- James L. Day Middle School
- Math 8
Triggs, Michelle
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Math 8
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Math 8 Information
Math 8 Class Information Letter
Semester 1 Topics
Unit 1: Rigid Transformations and Congruence
Big Ideas
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- Describe and perform translations, rotations, and reflections on a grid
- Determine whether two figures are congruent using rigid transformations
- Use transformations and angle relationships created by a transversal with parallel lines to determine unknown measurements
Required Skills
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- Perform rotations, reflections, & translations on a grid and using coordinate rule
- Determine whether a transformation on a given two-dimensional figure results in a congruent figure
- Describe a sequence of rigid transformations that would take one given figure to another
- Understand and use facts about angle sum and exterior angles of triangles, corresponding angles, alternate & same-side interior and exterior angles
Unit 2 – Dilation, Similarity, and Introducing Slope
Big Ideas
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- Describe dilations in terms of their center and scale factor
- Dilate figures on and off coordinate plane
- Identify similar figures and properties of similar figures using transformations
- Explain slope in terms of similar triangles on same line and determine slopes of given lines
Required Skills
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- Perform dilations
- Describe the effect of a transformation on a given two-dimensional figure that creates a similar figure
- Describe the sequence of transformations that would take one given figure to another
- Understand and use facts about the angle-angle criterion for similarity of triangles
Unit 3 – Proportional and Linear Relationships
Big Ideas
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- Compare proportional relationships using their equations, tables, and graphs
- Interpret the intercepts and slope of a graph or equation of a linear relationship
- Use the concept that a graph represents all solutions of an equation to solve problems
Required Skills
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- Identify and graph linear equations using table of values and using slope and y-intercept
- Interpret rate of change and initial value of a linear relationship in terms of a situation it models
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- Describe key elements of a graph (linear vs. nonlinear; increasing, decreasing, or constant intervals)
- Examine rates, ratios, and slope relationships
Unit 4 – Linear Equations and Linear Systems
Big Ideas
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- Write and solve linear equations
- Use graphs and algebraic methods to solve systems of linear equations in two variables
Required Skills
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- Review how to perform operations on rational numbers (add, subtract, multiply, & divide)
- Solve multi-step linear equations with rational coefficients
- Identify whether a given linear equation will have one solution, no solution, or infinitely many solutions
- Model situations using linear equations
- Solve linear systems of equation by graphing, substitution, & elimination
Semester 2 Topics
Unit 5 – Functions and Volume
Big Ideas
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- Determine whether or not graphs, tables, or rules represent functions
- Create and interpret graphs of functions that represent stories
- Calculate and compare volume of cylinders, cones, and spheres
- Use the relationships between height, radius, and volume to calculate missing dimensions
Required Skills
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- Determine whether given relations are functions
- Interpret and compare functions described using different models: verbal descriptions, tables, algebraic expressions/equations, graphs
- Construct functions to model relationship between two quantities
- Use formulas for volumes of cones, cylinders, and spheres to solve problems
Unit 6 – Exponents and Scientific Notation
Big Ideas
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- Identify and create equivalent expressions involving positive, negative, and zero exponents
- Express and perform operations with very large or very small quantities using powers of 10 and scientific notation
Required Skills
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- Use rational exponents & rules of exponents to simplify expressions
- Convert numbers between standard form and scientific notation
- Perform operations (add, subtract, multiply, & divide) numbers written in scientific notation
Unit 7 – The Pythagorean Theorem and Irrational Numbers
Big Ideas
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- Understand that square roots and cube roots represent the edge lengths of squares and cubes, and approximate their values
- Use the Pythagorean theorem and its converse to reason about right triangles and find unknown measurements
- Determine fractions and decimal approximations for rational and irrational numbers
Required Skills
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- Convert terminating and repeating decimals to fractions and vice-versa
- Identify whether real numbers are rational or irrational, locate on number line, and compare
- Take the square root and cube root of a given number, estimate roots if not perfect
- Solve simple equations involving square roots and cube roots
- Prove the Pythagorean Theorem using visual proof
- Use Pythagorean Theorem to solve problems, such as finding distance between two points and unknown side lengths of a right triangle
Unit 8 – Association in Data
Big Ideas
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- Examine different ways to organize bivariate data (scatter plots & two-way tables)
- Use scatter plots and fitted lines to analyze numerical data and identify associations
- Use two-way tables and bar graphs to identify associations in categorical data
Required Skills
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- Construct and interpret scatter plots
- Discuss patterns (clustering, outliers, and association)
- Draw lines of best fit, find their equations, and use to make interpolations/extrapolations
- Construct and investigate patterns of associations that occur in two-way frequency tables
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- the California Math CCSS Course 3 on-line textbook
- i-Ready
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