Last updated: 2/12/2024

Math Grade 8 PJMS

20 Days

Module 1: Integer Exponents and Scientific Notation

(1)	8.EE.1	Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² * 3^-5 = 3^-3=1 / 3³ – 1 / 27.
(1)	8.EE.3	Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10⁸ and the population of the world as 7 times 10⁹, and determine that the world population is more than 20 times larger.
(1)	8.EE.4	Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Why is it helpful to write numbers in different ways?

1. Exponential Notation

2. Multiply & Divide Monomials

3. Powers of Monomials

4. Negative Exponents

5. Estimating Quantities

6. Scientific Notation

7. Comparing and Ordering Numbers in Scientific Notation

8. Compute with Scientific Notation

Power

Base

Monomial

Scientific Notation

Exponent

Evaluate

Coincide

I can write repeated multiplication using powers.

I can simplify real number expressions by multiplying and dividing monomials.

I can apply the laws of exponents to find powers of monomals.

I can write and evaluate expressions using negative exponents.

I can use scientific notation to write large and small numbers.

I can compute numbers written in scientific notation.

Multiplying Exponents

Dividing Exponents

Powers of Products and Quotients

Scientific Notation

Scientific Notation- Computing

Scientific Notation- Adding/Subtracting

25 Days

Module 2: Concept of Congruence

(1)	8.G.1	Verify experimentally the properties of rotations, reflections, and translations:
(1)	8.G.1.a	Lines are taken to lines, and line segments to line segments of the same length.
(1)	8.G.1.b	Angles are taken to angles of the same measure.
(1)	8.G.2	Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

How can you determine congruence and similarity?

How can you best describe the change in position of a figure?

1. Translations

2. Reflections

3. Rotations

4. Sequences of Rigid Motion

5. Parallel Lines Cut By Transversal

6. Angle Pair Relationship

7. Exterior Angle of Triangles

Rotation

Reflection

Congruent

Image

Pre-Image

Line of Reflection

Transformation

Translation

Parallel Lines

Perpendicular

Transversal

Interior Angles

Exterior Angles

Alternate Interior

Alternate Exterior

Corresponding

Vertical

Supplementary

I can graph and descibe tanslations on the coordinate plane.

I can graph and describe reflections on the coordinate plane.

I can graph and describe rotations on the coordinate plane.

I can graph and desribe a sequence of rigid motion.

Parallel Lines and Transversals

Parallel Lines and Transversals Finding Angles

Angle Pair Relationships

Angles in Triangles

Exterior Angle of a Triangle

15 Days

Mod 3 (Similarty) blends in with Mod 2 (Congruence). Include Transformations with Dilations

Module 3: Similarity

(1)	8.G.3	Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
(1)	8.G.4	Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
(1)	8.G.5	Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

How can you determine congruence and similarity?

How can you best describe the change in position of a figure?

What Lies behind "Same Shape"?

Dilations on the Coordinate Plane

Similarity

Basic Properties of Similarity

Sequences of Rigid Motions Including Dilations

Dilation

Scale Drawing

Similar

Similarity Transformation

Scale Factor

I can identify a dilation.

I can construct a dilation on coordinate plane.

I can describe the effect of dilations on two-dimensional figures using coordinate.

I can map an object onto another by applying a sequence of transformations.

Dilations Worksheet

Scale Factors

40 Days

Module 4- Equations

(1)	8.EE.6	Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
(1)	8.EE.7	Solve linear equations in one variable.
(1)	8.EE.8	Analyze and solve pairs of simultaneous linear equations.

How can you communicate mathematical ideas effectively?

What is equivalence?

Why are graphs helpful?

Writing equations using symbols

One step equations

Two step equations

combining like terms

Variables on both sides

Distributive property

Multi-Step equations

Solving equations to discover number of solutions: No solution, infinite solution, one solution

Applying geometry concept to equations

Finding slope of a linear lines: table of values, 2 ordered pairs, given a a line

Graphing a linear line: y = mx + b

Finding slope and y-intercept

Systems of equations- graphing, substitution, elimination

System of equation word problems

coefficient

multiplicative inverse

identity

null set

two-step equation

constant of proportionality

constant rate of change

linear relationships

point-slop form

rise

run

slope

slope-intercept form

standard form

systems of equations

x-intercept

y-intercept

I can write mathematical statements using symbols to represent numbers.

I can solve one step equations.

I can solve one step equations with rational coefficients.

I can solve two step equations.

I can solve two step equations with rational coefficients.

I can simplify expressions by combining like terms.

I can solve equations with variables on both sides of the equation.

I can solve multi-step equations.

I can solve multi-step equations inlcluding the identity solution and nul sets.

I can apply geometry concepts to solving and writing equations.

I can identify, by inspection, when an equations has one solution, infinitely many solutions, or no solutions.

Writing verbal and variable expressions

One Step Equations

Two Step Equations

Combining Like Terms

Variables on Both Sides

Distributive Property

Multi Step Equations

Number of Solutions to Equations

Applying Geometry Concepts to Equations

Finding Slop of a Graph

Finding Slope from Two Points

Finding Slope From an Equation

Graphing Linear Lines

Writing Linear Equations

Solve Systems of Equations by Graphing

Solve Systems of Equations by Elimination

Solve Systems of Equations by Substitution

Systems of Equations Word Problems

15 Days

Module 5- Functions

(1)	8.F.1	Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
(1)	8.F.2	Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
(1)	8.F.3	Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
(1)	8.F.4	Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
(1)	8.F.5	Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

How can you find and use patterns to model real-world situations?

How can we model relationships between quantities?

What is a Relation?

What is a Function?

Vertical Line Test

Compare Functions

Linear vs Non Linear

continuous data

dependent variable

domain

function

linear equations

linear functions

nonlinear function

range

relation

I can use the coordinate plane to represent relations.

I can apply the vertical line test to determine if a relation is a function.

I can use the definition of a function to determine if a set of data is representing a functional relationship.

I can compare properties of fuctions.

I can determine if a function is linear of non linear.

Relations, functions, domain, range

vertical line test

Comparing Functions

Domain and Range

Function vs not a Function

Function Tables

Linear vs Non Linear Functions

10 Days

Mod 6- Volume and Surface Area

(1)

8.G.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Why are formulas important in math and science?

What is the volume of a cylinder?

What is the volume of a sphere?

What is the volum of a cylinder?

How can we find the volume of composite shapes?

Volume

Area (review)

Cylinder

Sphere

Cylinder

I can find the volume of a cylinder.

I can find the volume of a sphere.

I can find the volume of a cone.

I can find the volume of composite shapes.

Volume of a cone

Volume of a cylinder

Volume of a sphere

Volume of mixed shapes

25 Days

Mod 7-

Rational & Irrational Numbers

(1)	8.G.6	Explain a proof of the Pythagorean Theorem and its converse.
(1)	8.G.7	Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
(1)	8.G.8	Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
(1)	8.NS.1	Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
(1)	8.NS.2	Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Why is it helpful to write numbers in different ways?

What happens when you add, subtract, multiply, and divide fractions?

How can algebraic concepts by applied to geometry?

What is a rational number?

What is an irrational number?

Square Roots

Perfect Squares

Simplifying square roots

Intro to the pythagorean theorem.

Applying the pythagorean theorem

Pythagorean Theorem Applications

Finding the Distance on a the coordinate plane by applying the pythagorean theoream

Rational Number

Irrational Number

Square Root

Perfect Square

Radical sign

Repeating Decimal

Terminating Decimal

Pythagorean Theoream

Legs

Hypotenuse

I can identify a rational and irrational number.

I can identify perfect squares.

I can simplify a square root.

I can apply the pythagorean Theorem.

I can find the distance between two points by using the pythagorean theorem.

Rational vs. Irrational

Square Roots

Simplifying Square Roots

Pythagorean Theorem

Pythagoren Theorem B

Find the Distance Between two points

Post Test Topics

Mod 4: Systems of Equations

8.EE 7 Solve Linear Equations in one variable.

8. E.E 8 Analyze and solve pairs of simultaneous linear equations.