Sub Unit 1: Area
Calculate the area of parallelograms and triangles.
Calculate the area of polygons by decomposing them into rectangles and triangles or by enclosing and subtracting.
Describe the relationship betwee a base of a parallelogram or triangle and its corresponding height using mathematically precise language.
Analyze strategies for determining the area of polygons using mathematically precise language.
Sub Unit 2: Surface Area
Connect polyhedra with nets that represent them.
Calculate the surface area of polyhedra made up of rectangles and triangles.
Describe the polyhedron that can be assembled from a given net using mathematically precise language, including terms such as face, edge, prism, and pyramid.
Analyze strategies for determining the surface area of polyhedra using mathematically precise language, including terms such as face ,edge, base, and height.
Sub Unit 1: Ratios
Use tables, double number lines, and ratios per 1 to solve problems with equivalent ratios.
Describe ratio relationships between two quantities using appropriate notation and mathematically precise language.
Analyze strategies for solving problems involving equivalent ratios, including using tables and double number lines.
Sub Unit 2: Common Factors and Multiples
Determine the least common multiple and greatest common factor of two numbers.
Interpret least common multiples and greatest common factors in mathematical and real-world situations.
Sub Unit 3: Solving Problems with Ratios
Compare ratios in context using a variety of strategies.
Solve real-world and mathematical problems using double number lines and tables of equivalent ratios.
Describe strategies for comparing ratios in context.
Interpret different representations of a ratio relationship to make sense of a situation in context.
Sub Unit 1: Units and Measurement
Use ratio reasoning to convert between units of measurement.
Explain why it takes more of a smaller unit or fewer of a larger unit to measure the same quantity.
Describe connections between units of measurement and the measurements of everyday objects.
Sub Unit 2: Unit Rates
Recognize and calculate two unit rates for the same ratio relationship.
Use unit rates to solve problems involving tables of equivalent ratios.
Identify and describe the two unit rates associated with a ratio (i.e., a/b and b/a for the ratio a:b)
Sub Unit 3: Percentages
Use ratio reasoning to determine unknown parts, wholes, and percentages.
Describe connections between percentages, ratios, and rates.
Sub Unit 1: Introduction to Dividing Fractions
Create and interpret diagrams that represent dividing whole numbers by fractions.
Analyze diagrams that represent dividing whole numbers by fractions.
Sub Unit 2: Dividing Fractions
Use a variety of strategies to calculate quotients of fractions.
Solve problems that involve dividing fractions.
Describe connections between division problems, diagrams, and questions asking "How many groups?" or "How many in 1 group?" and explain a solution method using mathematically precise language.
Sub Unit 3: Area and Volume with Fractions
Use division of fractions to compare lengths.
Solve problems about areas and volumes with fractional dimensions.
Analyze strategies for solving problems involving fractional lengths using mathematically precise language.
Sub Unit 1: Adding and Subtracting Decimals
Add and subtract multi-digit decimals using a variety of strategies.
Explain how to attend to place value when adding and subtracting multi-digit decimals.
Sub Unit 2: Multiplying Decimals
Multiply multi-digit decimals using a variety of strategies.
Compare and contrast different strategies for multiplying multi-digit decimals.
Sub Unit 3: Division and Dividing Decimals
Divide multi-digit decimals using a variety of strategies.
Divide multi-digit numbers with and without remainders using long division.
Compare and contrast different strategies for dividing multi-digit decimals.
Sub Unit 4: Solving Problems with Decimals
Use decimal operations to solve problems in context.
Explain how operations with decimals relate to real-world problems.
Sub Unit 1: Solving Equations
Write and solve equations in the form of x + p = q and px=q.
Describe a situation that could be represented by an equation of the form x + p = q or px=q, for a rational number p and unknown x.
Interpret diagrams that represent equations of the form x + p = q or px=q.
Sub Unit 2: Equivalent Expressions
Use properties to write equivalent expressions with variables.
Analyze expressions to determine if they are equivalent.
Caregiver Support Resource (Lessons 1-9)
Sub Unit 3: Expressions Involving Exponents
Evaluate numerical and variable expressions with whole number exponents and one or more other operations.
Describe a pattern that could be expressed using exponents.
Interpret expressions with exponents using language like to the power.
Sub Unit 4: Introduction to Representing Relationships
Use tables, equations, and graphs to represent relationships.
Interpret an equation that represents the relationship between two quantities by identifying dependent and independent variables.
Analyze the relationship between quantities using tables, equations, and graphs.
Caregiver Support Resource (Lessons 10-16)
Sub Unit 1: Negative Numbers and Absolute Values
Order and compare positive numbers, negative numbers, and 0.
Evaluate, order, and compare absolute values.
Interpret positive numbers, negative numbers, 0, and absolute value in context.
Sub Unit 2: Inequalities
Write inequalities using symbols and words.
Graph solutions to inequalities on a number line.
Interpret the meaning of an inequality in context.
Justify whether a number is a solution to an inequality.
Sub Unit 3: The Coordinate Plane
Graph points with positive and negative coordinates.
Draw polygons on the coordinate plane and determine their vertical and horizontal side lengths.
Describe the relationship between ordered pairs that differ only by the signs of their coordinates.
Interpret the meaning of an ordered pair in context.