M07.A-N: The Number System

M07.A-N.1: Apply and extend previous understandings of operations to add, subtract, multiply, and divide rational numbers.

M07.A-N.1.1: Solve real-world and mathematical problems involving the four operations with rational numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Population Size
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

M07.A-N.1.1.1: Apply properties of operations to add and subtract rational numbers, including real-world contexts.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Sums and Differences with Decimals

M07.A-N.1.1.2: Represent addition and subtraction on a horizontal or vertical number line.

Adding and Subtracting Integers
Adding on the Number Line
Fractions Greater than One (Fraction Tiles)

M07.A-N.1.1.3: Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

M07.A-R: Ratios and Proportional Relationships

M07.A-R.1: Demonstrate an understanding of proportional relationships.

M07.A-R.1.1: Analyze, recognize, and represent proportional relationships and use them to solve real-world and mathematical problems.

M07.A-R.1.1.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Road Trip (Problem Solving)
Unit Conversions

M07.A-R.1.1.2: Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

M07.A-R.1.1.3: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Beam to Moon (Ratios and Proportions)
Dilations
Direct and Inverse Variation
Perimeters and Areas of Similar Figures
Similar Figures

M07.A-R.1.1.4: Represent proportional relationships by equations.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Geometric Probability
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers
Theoretical and Experimental Probability

M07.A-R.1.1.5: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.

Direct and Inverse Variation

M07.A-R.1.1.6: Use proportional relationships to solve multi-step ratio and percent problems.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Proportions and Common Multipliers

M07.B-E: Expressions and Equations

M07.B-E.1: Represent expressions in equivalent forms.

M07.B-E.1.1: Use properties of operations to generate equivalent expressions.

M07.B-E.1.1.1: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Algebraic Equations II

M07.B-E.2: Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

M07.B-E.2.1: Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

M07.B-E.2.1.1: Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

M07.B-E.2.2: Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.

M07.B-E.2.2.1: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

Absolute Value Equations and Inequalities
Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Order of Operations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

M07.B-E.2.2.2: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.

Absolute Value Equations and Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

M07.C-G: Geometry

M07.C-G.1: Demonstrate an understanding of geometric figures and their properties.

M07.C-G.1.1: Describe and apply properties of geometric figures.

M07.C-G.1.1.1: Solve problems involving scale drawings of geometric figures, including finding length and area.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

M07.C-G.1.1.2: Identify or describe the properties of all types of triangles based on angle and side measures.

Concurrent Lines, Medians, and Altitudes

M07.C-G.1.1.3: Use and apply the triangle inequality theorem.

Triangle Inequalities

M07.C-G.2: Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.

M07.C-G.2.1: Identify, use, and describe properties of angles and their measures.

M07.C-G.2.1.1: Identify and use properties of supplementary, complementary, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Investigating Angle Theorems
Triangle Angle Sum

M07.C-G.2.1.2: Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).

Triangle Angle Sum

M07.C-G.2.2: Determine circumference, area, surface area, and volume.

M07.C-G.2.2.1: Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.

Circumference and Area of Circles

M07.C-G.2.2.2: Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

M07.D-S: Statistics and Probability

M07.D-S.1: Use random sampling to draw inferences about a population.

M07.D-S.1.1: Use random samples.

M07.D-S.1.1.1: Determine whether a sample is a random sample given a real-world situation.

Polling: City

M07.D-S.1.1.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Polling: City
Polling: Neighborhood
Populations and Samples

M07.D-S.2: Draw comparative inferences about populations.

M07.D-S.2.1: Use statistical measures to compare two numerical data distributions.

M07.D-S.2.1.1: Compare two numerical data distributions using measures of center and variability.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

M07.D-S.3: Investigate chance processes and develop, use, and evaluate probability models.

M07.D-S.3.1: Predict or determine the likelihood of outcomes.

M07.D-S.3.1.1: Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event).

Independent and Dependent Events
Spin the Big Wheel! (Probability)

M07.D-S.3.2: Use probability to predict outcomes.

M07.D-S.3.2.1: Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability.

Probability Simulations
Theoretical and Experimental Probability

M07.D-S.3.2.2: Find the probability of a simple event, including the probability of a simple event not occurring.

Independent and Dependent Events
Theoretical and Experimental Probability

M07.D-S.3.2.3: Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation.

Independent and Dependent Events
Theoretical and Experimental Probability