ALGEBRA 100 HONORS GRADE: 8

Size: px
Start display at page:

Download "ALGEBRA 100 HONORS GRADE: 8"

Transcription

1 ALGEBRA 100 HONORS GRADE: 8 Prerequisite: Pre Algebra, Grade 7 or Pre Algebra Honors, Grade 7; teacher recommendation Credits: 5 ABSTRACT This full year course prepares students for more rigorous study in higher honors mathematics courses by providing the necessary foundations of algebraic concepts and skills. In order to accomplish this, emphasis will be placed on the following: developing number sense and an ability to represent numbers in a variety of forms; understanding, selecting and applying various methods of performing numerical operations; understanding the symbolism of algebra, using exponents, solving linear equations and inequalities; applying absolute value; factoring expressions; exploring real numbers; understanding the basic concepts of coordinate geometry, developing spatial sense and an ability to use geometric properties and relationships; identifying quadratic functions; introducing basic trigonometric functions; developing the understanding of patterns, relationships and functions to analyze real world situations; using statistical analysis and probability to describe data; model situations and support appropriate inferences and arguments; applying the concepts of discrete mathematics to model and explore a variety of practical situations; using a variety of estimation strategies and recognizing situations in which estimation is appropriate. Students will use all available technology to enhance mathematical knowledge and application. Technology usage is recommended through the use of graphing calculators and computers. They will analyze relationships among variables and quantities and use these relationships to solve real-world problems, ranging from everyday applications to the

2 sciences. They will develop reasoning ability and will become self-reliant, independent mathematical thinkers willing to take part in decision-making and risk-taking in order to arrive at reasonable conclusions. They will be able to pose and solve mathematical problems found in all disciplines. UNIT: 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November ESTABLISHED GOALS: (NJ CCCS and/or CCS) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Math CCSS EE.8.7, SP.8.1 A-REI.1 Math CCSS EE.8.7 A-CED.1, A-REI.3 Math CCSS EE.8.5 A-SSE.1 Technology CCCS 8.1, 8.2 Technology CCCS 8.1, 8.2 Technology CCCS 8.1, 8.2 ENDURING UNDERSTANDINGS: (Students will Understand that...) 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 will use variables to transform English phrases into mathematical expressions. will extend your ability to calculate with whole numbers, decimals, and factions to include integers. will use the order of operations and the distributive property to simplify expressions. will show the relationship between two sets of real-world data, using a scatter plot. 2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 will solve equations, including equations with variables on both sides, using properties of equality. will develop the ability to solve problems by defining variables, relating them to one another, and writing an equation. will use measures of central tendency to describe a set of data. will learn how to graph inequalities. will solve inequalities, noting the differences from the methods used 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 will find ratios and rates to model real-world situations. will use proportions to measure objects indirectly. will solve problems that involve discounts, taxes, and interest.

3 ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) 1: Tools of Algebra September Why do you sometimes need variables when writing equations to represent real-world situations? Why are the rules for the order of operations necessary? How can you express an integer as a rational number? How would you explain the process for graphing a point on a coordinate plane to another student? 2: Solving Equations & Inequalities October-November 24 days for solving equations. will write and solve compound inequalities by interpreting phrases that use and or or. When solving equations, what type of operations must you use to get the variable alone on one side of the equal sign? How can you clear an equation of fractions or decimals? How is solving an equation with 2 variable terms on the same side of the equal sign different than solving an equation with variable terms on both sides of the equal sign? What are the two ways to help set up a distance problem? When should the mean be used to describe data and when should the median be used? What is the main difference between solving inequalities using multiplication and division and solving equations using multiplication and division? 3: Solving & Applying Proportions November How can you use proportions to find a distance that is difficult to measure? What are two ways to write percent problems? What are the differences between theoretical probability and experimental probability? How does finding the probability of independent events differ from finding the probability of dependent events? 3

4 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) Assessments of each learning activity Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes 4 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes

5 RESOURCES: 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November Homework Homework Homework Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Lessons EE.8.7. 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 5 EE.8.7. 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 EE.8.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. A-SSE.1. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by

6 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November equations whose solutions require expanding expressions using the distributive property and collecting like terms. SP.8.1. 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. A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an expanding expressions using the distributive property and collecting like terms. A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, 6

7 CROSS-CURRICULAR / DIFFERENTIATION: 1: Tools of Algebra September understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses 7 2: Solving Equations & Inequalities October-November 24 days global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses 3: Solving & Applying Proportions November and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses

8 (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) (What type of differentiated instruction will be used for ELL, SP.ED. and G&T students?) 1: Tools of Algebra September Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. 8 2: Solving Equations & Inequalities October-November 24 days Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. 3: Solving & Applying Proportions November Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional

9 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. *WHERETO W = Help the students know WHERE the unit is going and WHAT is expected. Help the teacher know WHERE the students are coming from (prior knowledge, interests). H = HOOK all students and HOLD their interest. E = EQUIP students, help them EXPERIENCE the key ideas and EXPLORE the issue. R = Provide opportunities to RETHINK and REVISE their understandings and work. E = Allow students to EVALUATE their work and its implications. T = TAILORED to the different needs, interests, and abilities of learners. O = ORGANIZE to maximize initial and sustained engagement as well as effective learning. UNIT: 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days 9

10 ESTABLISHED GOALS: (NJ CCCS and/or CCS) ENDURING UNDERSTANDINGS: (Students will Understand that they will...) 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Math CCSS F.8.1, F.8.2 F-IF.1, F-IF.2, F.BF.2, F-LE.2 Technology CCCS 8.1, st Century Life and Careers CCCS 9.1, 9.2, 9.3 move from the specific case of equations in one variable to the study of functions in two variables. learn about the function rules, and model data using equations, tables, and graphs. learn how to use inductive reasoning for recognizing number patterns called sequences Math CCSS EE.8.6, F.8.3, F.8.4, F.8.5, SP.8.2 A-REI.10, F-IF.5, F-IF.6, F-IF.7a, F-BF.3, F-LE.5 Technology CCCS 8.1, st Century Life and Careers CCCS 9.1, 9.2, 9.3 learn how to write linear equations and recognize their different forms. by working with rate of change, interpret the slope in real-world situations. determine whether the graphs of two linear equations are parallel or perpendicular. 6: Systems of Equations & Inequalities January-February 12 days Math CCSS EE.8.8 A-CED.2, A-REI.5, A-REI.6, A-REI.11 A-REI.12 Technology CCCS 8.1, st Century Life and Careers CCCS 9.1, 9.2, 9.3 extend your ability to solve equations to include solving a system of two equations with two variables. learn methods of solving a linear system and how to determine which method is best for a given situation. graph the solution to a system of linear inequalities. 10

11 ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) 4: Graphs & November-December What are the key differences between relations and functions? What are the advantages and disadvantages of representing functions using rules, tables and graphs? 5: Linear Equations & Their Graphs December-January 13 days What are the two ways to find the slope of a line? How does changing the value of the slope affect the graph of the line? How does changing the value of the y-intercept affect the graph of the line? How do you find the x- and y- intercepts of a linear equation? What is the difference between a trend line and a line of best fit? 6: Systems of Equations & Inequalities January-February 12 days Why is it sometimes easier to solve equations using substitution rather than graphing? When is it best to solve a linear system by elimination and by using substitution? Compare graphing linear inequalities with graphing linear equations. STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Assessments of each learning activity Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in 11 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

12 OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) 4: Graphs & November-December repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 5: Linear Equations & Their Graphs December-January 13 days Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 6: Systems of Equations & Inequalities January-February 12 days Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework RESOURCES: Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as F.8.1. 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 12 EE.8.6. 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 EE.8.8. Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two

13 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days a result of the unit?) input and the corresponding output.1 F.8.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-BF.2. Write arithmetic and geometric equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. F.8.3. 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. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. F.8.4. 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. F.8.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 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. A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation 13

14 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function 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. SP.8.2. 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. A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F-IF.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. and a multiple of the other produces a system with the same solutions. A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A-REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 8.1 All students will use digital tools to 14

15 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F-BF.3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F-LE.5. Interpret the parameters in a linear or exponential function in terms access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation 15

16 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days of a context. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. in order to navigate the globally competitive work environment of the information age. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures : All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy.

17 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days CROSS-CURRICULAR: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) Centers Tiered Lessons Open-Ended Responses Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments : All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Centers Tiered Lessons Open-Ended Responses Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented:

18 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. 18

19 7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days ESTABLISHED GOALS: (NJ CCCS and/or CCS) ENDURING UNDERSTANDINGS: (Students will Understand that they will...) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Math CCSS EE.8.1, EE.8.3, EE.8.4 F-IF.7e, F-IF.8b, F.BF.2, F-LE.2 Technology CCCS 8.1, st Century Life and Careers CCCS 9.1, 9.2, 9.3 extend their knowledge about exponents to include zero and negative exponents. learn the properties of exponents, and how exponents are used to write a geometric sequence. graph exponential functions by making a table of values. Math CCSS A-SSE.2, A-APR.1, A-APR.7 Technology CCCS 8.1, st Century Life and Careers CCCS 9.1, 9.2, 9.3 categorize polynomials by their degree and number of terms. learn to add, subtract, and multiply polynomials. Math CCSS NS.8.2 A-SSE.3, A-APR.3, A-REI.4, A-REI.10, F-IF.7, F.IF.8, F-LE.1 Technology CCCS 8.1, st Century Life and Careers CCCS 9.1, 9.2, 9.3 examine quadratic graphs and their equations. solve quadratic equations by various techniques. determine an appropriate linear, quadratic, or exponential model for real-world data. 19

20 7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) What is the meaning of a zero exponent? What is the meaning of a negative exponent? How is dividing powers with the same base different from multiplying powers with the same base? How is raising a quotient to a power different than raising a power to a power? How do you square a binomial? How do you determine what numbers are used in the binomial factors when factoring expressions of the type x 2 + bx + c.? What is the first thing you should look for when factoring a trinomial? How do a and c affect a quadratic graph? How many solutions does a quadratic equation have? How can you determine the number of solutions from the graph? How do you complete the square? When is the quadratic formula useful? What is the discriminant and how is it useful? How do you choose between a linear, quadratic, or exponential model for data? STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Assessments of each learning activity Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 20

21 OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) 7: Exponents & Exponential February-March 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 8: Polynomials & Factoring March 15 days 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 9: Quadratic Equations & March-April 16 days 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework RESOURCES: Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 Manipulatives NJ ASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. 21

22 7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) EE.8.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3 3 = 1/3 3 = 1/27. EE.8.3. Use numbers expressed in the form of a single digit times a wholenumber power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10 8 and the population of the world as 7 times 10 9, and determine that the world population is more than 20 times larger. EE.8.4. 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. F-IF.7. Graph functions expressed A-SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. NS.8.2. 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 (e.g., π 2 ). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t t to reveal the approximate 22

23 7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01) 12t, y = (1.2) t/10, and classify them as representing exponential growth or decay. F-BF.2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. equivalent monthly interest rate if the annual rate is 15%. A-APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A-REI.4. Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A-REI.10. Understand that the graph of an equation in two variables is the set of 23

24 7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days situations, and translate between the two forms. F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root and cube root functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential functions, showing intercepts and end behavior. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different 24

Statewide Framework Document for:

Statewide Framework Document for: Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance

More information

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best

More information

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic

More information

Grade 6: Correlated to AGS Basic Math Skills

Grade 6: Correlated to AGS Basic Math Skills Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and

More information

Mathematics subject curriculum

Mathematics subject curriculum Mathematics subject curriculum Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research on 24 June

More information

Extending Place Value with Whole Numbers to 1,000,000

Extending Place Value with Whole Numbers to 1,000,000 Grade 4 Mathematics, Quarter 1, Unit 1.1 Extending Place Value with Whole Numbers to 1,000,000 Overview Number of Instructional Days: 10 (1 day = 45 minutes) Content to Be Learned Recognize that a digit

More information

Cal s Dinner Card Deals

Cal s Dinner Card Deals Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help

More information

Honors Mathematics. Introduction and Definition of Honors Mathematics

Honors Mathematics. Introduction and Definition of Honors Mathematics Honors Mathematics Introduction and Definition of Honors Mathematics Honors Mathematics courses are intended to be more challenging than standard courses and provide multiple opportunities for students

More information

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in

More information

Math 121 Fundamentals of Mathematics I

Math 121 Fundamentals of Mathematics I I. Course Description: Math 121 Fundamentals of Mathematics I Math 121 is a general course in the fundamentals of mathematics. It includes a study of concepts of numbers and fundamental operations with

More information

Mathematics Assessment Plan

Mathematics Assessment Plan Mathematics Assessment Plan Mission Statement for Academic Unit: Georgia Perimeter College transforms the lives of our students to thrive in a global society. As a diverse, multi campus two year college,

More information

Math 098 Intermediate Algebra Spring 2018

Math 098 Intermediate Algebra Spring 2018 Math 098 Intermediate Algebra Spring 2018 Dept. of Mathematics Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: MyMathLab Course ID: Course Description This course expands on the

More information

Technical Manual Supplement

Technical Manual Supplement VERSION 1.0 Technical Manual Supplement The ACT Contents Preface....................................................................... iii Introduction....................................................................

More information

GUIDE TO THE CUNY ASSESSMENT TESTS

GUIDE TO THE CUNY ASSESSMENT TESTS GUIDE TO THE CUNY ASSESSMENT TESTS IN MATHEMATICS Rev. 117.016110 Contents Welcome... 1 Contact Information...1 Programs Administered by the Office of Testing and Evaluation... 1 CUNY Skills Assessment:...1

More information

CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011

CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011 CAAP Content Analysis Report Institution Code: 911 Institution Type: 4-Year Normative Group: 4-year Colleges Introduction This report provides information intended to help postsecondary institutions better

More information

Math 96: Intermediate Algebra in Context

Math 96: Intermediate Algebra in Context : Intermediate Algebra in Context Syllabus Spring Quarter 2016 Daily, 9:20 10:30am Instructor: Lauri Lindberg Office Hours@ tutoring: Tutoring Center (CAS-504) 8 9am & 1 2pm daily STEM (Math) Center (RAI-338)

More information

Learning Disability Functional Capacity Evaluation. Dear Doctor,

Learning Disability Functional Capacity Evaluation. Dear Doctor, Dear Doctor, I have been asked to formulate a vocational opinion regarding NAME s employability in light of his/her learning disability. To assist me with this evaluation I would appreciate if you can

More information

Probability and Statistics Curriculum Pacing Guide

Probability and Statistics Curriculum Pacing Guide Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods

More information

Characteristics of Functions

Characteristics of Functions Characteristics of Functions Unit: 01 Lesson: 01 Suggested Duration: 10 days Lesson Synopsis Students will collect and organize data using various representations. They will identify the characteristics

More information

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Title: Considering Coordinate Geometry Common Core State Standards

More information

Montana Content Standards for Mathematics Grade 3. Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011

Montana Content Standards for Mathematics Grade 3. Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011 Montana Content Standards for Mathematics Grade 3 Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011 Contents Standards for Mathematical Practice: Grade

More information

Dublin City Schools Mathematics Graded Course of Study GRADE 4

Dublin City Schools Mathematics Graded Course of Study GRADE 4 I. Content Standard: Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems and reasonable estimates using paper and pencil, technology-supported

More information

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community

More information

SAT MATH PREP:

SAT MATH PREP: SAT MATH PREP: 2015-2016 NOTE: The College Board has redesigned the SAT Test. This new test will start in March of 2016. Also, the PSAT test given in October of 2015 will have the new format. Therefore

More information

Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.

More information

Math 150 Syllabus Course title and number MATH 150 Term Fall 2017 Class time and location INSTRUCTOR INFORMATION Name Erin K. Fry Phone number Department of Mathematics: 845-3261 e-mail address erinfry@tamu.edu

More information

Focus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multi-digit whole numbers.

Focus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multi-digit whole numbers. Approximate Time Frame: 3-4 weeks Connections to Previous Learning: In fourth grade, students fluently multiply (4-digit by 1-digit, 2-digit by 2-digit) and divide (4-digit by 1-digit) using strategies

More information

BENCHMARK MA.8.A.6.1. Reporting Category

BENCHMARK MA.8.A.6.1. Reporting Category Grade MA..A.. Reporting Category BENCHMARK MA..A.. Number and Operations Standard Supporting Idea Number and Operations Benchmark MA..A.. Use exponents and scientific notation to write large and small

More information

LLD MATH. Student Eligibility: Grades 6-8. Credit Value: Date Approved: 8/24/15

LLD MATH. Student Eligibility: Grades 6-8. Credit Value: Date Approved: 8/24/15 PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION LLD MATH Length of Course: Elective/Required: School: Full Year Required Middle Schools Student Eligibility: Grades 6-8 Credit Value:

More information

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade The third grade standards primarily address multiplication and division, which are covered in Math-U-See

More information

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a

More information

Radius STEM Readiness TM

Radius STEM Readiness TM Curriculum Guide Radius STEM Readiness TM While today s teens are surrounded by technology, we face a stark and imminent shortage of graduates pursuing careers in Science, Technology, Engineering, and

More information

STA 225: Introductory Statistics (CT)

STA 225: Introductory Statistics (CT) Marshall University College of Science Mathematics Department STA 225: Introductory Statistics (CT) Course catalog description A critical thinking course in applied statistical reasoning covering basic

More information

TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system

TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Curriculum Overview Mathematics 1 st term 5º grade - 2010 TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Multiplies and divides decimals by 10 or 100. Multiplies and divide

More information

Written by Wendy Osterman

Written by Wendy Osterman Pre-Algebra Written by Wendy Osterman Editor: Alaska Hults Illustrator: Corbin Hillam Designer/Production: Moonhee Pak/Cari Helstrom Cover Designer: Barbara Peterson Art Director: Tom Cochrane Project

More information

Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: Addison-Wesley.

Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: Addison-Wesley. Course Syllabus Course Description Explores the basic fundamentals of college-level mathematics. (Note: This course is for institutional credit only and will not be used in meeting degree requirements.

More information

Introducing the New Iowa Assessments Mathematics Levels 12 14

Introducing the New Iowa Assessments Mathematics Levels 12 14 Introducing the New Iowa Assessments Mathematics Levels 12 14 ITP Assessment Tools Math Interim Assessments: Grades 3 8 Administered online Constructed Response Supplements Reading, Language Arts, Mathematics

More information

Foothill College Summer 2016

Foothill College Summer 2016 Foothill College Summer 2016 Intermediate Algebra Math 105.04W CRN# 10135 5.0 units Instructor: Yvette Butterworth Text: None; Beoga.net material used Hours: Online Except Final Thurs, 8/4 3:30pm Phone:

More information

First Grade Standards

First Grade Standards These are the standards for what is taught throughout the year in First Grade. It is the expectation that these skills will be reinforced after they have been taught. Mathematical Practice Standards Taught

More information

This scope and sequence assumes 160 days for instruction, divided among 15 units.

This scope and sequence assumes 160 days for instruction, divided among 15 units. In previous grades, students learned strategies for multiplication and division, developed understanding of structure of the place value system, and applied understanding of fractions to addition and subtraction

More information

Instructor: Matthew Wickes Kilgore Office: ES 310

Instructor: Matthew Wickes Kilgore Office: ES 310 MATH 1314 College Algebra Syllabus Instructor: Matthew Wickes Kilgore Office: ES 310 Longview Office: LN 205C Email: mwickes@kilgore.edu Phone: 903 988-7455 Prerequistes: Placement test score on TSI or

More information

Common Core Standards Alignment Chart Grade 5

Common Core Standards Alignment Chart Grade 5 Common Core Standards Alignment Chart Grade 5 Units 5.OA.1 5.OA.2 5.OA.3 5.NBT.1 5.NBT.2 5.NBT.3 5.NBT.4 5.NBT.5 5.NBT.6 5.NBT.7 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.5 5.NF.6 5.NF.7 5.MD.1 5.MD.2 5.MD.3 5.MD.4

More information

UNIT ONE Tools of Algebra

UNIT ONE Tools of Algebra UNIT ONE Tools of Algebra Subject: Algebra 1 Grade: 9 th 10 th Standards and Benchmarks: 1 a, b,e; 3 a, b; 4 a, b; Overview My Lessons are following the first unit from Prentice Hall Algebra 1 1. Students

More information

Missouri Mathematics Grade-Level Expectations

Missouri Mathematics Grade-Level Expectations A Correlation of to the Grades K - 6 G/M-223 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley Mathematics in meeting the

More information

Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30%

Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30% COURSE SYLLABUS FALL 2010 MATH 0408 INTERMEDIATE ALGEBRA Course # 0408.06 Course Schedule/Location: TT 09:35 11:40, A-228 Instructor: Dr. Calin Agut, Office: J-202, Department of Mathematics, Brazosport

More information

Rendezvous with Comet Halley Next Generation of Science Standards

Rendezvous with Comet Halley Next Generation of Science Standards Next Generation of Science Standards 5th Grade 6 th Grade 7 th Grade 8 th Grade 5-PS1-3 Make observations and measurements to identify materials based on their properties. MS-PS1-4 Develop a model that

More information

Mathematics process categories

Mathematics process categories Mathematics process categories All of the UK curricula define multiple categories of mathematical proficiency that require students to be able to use and apply mathematics, beyond simple recall of facts

More information

Florida Mathematics Standards for Geometry Honors (CPalms # )

Florida Mathematics Standards for Geometry Honors (CPalms # ) A Correlation of Florida Geometry Honors 2011 to the for Geometry Honors (CPalms #1206320) Geometry Honors (#1206320) Course Standards MAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular

More information

Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple

Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple Unit Plan Components Big Goal Standards Big Ideas Unpacked Standards Scaffolded Learning Resources

More information

Common Core State Standards

Common Core State Standards Common Core State Standards Common Core State Standards 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Mathematical Practices 1, 3, and 4 are aspects

More information

1.11 I Know What Do You Know?

1.11 I Know What Do You Know? 50 SECONDARY MATH 1 // MODULE 1 1.11 I Know What Do You Know? A Practice Understanding Task CC BY Jim Larrison https://flic.kr/p/9mp2c9 In each of the problems below I share some of the information that

More information

OFFICE SUPPORT SPECIALIST Technical Diploma

OFFICE SUPPORT SPECIALIST Technical Diploma OFFICE SUPPORT SPECIALIST Technical Diploma Program Code: 31-106-8 our graduates INDEMAND 2017/2018 mstc.edu administrative professional career pathway OFFICE SUPPORT SPECIALIST CUSTOMER RELATIONSHIP PROFESSIONAL

More information

Edexcel GCSE. Statistics 1389 Paper 1H. June Mark Scheme. Statistics Edexcel GCSE

Edexcel GCSE. Statistics 1389 Paper 1H. June Mark Scheme. Statistics Edexcel GCSE Edexcel GCSE Statistics 1389 Paper 1H June 2007 Mark Scheme Edexcel GCSE Statistics 1389 NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional

More information

Are You Ready? Simplify Fractions

Are You Ready? Simplify Fractions SKILL 10 Simplify Fractions Teaching Skill 10 Objective Write a fraction in simplest form. Review the definition of simplest form with students. Ask: Is 3 written in simplest form? Why 7 or why not? (Yes,

More information

Julia Smith. Effective Classroom Approaches to.

Julia Smith. Effective Classroom Approaches to. Julia Smith @tessmaths Effective Classroom Approaches to GCSE Maths resits julia.smith@writtle.ac.uk Agenda The context of GCSE resit in a post-16 setting An overview of the new GCSE Key features of a

More information

Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall Phone:

Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall Phone: Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall 2011 Instructor s Name: Ricky Streight Hours Credit: 3 Phone: 405-945-6794 email: ricky.streight@okstate.edu 1. COURSE: Math 2103

More information

Unit 3 Ratios and Rates Math 6

Unit 3 Ratios and Rates Math 6 Number of Days: 20 11/27/17 12/22/17 Unit Goals Stage 1 Unit Description: Students study the concepts and language of ratios and unit rates. They use proportional reasoning to solve problems. In particular,

More information

Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C

Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C Using and applying mathematics objectives (Problem solving, Communicating and Reasoning) Select the maths to use in some classroom

More information

Pre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value

Pre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value Syllabus Pre-Algebra A Course Overview Pre-Algebra is a course designed to prepare you for future work in algebra. In Pre-Algebra, you will strengthen your knowledge of numbers as you look to transition

More information

Grade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

Grade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology

More information

Algebra 2- Semester 2 Review

Algebra 2- Semester 2 Review Name Block Date Algebra 2- Semester 2 Review Non-Calculator 5.4 1. Consider the function f x 1 x 2. a) Describe the transformation of the graph of y 1 x. b) Identify the asymptotes. c) What is the domain

More information

INTERMEDIATE ALGEBRA PRODUCT GUIDE

INTERMEDIATE ALGEBRA PRODUCT GUIDE Welcome Thank you for choosing Intermediate Algebra. This adaptive digital curriculum provides students with instruction and practice in advanced algebraic concepts, including rational, radical, and logarithmic

More information

South Carolina College- and Career-Ready Standards for Mathematics. Standards Unpacking Documents Grade 5

South Carolina College- and Career-Ready Standards for Mathematics. Standards Unpacking Documents Grade 5 South Carolina College- and Career-Ready Standards for Mathematics Standards Unpacking Documents Grade 5 South Carolina College- and Career-Ready Standards for Mathematics Standards Unpacking Documents

More information

TabletClass Math Geometry Course Guidebook

TabletClass Math Geometry Course Guidebook TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course

More information

Math Techniques of Calculus I Penn State University Summer Session 2017

Math Techniques of Calculus I Penn State University Summer Session 2017 Math 110 - Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg E-mail: sxz38@psu.edu Office phone: 814-865-4291 Office Hours:

More information

Arizona s College and Career Ready Standards Mathematics

Arizona s College and Career Ready Standards Mathematics Arizona s College and Career Ready Mathematics Mathematical Practices Explanations and Examples First Grade ARIZONA DEPARTMENT OF EDUCATION HIGH ACADEMIC STANDARDS FOR STUDENTS State Board Approved June

More information

Helping Your Children Learn in the Middle School Years MATH

Helping Your Children Learn in the Middle School Years MATH Helping Your Children Learn in the Middle School Years MATH Grade 7 A GUIDE TO THE MATH COMMON CORE STATE STANDARDS FOR PARENTS AND STUDENTS This brochure is a product of the Tennessee State Personnel

More information

Afm Math Review Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database

Afm Math Review Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database Afm Math Free PDF ebook Download: Afm Math Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database C++ for Game Programming with DirectX9.0c and Raknet. Lesson 1.

More information

Problem of the Month: Movin n Groovin

Problem of the Month: Movin n Groovin : The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of

More information

NCSC Alternate Assessments and Instructional Materials Based on Common Core State Standards

NCSC Alternate Assessments and Instructional Materials Based on Common Core State Standards NCSC Alternate Assessments and Instructional Materials Based on Common Core State Standards Ricki Sabia, JD NCSC Parent Training and Technical Assistance Specialist ricki.sabia@uky.edu Background Alternate

More information

Math 181, Calculus I

Math 181, Calculus I Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,

More information

MAT 122 Intermediate Algebra Syllabus Summer 2016

MAT 122 Intermediate Algebra Syllabus Summer 2016 Instructor: Gary Adams Office: None (I am adjunct faculty) Phone: None Email: gary.adams@scottsdalecc.edu Office Hours: None CLASS TIME and LOCATION: Title Section Days Time Location Campus MAT122 12562

More information

SURVIVING ON MARS WITH GEOGEBRA

SURVIVING ON MARS WITH GEOGEBRA SURVIVING ON MARS WITH GEOGEBRA Lindsey States and Jenna Odom Miami University, OH Abstract: In this paper, the authors describe an interdisciplinary lesson focused on determining how long an astronaut

More information

Mathematics Success Level E

Mathematics Success Level E T403 [OBJECTIVE] The student will generate two patterns given two rules and identify the relationship between corresponding terms, generate ordered pairs, and graph the ordered pairs on a coordinate plane.

More information

Answers To Hawkes Learning Systems Intermediate Algebra

Answers To Hawkes Learning Systems Intermediate Algebra Answers To Hawkes Learning Free PDF ebook Download: Answers To Download or Read Online ebook answers to hawkes learning systems intermediate algebra in PDF Format From The Best User Guide Database Double

More information

MTH 141 Calculus 1 Syllabus Spring 2017

MTH 141 Calculus 1 Syllabus Spring 2017 Instructor: Section/Meets Office Hrs: Textbook: Calculus: Single Variable, by Hughes-Hallet et al, 6th ed., Wiley. Also needed: access code to WileyPlus (included in new books) Calculator: Not required,

More information

SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106

SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106 SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106 Title: Precalculus Catalog Number: MATH 190 Credit Hours: 3 Total Contact Hours: 45 Instructor: Gwendolyn Blake Email: gblake@smccme.edu Website:

More information

SANTIAGO CANYON COLLEGE Reading & English Placement Testing Information

SANTIAGO CANYON COLLEGE Reading & English Placement Testing Information SANTIAGO CANYON COLLEGE Reaing & English Placement Testing Information DO YOUR BEST on the Reaing & English Placement Test The Reaing & English placement test is esigne to assess stuents skills in reaing

More information

TABE 9&10. Revised 8/2013- with reference to College and Career Readiness Standards

TABE 9&10. Revised 8/2013- with reference to College and Career Readiness Standards TABE 9&10 Revised 8/2013- with reference to College and Career Readiness Standards LEVEL E Test 1: Reading Name Class E01- INTERPRET GRAPHIC INFORMATION Signs Maps Graphs Consumer Materials Forms Dictionary

More information

Page 1 of 8 REQUIRED MATERIALS:

Page 1 of 8 REQUIRED MATERIALS: INSTRUCTOR: OFFICE: PHONE / EMAIL: CONSULTATION: INSTRUCTOR WEB SITE: MATH DEPARTMENT WEB SITES: http:/ Online MATH 1010 INTERMEDIATE ALGEBRA Spring Semester 2013 Zeph Smith SCC N326 - G 957-3229 / zeph.smith@slcc.edu

More information

Diagnostic Test. Middle School Mathematics

Diagnostic Test. Middle School Mathematics Diagnostic Test Middle School Mathematics Copyright 2010 XAMonline, Inc. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by

More information

Math Grade 3 Assessment Anchors and Eligible Content

Math Grade 3 Assessment Anchors and Eligible Content Math Grade 3 Assessment Anchors and Eligible Content www.pde.state.pa.us 2007 M3.A Numbers and Operations M3.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among

More information

EQuIP Review Feedback

EQuIP Review Feedback EQuIP Review Feedback Lesson/Unit Name: On the Rainy River and The Red Convertible (Module 4, Unit 1) Content Area: English language arts Grade Level: 11 Dimension I Alignment to the Depth of the CCSS

More information

South Carolina English Language Arts

South Carolina English Language Arts South Carolina English Language Arts A S O F J U N E 2 0, 2 0 1 0, T H I S S TAT E H A D A D O P T E D T H E CO M M O N CO R E S TAT E S TA N DA R D S. DOCUMENTS REVIEWED South Carolina Academic Content

More information

AP Statistics Summer Assignment 17-18

AP Statistics Summer Assignment 17-18 AP Statistics Summer Assignment 17-18 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic

More information

Using Proportions to Solve Percentage Problems I

Using Proportions to Solve Percentage Problems I RP7-1 Using Proportions to Solve Percentage Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by

More information

Curriculum Guide 7 th Grade

Curriculum Guide 7 th Grade Curriculum Guide 7 th Grade Kesling Middle School LaPorte Community School Corporation Mr. G. William Wilmsen, Principal Telephone (219) 362-7507 Mr. Mark Fridenmaker, Assistant Principal Fax (219) 324-5712

More information

Physics 270: Experimental Physics

Physics 270: Experimental Physics 2017 edition Lab Manual Physics 270 3 Physics 270: Experimental Physics Lecture: Lab: Instructor: Office: Email: Tuesdays, 2 3:50 PM Thursdays, 2 4:50 PM Dr. Uttam Manna 313C Moulton Hall umanna@ilstu.edu

More information

CUNY ASSESSMENT TESTS Webinar for International Students

CUNY ASSESSMENT TESTS Webinar for International Students CUNY ASSESSMENT TESTS Webinar for International Students 1 Today s Agenda ITEM 1 Description Overview of the CUNY ASSESSMENT TEST (CAT) What is the CUNY Assessment Test Why students need to take the CAT

More information

Course Syllabus for Math

Course Syllabus for Math Course Syllabus for Math 1090-003 Instructor: Stefano Filipazzi Class Time: Mondays, Wednesdays and Fridays, 9.40 a.m. - 10.30 a.m. Class Place: LCB 225 Office hours: Wednesdays, 2.00 p.m. - 3.00 p.m.,

More information

Algebra 1 Summer Packet

Algebra 1 Summer Packet Algebra 1 Summer Packet Name: Solve each problem and place the answer on the line to the left of the problem. Adding Integers A. Steps if both numbers are positive. Example: 3 + 4 Step 1: Add the two numbers.

More information

Content Language Objectives (CLOs) August 2012, H. Butts & G. De Anda

Content Language Objectives (CLOs) August 2012, H. Butts & G. De Anda Content Language Objectives (CLOs) Outcomes Identify the evolution of the CLO Identify the components of the CLO Understand how the CLO helps provide all students the opportunity to access the rigor of

More information

GCSE Mathematics B (Linear) Mark Scheme for November Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education

GCSE Mathematics B (Linear) Mark Scheme for November Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education GCSE Mathematics B (Linear) Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education Mark Scheme for November 2014 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge

More information

MATH 108 Intermediate Algebra (online) 4 Credits Fall 2008

MATH 108 Intermediate Algebra (online) 4 Credits Fall 2008 MATH 108 Intermediate Algebra (online) 4 Credits Fall 2008 Instructor: Nolan Rice Math Lab: T 2:00 2:50 Office: SHL 206-F Office Hours: M/F 2:00 2:50 Phone/Voice Mail: 732.6819 W 4:30 5:20 E-mail: nrice@csi.edu

More information

School of Innovative Technologies and Engineering

School of Innovative Technologies and Engineering School of Innovative Technologies and Engineering Department of Applied Mathematical Sciences Proficiency Course in MATLAB COURSE DOCUMENT VERSION 1.0 PCMv1.0 July 2012 University of Technology, Mauritius

More information

Ohio s Learning Standards-Clear Learning Targets

Ohio s Learning Standards-Clear Learning Targets Ohio s Learning Standards-Clear Learning Targets Math Grade 1 Use addition and subtraction within 20 to solve word problems involving situations of 1.OA.1 adding to, taking from, putting together, taking

More information

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology Michael L. Connell University of Houston - Downtown Sergei Abramovich State University of New York at Potsdam Introduction

More information

Functional Skills Mathematics Level 2 assessment

Functional Skills Mathematics Level 2 assessment Functional Skills Mathematics Level 2 assessment www.cityandguilds.com September 2015 Version 1.0 Marking scheme ONLINE V2 Level 2 Sample Paper 4 Mark Represent Analyse Interpret Open Fixed S1Q1 3 3 0

More information

Getting Started with TI-Nspire High School Science

Getting Started with TI-Nspire High School Science Getting Started with TI-Nspire High School Science 2012 Texas Instruments Incorporated Materials for Institute Participant * *This material is for the personal use of T3 instructors in delivering a T3

More information