Grade 7 Math Practice

Students will substitute given values for variables and evaluate algebraic expressions to find their numerical value.

Students will graph linear equations in two variables, understanding the relationship between the equation and its graphical representation.

Students will recognize when two algebraic expressions are equivalent and generate equivalent expressions using properties of operations.

Students will interpret algebraic expressions as representing a quantity in a real-world context.

Students will learn to write and simplify algebraic expressions involving variables, constants, and arithmetic operations.

Students will represent relationships between quantities using equations and use these equations to solve problems.

Students will solve one-step linear equations in one variable by using inverse operations to isolate the variable.

Students will solve one-step linear inequalities in one variable and represent the solution set on a number line.

Students will translate verbal phrases and word problems into algebraic expressions and vice versa.

Students will use properties of operations (commutative, associative, distributive) to generate equivalent expressions.

Students will understand that a variable represents an unknown quantity and that an equation expresses a relationship between quantities.

Students will write and solve two-step linear equations in one variable, understanding the process of undoing operations.

This topic covers performing addition, subtraction, multiplication, and division with integers, fractions, and decimals, including those involving negative numbers.

This topic deepens the understanding of operations (addition, subtraction, multiplication, division) with positive and negative integers and rational numbers.

Students will apply their understanding of percentages to solve problems involving discounts, interest, taxes, and markups.

Students will analyze proportional relationships and understand how to calculate and interpret unit rates in various contexts.

This topic focuses on solving real-world and mathematical problems that require multiple steps and involve addition, subtraction, multiplication, and division of rational numbers.

Analyze and compare datasets using measures of center and measures of variability, understanding how to interpret and draw conclusions from statistical information.

Use a variety of tools to perform geometric constructions, including bisecting a segment, bisecting an angle, and constructing perpendicular lines, and understand the reasoning behind these constructions.

Develop probability models and use them to find probabilities of simple events, understanding the relationship between experimental and theoretical probability.

Explore and apply the properties of operations (associative, commutative, distributive) to sums, differences, products, and quotients of rational numbers, including those involving variables.

Understand and apply the properties of angles formed by intersecting lines, including vertical angles, adjacent angles, and angles formed by parallel lines and transversals. This also includes the sum of interior angles of a triangle.

Apply formulas for the circumference and area of a circle, understanding the role of pi. Students will solve problems involving circles, including finding missing dimensions when given area or circumference.

Develop and apply formulas for the circumference and area of circles. Students will understand the relationship between the radius, diameter, circumference, and area, and solve problems involving these concepts.

Describe the two-dimensional shapes that result from slicing three-dimensional figures (e.g., cubes, prisms, pyramids) in various ways.

Explore and apply properties of geometric figures, including angles formed by parallel lines and transversals, and the sum of angles in a triangle. This also includes understanding the relationships between sides and angles in various polygons.

Understand the relationship between scale drawings and the actual lengths, areas, and volumes of geometric figures. This includes calculating actual measurements from scale drawings and creating scale drawings from given measurements.

Calculate the surface area of prisms and cylinders. This involves understanding the concept of surface area and applying formulas to find the total area of all faces.

Solve real-world and mathematical problems involving area, volume, and surface area of two-dimensional and three-dimensional objects. This includes calculating these measures for composite shapes.

Calculate the volume of prisms and cylinders. Students will use formulas to find the amount of space occupied by these three-dimensional figures.

Compare observational data from two populations, using measures of center and variability, to draw informal comparative inferences.

Calculate the probability of compound events by using systematic lists, tables, tree diagrams, or simulations, and understand the difference between independent and dependent events.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring, and use probability models to describe probability.

Use measures of center (median, mean) and measures of variability (interquartile range, mean absolute deviation) to draw informal comparative inferences about two populations.

Understand that random sampling is a process to draw conclusions about a population from a sample, and recognize that larger samples are more likely to be representative.