Virtual Nerd
 statistics
 algebra
 geometry
 graphing
 momentum
 motion
 physics
 problem solving
 thinking critically
 test prep
Pros
Tutorials are highquality and give kids clear opportunities to practice what they learn.Cons
Learning can be repetitive, and there could be a better variety of questions.Bottom Line
Highquality math and physics tutorials are a great classroom supplement, plus they're aligned to Common Core standards.Virtual Nerd provides a My Classroom menu for teachers to manage their class rosters and student passwords. You can: • Create and assign playlists with a combination of tutorials, practice problems, and assessments. • Customize their playlists by adding comments or uploading a Prezi presentation. • View the amount of time students have spent viewing tutorials • See the questions that kids have answered right or wrong, or have skipped.
Though clear and visually appealing, the tutorials are no more engaging than any other straightforward lecture. Kids may have to be extra motivated to pursue Virtual Nerd study.
Through watching these lecture videos at home, kids can have a different experience during class time, allowing for more individualized teacher attention, group work, and communication.
Subscribers can view content in three ways  video, stepbystep notes, and a diagram  which is very helpful to different learning styles. Bummer: It's only available in English.
Teachers looking to build a "flipped classroom" (using technology to allow kids to learn at home, then come to class for interactive work) will love that clear tutorials are already created. Students can watch the straightforward instruction and take notes at home, saving class time to focus on applying the concepts and working on cooperative projects. You can input students into the Virtual Nerd account roster and provide them an access code to log in. They can then build playlists with tutorials, multiplechoice practice problems, and assessments. To build an assessment, you can choose from an unfortunately limited group of questions for each topic, some of which are the same as the practice problems.
Read More Read LessVirtual Nerd is a website featuring tutorials to supplement learning in middle and high school math and physics classes. Hundreds of tutorials are available for sixth through eighthgrade math, PreAlgebra, Algebra 1, Algebra 2, Geometry, and Introductory Physics. Each tutorial provides a video of a teacher lecturing on a topic and writing on a whiteboard. At the same time, a diagram and stepbystep notes appear to the right.
Standout tutorials and questions:
"How do you find the probability of a simple event?" – Kids get a video, a diagram, and stepbystep directions showing them how to find the probability of getting a green or blue marble from a bag of marbles.
"Curtains at Jordan’s" – A multiplechoice problem where kids use a tree diagram to determine all the possible combinations of curtains at the store.
Read More Read LessHigh school students should find a lot to work with here. ACT and SAT math tutorials provide opportunities for kids to review key concepts in preparation for these nervewracking, highstakes tests. Tutorials are separated by each subject and organized by topic or according to several popular textbooks, which could work well if kids are already familiar with a particular textbook series. Good news: Concepts are aligned to a broad range of Common Core Math Standards. Physics concepts are appropriate for kids in a standard high school physics class or for those reviewing basic physics concepts in preparation for AP or IB Physics. Virtual Nerd’s "Dynamic Whiteboard" platform is distinctive because it allows kids to view instruction in three ways simultaneously.
A few nits to pick: It would be nice if Virtual Nerd had a larger pool of questions; sometimes they repeat. Adding more resources for kids to apply and extend their learning would also strengthen the site's reach.
Read More Read LessKey Standards Supported
Arithmetic With Polynomials And Rational Expressions  
HSA.APR: Perform Arithmetic Operations On Polynomials  
HSA.APR.1  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. 
Rewrite Rational Expressions  
HSA.APR.6  Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. 
HSA.APR.7  (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. 
Building Functions  
HSF.BF: Build A Function That Models A Relationship Between Two Quantities  
HSF.BF.2  Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ 
Build New Functions From Existing Functions  
HSF.BF.4  Find inverse functions. 
Circles  
HSG.C: Find Arc Lengths And Areas Of Sectors Of Circles  
HSG.C.5  Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 
Conditional Probability And The Rules Of Probability  
HSS.CP: Understand Independence And Conditional Probability And Use Them To Interpret Data  
HSS.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. 
Congruence  
HSG.CO: Experiment With Transformations In The Plane  
HSG.CO.1  Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 
HSG.CO.2  Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). 
HSG.CO.4  Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 
HSG.CO.5  Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 
Prove Geometric Theorems  
HSG.CO.11  Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. 
HSG.CO.9  Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. 
Understand Congruence In Terms Of Rigid Motions  
HSG.CO.6  Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. 
HSG.CO.7  Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. 
HSG.CO.8  Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. 
Creating Equations  
HSA.CED: Create Equations That Describe Numbers Or Relationships  
HSA.CED.1  Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 
HSA.CED.2  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 
HSA.CED.3  Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 
HSA.CED.4  Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. 
Expressing Geometric Properties With Equations  
HSG.GPE: Use Coordinates To Prove Simple Geometric Theorems Algebraically  
HSG.GPE.5  Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 
Expressions And Equations  
6.EE: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.  
6.EE.1  Write and evaluate numerical expressions involving wholenumber exponents. 
6.EE.2  Write, read, and evaluate expressions in which letters stand for numbers. 
6.EE.3  Apply the properties of operations to generate equivalent expressions. 
Reason About And Solve OneVariable Equations And Inequalities.  
6.EE.5  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 
6.EE.6  Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 
6.EE.7  Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 
6.EE.8  Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 
7.EE: Solve RealLife And Mathematical Problems Using Numerical And Algebraic Expressions And Equations.  
7.EE.3  Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 
7.EE.4  Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 
Use Properties Of Operations To Generate Equivalent Expressions.  
7.EE.1  Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 
8.EE: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations.  
8.EE.7  Solve linear equations in one variable. 
8.EE.8  Analyze and solve pairs of simultaneous linear equations. 
Understand The Connections Between Proportional Relationships, Lines, And Linear Equations.  
8.EE.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 distancetime graph to a distancetime equation to determine which of two moving objects has greater speed. 
8.EE.6  Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical 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. 
Work With Radicals And Integer Exponents.  
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. 
8.EE.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. 
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. 
Geometric Measurement And Dimension  
HSG.GMD: Explain Volume Formulas And Use Them To Solve Problems  
HSG.GMD.1  Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. 
HSG.GMD.3  Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★ 
Geometry  
6.G: Solve RealWorld And Mathematical Problems Involving Area, Surface Area, And Volume.  
6.G.1  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 
6.G.2  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 
7.G: Solve RealLife And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume.  
7.G.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. 
7.G.5  Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. 
7.G.6  Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 
8.G: Solve RealWorld And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres.  
8.G.9  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. 
Understand And Apply The Pythagorean Theorem.  
8.G.6  Explain a proof of the Pythagorean Theorem and its converse. 
8.G.7  Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. 
8.G.8  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 
Understand Congruence And Similarity Using Physical Models, Trans Parencies, Or Geometry Software.  
8.G.2  Understand that a twodimensional 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. 
8.G.3  Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. 
8.G.4  Understand that a twodimensional 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. 
Interpreting Categorical And Quantitative Data  
HSS.ID: Interpret Linear Models  
HSS.ID.7  Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 
HSS.ID.8  Compute (using technology) and interpret the correlation coefficient of a linear fit. 
Summarize, Represent, And Interpret Data On Two Categorical And Quantitative Variables  
HSS.ID.6  Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 
Interpreting Functions  
HSF.IF: Analyze Functions Using Different Representations  
HSF.IF.7  Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ 
HSF.IF.8  Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 
Interpret Functions That Arise In Applications In Terms Of The Context  
HSF.IF.4  For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ 
HSF.IF.6  Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ 
Understand The Concept Of A Function And Use Function Notation  
HSF.IF.1  Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). 
HSF.IF.2  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 
Linear, Quadratic, And Exponential Models  
HSF.LE: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems  
HSF.LE.1  Distinguish between situations that can be modeled with linear functions and with exponential functions. 
HSF.LE.2  Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 
HSF.LE.3  Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 
Interpret Expressions For Functions In Terms Of The Situation They Model  
HSF.LE.5  Interpret the parameters in a linear or exponential function in terms of a context. 
Quantities  
HSN.Q: Reason Quantitatively And Use Units To Solve Problems.  
HSN.Q .1  Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. 
Ratios And Proportional Relationships  
6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.  
6.RP.1  Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 
6.RP.2  Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1 
6.RP.3  Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 
7.RP: Analyze Proportional Relationships And Use Them To Solve RealWorld And Mathematical Problems.  
7.RP.1  Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 
7.RP.2  Recognize and represent proportional relationships between quantities. 
7.RP.3  Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 
Reasoning With Equations And Inequalities  
HSA.REI: Represent And Solve Equations And Inequalities Graphically  
HSA.REI.10  Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 
HSA.REI.12  Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. 
Solve Equations And Inequalities In One Variable  
HSA.REI.3  Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 
HSA.REI.4  Solve quadratic equations in one variable. 
Solve Systems Of Equations  
HSA.REI.5  Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 
HSA.REI.6  Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 
Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning  
HSA.REI.1  Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 
HSA.REI.2  Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. 
Seeing Structure In Expressions  
HSA.SSE: Interpret The Structure Of Expressions  
HSA.SSE.1  Interpret expressions that represent a quantity in terms of its context. 
HSA.SSE.2  Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). 
Write Expressions In Equivalent Forms To Solve Problems  
HSA.SSE.3  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ 
Similarity, Right Triangles, And Trigonometry  
HSG.SRT: Define Trigonometric Ratios And Solve Problems Involving Right Triangles  
HSG.SRT.8  Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★ 
Statistics And Probability  
7.SP: Investigate Chance Processes And Develop, Use, And Evaluate Probability Models.  
7.SP.7  Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 
7.SP.8  Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 
8.SP: Investigate Patterns Of Association In Bivariate Data.  
8.SP.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. 
8.SP.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. 
The Complex Number System  
HSN.CN: Perform Arithmetic Operations With Complex Numbers.  
HSN.CN.2  Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 
HSN.CN.3  (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. 
Represent Complex Numbers And Their Operations On The Complex Plane.  
HSN.CN.4  (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. 
HSN.CN.5  (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (–1 + √3 i)3 = 8 because (–1 + √3 i) has modulus 2 and argument 120°. 
HSN.CN.6  (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. 
Use Complex Numbers In Polynomial Identities And Equations.  
HSN.CN.7  Solve quadratic equations with real coefficients that have complex solutions. 
The Number System  
6.NS: Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.  
6.NS.1  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? 
Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.  
6.NS.5  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 
6.NS.6  Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 
6.NS.7  Understand ordering and absolute value of rational numbers. 
6.NS.8  Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 
Compute Fluently With MultiDigit Numbers And Find Common Factors And Multiples.  
6.NS.2  Fluently divide multidigit numbers using the standard algorithm. 
6.NS.3  Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. 
6.NS.4  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). 
7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers.  
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. 
7.NS.2  Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 
7.NS.3  Solve realworld and mathematical problems involving the four operations with rational numbers. 
8.NS: Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers.  
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 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. 
The Real Number System  
HSN.RN: Use Properties Of Rational And Irrational Numbers.  
HSN.RN.3  Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. 
Vector And Matrix Quantities  
HSN.VM: Perform Operations On Matrices And Use Matrices In Applications.  
HSN.VM.10  (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. 
HSN.VM.7  (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. 
HSN.VM.8  (+) Add, subtract, and multiply matrices of appropriate dimensions. 
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