Key Learning: Students will demonstrate an understanding of expression and equations with respect to linear equations. Unit Essential Question

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1 Student Learning Map for Unit Topic: PA Common Core: M08.B-E.1 Demonstrate an understanding of expressions and equations with radicals and integer exponents. M08.B-E.2 Understand the connections between proportional relationships, lines, and linear equations. M08.B-E.3 Analyze and solve linear equations and pairs of simultaneous linear equations. Key Learning: Students will demonstrate an understanding of expression and equations with respect to linear equations. Unit Essential What is the relationship between a system of linear equations and their slopes? Lesson Topic 1: Equivalent Expressions Lesson Topic 2: Solving Equations Lesson Topic 3: Graphing Linear Equations s: How is PEMDAS related to simplifying algebraic expressions? s: What are the steps used in solving an equation with a variable on both sides? s: What is the representation of slopeintercept form on a graph? Integers, exponent, square root, cube root, scientific notation, numerical expression, algebraic expression : Equation, variable, solution, addition property of equality, multiplication property of equality, distributive property, inverse operations, : Linear equation, y=mx+b, slope, origin, y-intercept, systems of equations Understand: Scientific Notation is used to write very large or very small numbers. To solve an equation, remember whatever you do to the left, you must do to the right. The formula y=mx+b is an equation of a line. It becomes proportional when b=0. Understand a negative exponent is a reciprocal of the base number.

2 Course/Subject: 8 th Grade math Topic: Functions Days: Grade Level: Key Learning Functions Unit Essential How will a function help us to understand graphs, equations, and tables? What is a function? Standards: BM08.B-F.1 Analyze and interpret functions Functions and Graphs Standards: BM08.B-F.1 Analyze and interpret functions Y=mx+b Standards: M08.B-F.2 Use functions to model relationships between quantities. How do I know when a relation is not a function? How can we interpret functional relationships represented by graphs, equations, and tables? How does y=mx+b model a linear graph? Relation, function, domain, range, x-intercept, y-intercept, Slope (m), (0,b), slopeintercept form, Standards: Standards: Standards:

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4 Student Learning Map for Unit Topic: PA Common Core: M08.C-G.1 Demonstrate an understanding of geometric transformations.-g.1 M08.C-G.2 Understand and apply the Pythagorean Theorem. M08.C-G.3 Solve real-world and mathematical problems involving volume. Key Learning: Students will demonstrate an understanding of transformations, Pythagorean theorem, and volume. Unit Essential What spatial relations exist on a coordinate plane, in a right triangle, and 3-dimensional figures? Lesson Topic 1: Transformations Lesson Topic 2: Pythagorean Theorem Lesson Topic 3: Volume s: How are rotations, reflections, and translations alike and different? s: What is relationship between the Pythagorean Theorem and right triangles? s: Why are the units in volume always cubed? Rotation, reflection, translation, congruent, similar, sequence, dilation, coordinates, Cartesian coordinate system : Right, triangle, hypotenuse, leg, Pythagorean Theorem, converse, a 2 + b 2 = c 2 distance on coordinate system : Volume, cone, cylinder, sphere, V = 1 3 πr2 h ; V = πr 2 h ; V = 4 3 πr3 Understand: a 2 + b 2 = c 2 can only be used with right triangles Transformation and translation are different. Volume is the amount of space inside a 3-dimensional shape.

5 Student Learning Map for Unit Topic: PA Common Core: M08.A-N Number Systems Key Learning: Students will demonstrate an understanding of rational and irrational numbers. Unit Essential How are rational and irrational numbers related? Lesson Topic 1: Define rational & irrational Lesson Topic 2: Comparing and Ordering Rational and Irrational Nbrs Lesson Topic 3: Applying Rationals & Irrationals s: What is the difference between a rational and irrational number? s: How do rational numbers help us compare irrational numbers? s: How can you represent rational and irrational numbers on a number line? Terminating, Repeating Rational, Irrational Quotient, Division Square Root ( perfect square Numerator, Denominator Estimate, Round : Number Line Symbols <, >, = : Understand: All rational numbers repeat. All irrational numbers never repeat. Perfect Squares have whole number answers. The square root of any non-perfect ( is irrational π is irrational.

6 Course/Subject: 8 th Grade math Topic: M08.D-S Statistics and Probability Days: Grade Level: 8th Key Learning Investigating patterns of bivariate data Unit Essential How can bivariate data be represented to find patterns? Scatter Plots Standards: M08.D-S.1 Investigate patterns of association in bivariate data. Analyzing Bivariate Data Standards: M08.D-S.1 Investigate patterns of association in bivariate data. Standards: How can scatter plots help us determine relationships in bivariate data? What patterns can be used to infer conclusions associated with bivariate data? Scatter plot, correlation: (pos/neg/no trend), line of best fit, Max, min, outliers, relative frequency, cluster, Standards: Standards: Standards:

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