Identify absolute value, graph and compare rational numbers on a number line. 

Add and subtract rational numbers. 

How can understanding absolute value and the placement of rational numbers on a number line help us compare, add, and subtract them effectively?

Multiply and divide rational numbers. 

Convert between fractions and decimals. 

How can understanding the relationships between fractions, decimals, and rational numbers help us perform operations and solve real-world problems?

Simplify algebraic expressions by combining like terms.

Add and subtract linear expressions.

Apply the Distributive Property to create equivalent expressions.

Factor algebraic expressions.

How can simplifying and creating equivalent algebraic expressions help us understand and solve mathematical problems more efficiently?

Write and solve equations using addition or subtraction.

Write and solve equations using multiplication or division.

Write and solve two-step equations.

 How can you use properties of equality to solve equations?

Writing and solving proportions with variables.    

Use proportions to solve ratio problems.

Determine if two quantities represent a proportional relationship. 

Convert from percent to decimal & from decimal to percent. 

Convert percents to simplified fractions & fractions to percents.

Compare & Order Fractions, Decimals & Percents

Solve percent problems using proportional relationships (parts & wholes) and equations.

Calculate and explain percent increase & decrease

Calculate and explain mark ups & discounts

How can understanding proportions, ratios, and percents help us analyze relationships, solve problems, and make informed decisions in real-world situations?

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring

Explain and interpret the likelihood of an event occuring using a number between 0 and 1. 

Approximate the probability of an event by collecting data

Develop a model and use it to determine the probability of an event

Explain and identify the probability of compound events

Represent compound events using a model

Design a simulation for compound events

How can understanding and modeling probability help us predict and analyze the likelihood of single and compound events in real-world situations?

Explain the relationship between the diameter and circumference of a circle.

Use a formula to find the circumference of a circle.

Estimate the area of a circle. 

Use a formula to find the area of a circle

Use a grid to estimate perimeters and areas. 

Identify the shapes that make up a composite figure. 

Find the perimeters and areas of shapes that make up composite figures. 

Use technology to draw polygons.

Determine whether given measures result in one triangle, many triangles, or no triangle.

Draw polygons given angle measures or side lengths. 

Identify adjacent, complementary, supplementary, and vertical angles.

Use equations to find unknown angle measures. 

Find unknown angle measures in real-life situations.

How can understanding the properties of circles, polygons, and angles help us solve problems involving measurement, geometry, and real-world applications?

Find missing angle measures created by the intersections of lines.

Understand properties of interior and exterior angles of triangles.

Find interior angle measures of polygons.

Use similar triangles to find missing measures.

How can understanding the relationships between angles, triangles, and polygons help us solve problems and find missing measures in geometric figures?

Calculate the surface area of a prism. 

Calculate the surface area of a cylinder.

Calculate the surface area of a pyramid.

Calculate the volume of a prism. 

Calculate the volume of a pyramid.

Describe the cross section of a solid.

How can understanding surface area, volume, and cross-sections help us analyze and solve problems involving three-dimensional shapes?

Find the volume of a cylinder.

Find the volume of a cone.

Find the volume of a sphere.

Find the surface areas and volumes of similar solids.

How can understanding the formulas for volume and surface area help us solve problems involving cylinders, cones, spheres, and similar solids?

Use exponents to write and evaluate expressions. 

Understand the concept of scientific notation.

How can understanding exponents and scientific notation help us represent and work with very large or very small numbers in real-world and mathematical contexts?

Understand the concept of a square root of a number

Understand the Pythagorean Theorem.

Understand the concept of a cube root of a number

How can understanding square roots, cube roots, and the Pythagorean Theorem help us solve problems involving geometry and the relationships between numbers?

Translate figures in the coordinate plane.

Reflect figures in the coordinate plane.

Rotate figures in the coordinate plane.

Understand the concept of congruent figures.

Dilate figures in the coordinate plane.

Understand the concept of similar figures.

Find perimeters and areas of similar figures.

How can transformations in the coordinate plane help us understand congruence, similarity, and the relationships between shapes and their measurements?