Math 8

Adopted June 7, 2022

Download/ Print Math 8

Grades 6-8 Math Competency Checklist

K-12 Math Competencies

Download/ Print Math Curriculum

Suggested Pacing Guide for iReady

Recommended Middle School Pathways

Decision Point Guide for MS Placement

Appendix

Additional Educator Resources

AK Standards for Mathematical Practice

Course Details:

Grades: 7-8

Length: two semesters

Prerequisite:

- Math 7 or
- Math 6 and teacher recommendation

Placement recommendation:

When making decisions about placement, always consider student reflection, assessment data, teacher recommendation, and parent input. (See the flowchart.)

Course Description:

In Math 8, students make several advances in their algebraic reasoning, particularly as it relates to linear equations. Students extend their understanding of proportional relationships to include all linear equations, and they consider what a “solution” looks like when it applies to a linear equation. They learn that linear equations can be a useful representation to model bivariate data and to make predictions. Lastly, students study figures, lines, and angles in two-dimensional and three-dimensional space, investigating how these figures move, and how they are measured. This course prepares students to take Algebra 1.

Mathematical Topics

(Recommended Order)

Semester 1

Solving Linear Equations and Inequalities (One Variable)
Rigid Transformations, Congruence, and Similarity
Angle Relationships
Linear Equations and Graphs

Semester 2

Integer Exponents and Scientific Notation
Numeracy (Rational and Irrational Numbers): can easily be covered within other units
Pythagorean Theorem
Volumes (Cylinders, Cones and Spheres)
Two-Way Categorical Tables and Associations

Course/ Grade Competencies

Semester 1

M1.7-8.1: The learner will reason abstractly and manipulate symbolic expressions to represent relationships and interpret expressions and equations in terms of a given context for determining an unknown value.
M2.7-8.1: The learner will expand their understanding of number systems thinking flexibly and attending to precision and reasonableness when solving problems using rational and irrational numbers.
M3.7-8.1: The learner will expand the use of computational strategies, algorithms, and proportional reasoning to rational and irrational numbers.
M3.7-8.2: The learner will use reasoning and metacognitive skills through making conjectures, justifying, and effectively communicating mathematical solutions and arguments.
M4.7-8.1: The learner will strategically use tools and apply proportional reasoning and precision to solve measurement problems in pure/ theoretical and authentic applied contexts.
M5.7-8.1: The learner will make use of structure to describe and compare situations that involve proportionality, change, or patterns, and use the information to make conjectures and justify conclusions/ solutions.
M6.7-8.1: The learner will solve problems involving reasoning using properties of two- and three- dimensional shapes to analyze, represent, and model geometric relationships in pure/ theoretical and authentic applied contexts.

Semester 2

M1.7-8.1: The learner will reason abstractly and manipulate symbolic expressions to represent relationships and interpret expressions and equations in terms of a given context for determining an unknown value.
M2.7-8.1: The learner will expand their understanding of number systems thinking flexibly and attending to precision and reasonableness when solving problems using rational and irrational numbers.
M3.7-8.1: The learner will expand the use of computational strategies, algorithms, and proportional reasoning to rational and irrational numbers.
M3.7-8.2: The learner will use reasoning and metacognitive skills through making conjectures, justifying, and effectively communicating mathematical solutions and arguments.
M4.7-8.1: The learner will strategically use tools and apply proportional reasoning and precision to solve measurement problems in pure/ theoretical and authentic applied contexts.
M5.7-8.1: The learner will make use of structure to describe and compare situations that involve proportionality, change, or patterns, and use the information to make conjectures and justify conclusions/ solutions.
M6.7-8.1: The learner will solve problems involving reasoning using properties of two- and three- dimensional shapes to analyze, represent, and model geometric relationships in pure/ theoretical and authentic applied contexts.
M7.7-8.1: The learner will design investigations and conduct probability experiments involving populations.

Solving Linear Equations & Inequalities With One Variable

Graduate-Level Competency:

M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.

M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.1

M3.7-8.2

Content Objectives:

Must be Covered:

The learner will:

- Know the definitions of a constant and a coefficient.
- Know the difference between an expression and an equation.
- Be able to evaluate expressions using substitution.
- Be able to simplify expressions by combining like terms and or applying the distributive property.
- Know that for the expression x, the coefficient is 1 and the constant is 0.

Standards:

AKSS

Mathematical Practices

All mathematical practices are present in each unit.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.2

M5.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Solve one- or two-step equations by isolating x, or changing the associated constant to 0 with addition or subtraction and the coefficient to 1 with multiplication or division.
- Solve multistep equations and understand there are multiple ways to do this.
- Solve equations with variables on both sides.
- Solve equations involving simplifying one or both sides by distributing and or combining like terms.
- Recognize when equations have infinite or no solutions.
- Write and solve equations based on word problems, including those where one variable must be written in terms of another.

Can be Covered:

The learner will:

Solving equations where clearing of fractions or cross-multiplying is involved.

Standards:

AKSS

Mathematical Practices

All mathematical practices are present in each unit.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.2

M5.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Understand inequalities and their symbols.
- Graph inequalities on the number line.
- Write inequalities given a graph on the number line.
- Solve simple multi-step inequalities, including those where the inequality must be flipped.

Standards:

AKSS

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

iReady unit 3, lessons 10 and 11

Rigid Transformations, Congruence, & Similarity

Graduate-Level Competency:

M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.

M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.

M6 - Geometry: The learner will solve problems involving spatial reasoning and model geometric concepts in applied contexts.

Course/ Grade Competencies:

M3.7-8.2

M4.7-8.1

M6.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Know what congruent means and be able to recognize congruent figures.
- Know that if two figures are congruent, then one can be mapped onto the other with a sequence of rigid transformations
- Know the three rigid transformations are translations, reflections, and rotations.
- Be able to perform each transformation given the specific rule and graph paper (reflections will be over simple vertical or horizontal lines, and rotations will be in increments of 90 degrees).
- Be able to write the rule for transformations given an image on the coordinate plane (reflections will be over simple vertical or horizontal lines, and rotations will be in increments of 90 degrees).
- Be able to perform or write rules for simple sequences of translations.

Standards:

AKSS

8.G.1,

8.G.2

Mathematical Practices

All mathematical practices are present in each unit.

Course/ Grade Competencies:

M1.7-8.1

M3.7-8.1

M4.7-8.1

M5.7-8.1

M6.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Define, describe, and perform dilations in the coordinate plane.
- Determine if two figures are similar using transformations and dilations.
- Understand angle measurement and parallel or perpendicular relationships are preserved under similarity.
- Find and use scale factor.
- Use properties of similar triangles to model and solve problems.

Standards:

AKSS

8.G.3,

8.G.4

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

- Tessellation art project
- iReady units 1 and 2 (not lessons 6 and 7)

Angle Relationships

Graduate-Level Competency:

M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.

M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.

M6 - Geometry: The learner will solve problems involving spatial reasoning and model geometric concepts in applied contexts.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.2

M4.7-8.1

M6.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Identify vertical, supplementary, and complementary angles.
- Identify corresponding angles, alternate interior and alternate exterior angles in parallel lines and transversals.
- Know the relationships between all of the above angles.
- Define and use the interior angle sum for triangles.
- Define and use the exterior angle sum for triangles.
- Define and use the angle-angle criterion for similar triangles.
- Solve for missing angles and or variables using equations.

Can be Covered:

The learner will:

Use the interior angle sum to derive the formula (n-2)180 for finding the sum of interior angles for any polygon with n sides.

Standards:

AKSS

8.G.5

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

iReady unit 2, lessons 6 and 7

Linear Equations & Graphs

Graduate-Level Competency:

M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.

Course/ Grade Competencies:

M5.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Know that linear equations can be represented in tables, graphs, and equations.
- Know the four quadrants of the coordinate plane.
- Know the x and y axes and the origin.
- Be able to interpret scale for both axes.
- Understand that x is the independent variable and y is the dependent variable.
- Be able to graph linear equations from a table of values.
- Understand slope as rise over run or a unit rate.
- Determine slopes from graphs or word problems.
- Understand the meaning of y intercept as the value of y when x is 0.
- Be able to identify the y intercept from graphs or simple word problems
- Recognize slope intercept form as y = mx + b, where m or slope is the coefficient of x.
- Recognize the effect of slope on the steepness or direction of a graph.
- Graph equations written in slope intercept form or written in word problems.
- Know that proportional relationships are linear equations where the constant of proportionality is the slope and the y intercept is 0.
- Know horizontal lines are linear equations where slope is 0 leading to the form y = b.
- Know vertical lines have undefined slope because the change in x is 0 and division by 0 is undefined.
- Know vertical lines are written as x = a constant.

Can be Covered:

The learner will:

Find the slope from a table or two coordinate pairs.
Write the slope intercept form of a linear equation when only given two points.

Standards:

AKSS

8.EE.5,

8.F.2, 8.F.4

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

iReady unit 3 (not lessons 10 and 11)

Integer Exponents & Scientific Notation

Graduate-Level Competency:

M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.

M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.1

M5.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Identify equivalent exponential expressions.
- Evaluate numerical or algebraic expressions with exponents using the order of operations.
- Understand the effect of positive and negative bases with odd and even exponents.
- Understand the properties of exponents including product property, quotient property, and power to a power property.
- Recognize zero and negative (integer) exponents.
- Simplify exponential expressions using all properties.

Standards:

AKSS

8.EE.1, 8.EE.2

Mathematical Practices

All mathematical practices are present in each unit.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.1

M5.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Write small or large numbers as powers of 10.
- Write numbers in scientific notation.
- Convert numbers written in scientific notation into standard form.
- Compare numbers written in either form.
- Multiply, divide, add, and subtract numbers written in scientific notation, using exponential properties.
- Interpret scientific notation values on calculators.

Standards:

AKSS

8.EE.1, 8.EE.3,

8.EE.4

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

iReady unit 5

Numeracy

Graduate-Level Competency:

M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

Course/ Grade Competencies:

M2.7-8.1

M3.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Define, evaluate, or estimate square and cube roots.
- Understand that squares and square roots and cubes and cube roots are inverse operations.
- Define and be able to identify rational numbers.
- Define and be able to identify irrational numbers, including pi and square roots of nonperfect squares.
- Approximate the value of irrational numbers and locate on a number line.
- Compare values of rational and irrational numbers.

Can be Covered:

The learner will:

Know why there is no real square root to a negative number, and that square roots of negative numbers are classified as imaginary numbers.

Standards:

AKSS

8.NS.1, 8.NS.2,

8.EE.2

Mathematical Practices

All mathematical practices are present in each unit.

Course/ Grade Competencies:

M2.7-8.1

M3.7-8.2

Content Objectives:

Must be Covered:

The learner will:

Understand that division of zero is not possible; for example a vertical line has undefined slope because the “run” in “rise over run” is 0.

Standards:

AKSS

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

iReady unit 6, lessons 23-25

Pythagorean Theorem

Graduate-Level Competency:

M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.

M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.

M6 - Geometry: The learner will solve problems involving spatial reasoning and model geometric concepts in applied contexts.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.1

M3.7-8.2

M4.7-8.1

M6.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Learn the Pythagorean Theorem.
- Use the converse to determine if a triangle is a right triangle.
- Use the Pythagorean Theorem to find missing side lengths of right triangles, slant height of cones, or distance between points in the coordinate plane.
- Apply the Pythagorean Theorem in area and perimeter problems and other real-world problems.

Standards:

AKSS

8.EE.2, 8.G.6,

8.G.7, 8.G.8

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

iReady unit 6, lessons 26-27

Volume of Cylinders, Cones, & Spheres

Graduate-Level Competency:

M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.

M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.

M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.

M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.

M6 - Geometry: The learner will solve problems involving spatial reasoning and model geometric concepts in applied contexts.

Course/ Grade Competencies:

M1.7-8.1

M2.7-8.1

M3.7-8.1

M4.7-8.1

M6.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Find the volume of cylinders, cones, and spheres.
- Understand the proportional relationship between a cylinder and cone with equal radius and height.
- Be able to find missing dimensions when given the volume of cones, cylinders, or spheres.
- Find the volumes of composite shapes that include cylinders, cones, or spheres.

Standards:

AKSS

8.EE.2, 8.G.9

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

Lab to derive volume of cones based on cylinders.
iReady unit 6, lessons 28-29

Two-Way Categorical Tables & Associations

Graduate-Level Competency:

M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.

Course/ Grade Competencies:

M7.7-8.1

Content Objectives:

Must be Covered:

The learner will:

- Know the difference between numerical and categorical data.
- Create and analyze two-way tables of bivariate categorical data for associations.
- Calculate relative frequencies in two-way tables to investigate associations.

Standards:

AKSS

8.SP.4

Mathematical Practices

All mathematical practices are present in each unit.

Suggested Activities, Materials, and Resources:

- Gather data on “the dress” (is it black and blue or white and gold), and look for associations between gender and color seen or age and color seen.
- iReady unit 7

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