Middle School Math for Digital White Boards. Common Core State Standards for Mathematics

Transcription

1 Middle School Math for Digital White Boards Correlations to Common Core State Standards for Mathematics OnBoard Academics, Inc. 44 Merrimac Street Newburyport MA Telephone: FAX:

2 Contents Scope and Sequence. Page 3 State Correlations Page 11 Page 2 of 28

3 Middle School Math for Digital White Boards Scope & Sequence Scope and Sequence Grade 6 STRAND KEY A = Algebra D = Data Analysis & Probability G = Geometry M = Measurement N = Number and Operations Code Strand Title Objective 6N001 N Words and Numbers Review word numbers and place value up to billions. Write numbers as word numbers. Write word numbers as numbers. 6N002 N Expanded Notation Write numbers using both expanded notation and standard form, up to billions. 6N003 N Compare and Order Integers Compare and order integers using number lines and greater than and less than symbols. 6N004 N Rounding Integers Practice rounding numbers to the nearest thousand, ten thousand, hundred thousand and million. Students should be familiar with rounding numbers up to at least the nearest thousand. 6N005 N Integers on a Number Line 6N006 N Adding Integers Using a Chip Board 6N007 N Subtracting Integers Using a Chip Board 6N008 N Adding and Subtracting Integers 6N009 N Multiplying and Dividing Integers Model adding and subtracting integers using a number line. Find the missing values in addition and subtraction problems. Given the answer write the addition or subtraction problem. Model adding integers using a chip board. Use the chip board to create your own addition problems. Model subtracting integers using a chip board. Use the chip board to create your own subtraction problems. Add and subtract integers in real-life situations including temperature, bank account balances and sea level. Investigate multiplying negative numbers by looking at number patterns and summarize the rules for multiplying and dividing with negative numbers. 6N010 N Absolute Value Introduce absolute value and apply to find the absolute value of an integer. 6N011 N Order of Operations Apply the order of operations to solve number problems. Arrange numbers and symbols to come up with a given answer. Insert parentheses correctly into a number problem, given the answer. 6N012 N Exponents Use exponents. Calculate with exponents. Compare numbers written with exponential notation. 6N013 N Multiples and Least Common Multiples Review multiples. Find the Least Common Multiple (LCM) of two or more numbers. Solve problems using multiples and LCM. 6N014 N Factoring Find the factors of a given number. Model the factors of a number using rectangle. Find missing factors. Page 3 of 28

4 Scope and Sequence Grade 6 (cont d) Code Strand Title Objective 6N015 N Greatest Common Factor 6N016 N Prime and Composite Numbers Find the Greatest Common Factor (GCF) of two or more numbers and apply to solve real-world problems. Identify prime and composite numbers. Find prime numbers less than 100 using the Sieve of Eratosthenes. Solve word problems. 6N017 N Prime Factorization Find the prime factors of a number. Complete factor trees. Write prime factors using exponent form. Apply to solve real-life problems. 6N018 N Divisibility Tests Determine whether a number is divisible by 2, 3, 4, 5, 6, 9, or 10 using divisibility tests. Use divisibility tests to solve a contextual problem. 6N019 N Identifying Fractions Review using fractions models to identify fractions. Introduce equivalent fractions. 6N020 N Equivalent Fractions Recognize simple relationships between equivalent fractions. Find equivalent fractions. Find missing numerators and denominators in equivalent fractions. 6N021 N Simplifying Fractions Write fractions in simplest terms by dividing the numerator and denominator by their greatest common factor (GCF). 6N022 N Compare and Order Fractions 6N023 N Mixed Numbers and Improper Fractions 6N024 N Estimating and Calculating with Fractions 6N025 N Adding and Subtracting Fractions with Common Denominators 6N026 N Adding and Subtracting Fractions with Unlike Denominators 6N027 N Adding and Subtracting Mixed Numbers with Common Denominators 6N028 N Adding and Subtracting Mixed Numbers with Unlike Denominators Compare and order fractions by finding equivalent fractions with a common denominator using pictures, number lines, and by writing fractions as decimals. Convert between mixed numbers and improper fractions. Use different strategies to write mixed numbers as improper fractions and improper fractions as mixed numbers. Use a contextual theme to estimate and calculate fractions. Model fractions using fractions strips. Modeling adding and subtracting fractions with common denominators. Progress to solving fraction problems without modeling, simplifying fractions. Use fraction models to add and subtract fractions with unlike denominators, and progressing to solve addition and subtraction problems without modeling. Add and subtract fractions and mixed numbers with common denominators. Use fraction models to add and subtract mixed numbers with unlike denominators, and progressing to solving mixed number problems without modeling. 6N029 N Multiplying Fractions The objective of this lesson is to multiply fractions using fractions models. Write the product in simplest form. Page 4 of 28

5 Scope and Sequence Grade 6 (cont d) Code Strand Title Objective 6N030 N Multiplying Mixed Numbers 6N031 N Dividing Fractions Using Fraction Models 6N032 N Dividing Fractions and Mixed numbers Multiply a mixed number by a mixed number; multiply a whole number by a mixed number. Apply to solve contextual problems. Divide whole numbers by fractions, and fractions by fractions, using fraction models. Dividing fractions and mixed numbers. Apply to contextual problems. 6N033 N Decimal Place Value Review decimal place value and equivalent decimals. 6N034 N Compare and Order Decimals Compare and order decimals. Order decimals on a number line. Use the greater than, less than or equal to symbols to compare decimals. Identify equivalent decimals. Order times heights and times in a race. 6N035 N Rounding Decimals Rounding decimals to the nearest whole number, tenth, hundredth, and thousandth. 6N036 N Adding and Subtracting Decimals Add and subtract decimals, with instruction and practice targeted at correctly organizing numbers to avoid typical computational errors. 6N037 N Multiplying Decimals Extend understanding, and introduce strategies, for multiplying decimals by whole numbers and by decimals 6N038 N Dividing Decimals Extend understanding, and introduce strategies, for dividing decimals by whole numbers and by decimals 6N039 N Estimation Use a range of estimation strategies (rounding, front end and clustering) in order to make reasonable estimates and to be able to estimate efficiently. 6N040 N Writing Numbers as Percents 6N041 N Fractions, Decimals and Percents 6N042 N Finding the Percent of a Number 6N043 N Sales Tax, Tips and Discounts Finding percents by writing numbers as a ratio. Apply to solve contextual questions. Write numbers as percents, fractions and decimals. Match equivalent fractions, decimals and percents. Find the percent of a number and apply in real-life scenarios. Find the percent of a number and apply to real-life scenarios such as adding interest, tipping, sales tax, and sales discounts. 6N044 N Ratio Write ratios and apply to solve simple ratio problems. Find the number of boys and girls in a class given the ratio of boys to girls. 6N045 N Proportion Introduce strategies for solving proportion problems including 'common sense' computation, equivalent fractions and cross multiplication. 6A001 A Patterns Investigate sequences and rules using different shape patterns. Represent and generalize the patterns using tables, words and symbols. Page 5 of 28

6 Scope and Sequence Grade 6 (cont d) Code Strand Title Objective 6A002 A Algebraic Expressions Write verbal expressions and sentences as algebraic expressions; evaluate algebraic expressions. 6A003 A Simplifying Algebraic Expressions Identify like terms. Simplify algebraic expressions by combining like terms. Like terms can be dragged together on the page and simplified. 6A004 A Solving Equations Solve simple word problems using equations by translating a situation explained in words into a mathematical equation using symbols. 6A005 A Graphing Linear Functions Recognize and continue a number pattern and find rules. Complete a function based on a given rule. Represent patterns and functions with tables and graphs; extend to using symbols. 6M001 M Customary Measure Identify and convert units of length, weight and capacity within the customary system of measurement. 6M002 M Metric Measure for Length 6M003 M Metric Measure for Mass and Capacity Develop estimation skills using metric units of measure for length and consolidate understanding of measuring length in metric units. Develop estimation skills using metric units of measure for capacity and mass, and convert within metric measures for mass and capacity. 6M004 M Perimeter Investigation Investigate perimeters of irregular figures. Find the largest and smallest perimeter given the area. 6M005 M Perimeters of Irregular Figures Find the perimeter of irregular figures. Find missing dimensions of irregular figures. Solve real-life problems. Given the perimeter find the missing dimensions. 6M006 M Area of a Parallelogram Find the area of a parallelogram. Given the area find the height or base of a parallelogram. 6M007 M Area of a Triangle Find the area of triangles. Find the height of a triangle given the area. 6M008 M Area of Irregular Figures 6M009 M Circumference of a Circle Find the area of irregular figures by dividing them into familiar shapes (rectangles and triangles.) Identify the attributes of a circle. Find the diameter and circumference of a circle by measuring. Explore and state the relationship between the radius, diameter, and circumference of a circle. Find the circumference of a circle, given the radius or diameter and find the radius (or diameter) of a circle given the circumference. 6M010 M Area of a Circle Derive the formula for the area of a circle. Find the area of a circle given the radius or diameter of a circle. 6M011 M Triangle Classification Classify triangles by lengths of their sides. Classify triangles by the measures of their angles. 6M012 M Nets and Surface Area Draw the net of a cube. Find the surface area of a cube. Extend to find the surface area of rectangular prisms. Page 6 of 28

7 Scope and Sequence Grade 6 (cont d) Code Strand Title Objective 6M013 M Volume of a Rectangular Prism 6M014 M Three-Dimensional Figures Find the volume of a rectangular prism. Solve contextual problems. Find the largest and smallest volume for a piece of luggage. Identify three-dimensional figures, including prisms, pyramids, cones and spheres. Identify the vertices, faces and edges of pyramids and prisms. 6G001 G The Coordinate Plane Graph points on a coordinate plane. Identify quadrants. Locate the vertices of a shape on the coordinate plane. Find the area and perimeter of the shapes. 6G002 G Exploring Line Symmetry 6G003 G Exploring Rotational Symmetry 6G004 G Parallel and Perpendicular Lines Identify line symmetry in figures and the mirror lines for various figures. Determine whether or not a figure has line symmetry. Identify properties of rotational symmetry. Complete figures so that they have rotational symmetry. Review parallel and perpendicular lines. Determine if lines are parallel or perpendicular. Identify parallel and perpendicular lines in shapes. 6G005 G Angle Properties Review angle names, estimate and find the measure of angles. Find angles on a straight line. 6G006 G Tessellations Tessellate regular polygons. Use the properties of tessellated polygons to find the interior angles of regular polygons. 6G007 G Transversals and Parallel Lines - Angle Animations 6G008 G Angles Formed by Transversal and Parallel Lines Definitions and properties of angles formed by transversals and parallel lines. Animate corresponding, opposite and alternate angles. Determine the measure of angles formed by transversals and parallel lines. Determine the measure of angles formed by transversals and parallel lines. Find corresponding, opposite and alternate angles. 6G009 G Transformations Identify translations, reflections and rotations. Given the result of a transformation, determine whether it is a translation, rotation or reflection. 6G010 G Transformations in the Coordinate Plane 6D001 D Measures of Central Tendency the Mean 6D002 D Pictographs and Bar Graphs Perform translations and reflections in the coordinate plane. Identify the mirror line in a reflection. Find the arithmetic mean for a set of data. Find the missing value in a set of data given the mean. Read and interpret bar graphs. Make and interpret pictographs. 6D003 D Line Plots The objective of this lesson is display data using line plots. Use line plots to find measures of central tendency. Interpret data using a line plot. 6D004 D Stem-and-Leaf Plots The objective of this lesson is to display data using stem-and-leaf plots. Find measures of central tendency. Interpret stem-and-leaf plots. Page 7 of 28

8 Scope and Sequence Grade 6 (cont d) Code Strand Title Objective 6D005 D Circle Graphs Draw and interpret circle graphs. Use the data to find the degrees needed for each piece of a pie graph. 6D006 D Probability The objective of this lesson is to define probability, discuss the vocabulary associated with probability, learn different ways to express probability, and develop understanding of strategies for solving probability problems including sample space and tree diagrams. Page 8 of 28

9 Scope and Sequence Grade 7 STRAND KEY A = Algebra D = Data Analysis & Probability G = Geometry M = Measurement N = Number and Operations Code Strand Title Objective 7N001 N Compare and Order Rational Numbers Compare and order rational numbers: positive and negative integers, whole numbers, fractions, terminating and repeating decimals 7N002 N Real Numbers Differentiate between rational and irrational numbers. Compare and order rational and irrational numbers on a number line. 7N003 N GCF and LCM Find the Least Common Multiple and Greater Common Factor of two or more numbers. Apply to solve word problems using LCM and GCF. 7N004 N Simplifying Fractions Simplify fractions. Find the GCF of the numerator and denominator and use this to reduce fractions to their least terms. 7N005 N Adding and Subtracting Fractions and Mixed Numbers Using fraction models to add and subtract fractions and mixed numbers with unlike denominators, and progressing to solving fraction problems without modeling. 7N006 N Multiplying Fractions Review different methods for finding the product of two fractions, and apply to finding the product of negative fractions. 7N007 N Multiplying Mixed Numbers 7N008 N Dividing Fractions and Mixed numbers Multiply mixed numbers. Multiply positive and negative mixed numbers. Solve problems involving mixed numbers. Dividing integers, mixed numbers and fractions by fractions and mixed numbers. Solve word problems involving mixed numbers and fractions. 7N009 N Fractions and Decimals Write fractions as either terminating or repeating decimals. Convert between fractions and decimals. Identify terminating and repeating decimals. 7N010 N Decimals Solve contextual problems by adding, subtracting, multiplying and dividing decimals. 7N011 N Proportions Solve proportion problems. Use proportions to find percents. Find the percent of a number using proportions. Find the number given a percent. 7N012 N Ratio Use ratios to solve problems. Write ratios in simplest form. Solve ratio problems by modeling. 7N013 N Rate and Unit Rate Calculate rate and unit rate. Compare rates. Solve ratio and rate problems. 7N014 N Estimating with Percents 7N015 N Percents (greater than 100% and less than 1%) Estimating percents of a number using near fractions. Solve percent problems by estimation. Model percents greater than 100% and percents less than 1%. Find percents greater than one hundred and less than one. Page 9 of 28

10 Scope and Sequence Grade 7 (cont d) Code Strand Title Objective 7N016 N Percents, Sales Tax and Discounts Solve real-world problems using percents. Calculate sales tax, commission, tips and discounts. 7N017 N Simple Interest Solve problems using percents and apply the formula for simple interest. 7N018 N Exponents Understand and apply exponents with fractional and negative bases. Evaluate exponents. 7N019 N Order of Operations with Exponents Evaluate expressions with exponents using order of operations. Given the answer, insert parentheses into an expression. 7N020 N Absolute Value The objective of this lesson is to review absolute value, to simplify and evaluate absolute value expressions. 7N021 N Radicals and Square Roots Find the roots of perfect squares. Estimate square roots using a number line. 7N022 N Scientific Notation Write numbers (greater than one) in scientific notation, and convert between scientific notation and standard form. Solve problems using scientific notation. 7A001 A Algebraic Expressions Write and evaluate algebraic expressions using both positive and negative numbers. 7A002 A Properties of Algebra Understand and use the distributive, commutative, associative and identity properties to solve problems. 7A003 A Solving Problems Using Equations 7A004 A Solving One-Step and Two-Step Equations 7A005 A Solving Two-Step Equations Write and use equations to solve word problems. Write equations to solve money, age and perimeter problems. Find an unknown number in a one-step addition, subtraction, multiplication or division problem. Find an unknown number in two-step equations (equations involving more than one operation). Use equations to solve word problems. Solve two-step equations with fractional coefficients by finding the multiplicative inverse of the coefficient. 7A006 A Algebra Balance Solving equation with variables on each side. In this activity, manipulatives are used to model and solve algebraic equations using a balance beam to represent the equality of the equation. 7A007 A Solving Inequalities Solving one-step inequalities using a number line. Graph the solution set of an inequality on a number line 7A008 A Exploring Sequences Extend, represent, analyze, and generalize a variety of patterns with tables. Find missing terms in a sequence. Find rules and express using algebra. 7A009 A Functions Complete function tables, and use function tables to write equations, and to graph linear functions. Also introduce non-linear functions. 7A010 A Line and Slope Find the slope of a line. Find the slope given the coordinates of two points on the line. Page 10 of 28

11 Scope and Sequence Grade 7 (cont d) Code Strand Title Objective 7M001 M Customary and Metric Measure Convert between customary and metric units of measure for weight/mass and length. 7M002 M Scale Drawing Solve problems involving scale drawings and scale models; find scale factors. 7M003 M Area of a Trapezoid Find the area of a trapezoid by using compound figures and by deriving the formula for the area of a trapezoid. Find the height given the area. 7M004 M Area of Irregular Figures 7M005 M Surface Area of Rectangular Prisms Find the areas of complex or irregular figures by dividing them into familiar shapes. Find the areas of each shape and sum them to find the total area. Find the surface area of rectangular prisms. Solve problems involving surface area. 7M006 M Nets and Surface Area Draw nets and find the surface areas of three dimensional figures, including cubes, rectangular prisms and triangular prisms. 7M007 M Surface Area of a Cylinder Discover and create the formula for the surface area of a cylinder. Apply this formula to calculate the surface area of various cylinders. 7M008 M Volume of a Cylinder Find the volume of a cylinder. Solve problems involving the volume. Find the volume of similar cylinders. 7M009 M Volume of a Prism Find the volume of rectangular prisms and triangular prisms. Compare volumes of prisms of equal height. Find the volumes of similar prisms. 7G001 G Lines and Angles Introduce naming conventions for lines, line segments, rays, points and angles. 7G002 G Angle Properties Identify angles as complementary, supplementary or opposite, and solve angle measure problems. 7G003 G Constructions Construct various shapes and geometrical figures using only a compass and a straight edge. Stress to students that no measurement of lengths or angles is allowed. 7G004 G Interior and Exterior Angles of a Polygon 7G005 G Transformations in the Coordinate Plane 7G006 G The Pythagorean Theorem Investigating the interior and exterior angles of polygons. Derive the formula for finding the sum of the interior angles of a polygon. Use this to find the interior angles of a regular polygon. Find the sum of the exterior angles of a polygon. Use this to find the exterior angles of a regular polygon. Identify, describe and perform transformations involving translations, reflections, and rotations. Look for relationships between the lengths of the sides of a right triangle, leading to the Pythagorean Theorem. Apply the theorem to find the hypotenuse and legs of a right triangle. 7G007 G Similar Figures Understand similarity, investigate the ratios and lengths of similar figures, and solve problems using proportions. 7D001 D Which Average? Find mean, median, mode and range. Determine which measure of central tendency is most appropriate for a given set of data. Page 11 of 28

12 Scope and Sequence Grade 7 (cont d) Code Strand Title Objective 7D002 D Sampling Describe and discuss different techniques for selecting a representative sample from a population. 7D003 D Box-and-Whisker Plots Construct and interpret box-and-whisker plots. Find the median and quartile values. Find the interquartile range and identify outliers. 7D004 D Bar Graphs and Histograms Display and interpret bar graphs and histograms. Compare bar graphs and histograms. 7D005 D Displaying Data Review the various ways of displaying data, and analyze, discuss and understand the efficacy of particular graphs for particular data sets. 7D006 D Making Predictions Introduce the basic concept of predictions. Use linear graphs and scatter plots to make predictions and determine if a correlation exists, and, if so, whether it is a positive or negative correlation. 7D007 D Venn diagrams Use and interpret Venn diagrams. Find common factors using Venn diagrams. Apply to solve problems. 7D008 D Misleading Statistics Analyze data and identify when data and/or graphs are misleading. Draw misleading graphs. 7D009 D Fundamental Counting Principle 7D010 D Permutations and Combinations 7D011 D Theoretical and Experimental Probability 7D012 D Independent and Dependent Events Introduce the Fundamental Counting Principle as a method to calculate the number of possible outcomes for real-life problems. The objective of this lesson is to distinguish between permutations and combinations and apply to solve permutation and combination problems. Compare experimental to theoretical probabilities. Use interactive manipulatives to simulate experimental probabilities. Determine if an event is dependent or independent. Find the probability of dependent and independent events. Page 12 of 28

13 Scope and Sequence Grade 8 STRAND KEY A = Algebra D = Data Analysis & Probability G = Geometry M = Measurement N = Number and Operations Code Strand Title Objective 8N001 N Adding and Subtracting Rational numbers 8N002 N Multiplying Rational numbers 8N003 N Dividing Rational Numbers Add and subtract rational numbers including negative fractions. Use absolute value to solve addition and subtraction problems. Multiply rational numbers. Solve problems by multiplying rational numbers including negative fractions. Divide rational numbers. Solve contextual problems. Divide negative fractions. 8N004 N Order of Operations Use order of operations to evaluate both numerical and algebraic expressions. 8N005 N Multiply and Dividing Exponents Use and apply the exponent laws for multiplying and dividing with powers. 8N006 N Prime Factorization Find and write the prime factors of a number. Use prime factorization to solve problems. 8N007 N Estimation Strategies Use a range of estimation strategies, including: rounding, front-end, clustering, compatible numbers, in order to make reasonable estimates and to estimate efficiently. 8N008 N Decimals Review adding, subtracting, multiplying and dividing decimals. Answer contextual questions using fractions. Review writing fractions as decimals. 8N009 N Decimals as Fractions Write both terminating and repeating decimals as fractions. Write fractions as decimals. 8N010 N Real Numbers Compare and order rational and irrational numbers and solve problems with irrational numbers. 8N011 N Scientific Notation Write numbers in scientific notation, and convert between scientific notation and standard form. Compare numbers written in scientific notation. 8N012 N Scientific Notation Calculations 8N013 N Solve Proportion Problems Use scientific notation in calculations and solve problems with numbers written in scientific notation. Compare numbers written in scientific notation. Solve proportion problems using rates, similarity and percents. 8N014 N Ratios and Rates Calculate ratios, rates and units rates. Solve problems using unit rate. 8N015 N Percent of Change Find a percent increase or a percent decrease. Solve problems in involving percent increase or percent decrease. Page 13 of 28

14 Scope and Sequence Grade 8 (cont d) Code Strand Title Objective 8A001 A Algebraic Fractions Simplify algebraic fractions. Add, subtract, multiply and divide algebraic fractions. 8A002 A Factoring Algebraic Expressions 8A003 A Review One-Step and Two-Step Equations 8A004 A Solving Multistep Equations 8A005 A Solving Equations With Variables on Both Sides 8A006 A Absolute Value Equations Factor algebraic expressions. Find the factors of terms in an algebraic expression, find the common factors and rewrite the expression as a product of common factors. Find an unknown number in a one-step addition, subtraction, multiplication or division problem. Find an unknown number in two-step equations, i.e. equations involving more than one operation. Use equations to solve word problems. Solve multi-step equations by combining like terms and using the distributive property. Solve equations with variables on both sides. Solve algebraic problems with variables on both sides. Solve absolute value equations. Set up absolute value equations and solve using the property that both positive and negative answers become positive. 8A007 A Formulas Use formulas to solve problems. Convert between Fahrenheit and Celsius temperatures. 8A008 A Arithmetic and Geometric Sequences Identify and extend arithmetic and geometric sequences. Find the common differences of arithmetic sequences. Find the common ratio of geometric sequences. Find the nth term of an arithmetic or geometric sequence. 8A009 A Slope Find the slope of a line. Find the slope given the coordinates of two points on the line. 8A010 A Slope-Intercept Form Determine the equation of a line given the slope and the y-intercept 8A011 A Slope as Rate of Change Find rates of change. Determine rate of change from the slope of a line. 8A012 A Systems of Equations Solve systems of equations by graphing. Solve contextual problems using systems of equations. 8A013 A Linear and Non Linear Functions Distinguish between linear and nonlinear functions using tables, graphs and equations. 8A014 A Solving Inequalities Solve inequalities by adding, subtracting, multiplying and dividing. Graph solutions on a number line. Solve contextual problems using inequalities. 8A015 A Solving Multi-Step Inequalities. 8A016 A Graphing Linear Inequalities Solve multi-step inequalities. Graph solutions on a number line. Graph linear inequalities. Find solutions to problems by graphing linear inequalities. Page 14 of 28

15 Scope and Sequence Grade 8 (cont d) Code Strand Title Objective 8A017 A Introduction to Polynomials Define and evaluate polynomial expressions. Distinguish between polynomials and non-polynomial expressions. Identify monomials, binomial and trinomial expressions. 8A018 A Degrees of polynomials Understand and state the degree of a polynomial. Name polynomials according to their degree (quadratic, cubic etc). 8A019 A Adding and Subtracting Polynomials 8A020 A Multiplying Polynomials 8A021 A Multiplying a Binomial by a Binomial Add, subtract, multiply and divide monomials and polynomials; expand polynomials by multiplying; apply properties of exponents. Multiplying monomials by monomials. Multiplying monomials by binomials. Multiplying polynomials, specifically binomials by binomials. 8A022 A Algebra Tiles Model operations with polynomial expressions using algebra tiles. Add, subtract, multiply and divide polynomials. 8A023 A Graphing Quadratic Functions 8A024 A Solving Quadratic Equations by Taking Square Roots 8A025 A Solving Quadratic Equations by Graphing 8A026 A Solving Quadratic Equations by Factoring (using Algebra Tiles) 8M001 M Customary and Metric Units 8M002 M Area of Irregular Figures 8M003 M Surface Area of Prisms and Cylinders 8M004 M Surface Area of Pyramids and Cones 8M005 M Surface Area of a Sphere 8M006 M Volume of Prisms and Cylinders Graphing quadratic functions. Complete a table of values, identify the x and y- intercepts and axis of symmetry for a quadratic function. Graph translations of quadratic functions. Solve equations with exponents. Estimate square and cube roots. Solve quadratic equations by graphing. Find the axis of symmetry, complete the table of values, graph the equation and identify the x-intercepts). Use algebra tiles to model factoring trinomial expressions. The final section of the lesson covers solving quadratic equations by factoring. Convert between metric units and convert between customary units. Find the areas of complex figures by dividing them into familiar shapes. Find the areas of each shape and sum to find the total area. Find and compare the volume of prisms and cylinders. Find the volumes of similar three dimensional figures. Find the surface area of pyramids and cones. Apply to solve contextual problems. Find the surface area of a sphere. Apply to contextual problems. Find the volume of prisms and cylinders. Apply to contextual problems. Page 15 of 28

16 Scope and Sequence Grade 8 (cont d) Code Strand Title Objective 8M007 M Volume of Pyramids and Cones Find the volume of pyramids and cones. Apply to contextual problems. 8G001 G Transformations in the Coordinate Plane Identify, describe and perform transformations involving translations, reflections, and rotations. 8G002 G Dilations Investigate dilations and reductions. Find the center of dilation and the scale factor. 8G003 G Applying The Pythagorean Theorem 8G004 G The Distance between Two Points Use and apply the Pythagorean theorem to find the hypotenuse and the legs of a right triangle. Find the distance between two points in the coordinate plane using the Pythagorean Theorem. 8G005 G The Midpoint Formula Find the midpoint of a line segment. Apply the midpoint formula. 8G006 G Use Algebra to Solve Geometry Problems. 8G007 G Views of Three Dimensional Figures Use algebra to solve geometry problems. Review angle properties for angles on a straight line, angles in a triangle, complementary, supplementary, interior, exterior and opposite angles. Draw front, side and top views of three-dimensional figures built from cubes. Build a three-dimensional figure when given the front, side and top views. 8D001 D Displaying Data The objective of this lesson is to choose the most appropriate graph to display the data in a given scenario. 8D002 D Measures of Central Tendency 8D003 D Scatterplots and Correlation 8D004 D Probability of Compound Events 8D005 D Permutations and Combinations Compare data sets using measures of central tendency. Find measures of central tendency from line plots. Find the missing value in a data set, given the mean. Determine if there is a positive, negative or no correlation for data. Draw a line of best fit. Use scatter plots to make predictions. Determine if an event is dependent or independent. Find the probability of dependent and independent events. Determine if events are independent or mutually exclusive. Find the probability of mutually exclusive events. The objective of this lesson is to distinguish between permutations and combinations and to solve permutation and combination problems. Page 16 of 28

17 6-8 Math for Digital White Boards Correlations Core Reference Standard Description Grade Math Correlations Ratios & Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. Correlation G5M011 G5M012 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. G5M011 G5M012 G6M016 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multidigit numbers and find common factors and multiples. Compute fluently with multi-digit numbers and find common factors and multiples. G6M016 G6M020 G5M012 G6M014 G6M015 G6M016 G6M009 6.NS.2. Fluently divide multi-digit numbers using the standard algorithm. G5M005 G6M012 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. G5M010 G6M011 G6M012 Page 17 of 28

18 Core Reference 6.NS.4. Standard Description Grade Math Correlations Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers. Correlation G4M006 G6M002 G6M003 Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. G5M014 6N005 6N008 6.NS.6. 6.NS.7. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand ordering and absolute value of rational numbers. G5M014 6N005 6N008 G6M020 G6M021 G5M014 G6M020 6N005 6N008 6.NS.8. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 o C > 7 o C to express the fact that 3 o C is warmer than 7 o C. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. G5M014 6N003 6N005 6N008 G5M014 6N003 6N008 6N010 7N020 6N003 6N010 7N020 G6M018 G6M020 6G001 Page 18 of 28

19 Core Reference Standard Description Grade Math Correlations Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Correlation 6.EE.1. Write and evaluate numerical expressions involving whole-number exponents. G5M006 6N012 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.3. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. G6M017 6A002 6A003 G6M017 6A002 6A003 7A001 7A002 G6M001 G6M019 6A002 6A003 7N019 G6M001 G6M017 7A002 6.EE.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Reason about and solve one-variable equations and inequalities. Reason about and solve one-variable equations and inequalities. 6.EE.5. 6.EE.6. 6.EE.7. 6.EE.8. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Solve real-world and mathematical problems by writing and solving equations of the form x +p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. G6M017 7A002 G6M019 6A004 7A003 7A004 G6M017 6A004 7A003 7A004 G6M016 G6M019 6A004 7A003 7A004 7A007 Page 19 of 28

20 Core Reference Standard Description Grade Math Correlations Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1. 6.G.2. 6.G.3. 6.G.4. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Develop understanding of statistical variability. 6.SP.1. Statistics & Probability Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages. Correlation G6M017 G6M018 G6M019 6A005 7A009 7A010 G5M024 G5M025 G6M024 6M006 6M007 6M008 6M013 G6M026 G6M020 6G001 G6M025 6M012 6D003 6D004 6.SP.2. 6.SP.3. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. G6M027 G6M028 6D001 6D003 6D004 6D001 6D003 6D004 Page 20 of 28

21 Core Reference Standard Description Summarize and describe distributions. Grade Math Correlations Correlation 6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. G6M027 G6M028 6D003 6D004 7D003 6.SP.5. Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations. G6M028 6D003 Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. G6M028 6D003 6D004 G6M027 G6M028 6D001 6D003 G6M027 G6M028 6D001 6D003 Page 21 of 28

22 Core Reference Standard Description Grade Math Correlations Ratios & Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.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. Correlation 8N014 8M001 7.RP.2. 7.RP.3. Recognize and represent proportional relationships between quantities. 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. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 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. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7N013 7N015 7N016 7N017 6N005 6N006 6N005 6N006 6N008 6N005 6N006 6N010 7.NS.2. Apply properties of operations as strategies to add and subtract rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 7N006 7N007 Page 22 of 28

23 Core Reference Standard Description Grade Math Correlations Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. Correlation 7N008 Apply properties of operations as strategies to multiply and divide rational numbers. 7N006 7N007 7N008 Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 7N009 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. 7N005 7N006 7N007 7N008 Expressions & Equations Use properties of operations to generate equivalent expressions. 7.EE.1. 7.EE.2. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 7A001 7A002 7A004 7A005 7N015 7A002 7A004 7N005 7N006 7N007 7N008 7N009 7N010 7N016 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 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? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. 7A002 7A003 7A004 7A005 7A007 Page 23 of 28