Central Valley School District Math Curriculum Map Grade 8. August - September

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Ashlyn Atkinson
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1 August - September Decimals Add, subtract, multiply and/or divide decimals without a calculator (straight computation or word problems) Convert between fractions and decimals ( terminating or repeating decimals) Scientific Notation Convert between decimal notation and scientific notation percents, exponents, scientific notation, square roots, absolute values) B Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions percents, exponents, scientific notation, square roots, absolute values) Fractions Use divisibility rules for 2, 3, 4, 5, 6, 8, 9 and10 Add, subtract, multiply and/or divide fractions without a calculator (straight computation or word problems) Convert between fractions, decimals and/or percents (e.g., 20% = 0.2 = 1/5) Identify and use rational number properties Problem Solving Solve problems involving operations (+, -, x, ) of whole numbers, decimals, fractions, or mixed numbers (straight computation or word problems) Choose the best method of computation for solving a problem Solve problems by determining reasonable answers D Extend place-value concepts to represent large numbers using exponential, scientific and calculator notation percents, exponents, scientific notation, square roots, absolute values) B Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions A Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, apply estimation skills as appropriate, check whether the plan makes sense and explain how the problem was solved in grade appropriate contexts B Use precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams to explain and interpret results 1

2 October Integers Locate or plot integers on a number line A Model and compare values of integers and rational numbers Find the absolute value and opposite of an integer Compare and/or order a set of integers from least to greatest and from greatest to least Add and subtract integers without a calculator (straight computation or word problems) Multiply and divide integers without a calculator (straight computation or word problems) Expressions Simplify numeric expressions involving integers, using the order of operations. (May include all types of grouping symbols. No combining negatives with exponents [4^-3] or compound exponents.) Find the square or cube of a whole number (single digit) and/or the square root of a perfect square (without a calculator) and explain the relationship between the two (i.e. square and square root) Determine the value of an algebraic expression by simplifying and/or substituting a number for the variable Equations Use addition and subtraction to solve one-step equations Use multiplication and division to solve one-step equations Solve two-step equations Inequalities Solve and graph one-step Solve and graph two-step percents, exponents, scientific notation, square roots, absolute values) B Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions F Understand the concepts of exponents and roots and use the inverse relationships between exponents and roots to determine unknown quantities in equations C Use the order of operations to evaluate numerical expressions A Use the concept of equality to demonstrate understanding of the inverse properties of numbers and the addition and multiplication properties of equality A Use the concept of equality to demonstrate understanding of the inverse properties of numbers and the addition and multiplication properties of equality Problem Solving Match a written situation to its numeric and/or algebraic expression, equation or inequality (up to two variables in equations or expressions one variable with ) A Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, apply estimation skills as appropriate, check whether the plan makes sense and explain how the problem was solved in grade appropriate contexts B Use precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams to explain and interpret results E Use combinations of symbols and numbers to create expressions, equations in one or two variables and in one variable that model problem situations F Interpret the results of solving equations in one or two variables and in one variable in the context of the situation that motivated the model

3 November Ratio, Rate, Proportion and Percent Express ratios as fractions in simplest form Represent or solve rate problems (e.g., unit rates, simple interest, distance, etc.) Students percents, exponents, scientific notation, square roots, absolute values) may be asked to solve for any term (formulas provided on the reference sheet for distance and interest) C Use ratio and proportion to model relationships between quantities Solve proportions Solve problems by using proportions (include similar figures, scale drawings, etc.) B Add, subtract, multiply and divide different kinds and forms of rational numbers Convert between percents, decimals and fractions (include percent greater than 100 or less including integers, decimal fractions, percents and proper and improper fractions than 1) Solve problems involving percents (e.g., tax, discounts, etc) Do not include percent F Estimate and verify measurements of rate and mass increase or decrease Solve problems by using the percent equation A Use the concept of equality to demonstrate understanding of the inverse properties of numbers and the addition and multiplication properties of equality E Use combinations of symbols and numbers to create expressions, equations in one or two variables and in one variable that model problem situations Estimation Identify, use and/or explain when it is appropriate to round up or round down Identify, apply and/or explain when an exact answer is needed or when estimation is appropriate Estimating with percents F Interpret the results of solving equations in one or two variables and in one variable in the context of the situation that motivated the model D Estimate the values of irrational numbers and the results from calculations with basic operations of fractions and percents and check the reasonableness 3

4 December Unit Conversion Convert among metric measurements (milli, centi, kilo using meter, liter and gram) (table of equivalency provided on the reference sheet) Convert customary measurements up to 2 units above or below the given unit (e.g., inches to yards, pints to gallons) (table of equivalency provided on the reference sheet) Convert time up to 2 units above or below given unit (e.g., seconds to hours) Convert from Fahrenheit to Celsius or Celsius to Fahrenheit (formulas provided on the reference sheet) Measures of Angles of Polygons Determine the total number of degrees in the interior angles of a polygon in 3-8 sided figures (formula provided on the reference sheet) Determine the measurement of one interior angle of a regular polygon (3-8 sided polygons, formula provided on the reference sheet) Determine the number of sides of a polygon given the total number of degrees in the interior angles (3-8 sided polygons, formula provided on the reference sheet) D Perform conversions within the metric system and within the customary system including scale measurements, between units of time and between units of temperature A Name, describe and apply geometric relations for 1- dimensional shapes and 2-4

5 January Two-Dimensional Measurement Find perimeter of regular and irregular polygons (formula provided on the reference sheet) B Develop strategies for determining areas and volumes of compound shapes and solids Find the circumference of circles (formula provided on the reference sheet) Find the area of triangles, quadrilaterals, circles and compound figures (formula provided A Name, describe and apply geometric relations for 1- dimensional shapes and 2- on the reference sheet) Three-Dimensional Measurement Match the three-dimensional figure with its net (cube, cylinder, cone, prism, pyramid). Any C Calculate volume, surface area, and degrees of angles; calculate circumference and area measurements used should be consistent in the stem and answer choices of circles, and use a measurement formula to solve for a missing quantity Calculate the surface area of cubes and rectangular prisms (formula provided on the reference sheet) A Name, describe and apply geometric relations for 1- dimensional shapes and 2- Calculate the volume of cubes and rectangular prisms (formulas provided on the reference sheet) Problem Solving Determine the appropriate type of measurement (circumference, perimeter, area, surface area, volume) for a given situation (e.g., which measurement is needed to determine the amount of carpeting for a room) Analyze effects of changes in a linear dimension B Develop strategies for determining areas and volumes of compound shapes and solids E Describe how a change in linear dimension of an object affects its perimeter, area and volume The Coordinate Plane Plot, locate or identify ordered pairs on a coordinate plane (the point may be a vertex of a polygon) A Name, describe and apply geometric relations for 1- dimensional shapes and C Plot ordered pairs and 2-dimensional shapes that satisfy given conditions on a 2- dimensional coordinate system 5

6 February Properties of Angles Define, identify and/or use properties of angles formed by intersecting lines A Name, describe and apply geometric relations for 1- dimensional shapes and 2- (complementary, supplementary, adjacent and/or vertical angles) Define, identify and/or use properties of angles formed when two parallel lines are cut by a transversal (alternate interior, alternate exterior, vertical corresponding) Triangles Classify by angles and sides and determine the measures of missing angles A Name, describe and apply geometric relations for 1- dimensional shapes and 2- The Pythagorean Theorem Estimate square roots Use the Pythagorean Theorem to find the measure of a missing side of a right triangle (formula provided on the reference sheet whole numbers only) Solve problems using the Pythagorean Theorem D Estimate the values of irrational numbers and the results from calculations with basic operations of fractions and percents and check the reasonableness A Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships Quadrilaterals Identify and/or describe properties of all types of quadrilaterals A Name, describe and apply geometric relations for 1- dimensional shapes and 2- Patterns Continue a numeric or algebraic pattern (pattern must show 3 repetitions may include up to 2 operations, squares and square roots) Find missing elements in numeric or geometric patterns and/or functions (may be given a table or rule pattern must show 3 repetitions) Determine the rule of a function (given elements in an input-output table, chart or list limit to linear functions) Linear Functions Graph a linear function based on an x/y table (integers only) Match the graph of a linear function to its x/y table (integers only) Match the linear equation (y = mx + b form) to the x/y table (integers only in the table) C Find the missing elements and recognize, describe and extend patterns to include linear, exponential, and simple quadratic equations D Create a table or graph from a function a1 rule E Use combinations of symbols and numbers to create expressions, equations in one or two variables and in one variable that model problem situations 6

7 Data Analysis Determine the mean, median, mode, range and quartiles of a set of data Analyze data and/or answer questions pertaining to data shown in multiple line graphs, circle graphs or histograms Interpret data shown in stem-and-leaf and box-and-whisker plots Fit a line to a scatter plot and/or describe any correlation between the two variables (positive, negative, strong, weak or none) Choose and/or explain the correct representation graph for a set of data Make predictions based on survey results or graphs (bar, line, circle, scatter plots, etc.) Analyze and recognize when graphs and statistics are misleading Probability Find the probability for a mutually exclusive or an independent event (written as a fraction in simplest form) Determine/show the number of permutations and/or combinations for an event using up to four choices (e.g., organized list, etc.) PSSA Review Numbers and Operations Measurement Geometry Algebra Data Analysis and Probability Open Ended March B Organize and display one-variable data using appropriate data display, such as stem and leaf and box-and whisker plots, and two variable data with scatter plots C Calculate quartiles for one-variable data and describe the correlation coefficient for twovariable data displayed in a scatter plot D Compare data sets graphically using double-bar and double-line graphs and numerically using mean, median, mode, range and quartiles E Determine the effect of extreme values on numerical summaries and calculate estimates based on survey results or graphs A Calculate the probability of an event involving and, or or not C Determine the number of combinations and permutations for an event E Find the experimental or theoretical probability of the outcomes of a simple or compound event 7

8 April Similar and Congruent Figures Identify corresponding parts of similar polygons and find missing measures of similar A Name, describe and apply geometric relations for 1- dimensional shapes and 2- polygons Identify and determine whether triangles are congruent by SSS, ASA and SAS properties Draw or identify a line of symmetry and rotational symmetry Transformations Graph translations on a coordinate plane B Predict and describe the result of a translation (slide), rotation (turn), or reflection (flip) Graph reflections on a coordinate plane of a 2- dimensional shape Graph rotations of 90 and 180 on a coordinate plane Graph dilations on a coordinate plane C Plot ordered pairs and 2-dimensional shapes that satisfy given conditions on a 2- Create Escher-like drawings using translations and rotations dimensional coordinate system Problem Solving Eliminate possibilities through problem solving Solve problems by finding and extending a pattern Recognize and extend arithmetic and geometric sequences Solve a problem by solving a similar problem Use inductive and deductive reasoning to solve a problem A Draw inductive and deductive conclusions within mathematical contexts A Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, apply estimation skills as appropriate, check whether the plan makes sense and explain how the problem was solved in grade appropriate contexts B Use precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams to explain and interpret results 8

9 Graphing Functions Find solutions of equations with two variables Use substitution to check the accuracy of a given value for an equation or inequality Graph linear functions Find the distance between points in the coordinate plane Graph systems of equations Graph quadratic function Discrete Math and Probability Use tree diagrams and multiplication counting principle to count outcomes Find the number of permutations of a set of objects Find the number of combinations of a set of objects Find the probability of compound events (include independent and dependent) Use sampling to predict outcomes Polynomials Classify and model polynomials Simplify polynomials Add polynomials May - June C Find the missing elements and recognize, describe and extend patterns to include linear, exponential, and simple quadratic equations D Create a table or graph from a function a1 rule A Understand and apply sampling techniques to gather data including simple random sampling and convenience sampling A Calculate the probability of an event involving and, or or not C Determine the number of combinations and permutations for an event E Find the experimental or theoretical probability of the outcomes of a simple or compound event 9

Prentice Hall Mathematics: Course Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 8)

Prentice Hall Mathematics: Course Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 8) M8.A Numbers and Operations M8.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M8.A.1.1 Represent numbers in equivalent forms.