)

Write word problems as algebraic expressions (EE.2)

Read and write algebraic expressions using parentheses (EE.2)

Evaluate one-step equations by combining like terms (EE.2)

## Big Idea 2: Nets and Surface Area of Pyramids (G.1, G.4, EE.2, EE.2c, EE.6)

See Big Idea 1

# Unit 5 Expressions and Equations

Unit 5 Research and Background Information (pdf)

## Big Idea 1: Writing, Interpreting, and Analyzing Expressions (EE.1-2, EE.4, G.1, G.4)

Write numerical expressions involving whole-number exponents (EE.1)

Evaluate numerical expressions by using whole-number exponents (EE.1)

Simplify addition and subtraction expressions: combining like terms (EE.2)

Read and write an algebraic expression containing a variable (EE.2)

Write word problems as algebraic expressions (EE.2)

Read and write algebraic expressions using parentheses (EE.2)

Evaluate one-step equations by combining like terms (EE.2)

Read and write equivalent expression with variables and exponents (EE.4)

Find the area of a right triangle (G.1)

Find the area of a parallelogram by decomposing (G.1)

Find the area of a trapezoid by decomposing a parallelogram (G.1)

Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids (G.1)

Identify the parts of three-dimensional solids (G.4)

Represent three-dimensional figures with nets (G.4)

Find surface area of a rectangular prism (G.4)

Find the surface area of a triangular prism (G.4)

## Big Idea 2: Equivalent Expressions (EE.1-4, NS.4)

Simplify algebraic expressions by combining like terms (EE.3)

Write equivalent expressions using the Distributive Property of Multiplication over Addition (EE.3)

Find the greatest common factor of two numbers (NS.4)

Find the GCF of two numbers using the distributive property (NS.4)

Find the least common multiple of two numbers (NS.4)

Find the GCF and LCM using prime factorization (NS.4)

## Big Idea 3: Representing and Describing Quantitative Relationships (EE.6, EE.9)

Understand how variables are used (EE.6)

Identify independent and dependent variables (EE.9)

Relate independent and dependent variables using a function table (EE.9)

## Big Idea 4: Solving Equations and inequalities (EE.2, EE.3, EE.5-9)

See Big Idea 1-3

Simplify addition and subtraction expressions: combining like terms (EE.2)

Read and write an algebraic expression containing a variable (EE.2)

Write word problems as algebraic expressions (EE.2)

Read and write algebraic expressions using parentheses (EE.2)

Evaluate one-step equations by combining like terms (EE.2)

Understand equations using a number line (EE.5)

Understand how variables are used (EE.6)

Solve addition and subtraction problems:using 1-step equations (EE.7)

Represent the solution set of an inequality using a number line (EE.8)

# Unit 6 Volume of a Rectangular Prism

Unit 6 Research and Background Information (pdf)

## Big Idea 1: Volume Formulas for Rectangular Prisms (G.1-2, G.4, EE.2, EE.6)

Find the area of a right triangle (G.1)

Find the area of a parallelogram by decomposing (G.1)

Find the area of a trapezoid by decomposing a parallelogram (G.1)

Find the volume of a rectangular prism by filling it with unit cubes (G.2)

Find the volume of a 3-dimensional figure composed of 2 rectangular prisms (G.2)

Identify the parts of three-dimensional solids (G.4)

Represent three-dimensional figures with nets (G.4)

Find surface area of a rectangular prism (G.4)

Find the surface area of a triangular prism (G.4)

Simplify addition and subtraction expressions: combining like terms (EE.2)

Read and write an algebraic expression containing a variable (EE.2)

Write word problems as algebraic expressions (EE.2)

Read and write algebraic expressions using parentheses (EE.2)

Evaluate one-step equations by combining like terms (EE.2)

Understand how variables are used (EE.6)

# Unit 7 Ratios and Rates with Fractions, Decimals, and Percents

Unit 7 Research and Background Information (pdf)

## Big Idea 1: Ratios, Fractions, Unit Rates, and Cross-Multiplying (RP.1-3, EE.6-7)

Visualize part-to-part ratios using pictures (RP.1)

Visualize part-to-total ratios using pictures (RP.1)

Understand the difference between fractions and ratios (RP.1)

Understand rates as a type of ratio (RP.2)

Graph ratios using a table (RP.3)

Compare ratios using tables and percents (RP.3)

Find missing values in ratio problems using a table (RP.3)

Solve ratio problems using double number lines (RP.3)

Find the total when the percent and part are known (RP.3)

Understand how variables are used (EE.6)

Solve addition and subtraction problems: using 1-step equations (EE.7)

## Big Idea 2: Ratios with Tape Diagrams and Equations (RP.1-3, EE.6-7)

See Big Idea 1

## Big Idea 3: Percent (RP.3, EE.6-7)

See Big Idea 1

## Big Idea 4: Relate Different Measurement Units (RP.1, RP.3, EE.6-7, EE.9, G.1, G.4)

Identify independent and dependent variables (EE.9)

Relate independent and dependent variables using a function table (EE.9)

Find the area of a right triangle (G.1)

Find the area of a parallelogram by decomposing (G.1)

Find the area of a trapezoid by decomposing a parallelogram (G.1)

Identify the parts of three-dimensional solids (G.4)

Represent three-dimensional figures with nets (G.4)

Find surface area of a rectangular prism (G.4)

Find the surface area of a triangular prism (G.4)

**Unit 8 Analyzing Statistics**

Unit 8 Research and Background Information (pdf)

## Big Idea 1: Displaying Data (SP.1, SP.4-5)

Construct a box plot (SP.4)

Determine the number of observations in a set of data by looking at histograms and line plots (SP.5)

Describe a data set (SP.5)

Summarize a data using the mean, median, and mode (SP.5)

Choose the best measure of center and variability (SP.5)

## Big Idea 2: Summarizing Data: The Mean, the Median (SP.2-5)

Analyze the shape of a graph to describe the distribution of data (SP.2)

Describe the shape of a dot plot (SP.2)

Describe the distribution of data using the mean absolute deviation (SP.2)

Express mean, median, and mode (SP.3)

Identify clusters, peaks, and gaps in a dot plot (SP.3)

## Big Idea 3: Describing Variability in Data (SP.1-5)

See Big Idea 1 and 2

# Unit 9 Rational Numbers and the Coordinate Plane

Unit 9 Research and Background Information (pdf)

## Big Idea 1: Discuss, Compare, and Graph Integers (NS.5-8)

Relate positive and negative quantities (NS.5)

Graph points on a coordinate plane (NS.6)

Reflect points over the x and y axes (NS.6)

Compare fractions: using less than 1/2 or more than 1/2 (NS.6)

Locate rational numbers using a number line (NS.6)

Understand the relationship between two numbers using a number line (NS.7)

Compare two positive or negative numbers in real-world situations (NS.7)

Find absolute value using a number line (NS.7)

Interpret absolute value in real-world situations (NS.7)

Use absolute value to find distance between points (NS.8)

## Big Idea 2: Discuss, Compare, and Graph Rational Numbers (NS.5-8, G.3)

Draw polygons using given coordinates as vertices (G.3)

Find perimeter and area by finding lengths of sides using coordinates (G.3)