# Grade 8 Common Core Math Curriculum

## Grade 8 Common Core Math Curriculum

#### Listed below are Math quizzes for 8th grade students based on the Common Core Math State Standards.

For grade level assignments, we adhere to the Common Core State Standards Initiative's curriculum, in addition to considering other course curriculums such as GCSE(UK), Singapore Math, Australian and Indian Math curriculums. These courses will help students to perform well in local and major international competitions such as the Science Bee, Math Olympiad, American Mathematics Competition and so on.

In grade 8, the focus is on three critical areas, namely

1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations;

2) grasping the concept of a function and using functions to describe quantitative relationships;

3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Some of the mathematical practices that you will learn are:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

### Grade 8: The Number System

8.NS.A.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.

Identifying Rational/Irrational Numbers

8.NS.A.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).

Approximating Irrational Numbers

### Expressions and Equations

You will use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems.

You will recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin.

You will understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m·A.

You will also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom).

At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires you to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.

You should be able to strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when you use the properties of equality and the concept of logical equivalence, you maintain the solutions of the original equation.

You will solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line.

You will use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

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

Simplify Exponents

Evaluate Exponents

8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Finding Square Roots

Finding Cube Roots

Determine Relative Square Root Value

Solving Equations With Square Roots and Cube Root

Solve Equations with Negative Powers

Evaluating Exponential Bases and Powers

8.EE.A.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.

Convert Numbers Into Scientific Notation

Solving Equations with Powers of Ten

8.EE.A.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. Interpret scientific notation that has been generated by technology

Solve Scientific Notation Problems

Solve Scientific Notation Multiplication Problems

Convert from Scientific Notation to Standard Form

8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Graphing Proportional Relationship

8.EE.A.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.

Find the Slope Using Similar Triangle

Evaluate Slope Attributes of the Line

Find Missing Rise/Run Using the Similar Triangle Approach

8.EE.A.7 Solve linear equations in one variable.

Solve Linear Equations with One Variable

8.EE.A.7A Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = aa = a, or a = b results (where aand b are different numbers).

Solve Simultaneous Linear Equations With Two Variables

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

Solve Linear Equations with Variables on Both Sides

8.EE.C.8A Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Identify the Point of Intersection with Equations

In this section, you will grasp the concept of a function as a rule that assigns to each input exactly one output.

You will understand that functions describe situations where one quantity determines another.

You can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and you will describe how aspects of the function are reflected in the different representations.

8.F.A.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.

Identify if the Equation Defines a Function or Not?

Evaluate Functions With Inputs

Identify if the Graph Defines a Function or Not?

Identify if the Table Defines a Function or Not?

8.F.A.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.

Compare Properties of Functions

Compare the Rate of Change

Draw Line with Different Rates of Change

Find the Rate of Change Using Description

Find the Rate of Change Using Equations

Find the Rate of Change Using Graphs

Find the Rate of Change Using Tables

Find the Y-intercept Using Tables

Find the Y-intercept Using Equation

Find the Y-intercept For Graphs

8.F.A.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.

Identify Linear and NonLinear Functions

Determine If the Graph Identifies a Linear Function

Determine If the Equation Identifies a Linear Function

Identify if the Table Defines a Linear Function or Not?

8.F.A.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.

Construct a Function to Model a NonLinear Function

8.F.A.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.

Interpret Graphs of Functions

You will use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems.

You will be able to show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines.

You will understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways.

You will apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. You can complete your work on volume by solving problems involving cones, cylinders, and spheres.

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

Verify rotations, reflections, and translations

8.G.A.1A Lines are taken to lines, and line segments to line segments of the same length

8.G.A.1B Angles are taken to angles of the same measure.

Identify Cross Sections of 3D Figures

8.G.A.1C Parallel lines are taken to parallel lines.

Finding Area and Circumference of Circles

8.G.A.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.

Understand Congruent Figures

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

Understand Similar Figures

8.G.A.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.

Understand Angles of Triangles and Parallel Lines

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

Prove Pythagoras Theorem

8.G.A.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Find the Length Using Pythagoras Theorem
8.G.A.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Find the Distance in a Coordinate System

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

### Grade 8: Statistics and Probability

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

Construct and Interpret Scatter Plots

8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Identify the Line of Best Fit

8.SP.B.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Interpret Slope and Intercept

8.SP.B.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.

Understand Association Between Two Variables