Course Title: Eighth Grade Mathematics - Course 3 [Units 1-5] Pre-Algebra [Course II Units 2-5 + Course III Units 1-5] Content Area: Mathematics Grade Level(s): Eighth Course Description: This course is designed for students planning to take Algebra 1 as freshmen. The course is in line with the areas of focus identified by the Common Core State Standards and the PARCC Model Content Frameworks. The curriculum will move the students from the concepts developed in grades 6 and 7; modeling relationships with variables and equations and ratio and proportional reasoning, to make connections between proportional relationships, lines, and linear equations. The idea of a function introduced in 8th grade is a precursor to concepts about functions that are included in the high school standards. Date Created: May 2014 Date Approved by Plumsted Township Board of Education: August 2014 Pacing Guide Unit 1 The Number System Unit 2 Expressions and Equations Unit 3 Functions Unit 4 Geometry Unit 5 Statistics and Probability 10 lessons (4 weeks) 13 lessons (10 weeks) 9 lessons (6 weeks) 24 lessons (10 weeks) 6 lessons (5 weeks) Unit 1 The Number System Unit Summary: Students develop an understanding of rational and irrational numbers. They express fractions as terminating or repeating decimals and terminating decimals as fractions. To use rational approximations of 1
irrational numbers to compare and order numbers. As with integers, students learn how to manipulate positive and negative fractions and mixed numbers using addition, subtraction, multiplication, and division to solve problems in everyday contexts. Students understand that it is often useful to convert numbers to other representations in order to solve problems. Primary interdisciplinary connections: Infused within the unit are connections to English Language Arts and Technology. 21st century themes: Through instruction in life and career skills, all students acquire the knowledge and skills needed to prepare for life as citizens and workers in the 21st century. For further clarification see NJ World Class Standards at www.nj.gov/education/aps/cccs/career/. CCSS 8.NS.1 8.NS.2 8.EE.1 8.EE.2 Common Core Standard Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. Know and apply the properties of integer exponents to generate equivalent numerical expressions. Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational. 8.EE.3 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. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology). Essential Questions: Why is it helpful to write numbers in different ways? 2
How can I determine if a number is a rational number How can I write repeated multiplication using powers? How can I use the properties of integer exponents to simplify algebraic and numeric expressions? How does the Product of Powers law apply to finding the power of a power? How are negative exponents and positive exponents related? How is scientific notation useful in the real world? How does scientific notation make it easier to perform computations with very large or very small numbers? Why would I need to use square roots and cube roots? How can I estimate the square root of a non-perfect square? How are real numbers different from irrational numbers? Instructional Outcomes Students will know... That every rational number is either a terminating or a repeating decimal and be able to convert terminating decimals into reduced fractions. How to read, write, classify, and compare rational numbers. Differentiate between rational and irrational numbers. Scientific notation is used to represent very small and very large numbers. Students will be able to Understand the real number system and how the subsets relate to one another. Understand the differences between the subsets of the real number system. Compare real numbers and order them on a number line. Use rational approximations or irrational numbers to compare numbers. Simplify real number expressions by multiplying and dividing monomials. Use the law of exponents to find powers of monomials. Write and evaluate expressions using negative exponents. Use scientific notation to write small and large numbers. Compute with numbers written in scientific notation. Find square roots and cube roots. Formative Assessments: Teacher observations Exit slips Technology/Manipulatives Homework Do Now Oral assessments Lesson notes and reflections Daily classwork 3
Whiteboards/Communicators Writing prompts Summative Assessments: Tests/Exams Quizzes Performance Based Assessments Unit Projects Presentations Suggested Learning Activities: Chapter 1 Lesson 1: Rational Numbers: o Write a fraction as a decimal o Write decimals as fractions o Write repeating decimals as mixed numbers Lesson 2: Powers and Exponents o Write expressions using powers o Evaluate powers o Evaluate algebraic expressions Lesson 3: Multiply and Divide o Product of powers o Quotient of powers o Simplify expressions Lesson 4: Powers of Monomials: Finding the power of a power o Power of a product o Find area Lesson 5: Negative Exponents o Write expressions using positive exponents o Negative exponents o Write expressions using negative exponents o Simplify expressions with negative exponents Lesson 6: Scientific Notation o Standard form o Compare and order with scientific notation Lesson 7: Compute With Scientific Notation o Multiply numbers written in scientific notation o Divide numbers written in scientific notation o Add numbers written in scientific notation o Subtract numbers in scientific notation Lesson 8: Roots 4
o Review number line o Principal square root o Both square roots o Find the square root o No real square root o Use square roots o Find cube roots Lesson 9: Estimating Roots o Estimate square roots o Estimate lengths with square roots Lesson 10: Compare Real Numbers o Classify real numbers o Compare real numbers o Order real numbers o Use real numbers Curriculum Development Resources: Glencoe textbooks and online support resources - Course III Teacher-generated assessments, worksheets, warm-ups, and quizzes Supplemental resources from various publishers Smart board, Chromebooks, ipads, and other devices Computer software and applications to support unit Math literacy resources (i.e. Sir Cumference series, Scholastic MATH Magazine, etc.) Academic vocabulary: http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/documents/ Vocabulary%20Documents/Vocab%20Cards/K-8%20CCSS%20Vocabulary%20Word%20List.pdf Internet based resources - videos, interactive manipulatives, online tutors o Khan Academy o Virtual Nerd o BuzzMath o Kuta Software o Sum Dog o YouTube 5
Unit 2 Expressions and Equations Unit Summary: Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original education. Interdisciplinary Connections/Content Area Integrations: Infused within the unit are connections to English Language Arts and Technology. 21st century themes: Through instruction in life and career skills, all students acquire the knowledge and skills needed to prepare for life as citizens and workers in the 21st century. For further clarification see NJ World Class Standards at www.nj.gov/education/aps/cccs/career/. CCSS 8.EE.5 8.EE.6 8.EE.7 8.EE.7a 8.EE.7b 8.EE.8 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Analyze and solve pairs of simultaneous linear equations. 8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 6
8.EE.8b 8.EE.8c 8.F.2 8.F.3 8.F.4 8.F.5 Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Solve real world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables or by verbal discussions). For example, given a linear function represented by an algebraic expression, determine which function had the greater rate of change. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Construct a function to model a linear relationship between two quantities. 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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Describe quantitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Essential Questions: How can linear equations be used to represent real-life situations? What are the connections between proportional relationships, lines, and linear equations? How can you use the work backward problem-solving strategy to solve a two-step equation? What it equivalence? How is the multiplicative inverse used to solve an equation that has a rational coefficient? Why is it important to define a variable before writing an equation? How is solving an equation with the variable in each side similar to solving a two-step equations? How many possible solutions are there to a linear equation in one variable? How can you use a table to determine if there is a proportional relationship between two quantities? In any linear relationship, why is the slope always the same? Why are graphs helpful? What is the relationship among the unit rate, slope, and constant rate of change of a proportional linear relationship? 7
How is the y-intercept represented in a table, an equation, and a graph? How can the x-intercept and y-intercept be used to graph a linear equation? How does using the point-slope form of a linear equation make it easier to write the equation of a line? How can you use a graph to solve a system of equations? Instructional Outcomes: Students will know... Expressions are simplified by various means. Equations can be solved using the properties of equality. Slope is a constant change. The solution of a one variable equation can be represented on a number line. Expressions are simplified by various means. Students will be able to Solve equations with rational coefficients Solve two-step equations Write two-step equations that represent real world situations Solve equations with variables on each side Solve multi-step equations Identify proportional and non-proportional linear relationships by finding a constant rate of change To find the slope of a line Use direct variation to solve problems Graph linear equations using the slope and y-intercept Graph a function using the x- and y-intercepts Write an equation of a line Solve systems of equations by graphing Solve systems of equations algebraically Formative Assessments: Teacher observations Exit slips Technology/Manipulatives Homework Do Now Oral assessments Lesson notes and reflections Daily classwork Whiteboards/Communicators Writing prompts 8
Summative Assessments: Tests/Exams Quizzes Performance Based Assessments Unit Projects Presentations Chapter 2 Lesson 1 o Solve Equations with Rational Coefficients o Solve Equations with Fractional Coefficients o Solve Equations with Decimal Coefficients Lesson 2 o Solve Two-Step Equations o Property of Equalities Lesson 3 o Write Two-Step Equations o Translate sentences into Equations o Write and Solve Two-step Equations Lesson 4 o Solve Equations with Variables on Each Side o Inquiry Lab- Equations with Variable on Each Side o Write and Solve Equations with Variables on Each Side o Equations with Rational Coefficients Lesson 5 o Solve Multi-Step Equations o Identities o Null Set or No Solution Chapter 3 Lesson 1 o Constant Rate of Change o Identify Linear Relationships o Identify Proportional Relationships o Inquiry Lab- Graphing Technology: Rate of Change Lesson 2 o Slope o Find slope o Find slope using a graph o Find slope using a table 9
o Find slope using coordinates Lesson 3 o Equations in y = mx form o Find the constant variation o Graph a direct variation o Compare proportional relationships Lesson 4 o Slope-Intercept form o Find slope and y-intercept o Write equations in slope-intercept form o Write an equation in slope-intercept form from a graph o Graph a line using a slope-intercept form o Interpret slope and y-intercept o Inquiry lab- slope triangles Lesson 5 o Graph a line using intercepts o Graph a function using intercepts o Find x- and y-intercepts o Interpret intercepts Lesson 6 o Write linear equations o Write an equation in point-slope form o Write an equation in point-slope form in slope-intercept form o Write an equation given two points o Inquiry Lab- Graphing Technology: Model Linear Behavior o Inquiry Lab- Graphing Technology: Systems of Equations Lesson 7 o Solve systems of equations by graphing o Write a system of equations o Solve a system of equations o Systems with no solution o Systems with infinitely many solutions o Analyze systems Lesson 8 o Solve systems of equations algebraically o Solve a system of equations o Write a system of equations o Inquiry Lab- Analyze Systems of Equations Curriculum Development Resources: Glencoe textbooks and online support resources - Course III 10
Teacher-generated assessments, worksheets, warm-ups, and quizzes Supplemental resources from various publishers Smart board, Chromebooks, ipads, and other devices Computer software and applications to support unit Math literacy resources (i.e. Sir Cumference series, Scholastic MATH Magazine, etc.) Academic vocabulary: http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/documents/voc abulary%20documents/vocab%20cards/k-8%20ccss%20vocabulary%20word%20list.pdf Internet based resources - videos, interactive manipulatives, online tutors o Khan Academy o Virtual Nerd o BuzzMath o Kuta Software o Sum Dog o YouTube 11
Unit 3 Functions Unit Summary: Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations. Interdisciplinary Connections/Content Area Integrations: Infused within the unit are connections to English Language Arts and Technology. 21st century themes: Through instruction in life and career skills, all students acquire the knowledge and skills needed to prepare for life as citizens and workers in the 21st century. For further clarification see NJ World Class Standards at www.nj.gov/education/aps/cccs/career/. CCSS 8.F.1 8.F.2 8.F.3 8.F.4 8.F.5 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables or by verbal discussions). For example, given a linear function represented by an algebraic expression, determine which function had the greater rate of change. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Construct a function to model a linear relationship between two quantities. 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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Construct a function to model a linear relationship between two quantities. 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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 12
Essential Questions: How can we model relationships between quantities? How can you use a graph to write an equation? How do tables and graphs represent relations? How does the domain affect the range in a function? Which representation of a pattern more clearly shows whether or not the pattern is linear: a table of values or a graph of the pattern? Are all functions linear? Are all lines functions? What do you expect to see in a graph given its equations? How can functions be used to solve real-world situations? What are the advantages and disadvantages to representing a function as an equation instead of a graph? How is the initial value of a function represented in a table and in a graph? How can you use a table or graph to determine if a function is linear or nonlinear? What does the graph of a quadratic function open upward or downward? What are some advantages of displaying the relationship between two quantities using a qualitative graph? Instructional Outcomes: Students will... Determine whether a relation is a function. Complete function tables. Represent linear functions using tables and graphs. Identify proportional and non proportional linear relationships by finding a constant rate of change. Find rate of change. Find slope of a line. Use direct variation to solve problems. Graph linear equations using slope and y-intercept. Use technology to investigate situations to determine if they display linear behavior. Graph and analyze slope triangles. Students will be able to Determine if relations are functions. Understand the rules of functions. Analyze the change in x-value and how it changes the y-value. Compare functions in their different forms (tables, graphs, and equations). Describe functional relationships (linear vs. nonlinear). Translate verbal expressions to create function equations. Graph equations in two variables by making a table of values and plotting points. Interpret unit rate as slope. Understand slope-intercept form and its components. 13
Interpret y = mx + b as a linear function. Graph an equation using the slope and y-intercept. Write an equation from the given graph using the slope and y-intercept. Formative Assessments: Teacher observations Exit slips Technology/Manipulatives Homework Do Now Oral assessments Lesson notes and reflections Daily classwork Whiteboards/Communicators Writing prompts Summative Assessments: Tests/Exams Quizzes Performance Based Assessments Unit Projects Presentations Suggested Learning Activities: Lesson 1 o Represent Relationships o Review- coordinate graphing/quadrants and evaluating expressions Lesson 2 o Relations o Inquiry Lab- Relations and Functions Lesson 3 o Functions o Function tables- independent and dependent variables Lesson 4 o Linear Functions Lesson 5 o Compare Properties of Functions Lesson 6 o Construct Functions 14
Lesson 7 o Linear and Nonlinear Functions Lesson 8 o Quadratic Functions o Inquiry Lab- Graphing Technology: Families of Nonlinear Functions (Graphing Calculators) Lesson 9 o Qualitative Graphs Curriculum Development Resources: Glencoe textbooks and online support resources - Course III Teacher-generated assessments, worksheets, warm-ups, and quizzes Supplemental resources from various publishers Smart board, Chromebooks, ipads, and other devices Computer software and applications to support unit Math literacy resources (i.e. Sir Cumference series, Scholastic MATH Magazine, etc.) Academic vocabulary: http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/documents/voc abulary%20documents/vocab%20cards/k-8%20ccss%20vocabulary%20word%20list.pdf Internet based resources - videos, interactive manipulatives, online tutors o Khan Academy o Virtual Nerd o BuzzMath o Kuta Software o Sum Dog o YouTube 15
Unit 4 Geometry Unit Summary: Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students understand the Pythagorean Theorem and apply it to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres. Interdisciplinary Connections/Content Area Integrations: Infused within the unit are connections to English Language Arts and Technology. 21st century themes: Through instruction in life and career skills, all students acquire the knowledge and skills needed to prepare for life as citizens and workers in the 21st century. For further clarification see NJ World Class Standards at www.nj.gov/education/aps/cccs/career/. CCSS 8.G.1 8.G.1a 8.G.1b 8.G.1c 8.G.2 8.G.3 8.G.4 8.G.5 Utilize the properties of rotation, reflection, and translation to model and relate pre-images of lines, line segments, and angles to their resultant image through physical representations and/or Geometry software/ Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations. Lines are taken to lines, and line segments to line segments of the same length. Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines. 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; given two congruent figures, describe a sequence that exhibits the congruence between them. Describe the effect of dilations, translations, rotations, and reflections, on two-dimensional figures using coordinates. 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 dilatons; given two similar two-dimensional figures, describe a sequence. Justify facts about angles created when parallel lines are cut by a transversal; Justify facts about the exterior angles of a triangle, the sum of the measures of the 16
interior angles of a triangle and the angle-angle relationship used to identify similar triangles. 8.G.6 8.G.7 8.G.8 8.G.9 8.EE.2 8.EE.6 Explain a proof of the Pythagorean Theorem and its converse. Utilize the Pythagorean Theorem to determine unknown side lengths of right triangles in two and three dimensions to solve real-world and mathematical problems. Use the Pythagorean Theorem to determine the distance between two points in the coordinate plane. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Evaluate square roots and cubic roots of small perfect squares and cubes respectively and use square and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p where p is a positive rational number; Identify 2 as irrational. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the original and the equation y=mx+b for a line intercepting the vertical axis at b. Essential Questions: How can you use different measurements to solve real-life problems? How can algebraic concepts be applied to geometry? How can you find the missing measure of an angle in a triangle if you know two of the interior angles? How can I find the sum of the interior angle measures of a polygon? What is the relationship among the legs and the hypotenuse of a right triangle? How do you solve a right triangle? How can we best show or describe the change in position of a figure? How are figures translated on the coordinate plane? How are the measures of angles related when parallel lines are cut by a transversal? How can you use the Pythagorean Theorem to find the distance between two points on the coordinate plane? How can you determine the coordinates of a figure after a reflection over either axis? What is the difference between rotating a figure about a given point that is a vertex and rotating the same figure about the origin if the rotation is less than 360? How are dilations similar to scale drawings? 17
How can you determine congruence and similarity? Why do translations, reflections, and rotations create congruent images? How can the coordinate plane help you determine that corresponding sides are congruent? What is the difference between using transformations to create congruent figures? How does the scale factor of a dilation relate to the ratio of two of the corresponding sides of the pre-image and the image? How do similar triangles make it easier to measure very tall objects? How is the slope of a line related to the similar slope triangles formed by the line? If you know two figures are similar and you are given the area of both figures, how can you determine the scale factor of the similarity? Why are formulas important in math and science? How is the formula for the volume of a cylinder similar to the formula for the volume of a rectangular prism? What would have a greater effect on the volume of a cone: doubling its radius or doubling its height? How are the volume of spheres and the volume of a cylinder with the same radius and the height of 2r related? How is a calculation affected if you round π to 3.14 or use the pi key on your calculator? How does the volume of a three-dimensional figure differ from its surface area? How is the volume of a prism affected when its dimensions are tripled? Instructional Outcomes: Students will... Examine angle relationships formed by parallel lines and a transversal. Identify relationships of angles formed by two parallel lines cut by a transversal. Explore the relationship among the angles of triangles. Identify similar polygons and find missing measures of similar polygons. Investigate parallel lines and similar triangles. Use the Pythagorean Theorem. Solve problems using the Pythagorean Theorem. Use special right triangles to solve problems. Graph translations on the coordinate planes. Identify rotational symmetry. Graph rotations on the coordinate plane. Use scale factor to graph dilations on the coordinate plane. Draw compositions of translations, reflections and rotations. Find volume of prisms and cylinders. Find volume of pyramids, cones, and spheres. Students will be able to Identify parallel and perpendicular lines. 18
Identify angles formed by a transversal. Identify types of angles. Find missing angles in shapes and sets of lines. Understand and apply a rotation about the origin. Understand and apply a reflection about the x-axis or y-axis. Understand and apply translations. Understand and apply dilations. Describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Determine that the image and pre-image are congruent figures or similar figures. Use scale factors to create scale drawings. Set up and solve proportions to find missing sides of similar shapes. Determine if a triangle is a right triangle using the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths. Apply the Pythagorean Theorem to solve real world problems. Determine the volume of cylinders and spheres. Apply the Pythagorean Theorem to determine the volume of cones. Formative Assessments: Teacher observations Exit slips Technology/Manipulatives Homework Do Now Oral assessments Lesson notes and reflections Daily classwork Whiteboards/Communicators Writing prompts Summative Assessments: Tests/Exams Quizzes Performance Based Assessments Unit Projects Presentations Lesson 1 o Volume of Cylinders 19
o Inquiry Lab- Three-Dimensional Figures Lesson 2 o Volume of Cones Lesson 3 o Volume of Spheres Lesson 4 o Surface Area of Cylinders o Inquiry Lab- Surface Area of Cylinders Lesson 5 o Surface Area of Cones o Inquiry Lab- Nets of Cones Lesson 6 o Changes in Dimensions o Inquiry Lab- Changes in Scale Curriculum Development Resources: Glencoe textbooks and online support resources - Course III Teacher-generated assessments, worksheets, warm-ups, and quizzes Supplemental resources from various publishers Smart board, Chromebooks, ipads, and other devices Computer software and applications to support unit Math literacy resources (i.e. Sir Cumference series, Scholastic MATH Magazine, etc.) Academic vocabulary: http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/documents/voc abulary%20documents/vocab%20cards/k-8%20ccss%20vocabulary%20word%20list.pdf Internet based resources - videos, interactive manipulatives, online tutors o Khan Academy o Virtual Nerd o BuzzMath o Kuta Software o Sum Dog o YouTube 20
Unit 5 Statistics and Probability Unit Summary: Students use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship in terms of the situation. Interdisciplinary Connections/Content Area Integrations: Infused within the unit are connections to English Language Arts and Technology. 21st century themes: Through instruction in life and career skills, all students acquire the knowledge and skills needed to prepare for life as citizens and workers in the 21st century. For further clarification see NJ World Class Standards at www.nj.gov/education/aps/cccs/career/. CCSS 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.2 8.SP.3 8.SP.4 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. Essential Questions: Why is learning mathematics important? How are patterns used when comparing two quantities? 21
What are the inferences that can be drawn from sets of data points having a positive association and a negative association? Why do we estimate a line of best fit for a scatter plot? How is a two-way table used when determining possible associations between two different categories from the same sample group? Instructional Outcomes: Students will... Use a scatter plot to investigate the relationship between two sets of data. Construct and make conjectures about scatter plots. Use models to predict. Draw lines of best fit and use them to make predictions about data. Create scatter plots and calculate lines of best fit using technology. Students will be able to Create and interpret scatter plots. Make predictions of correlations based on the data topics. Identify correlations of scatter plots. Determine the best-fit lines for the data. Find the equation of the best-fit lines. Use the best-fit line to predict values of data. Solve problems in the context of bivariate measurement data interpreting the slope and intercept. Use scatter plots to represent and interpret real data. Formative Assessments: Teacher observations Exit slips Technology/Manipulatives Homework Do Now Oral assessments Lesson notes and reflections Daily classwork Whiteboards/Communicators Writing prompts Summative Assessments: Tests/Exams Quizzes 22
Performance Based Assessments Unit Projects Presentations Suggested Learning Activities: Lesson 1 o Inquiry Lab: Scatter Plots o Scatter Plot instruction Lesson 2 o Inquiry Lab: Lines of Best Fit o Lines of Best Fit instruction o Inquiry Lab: Graphing Technology- Linear and Nonlinear Association Lesson 3 o Two Way Tables Curriculum Development Resources: Glencoe textbooks and online support resources - Course III Teacher-generated assessments, worksheets, warm-ups, and quizzes Supplemental resources from various publishers Smart board, Chromebooks, ipads, and other devices Computer software and applications to support unit Math literacy resources (i.e. Sir Cumference series, Scholastic MATH Magazine, etc.) Academic vocabulary: http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/documents/voc abulary%20documents/vocab%20cards/k-8%20ccss%20vocabulary%20word%20list.pdf Internet based resources - videos, interactive manipulatives, online tutors o Khan Academy o Virtual Nerd o BuzzMath o Kuta Software o Sum Dog o YouTube 23