FluidMath CCSS Lessons and Demonstrations

FluidMath Lessons and Demonstrations is a set of FluidMath documents aligned with the Common Core State Standards (CCSS). The documents include teacher demonstrations, student investigations, and practice applets.

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Grade 7Show

Ratios and Proportional Relationships Show

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7.RP.A.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.

Computing Unit Rates: Comparing Areas of Squares

7.RP.A.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Proportional Reasoning Practice 1: Juice Problem

7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Ratios and Proportional Relationships: Pizza Problem

7.RP.A.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Proportional Reasoning Practice 2: Juice Problem

The Number System (No content yet)

Expressions and Equations Show

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7.EE.B.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Construct Solve Equations Practice 1: Rectangles I

Construct Solve Equations Practice 1: Rectangles II

Geometry Show

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7.G.B.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.

Area of Circle with Varied Radius

Circumference of Circle with Varied Radius

Circumference of a Circle

Statistics and Probability (No content yet)

Grade 8Show

The Number System (No content yet)

Expressions & Equations Show

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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.

Compare Proportional Relations Practice 2: Juice

Compare Proportional Relations: Time Distance Graph

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

Linear Equations Rational Coefficients: Painting

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.

Solving System of Linear Equations Coincident

Solving System of Linear Equations Exploration 2

Solving System of Linear Equations Practice

8.EE.C.8b 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.

Solving System of Linear Equations: Foot Race

Functions Show

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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.

Interpret Equations Nonlinear Funcs: Area of Square

Geometry Show

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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.

Apply Pythagorean Theorem

Apply Pythagorean Theorem Practice 1

Statistics & Probatility (No content yet)

High School: Number and QuantityShow

The Real Number System Show

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HSN-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 513 to be the cube root of 5 because we want (513)3 = 5(13)3 to hold, so (513)3 must equal 5.

Rational Exponents

Quantities Show

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HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Interpret the Scale of a Graph

The Complex Number System Show

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HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

Quadratic Equations with Complex Solutions

Vector and Matrix Quantities Show

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HSN-VM.B.4a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

Adding Vectors

High School: AlgebraShow

Seeing Structure in Expressions (No content yet)

Arithmetic with Polynomials and Rational Expressions Show

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HSA-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Polynomial as Linear Factors

Creating Equations Show

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HSA-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Creating Equations 1 .

Creating Equations 2 .

Creating Equations 3 .

Creating Equations 4 .

Creating Equations 5 - College Costs .

Creating Equations 6 - Price and Demand .

Direct Variation

Direct or Inverse Variation Practice 1

Direct or Inverse Variation Practice 2

Inverse Variation

Reasoning with Equations and Inequalities Show

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HSA-REI.C.5 Fill in..

Systems of Equations 1 .

Systems of Equations 2 .

Systems of Equations 3 .

HSA-REI.C.6 Fill in..

System of Equations 4 .

System of Equations 5 .

Systems of Equations 6 .

HSA-REI.D.10 Fill in..

Algebra Reasoning with Equations 1 - Taxi .

Algebra Reasoning with Equations 2 - Ball Drop A .

Algebra Reasoning with Equations 3 - Ball Drop B .

HSA-REI.D.11 Fill in..

Algebra Reasoning w/ Equations 4 - Food Supply A .

Algebra Reasoning w/ Equations 5 - Food Supply B .

Algebra Reasoning w/ Equations 6 - Hoops .

HSA-REI.D.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 half-planes.

Inequality Graphing Practice 1

Inequality Graphing Practice 2

Inequality Graphing Practice 3

Reasoning with Equations and Inequalities 1 .

Reasoning with Equations and Inequalities 2 .

Reasoning with Equations and Inequalities 3 .

Reasoning with Equations and Inequalities 4 .

Reasoning with Equations and Inequalities 5 .

Reasoning with Equations and Inequalities 6 .

High School: FunctionsShow

Interpreting Functions Show

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HSF-IF.A.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).

Domain and Range Practice 1

Domain and Range Practice 2

Horizontal Lines

Vertical Lines

Vertical line test 1

Vertical line test 2

HSF-IF.B.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.

Graph Sketching 1 .

Graph Sketching 2 .

Graph Sketching 3 .

Intercept Practice 1 .

Intercept Practice 2 .

Intercept Practice 3 .

Interpret Functions - Swing

X-Intercept Practice 1

X-Intercept Practice 2

X-Intercept Practice 3

Y-Intercept Practice 1

Y-Intercept Practice 2

Y-Intercept Practice 3

HSF-IF.B.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.

Estimating slope

HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Graphing Functions 1 .

Graphing Functions 2 .

Graphing Functions 3 .

HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Sinusoidal Modeling

Sinusoidal Modeling Practice 1

Sinusoidal Modeling Practice 2

HSF-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Graphing Functions 4 .

Graphing Functions 5 .

Graphing Functions 6 .

Building Functions Show

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HSF-BF.A.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Exponential Functions - Temperature

HSF-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Seq: Recursive Equations 1b-Allowance

Arithmetic Seq: Recursive/Explicit Equations 1a

Functions - Arithmetic Sequence 1 .

Functions - Arithmetic Sequence 2 .

Functions - Arithmetic Sequence 3 - Savings .

Functions - Arithmetic Sequence 4 - Explicit .

Functions - Arithmetic Sequence 5 - Explicit - PT .

Functions - Arithmetic Sequence 6 - Allowance .

Functions - Geometric Seq 5 - Explicit - Half-Life .

Functions - Geometric Seq 6 - Explicit- Medicine .

Functions - Geometric Sequence 1 .

Functions - Geometric Sequence 2 .

Functions - Geometric Sequence 3 - Algae .

Functions - Geometric Sequence 4 - Explicit - Algae

Geometric Seq: Recursive Equations 1a

HSF-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Even Functions

Odd Functions

Transformations - Toolkit Functions 1

Transformations - Translations 2a

Transformations - Translations 2a .

Transformations - Translations 2b

Transformations - Translations 2b .

Transformations - Translations 2c

Transformations - Translations 2c .

Transformations - Translations 2d

Transformations - Translations 2d .

Transformations - Translations 2e

Transformations - Translations 2e .

Transformations - Translations 2f

Transformations - Translations 2f .

Transformations 1 .

Transformations 2 .

Transformations 3 .

Transformations 4 .

Transformations 5 .

Transformations 6 .

HSF-BF.B.4 Find inverse functions.

Inverse Points

HSF-BF.B.4b (+) Verify by composition that one function is the inverse of another.

Composition of Functions and Inverses

HSF-BF.B.4d (+) Produce an invertible function from a non-invertible function by restricting the domain.

Invertible Function

HSF-BF.B.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Exponential and Logarithmic Functions

Linear, Quadratic, and Exponential Models Show

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HSF-LE.A.1 Fill in..

Functions: Lin, Quad & Exp 5 - Fish Population .

Functions: Lin, Quad & Exp 6 - Car Value .

Functions: Lin, Quad & Exp 4 -Savings .

Linear versus Exponential Functions 1 .

Linear versus Exponential Functions 2 .

Linear versus Exponential Functions 3 .

HSF-LE.A.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Linear versus Exponential Functions 1

Linear versus Exponential Functions 2

Linear versus Exponential Functions 3

Trigonometric Functions Show

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HSF-TF.A.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number.

Trigonometric Values of Special Angles

High School: GeometryShow

Congruence (No content yet)

Similarity, Right Triangles, and Trigonometry (No content yet)

Circles (No content yet)

Expressing Geometric Properties with Equations Show

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HSG-GPE.B.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).

Parallel and Perpendicular Lines Practice 1

Parallel and Perpendicular Lines Practice 1 .

Parallel and Perpendicular Lines Practice 2

Parallel and Perpendicular Lines Practice 2 .

Parallel and Perpendicular Lines Practice 3

Parallel and Perpendicular Lines Practice 3 .

Parallel and Perpendicular Lines Practice 4 .

Parallel and Perpendicular Lines Practice 5 .

Parallel and Perpendicular Lines Practice 6 .

HSG-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Point on a Line Segment 1

Point on a Line Segment 2

HSG-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Maximum Area Given a Fixed Perimeter

Geometric Measurement and Dimension Show

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HSG-GMD.A.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 and agruments, Cavalieri's principle, and informal limit arguments.

Circumference of a Circle

Modeling with Geometry (No content yet)

High School: Statistics & ProbabilityShow

Interpreting Categorical and Quantitative Data Show

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HSS-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Shape, Center, and Spread 1

Shape, Center, and Spread 2

HSS-ID.B.6c Fit a linear function for a scatter plot that suggests a linear association.

Fitting a line to a scatterplot

Making Inferences and Justifying Conclusions (No content yet)

Conditional Probability & the Rules of Probability (No content yet)

Using Probability to Make Decisions (No content yet)


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