Curriculum Overview
In Grade 8, math instructional time will focus on three critical areas:
STANDARD 1 – THE NUMBER SYSTEM
Students know that there are numbers that are not rational and approximate them by rational numbers. Students know that every number has a decimal expansion and understand that rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number. Students learn to use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line to diagram and estimate the value of expressions.
STANDARD 2 – EXPRESSIONS AND EQUATIONS
Students know and apply the properties of integer exponents to generate equivalent numerical expressions. Students learn and 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. Students evaluate square roots of small perfect squares and cube roots of small perfect cubes. They know that √2 is irrational. Students also know how to 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. Students learn to perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. They use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Students interpret scientific notation that has been generated by technology. They understand the connections between proportional relationships, lines and linear equations. Students know how to graph proportional relationships as well as compare two different proportional relationships represented in different ways. Students also analyze and solve linear equations in one variable as well as with rational number coefficients including solutions requiring expanding expressions using distributive property. They also learn to analyze and solve pairs of simultaneous linear equations.
STANDARD 3 – FUNCTIONS
Students define, evaluate and compare functions. They understand that functions are rules that assign to each input exactly one output. Students learn to compare properties of two functions each represented in a different way. Students learn to interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Students use functions to model relationships between quantities and construct a function to model a linear relationship between two quantities. Students 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. They describe qualitatively the functional relationship between two quantities by analyzing a graph.
STANDARD 4 – GEOMETRY
Students understand congruence and similarity using physical models, transparencies or geometry software. They learn to verify experimentally the properties of rotations, reflections and translations. Students 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. Students describe the effect of dilations translations, rotations and reflections on two-dimensional figures using coordinates. Students also 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 dilation. Students 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 tranversal and the angle-angle criterion for similarity of triangles. Students understand and can apply the Pythagorean Theorem. Students also can solve real-world and mathematical problems involving volume of cylinders, cones and spheres by knowing and applying the formulas.
STANDARD 5 – STATISTICS AND PROBABILITY
Students construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Students know that straight lines are widely used to model relationships between two quantitative variables. Students also use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Students understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
- Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with linear equation and solving linear equations and systems of linear equations.
- Grasping the concept of a function and using functions to describe quantitative relationships.
- Analyzing two- and three-dimensional space and figures using distance, angles, similarity and congruence and understanding and applying the Pythagorean Theorem.
STANDARD 1 – THE NUMBER SYSTEM
Students know that there are numbers that are not rational and approximate them by rational numbers. Students know that every number has a decimal expansion and understand that rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number. Students learn to use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line to diagram and estimate the value of expressions.
STANDARD 2 – EXPRESSIONS AND EQUATIONS
Students know and apply the properties of integer exponents to generate equivalent numerical expressions. Students learn and 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. Students evaluate square roots of small perfect squares and cube roots of small perfect cubes. They know that √2 is irrational. Students also know how to 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. Students learn to perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. They use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Students interpret scientific notation that has been generated by technology. They understand the connections between proportional relationships, lines and linear equations. Students know how to graph proportional relationships as well as compare two different proportional relationships represented in different ways. Students also analyze and solve linear equations in one variable as well as with rational number coefficients including solutions requiring expanding expressions using distributive property. They also learn to analyze and solve pairs of simultaneous linear equations.
STANDARD 3 – FUNCTIONS
Students define, evaluate and compare functions. They understand that functions are rules that assign to each input exactly one output. Students learn to compare properties of two functions each represented in a different way. Students learn to interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Students use functions to model relationships between quantities and construct a function to model a linear relationship between two quantities. Students 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. They describe qualitatively the functional relationship between two quantities by analyzing a graph.
STANDARD 4 – GEOMETRY
Students understand congruence and similarity using physical models, transparencies or geometry software. They learn to verify experimentally the properties of rotations, reflections and translations. Students 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. Students describe the effect of dilations translations, rotations and reflections on two-dimensional figures using coordinates. Students also 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 dilation. Students 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 tranversal and the angle-angle criterion for similarity of triangles. Students understand and can apply the Pythagorean Theorem. Students also can solve real-world and mathematical problems involving volume of cylinders, cones and spheres by knowing and applying the formulas.
STANDARD 5 – STATISTICS AND PROBABILITY
Students construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Students know that straight lines are widely used to model relationships between two quantitative variables. Students also use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Students understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
Notes Pertaining to Current Unit of Study
review_vocab.docx | |
File Size: | 83 kb |
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review_vocab.pdf | |
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l5-1_lines_.pdf | |
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l5-4_polygons_and_angles_notes.pdf | |
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l1-8_roots.pdf | |
File Size: | 682 kb |
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l5-5_the_pythagorean_theorem.pdf | |
File Size: | 450 kb |
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l5-6_use_the_pythagorean_theorem.pdf | |
File Size: | 257 kb |
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l5-7_distance_on_the_coordinate_plane.pdf | |
File Size: | 369 kb |
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Blank Coordinate Grids
4_blank_coordinate_grids.pdf | |
File Size: | 38 kb |
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Fraction, Decimal, Percent Equivalents Chart
fraction_decimal_percent_chart.pdf | |
File Size: | 355 kb |
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