Kindergarten

## 8th Grade Math Common Core State Standards and Curriculum

It probably comes as no surprise that 8th grade math standards are of the highest complexity that your student has seen yet. 8th grade Common Core math standards are designed to finalize middle school math curriculum and prepare your student for high school math. A strong finish in 8th grade will ensure a smooth transition into 9th grade.

For better chances of success with 8th grade math Common Core standards, it is important that your student has succeeded in those of the year before. This is because there is a steady progression of education built into Common Core math standards. Grade 8 math is built upon the concepts learned in grade 7. Grade 7 math is built off of grade 6, and so on. For prosperity in 8th grade math, your student should be comfortable with:
• Multi-step ratio problems involving percentages.
• Students exiting 7th grade should have sufficient practice with proportional relationships. They should apply their knowledge of ratios to solve problems involving real-world examples with percentages. These include tipping rates, tax-related problems, and more. Students should also have developed strategies for representing these proportions with tables and graphs. They should be comfortable with plotting data on informational graphs and drawing conclusions based on their outcomes.
• The relationship between fractions, decimals, and percents.
• Students should be able to convert fluently between these three number forms by the end of 7th grade. They should understand why methods of conversion provide accurate results. Additionally, students should be able to apply these strategies to more efficiently solve problems involving these three forms. Moreover, students should be comfortable with negative integers. They should understand the properties associated with numbers below zero and relate them to real-world examples.
• Finding area of two-dimensional shapes and volume and surface area of three-dimensional shapes.
• Students should have a clear understanding of finding the area of rectangular shapes. They should also be fluent in determining the area of three-dimensional rectangular objects. Students should have practice finding the area of non-rectangular shapes, such as circles and triangles, and have familiarity with the properties associated with them.
The above subjects are key areas in 7th grade Common Core. 8th grade math standards will continue these subjects with the intention of creating complete fluency and competency in them. If you feel that your student is behind, consider creating a summer study plan. If necessary, contact your student’s teacher for pointers on priority subject matter. For esteemed and effective materials, look into ArgoPrep’s informative pages on 8th grade math. Common Core standards play an important role in your student’s education, and nobody knows it better than ArgoPrep. For the highest accuracy and relevance to their time in the classroom, ArgoPrep ensures careful alignment of Common Core in their curriculum.

### 8th Grade CCSS Math: The Three Focus Areas

Throughout math 8, Common Core standards dictate that students will hone in on three main areas of study. Before this year, they will have touched on these subjects and created the basis from which to build from. They will have informally practiced with some of these, such as patterns and trends in slope. Others will have been more concrete, such as their studies in geometry. Grade 8 math standards will take these concepts and create a firmer structure within them. The three focus areas of 8th grade math Common Core standards are:
• Area 1: Modeling, solving, and examining linear equations.
• Area 2: Define and examine representations of functions
• Area 3: Transformations of angles, shapes, and triangular properties

### CCSS 8th Grade Math: Focus Area Breakdowns and Study Suggestions

#### Area 1: Modeling, solving, and examining linear equations.

In this focus area, students will explore more concrete equations with plotting points on axis graphs. They will study trends and explore relationships between linear equations. Students will experiment with various operations within linear equations, noting the changes that the different operations create. They will become familiar with linear properties and compare sets of linear equations and their corresponding results on graphs. Students will relate unit rate of word problem examples to the calculated slope of linear equations. 8th graders will also come to understand more parts of the number system. They will come to recognize irrational numbers. To utilize these, they will develop methods for approximating them with rational numbers. They will also become familiar with scientific notation and incorporate this into expressions of numbers as a way of simplifying numbers and equations.

#### Study Suggestion for Area 1

Utilizing digital graphing tools is a great way to explore differences in linear expressions. Step-by-step tutorials, like the ones provided by ArgoPrep, may also prove highly useful and effective in achieving 8th grade Common Core standards. Math curriculum of this school year calls for as many visuals as possible. Graphing calculators and helpful videos will be a great study tool for your student.

#### Area 2: Define and examine representations of functions

In this area, students will explore functions. They will come to understand a function as an expression resulting in a single correct outcome for any given input. Students will experiment with multiple functions represented in equation and graph form. With these representations, students will identify characteristics and compare the properties of the functions.

#### Study Suggestion for Area 2

Not unlike linear equations, functions may be better understood with visual tools. Graphing calculators, online tools, and video tutorials will provide excellent visual aids to your student. While working with pen and paper, try using various colors for various functions. Creating colorful assortments will help distinguish between functions and better display their similarities and differences.

#### Area 3: Transformations of angles, shapes, and triangular properties

In the third and final area, students will study angles and two-dimensional shapes by way of transformations. Transformations involve rotations (by a number of degrees), dilations (reduction or enlargement to scale of a two dimensional shape), reflections (over x and y axes), and translations (sliding a plotted shape in a given direction on a graph). Students will study properties of triangular shapes using the Pythagorean theorem. Using this, students will determine unknown dimensions of triangles (such as an unknown length of one side) and apply these methods to real-world example problems.

#### Study Suggestion for Area 3

Online geometry graphing tools will come in handy in this study area. Different transformations require different methods, so experimenting with them (whether in the context of a problem or not) is important. When it comes to the Pythagorean theorem, practice makes perfect. Use different triangular items around your home for physical examples. Illustrations of triangular examples (such as a fence or frame) make for effective geometry practice.

## The Number System

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

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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). 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.

## Expressions & Equations

### Expressions and Equations Work with radicals and integer exponents.

#### CCSS.MATH.CONTENT.8.EE.A.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.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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. 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.

#### CCSS.MATH.CONTENT.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 (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology

### Understand the connections between proportional relationships, lines, and linear equations.

#### CCSS.MATH.CONTENT.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. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

#### CCSS.MATH.CONTENT.8.EE.B.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.

### Analyze and solve linear equations and pairs of simultaneous linear equations.

#### CCSS.MATH.CONTENT.8.EE.C.7

Solve linear equations in one variable.
##### CCSS.MATH.CONTENT.8.EE.C.7.A
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 = a, a = a, or a = b results (where a and b are different numbers).
##### CCSS.MATH.CONTENT.8.EE.C.7.B
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

#### CCSS.MATH.CONTENT.8.EE.C.8

Analyze and solve pairs of simultaneous linear equations.
##### CCSS.MATH.CONTENT.8.EE.C.8.A
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.
##### CCSS.MATH.CONTENT.8.EE.C.8.B
Solve systems of two linear equations in two variables algebraically, 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 5 and 6.
##### CCSS.MATH.CONTENT.8.EE.C.8.C
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

## Functions

### Define, evaluate, and compare functions.

#### CCSS.MATH.CONTENT.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.1

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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. 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.

### Use functions to model relationships between quantities.

#### CCSS.MATH.CONTENT.8.F.B.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.

#### CCSS.MATH.CONTENT.8.F.B.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.

## Geometry

### Understand congruence and similarity using physical models, transparencies, or geometry software.

#### CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:
##### CCSS.MATH.CONTENT.8.G.A.1.A
Lines are taken to lines, and line segments to line segments of the same length.
##### CCSS.MATH.CONTENT.8.G.A.1.B
Angles are taken to angles of the same measure.
##### CCSS.MATH.CONTENT.8.G.A.1.C
Parallel lines are taken to parallel lines.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.8.G.A.3

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

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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. 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.

### Understand and apply the Pythagorean Theorem.

#### CCSS.MATH.CONTENT.8.G.B.6

Explain a proof of the Pythagorean Theorem and its converse.

#### CCSS.MATH.CONTENT.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

#### CCSS.MATH.CONTENT.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

#### CCSS.MATH.CONTENT.8.G.C.9

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

## Statistics & Probability

### Investigate patterns of association in bivariate data.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.8.SP.A.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 slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

#### CCSS.MATH.CONTENT.8.SP.A.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, collect data 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?

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