8th Grade Math

In this unit, eighth graders will explore the movement of shapes using terms like “translations,” “rotations,” and “reflections,” describing and analyzing sequences of transformations on a coordinate plane. They’ll compare shapes before and after transformations, focusing on side lengths and angles to determine congruence. Students will also explore the effects of transformations on parallel and intersecting lines while calculating unknown angle measures using vertical, supplementary, and alternate interior angles. By applying the Triangle Sum Theorem, they will solve problems involving triangles and deepen their understanding of rigid transformations in real-world contexts.

• Unit 1.1: Describe the movement of shapes using the terms “clockwise,” “counterclockwise,” “translations,” “rotations,” and “reflections” of figures.
• Unit 1.2: Use the terms translation, rotation, and reflection to precisely describe transformations and explain a sequence of transformations that takes one figure to its image.
• Unit 1.3: Apply transformations to points on a coordinate plane and name the coordinates of points in the image of a transformation.
• Unit 1.4: Apply a sequence of transformations to points on a coordinate plane. Determine whether the order of a sequence of transformations has an effect on the image.
• Unit 1.5: Compare measurements of sides and angles on a shape before and after rigid transformations.
• Unit 1.6: Rotate a line segment 180 degrees around its midpoint, a point on the segment, and a point not on the segment. Generalize the outcomes of rotating a segment 180 degrees around different points.
• Unit 1.7: Describe the effects of a rigid transformation on a pair of parallel lines.
• Unit 1.8: Understand that a rotation by 180 degrees about a point of two intersecting lines moves each angle to the angle that is vertical to it.
• Unit 1.9: Determine whether two shapes are congruent by using properties of rigid transformations and each shape’s area and perimeter.
• Unit 1.10 Use the properties of a straight angle to calculate supplementary angle measures.
• Unit 1.11: Apply what you know about vertical angles and supplementary angles to calculate the measures of unknown angles.
• Unit 1.12: Calculate angle measures using alternate interior, vertical, and supplementary angles to solve problems.
• Unit 1.13: Apply the Triangle Sum Theorem and supplementary angles to calculate the unknown angles interior and exterior to triangles.

Click here to download a PDF version of Unit 1: Rigid Transformations and Congruence

In this unit, eighth graders will explore dilations by applying a scale factor to polygons, both from the origin and other centers of dilation. They will identify sequences of transformations to determine why two figures are similar and understand that similar polygons have congruent angles and proportional sides. Students will explore similarity in triangles by verifying congruent angles and using scale factors to calculate unknown side lengths. They’ll also recognize that the ratios of side lengths in similar triangles are equal. Additionally, students will find the slope of a line using slope triangles, write equations for lines, and determine whether a point lies on a given line using its equation.

• Unit 2.1: Dilate polygons given a scale factor and the origin as the center of dilation.
• Unit 2.2: Perform dilations given a scale factor and center of dilation that is not the origin.
• Unit 2.3: Identify a sequence of transformations that takes one figure on top of another to explain why two figures are similar.
• Unit 2.4: Understand that similar polygons have congruent corresponding angles and proportional corresponding sides.
• Unit 2.5: Determine that two triangles are similar by checking that two pairs of corresponding angles are congruent.
• Unit 2.6: Calculate unknown side lengths in similar triangles using the scale factor between similar triangles.
• Unit 2.7: Understand that the quotients of pairs of side lengths in similar triangles are equal.
• Unit 2.8: Find the slope of a line on a grid using properties of slope triangles.
• Unit 2.9: Write an equation for a line.
• Unit 2.10: Use an equation of a line to determine if a point is on the line.

Click here to download a PDF version of Unit 2: Dilations, Similarity, and Introducing Slope

In this unit, eighth graders will represent proportional relationships using graphs, equations, tables, and real-life contexts. They’ll explore the connections between unit rate, constant of proportionality, and slope, and determine the rate of change from various representations. Students will interpret pairs of values in relation to equations or graphs and represent linear relationships through different formats. They’ll analyze the y-intercept and slope to identify proportions and write equations for lines using points to find the y-intercept. Additionally, students will compare linear relationships, interpret and represent negative rates of change, and write equations for both horizontal and vertical lines.

• Unit 3.1: Represent proportions with graphs, equations, tables and stories.
• Unit 3.2: Connect the meaning of the unit rate, the constant of proportionality and the slope.
• Unit 3.3: Find the rate of change of a proportional relationship given the graph, equation, table, or situation.
• Unit 3.4: Make meaning of pairs of values that satisfy or do not satisfy a given equation or graph.
• Unit 3.5: Represent linear relationships with a graph, equation, table and story.
• Unit 3.6: Interpret the y-intercept and slope for linear graphs. Determine if they are proportions.
• Unit 3.7: Write an equation for the line by using two points to find the y-intercept.
• Unit 3.8: Compare linear relationships using the given context.
• Unit 3.9: Represent and interpret linear relationships with negative rates of change.
• Unit 3.10: Write an equation and find the x-intercept for linear relationships with negative rates of change.
• Unit 3.11:Write equations for horizontal and vertical lines.

Click here to download a PDF version of Unit 3: Linear Relationships

In this unit, eighth graders will master solving linear equations by performing balanced moves on both sides and using various strategies, including handling subtraction symbols, applying the distributive property, and combining like terms. They’ll solve equations with variables on both sides and determine if a linear equation has one solution, no solutions, or infinitely many solutions. Students will learn about systems of equations, identifying solutions and their meanings through graphs, and solving systems using methods such as substitution and elimination. They’ll also explore solutions for equations involving fractions and determine the nature of solutions for systems of equations using both graphical and algebraic methods.

• Unit 4.1: Solve linear equations by performing balanced moves on both sides.
• Unit 4.2: Solve linear equations by thinking about the subtraction symbol in two different ways.
• Unit 4.3: Solve linear equations with the distributive property.
• Unit 4.4: Solve linear equations with variables on both sides.
• Unit 4.5: Solve linear equations by combining like terms.
• Unit 4.6: Determine whether a linear equation has one solution, no solutions, or infinitely many solutions.
• Unit 4.7: Understand what a system of equations is. Determine whether a system of equations will have one solution, no solution or infinitely many solutions using graphs.
• Unit 4.8: Determine if a point is a solution to a system of equations and explain its meaning.
• Unit 4.9: Understand how to find a solution to a system of equations by setting two expressions equal to each other.
• Unit 4.10: Solve equations with fractions.
• Unit 4.11: Find the solution for a system of equations using substitution.
• Unit 4.12: Find the solution for a system of equations using elimination.
• Unit 4.13: Determine whether a system of equations will have one solution, no solutions or infinitely many solutions using equations.

Click here to download a PDF version of Unit 4: Rational Number Arithmetic

In this unit, eighth graders will explore the concept of exponents and their rules, beginning with expressions that represent repeated multiplication and division. They will generalize and apply exponent rules, including those for multiplication and division with a base of 10, and for negative exponents. Students will extend these rules to any nonzero base and use them to simplify expressions with positive exponents. They will describe and compare large and small numbers using powers of 10, and apply exponent rules to solve problems. Additionally, students will work with scientific notation, converting between forms, and perform operations such as multiplication, division, addition, and subtraction in scientific notation, using these skills to compare and solve problems.

• Unit 5.1: Compare quantities using expressions that represent repeated multiplication, and comprehend that repeated division of a number is equivalent to repeated multiplication by its reciprocal.
• Unit 5.2: Generalize the exponent rule 10n ∙ 10m = 10n+m and write equivalent exponential expressions of multiplication expressions with a base of 10.
• Unit 5.3: Explain and use a rule for raising a power of 10 to a power, that (10^n)^m = 10^(n•m)
• Unit 5.4: Generalize the exponent rule 10m 10n = 10n-m and write equivalent exponential expressions of division expressions with a base of 10.
• Unit 5.5: Generalize the exponent rule 10-n = 10n 1 and write equivalent exponential expressions involving negative exponents.
• Unit 5.6: Generalize exponent rules for bases other than 10, and use exponent rules to write equivalent exponent expressions for any nonzero base.
• Unit 5.7: Use an appropriate exponent rule to rewrite an expression with a single, positive exponent.
• Unit 5.8: Generalize a process for multiplying expressions with different bases having the same exponent.
• Unit 5.9: Describe large and small numbers as multiples of powers of 10.
• Unit 5.10: Compare large numbers using powers of 10.
• Unit 5.11: Represent small numbers as multiples of powers of 10, and compare numbers using powers of 10.
• Unit 5.12: Use exponent rules and powers of 10 to solve problems in context.
• Unit 5.13: Identify numbers written in scientific notation, and rewrite numbers written in different forms in scientific notation.
• Unit 5.14: Multiply and divide numbers in scientific notation, and use scientific notation and estimation to compare quantities.
• Unit 5.15: Add and subtract numbers in scientific notation.

Click here to download a PDF version of Unit 5: Exponents and Scientific Notation

In this unit, eighth graders will explore various concepts related to square and cube roots, starting with finding the area of a tilted square and using square root notation to determine the side length of a square given its area. They will classify rational and irrational numbers and find decimal approximations for square roots, placing these approximations on the number line. Students will learn about the Pythagorean Theorem, a2 + b2 = c2, including its proof and application for calculating unknown side lengths and identifying right triangles. They will use the theorem to solve contextual problems and calculate distances on the coordinate plane. Additionally, students will understand cube roots, represented by ∛a, and determine the whole numbers between which a cube root lies.

• Unit 6.1: Find the area of a tilted square
• Unit 6.2: Comprehend “square root” and use square root notation to express the side length of a square, given its area.
• Unit 6.4: Classify rational and irrational numbers
• Unit 6.4: Find decimal approximation for square roots
• Unit 6.5: Find a decimal approximation for square roots and locate its approximation on the number line
• Unit 6.6: Comprehend the term “Pythagorean Theorem” as the equation a2 + b2 = c2.
• Unit 6.7: Explain the Pythagorean Theorem proof and calculate unknown sides
• Unit 6.8: Calculate unknown side lengths using the Pythagorean Theorem
• Unit 6.9: Use the converse of the Pythagorean Theorem to determine right triangles
• Unit 6.10: Use the Pythagorean Theorem to solve problems within a context
• Unit 6.11: Calculate distance in the coordinate plane by using the Pythagorean Theorem
• Unit 6.12: Comprehend the term “cube root of a” and the notation ∛a
• Unit 6.13: Determine the whole numbers that a cube root lies between

Click here to download a PDF version of Unit 6: Pythagorean Theorem and Irrational Numbers