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Eighth Grade Mathematics Curriculum

Month Standard Code

Standard Learning Activities Assessment Interdisciplinary Connections

September 7.NS.1.a7.NS.1.b7.NS.1.c7.NS.1.d7.EE.1

Unit Title: Review of Algebraic fundamentals

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

a. Describe situations in which opposite quantities combine to make 0.

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse,p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Write variable expressions for word phrases

Use order of operations with variables

Add, subtract, divide, multiply of integers

Evaluate expressions

Understand the basic functions of your scientific calculator and graphing calculator

Checkpoint quizzes Test Teacher

Observation Class discussions Homework Problem of the day Journal entry

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2

PhysicalEducation and Health2.1.8.E.4

Technology8.1.4.A.18.1.P.C.1

21st Century Life and Career Skills9.1.8.A.19.1.12.A.19.1.4.B.19.1.8.B.1

Language ArtsL.8.2.aL.8.2.cSL.8.1.dW.8.1.cW.8.2.d

World Language7.1.NM.B.2


d. Apply properties of operations as strategies to add and subtract rational numbers.

7.EE.1 Use properties of operations to generate equivalent expressions.

1. Apply properties of operations as strategies to add, subtract, factor,and expand linear expressions with rational coefficients.

September – October

8.EE.7.a8.EE.7.bA-REI.3

Unit Title: Solving One-Step and Two-step and Multi-step Equations and Inequalities

8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations.:Solve linear equations in one variable:

a. Give examples of linear equations in one variable with onesolution, infinitely many solutions, or no solutions. Show whichof these possibilities is the case by successively transforming thegiven equation into simpler forms, until an equivalent equation ofthe form x = a, a = a, or a = b results (where a and b are different

Review key properties of identify, commutative, associative and distributive

Simplify variable expressions

Solve one step equations by addition or subtraction

Solve one step equations by multiplying or dividing

Solve inequalities by adding or subtracting

Solve inequalities by multiplying or

Daily Lesson Quizzes

Checkpoint quizzes Chapter Test Teacher

Observation Class discussions Homework Problem of the day Journal entry

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.25.2.8.E.1




numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

A-REI.3 Solve equations and inequalities in one variable

3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

dividing Solve two and

multi step equations and inequalities


October 8.NS.18.NS.2

8.EE.7.a8.EE.7.bA-REI.3

Unit Title: Using Decimals in Equations

8.NS Know that there are numbers that are not rational, and approximate them by rational numbers.

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

8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations.

Round and estimate decimals

Write formulas using a spreadsheet

Solve equations with decimals

Recognize that repeating decimals correspond to fractions and determine their fractional equivalents

Construct meanings for common irrational numbers, such pi and the square root of 2



Observation Class discussions Homework Problem of the day Journal entry Graphing calculator

activity – Mean and Median

Spreadsheet activity

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2

Technology8.1.4.A.18.1.8.A.48.1.P.C.1



Solve linear equations in one variable:

a. Give examples of linear equations in one variable with onesolution, infinitely many solutions, or no solutions. Show whichof these possibilities is the case by successively transforming thegiven equation into simpler forms, until an equivalent equation ofthe form x = a, a = a, or a = b results (where a and b are differentnumbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

A-REI.3 Solve equations and inequalities in one variable

3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.


November 8.EE.18.EE.38.EE.48.NS.18.NS.27.NS.3

Unit Title: Factors, Fractions, and Exponents

8.EE.1 1. Know and apply the properties of integer exponents to generate equivalent numerical

Use exponentiation to find whole number powers of numbers.

Use and explain procedures for



Observation

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2


expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

8.EE.3. Use numbers expressed in the form of a single digit times an integer 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 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

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 sizefor measurements of very large or very small quantities (e.g., usemillimeters per year for seafloor spreading). Interpret scientificnotation that has been generated by technology.

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

performing calculations involving addition, subtraction, multiplication, division and exponentiation with integers and all number types

Use negative exponents

Multiply and divide in scientific notation

Understand and use rational and irrational numbers

Solve least common multiple word problems

Find common factors and prime factorization of two or more numbers

Class discussions Homework Problem of the day Journal entry Graphing calculator

activity – Evaluating expressions

Calculator – Scientific Notation



Social Studies6.3.8.C.1

Language ArtsSL.8.1.dW.8.1.cW.8.2.d


8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number linediagram, and estimate the value of expressions (e.g., π2). For example,by truncating the decimal expansion of √2, show that √2 is between 1 and2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

7.NS Apply and extend previous understandings of operations withfractions to add, subtract, multiply, and divide rational numbers.

3. Solve real-world and mathematical problems involving the fouroperations with rational numbers

DecemberJanuary

8.NS.28.EE.1

8.EE.7.a8.EE.7.b

Unit Title: Operations with Fractions

8.NS Know that there are numbers that are not rational, and approximate them by rational numbers. 2. Use rational approximations of irrational numbers to compare the sizeof irrational numbers, locate them approximately on a number linediagram, and estimate the value of expressions (e.g., π2). For example,by truncating the decimal expansion of √2,

Compare and order numbers of all named types: rational numbers, percents, exponents, and numbers in scientific notation

Find the least common multiple

To write fractions as decimals

To write



Observation Class discussions Homework Problem of the day

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2


21st Century Life and


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.

8.EE.1 Work with radicals and integer exponents.1. Know and apply the properties of integer exponents to generateequivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

8.EE.7.aa. Give examples of linear equations in one variable with onesolution, infinitely many solutions, or no solutions. Show whichof these possibilities is the case by successively transforming thegiven equation into simpler forms, until an equivalent equation ofthe form x = a, a = a, or a = b results (where a and b are differentnumbers).

8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

terminating and repeating decimals as fractions

To add and subtract fractions and mixed numbers

To multiply and divide fractions

Use dimensional analysis to convert units of measure

Solving equations by adding or subtracting fractions

Solving equations by multiplying fractions

Solve multi-step equations with fractions and decimals

To find powers of products

To find powers of quotients

Career Skills9.1.8.A.19.1.12.A.19.1.4.B.19.1.8.B.1


January – February

8.EE.58.EE.8.a8.EE.8.b8.EE.8.c

8.F.18.F.2

Unit Title: Linear Functions

8.EE.5 Understand the connections between proportional relationships,lines, and linear equations.Graph proportional relationships,

To review the coordinate plane

To determine whether a relation is a function

To graph relations



Observation

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2


8.F.38.F.48.F.5

8.SP.18.SP.28.SP.38.SP.4

interpreting the unit rate as theslope of the graph. Compare two different proportional relationshipsrepresented in different ways. For example, compare a distance-timegraph to a distance-time equation to determine which of two movingobjects has greater speed.

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

a. Understand that solutions to a system of two linear equationsin two variables correspond to points of intersection of theirgraphs, because points of intersection satisfy both equationssimultaneously.

b. Solve systems of two linear equations in two variablesalgebraically, and estimate solutions by graphing the equations.Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x +2y = 6 have no solution because 3x + 2y cannot simultaneously be 5and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two variables.

8.F Define, evaluate, and compare

and functions To use tables,

graphs, or listed numerically to determine the slope of the function.

To find solutions of equations with two variables

To graph linear equations with two variables

To find the slope of a line

To use slope-intercept form in graphing a linear equation

To write a function rule for a word relationship

To write a function rule by analyzing a table or graph

To interpret and draw scatter plots

To use scatter plots to find trends

To solve systems of equations of linear equations by graphing

To solve systems of linear equations to solve problems

To solve systems of linear inequalities by graphing

Class discussions Homework Problem of the day Journal Graphing calculator

activities Rap song



Visual and Performing Arts1.3.8.B.21.3.8.B.4



functions.

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 pairsconsisting of an input and the corresponding output.1

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 tableof values and a linear function represented by an algebraic expression,determine which function has the greater rate of change.

3. Interpret the equation y = mx + b as defining a linear function, whosegraph 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 functionof 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.


4. Construct a function to model a linear relationship between twoquantities. Determine the rate of change and initial value of thefunction 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.

5. Describe qualitatively the functional relationship between twoquantities 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.

8.SP. Investigate patterns of association in bivariate data.

1. Construct and interpret scatter plots for bivariate measurementdata to investigate patterns of association between two quantities.Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.


2. Know that straight lines are widely used to model relationshipsbetween two quantitative variables. For scatter plots that suggest alinear association, informally fit a straight line, and informally assessthe model fit by judging the closeness of the data points to the line.

3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.For example, in a linear model for a biology experiment, interpret a slopeof 1.5 cm/hr as meaning that an additional hour of sunlight each day isassociated with an additional 1.5 cm in mature plant height.

4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible


association between the two variables. For example, collectdata from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

February – March

8.G.1.a8.G.1.b8.G.1.c8.G.28.G.38.G.48.G.5

Unit Title: Geometry – Spatial thinking

8.G.1 1. Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

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 asequence that exhibits the congruence between them.

Identify vertical angles

Identify complementary angles

Identify supplementary angles

Identify corresponding angles

Identify missing measures on a plane that had at least two parallel lines and one transversal

To identify corresponding parts of congruent triangles

To determine whether triangles are congruent

To graph translations

To describe translations



Observation Class discussions Homework Problem of the day Journal Graphing calculator

activities “Angle” challenge

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2





8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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 similaritybetween them.

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 oftriangles. 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.

To identify a line of symmetry

To graph a reflection of a geometric figure

To graph rotations To identify

rotational symmetry

To describe the effect of dilations on two-dimensional figures using coordinates

March 8.G.97.G.47.G.6

Unit Title: Area and Volume

8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-

Find the area and perimeter of geometric figures made by combining triangles,



Observation

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2


world and mathematical problems.

7.G. Solve real-life and mathematical problems involving angle measure,area, surface area, and volume.

4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

parallelograms, trapezoids, and circles or parts of circles

Review surface area of prisms, cylinders, cones, spheres

Find the volume of cones, cylinders, and spheres

Use the volume of cones, cylinders and spheres to solve real-world problems

Class discussions Homework Problem of the day Journal Volume Challenge




April - May 8.EE.28.G.68.G.78.G.8

8.NS.18.NS.2

Unit Title: Pythagorean Theorem and Square Roots

8.EE.2 Work with radicals and integer exponents.

2. Use square root and cube root symbols to represent solutions toequations of the form x2 = p and x3 = p, where p is a positive rational

To find square roots of numbers

To classify real numbers

Find square roots Find cube roots Use the

Pythagorean Theorem

Identify special properties of 45-



Observation Class discussions Homework Problem of the day Journal “Tree Angles”

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2

Science5.1.8.A.2


number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

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.

8.NS.2. Use rational approximations of irrational numbers to compare the sizeof irrational numbers, locate them approximately on a number linediagram, and estimate the value of expressions.

8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengthsin right triangles in real-world and mathematical problems in two andthree dimensions.

8.G.8. Apply the Pythagorean

45-90 and 30-60-90 triangles.

Use the distance and midpoint formulas





Theorem to find the distance between two points in a coordinate system.

MAY - JUNE S-CP.1S-CP.2S-CP.3

Unit Title: Probability

S-CP Understand independence and conditional probability and use them to interpret data

S-CP.1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S-CP.3. Understand the conditional probability of A given B as P(A andB)/P(B), and interpret independence of A and B as saying that theconditional probability of A given B is the same as the probabilityof A, and the conditional probability of B given A is the same as the probability of B.

To use a tree diagram and the Counting Principle

To find theoretical probability by counting outcomes

To calculate probabilities of independent events

To calculate probabilities of dependent events

To use permutations

To use combinations

To find experimental probability

To use simulations To choose a

sample for a survey of population

To make estimates about populations



Observation Class discussions Homework Problem of the day Journal Probability activity Scientific

Calculator activity Graphing

Calculator activity

Science5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2

Physical Education2.5.8.C.1




JUNE A-APR.1 Unit Title: Introduction to Adding and Daily Lesson Science


Polynomials

A-APR Arithmetic with Polynomials and Rational ExpressionsPerform arithmetic operations on polynomials1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

subtracting polynomials

Multiplying a polynomial by a polynomial

Multiplying binomials

Quizzes Checkpoint quizzes Chapter Test Teacher

Observation Class discussions Homework Problem of the day

5.1.8.A.25.1.8.B.25.1.8.C.25.1.8.D.15.1.12.D.2

Physical Education2.5.8.C.1




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