Grade 7 Mathematics

Classifying and ordering rational numbers, including positive and negative fractions and decimals, on a number line.

Understanding the addition and subtraction of positive and negative integers through number line models and real-world vectors.

Developing rules for multiplying and dividing integers and applying them to solve contextual problems.

Performing all four operations with positive and negative fractions and decimals, including complex fractions.

Connecting ratios to unit rates and using proportional reasoning to solve complex multi-step problems.

Identifying proportional relationships from tables, graphs, and equations, and understanding the constant of proportionality.

Applying percentage increases and decreases to financial literacy topics like discounts, taxes, and interest.

Solving problems involving finding the whole, finding the part, and finding the percent using various strategies.

Calculating simple interest and understanding its application in savings and loans.

Converting between different units of measurement using ratio reasoning and dimensional analysis.

Applying proportional reasoning to solve a variety of real-world problems, including those involving scale and mixtures.

Consolidating understanding of rational number operations and proportional reasoning through complex problem-solving.

Using variables to represent unknown quantities and simplifying expressions by combining like terms.

Translating verbal phrases into algebraic expressions and evaluating expressions for given variable values.

Applying the commutative, associative, and distributive properties to simplify algebraic expressions.

Mastering the balance method to isolate variables and solve for unknowns in linear equations.

Extending the balance method to solve equations requiring two inverse operations.

Solving one- and two-step equations involving fractions and decimals as coefficients and constants.

Representing ranges of possible solutions using inequalities and graphing them on a number line.

Solving inequalities using addition, subtraction, multiplication, and division, and graphing the solution sets.

Applying inverse operations to solve two-step inequalities and interpreting the solution in context.

Translating complex word problems into algebraic equations or inequalities and solving them.

Reviewing and applying all concepts related to expressions, equations, and inequalities through integrated problems.

Understanding the concept of a function as a rule that assigns each input exactly one output.

Investigating complementary, supplementary, vertical, and adjacent angles to solve for unknown values.

Discovering and applying the triangle sum theorem and exterior angle theorem.

Investigating the sum of interior and exterior angles in various polygons.

Discovering the constant relationship between circumference and diameter and calculating area.

Calculating the area of complex shapes by decomposing them into simpler geometric figures.

Using proportions to create and interpret scale versions of maps and blueprints.

Using tools like compass and straightedge to construct basic geometric shapes and angles.

Describing the 2D cross sections that result from slicing three-dimensional solids.

Understanding and performing translations of 2D figures on a coordinate plane.

Understanding and performing reflections of 2D figures across the x-axis, y-axis, and other lines.

Understanding and performing rotations of 2D figures around a point on a coordinate plane.

Understanding and performing dilations of 2D figures, including scale factor and center of dilation.

Visualizing 3D shapes through nets and identifying their faces, edges, and vertices.

Calculating the total surface area of rectangular and triangular prisms using nets and formulas.

Calculating the total surface area of square and triangular pyramids.

Developing the formula for volume by understanding layers of area.

Understanding the relationship between the volume of a pyramid and a prism with the same base and height.

Calculating the volume of cylinders and solving real-world problems involving cylindrical objects.

Applying surface area and volume concepts to solve multi-step real-world problems.

Exploring the basic properties of spheres and cones and their real-world applications.

Calculating the volume of cones and spheres using their respective formulas.

Understanding the concept of density and using it to solve problems involving mass and volume.

Comprehensive review of all 3D figure calculations and problem-solving strategies.

Discovering the relationship between the sides of a right triangle and applying the Pythagorean theorem.

Distinguishing between biased and representative samples to ensure valid conclusions.

Using data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Calculating and interpreting mean, median, and mode for various data sets.

Understanding and calculating range and interquartile range to describe data spread.

Using mean, median, and mean absolute deviation to compare two different populations.

Creating and interpreting box plots to identify trends and patterns, including quartiles and outliers.

Creating and interpreting histograms to display the distribution of numerical data.

Calculating the mathematical likelihood of simple and compound events.

Conducting trials and comparing observed results to expected theoretical values.

Using probability to assess risk and make informed predictions in games and insurance.