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Math 8 (Pre-Algebra) Curriculum Map 2011-2012 Quarter 1 Big Ideas 1. The real number system includes both rational and irrational numbers, each of which has distinguishing characteristics when expressed in decimal form. 2. Irrational numbers can be approximated by rational numbers. 3. There are laws that govern the use of integer exponents. 4. There is an inverse relationship between squares and square roots. 5. The Pythagorean Theorem is an historically and practically important application of squares and square roots. Textbook /Resource Correlation August Textbook Correlation for all of Q1 Smart Start Lesson 2, 3 Chapter 1 Lesson 1A-D Lesson 2A,B Standards Vocabulary Math Standards: Operations with rational numbers (integers, fractions, decimals, then integrate all three) 8.2.1 Conversions between and comparing fractions, decimals, and percents imbedded in 8.2.3, 8.2.4 Mental computation with rational numbers 8.2.4 Rational number, integer, inverse relationship, order of operations, reciprocal, terminating decimal, repeating decimal, absolute value, opposite Common Core Standards: CC8.NS.1 September Continue August Curriculum Chapter 2 Lesson 1A-C Lesson 2A-C Lesson 3A-D Chapter 9 Lesson 2A,D “Supplement” indicated that textbook does not sufficiently cover standard Math Standards: Positive exponents and square roots 8.1.6, 8.1.7 Number Sets (Rational and Irrational #s) 8.1.2, 8.1.3 Simplify and evaluate expressions that include exponents 8.3.4 Exponent laws 8.1.4, 8.1.5, 8.3.3 Common Core Standards: CC8.EE.1, CC8.EE.2 Exponent, laws of integer exponents, base, power, irrational number, real numbers, square, square root, radical, radicand Skills/Indicators of Success 8.2.1 Supplement Compute the solution to multi-step problems involving addition, subtraction, multiplication and division of integers, terminating decimals, fractions, and a combination of the three. 8.2.3 Decide whether answers to computations involving integers, fractions, decimals, and percents on a calculator are reasonable and justify your response using estimation techniques. (Classroom only, not ISTEP) 8.2.4 Compute with common fractions, decimals, powers, and percents using mental arithmetic. (Classroom only, not ISTEP) 8.1.6a Describe and provide an example of the inverse relationship between squaring and finding the square root involving a perfect square integer. 8.1.6b Supplement Simplify a problem involving a perfect square root squared, i.e. 144 2 144 (State suggests relating to Pythagorean Theorem, but PT will be covered in Q3) 8.1.7 Supplement Calculate the square root of a given number to the precision requested or required by the context. 8.1.2c Identify a given decimal as either rational or irrational and provide justification. 8.1.3 Determine and analyze the results of using addition, subtraction, multiplication, and division on rational and irrational numbers (other than zero) by doing the following: operating on two rationals, operating on one rational and one irrational, and operating on two irrationals. State and justify, in words, any generalizations that you can make. 8.3.4a Simplify algebraic expressions involving powers by using the correct order of operations. 8.3.4b Evaluate algebraic expressions involving powers by substitution. 8.1.4a Supplement Evaluate an exponential expression involving negative exponents without a calculator. 8.1.4b Simplify powers with variables as the base, the exponent, or both that involve negative exponents. Notes for Instruction and Pacing Suggested Formative and Summative Assessments Mental computation should be emphasized throughout Teach rules for computation of rational numbers with integers first, then fractions, decimals, and a combination. To be filled in by PLCs 8.1.3 assessed in classroom only, not ISTEP. ** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map. To be filled in by PLCs 8.1.4c & 8.3.3 Supplement Expand whole number powers involving negative exponents into multiplicative inverse (repeated division). 8.1.5a Describe the laws of exponents and explain how to use each one in a given scenario. 8.1.5b Evaluate division of same base expressions that have both positive and negative integer exponents by using the law of exponents. 8.1.5c Evaluate multiplication of same base expressions that have both positive and negative integer exponents by using the law of exponents. 8.3.3a Recognize the difference between a negative number raised to an exponent and the opposite of a positive number raised to an exponent. 8.3.3b Rewrite an exponential expression in expanded form. Textbook Correlation for all of Q1 Smart Start Lesson 2, 3 Chapter 1 Lesson 1A-D Lesson 2A,B October (Q1) Chapter 2 Lesson 1A-C Lesson 2A-C Lesson 3A-D Chapter 9 Lesson 2A,D “Supplement” indicated that textbook does not sufficiently cover standard Math Standards: Continue exponent laws with scientific notation application 8.1.1 Convert common measurements within the same system 8.5.1 Common Core Standards: CC8.EE.3, CC8.EE.4 Exponent, scientific notation, standard notation, dimensional analysis, proportion 8.1.1a Read orally decimals in scientific notation. 8.1.1b Write conversions of decimals from scientific notation to standard form. 8.1.1c Write conversions of decimals from standard form to scientific notation. 8.1.1d Use <, >, greater than or equal to, less than or equal to, and = to compare decimals in scientific notation. 8.1.1e Evaluate problems including +, -, x, and / of scientific notation. 8.1.1f Use scientific notation to solve word problems involving decimals. 8.5.1 Convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system. Discuss scientific notation with grade level science teachers to align instruction. If you teach conversions as a series of proportions, it is suggested that you teach conversions using dimensional analysis. (State suggests teaching conversions in the context of perimeter and area problems, but this will be covered more in Q3) ** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map. To be filled in by PLCs Quarter 2 Big Ideas 1. Relationships can be described and generalizations made for mathematical situations that repeat in a predictable way. These generalizations can then be represented in a variety of forms including tables, graphs, equations, and in words. 2. Relations can be used to assign members of one set to members of another set. A function, a specific type of relation, assigns each member of one set to a unique number of another set. 3. If a correlation exists within data plotted on a scatterplot, a line of best fit can be drawn and a linear equation formulated. 4. If two quantities vary proportionally, the relationship can be represented as a linear function. 5. Rules for arithmetic and algebra can be used together with notations of equivalence to transform equations and inequalities. 6. Nonlinear functions within families of functions have commonalities among their different representations. Textbook /Resource Correlation October (Q2) Textbook Correlation for all of Q2 November Chapter 3 Lesson 1 BCD Lesson 2 ABC Lesson 3 ABC Lesson 4 A Chapter 4 Lesson 1 ABC Lesson 2 ABCD December Chapter 5 Lesson 2 CD Lesson 3 BC Lesson 4 AB Chapter 6 Lesson 1 ABC Lesson 2 A Lesson 3 CD Chapter 9 Lesson 1 AB Additional Lesson #7 (Back of Book) Chapter 10 Lesson 3 B – F “Supplement” indicated that textbook does not sufficiently cover standard Standards Math Standards: Properties and algebraic expressions 8.3.4, imbedded in 8.3.1 One –step equations and inequalities 8.3.1 Common Core Standards: CC8.EE.7ab Math Standards: Two-step equations and inequalities 8.3.1 Multi-step equations 8.3.1 Vocabulary Commutative, associative, identity, distributive, coefficient, term, constant, expression, equation, inequality Common Core Standards: CC8.EE.7ab Math Standards: Relationship between tables, equations and linear graphs 8.3.5, 8.3.8 Linear vs. Non-linear functions 8.3.5, 8.3.8, 8.3.9, 8.3.10 Slope/Rate of Change 8.3.5, 8.3.6, 8.3.7 (If time allows, begin systems of equations) Common Core Standards: CC8.EE.5, CC8.EE.6, CC8.F.1, CC8.F.2, CC8.F.3, CC8.F.4, CC8.F.5, CC8.SP.3 Linear, parabola, quadratic, cubic, coordinate, function, relation, domain, range, independent, dependent, slope, rate of change, intercept, vertical change, horizontal change, input, evaluate, quadrant Skills/Indicators of Success 8.3.1a Define unknowns for a real-world problem. 8.3.1bcf Solve a linear equation or inequality for a given variable and verify solution. 8.3.1eg Write a linear equation or inequality to model a real-world problem. 8.3.1a Define unknowns for a real-world problem. 8.3.1bcf Solve a linear equation or inequality for a given variable and verify solution. 8.3.1eg Write a linear equation or inequality to model a real-world problem. 8.3.1d Find ordered pairs that are solutions to a linear equation and justify your reasoning. 8.3.5e Describe the change in y versus the change in x in terms of a table, a graph, an equation, or a written statement. 8.3.6a Calculate slope as rise/run and using the slope formula. 8.3.6b Determine the slope of a linear function given an equation, not necessarily in slope-intercept form. 8.3.6c Find the equation of a line given a graph or given the slope and a point on the line. 8.3.7a Explain in written form the relationship between one quantity with another quantity in terms of rate. 8.3.7b Write rates as the comparison of two quantities with appropriate labels. 8.3.7c Draw a graph of one quantity with respect to another quantity, i.e., time vs. distance. 8.3.10 Graph and compare functions of the form y nx 2 and y nx 3 , explain similarities and differences. 8.3.5a Identify linear functions from their graph. Description: Discuss with students the domain and range and which is allowed to have numbers repeat and still form a function (a good technique to use is the "vertical-line Notes for Instruction and Pacing Continue to emphasize word problems that can be solved by equations and inequalities. Continue to emphasize word problems that can be solved by equations and inequalities. Suggested Formative and Summative Assessments To be filled in by PLCs To be filled in by PLCs 8.3.10 Assessed in classroom only, not on ISTEP Make connections between tables, equations, and graphs. Emphasize translating equations into slope intercept form. Continue to spiral review these topics during bellringers and other assessments ** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map. To be filled in by PLCs December (continued) test"). 8.3.5b Identify linear functions from their table. Description: Discuss with students the domain and range and which is allowed to have numbers or variables repeat and still form a function. 8.3.5c Identify linear functions from their equation. 8.3.5d Identify the slope of a line as positive or negative from a graph. 8.3.6b Determine the slope of a linear function given an equation, not necessarily in slope-intercept form. 8.3.8 Translate between a table, equation (using y= or f(x)=), situation of words, and graph of a linear function given at least one of the representations. 8.3.9a Recognize and state in words what makes a quadratic function a quadratic in terms of its table, equation, and graph. 8.3.9bcd Produce a table, equation, or graph of a quadratic function, given a verbal description, graph, equation, or table. Quarter 3 Big Ideas ** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map. 1. Some attributes of objects are measurable and can be quantified using unit amounts. 2. Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes. These attributes are useful in solving problems involving or modeled by these objects. 3. Objects in space can be transformed in an infinite number of ways, and those transformations can be described and analyzed mathematically. 4. The Pythagorean Theorem and its converse can be used to calculate lengths of line segments in 2- and 3-dimensional geometric objects. Math Standards: Systems of equations 8.3.2 Pythagorean Theorem 8.4.5 Measurement (perimeter, area, volume, surface area) 8.5.4 January Common Core Standards: CC8.EE.8abc, CC8.G.6, CC8.G.7, CC8.G.8, CC8.G.9 Chapter 1 Lesson 1C Chapter 3 Lesson 1B,C February Chapter 7 Lesson 4B Chapter 8 Lesson 1B Lesson 2B,C Lesson 3A,B,D,E Chapter 9 Lesson 1A Lesson 2A Math Standards: Irregular 2D and 3D shapes 8.5.5 Scale factors 8.5.3 Convert common measurements 8.5.1 Common Core Standards: CC8.G.4, CC8.G.9 Chapter 12 Lesson 1B,C,E Lesson 2A,B Lesson 3B,C,D Scatter plot, line of best fit, correlation, systems of equations, no solution, one solution, infinitely many solutions, substitution, radius, diameter, surface area, volume, circumference, slant, height, cylinder, cone, cube, pyramid, sphere, face, area, right triangle, rectangular prism, right prism, similar, Pythagorean theorem, leg, hypotenuse, proportion Smart Start 5 March (Q3) Math Standards: Derived measurements 8.5.2 Simple and compound interest 8.2.2 Transformations 8.4.4 Common Core Standards: CC8.G.1, CC8.G.2, CC8.G.3, CC8.G.4 Transformation s, translation, rotation, reflection, dilation, simple and compound interest 8.3.2b Solve a system algebraically using substitution. 8.3.2c Write solutions to a system as intersection points or ordered pairs. 8.3.2d Determine the reasonableness of answers to realworld problems involving systems of equations and check solutions. 8.4.5ab Explain and use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle, given three side lengths. 8.4.5c Solve problems in two and three dimensions using the Pythagorean Theorem and its converse. Description: Use the Pythagorean Theorem to determine if three side lengths form a right triangle as well as finding the length of a missing side when given two side lengths. 8.5.1 Convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system. Description: Note: To prepare students for Algebra I, if you teach conversions as a series of proportions, we also suggest that you teach conversions using dimensional analysis. 8.5.3 Solve problems involving scale factors, area, and volume using ratio and proportion. 8.5.4a Solve problems involving perimeter and area of basic two-dimensional shapes, including rectangles, parallelograms, trapezoids, triangles, and circles 8.5.4b Solve problems involving surface area and volume of basic three-dimensional shapes including prisms, cylinders, spheres, cones, and pyramids. Description: Problems involving cones, pyramids and spheres are first found in 8th grade. 8.5.5a Compute and estimate the area of irregular twodimensional shapes. 8.5.5b Compute and estimate the volume of irregular threedimensional shapes. 8.5.2 & 8.2.2 Solve problems involving rates and derived measurements (e.g., simple and compound interest, velocity and density). 8.2.2 & 8.5.2 Solve problems involving simple and compound interest. 8.4.4 Draw the translation (slide), rotation (turn), reflection (flip), and dilation (stretch or shrink) of any given figure. Description: This is the only transformation that is introduced in 8th grade. ** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map. Quarter 4 Big Ideas 1. The chance of an event occurring can be described numerically by a number between 0 and 1 inclusive and used to make predictions about other events. 2. There are special numerical measures that describe the center and spread of numerical data sets. 3. Data can be represented visually using tables, charts, and graphs. The type of data determines the best choice of visual representation. 4. Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected and how best to collect it. Math Standards: Populations and samples 8.6.1, 8.6.2 Data displays (scatter plots and line of best fit) 8.6.3, 8.6.4, 8.6.5 March (Q4) Common Core Standards: CC8.SP.1, CC8.SP.2, CC8.SP.3, CC8.SP.4 Measure of central tendencies, outlier, quartiles, scatter plot, correlation, sample, bias Chapter 10 Lesson 1A,B,C Lesson 2A,B,C Lesson 3A-G April Chapter 11 Lesson 1A Lesson 3D,E Math Standards: Equally likely events 8.6.6 Counting principle 8.6.7 Geometric vocabulary and properties 8.4.1, 8.4.3 May Common Core Standards: CC8.G.5 Math Standards: Constructions 8.4.2 Common Core Standards: Probability, dependent, disjoint, equally likely, counting principle, tree diagram, bivariate data, supplementary, complementary , congruent, corresponding, altitude, bisector, midpoint, edge, compass, perpendicular 8.6.1a Identify claims based on statistical data. 8.6.1ac Identify possible sources of bias in selecting samples or in an existing sample. 8.6.1b Evaluate the reasonableness of the claims based on statistical data and design a study to investigate the claim. 8.6.2b Describe different methods of selecting samples, analyzing the strengths and weaknesses of each method. 8.6.3 Identify or compute the minimum value, the lower quartile, the median, the upper quartile, the interquartile range, and the maximum value of a data set, explaining what each represents in a data set and why each is useful 8.6.4ab Analyze, interpret, and display single-variable and two-variable data in appropriate bar, line, and circle graphs; stem-and-leaf plots; and box-and-whisker plots and explain which types of display are appropriate for various data sets. 8.6.5a Represent two-variable data with a scatterplot on the coordinate plane and describe how the data points are distributed. 8.6.5b Draw a line that appears to best fit the data in a scatterplot (if the pattern appears to be linear), and write the equation of that line. 8.6.6 Recognize and define equally likely events. 8.6.7 Find the number of possible arrangements of several objects by using the Basic Counting Principle 8.4.1 Identify and define basic properties of geometric shapes including altitudes, diagonals, angle and perpendicular bisectors, central angles, radii, diameters, and chords 8.4.3b Describe the results of the intersection of two or more geometric figures in a plane or space. 8.4.2 Using appropriate tools, accurately construct and justify the construction of: copies of segments and angles, bisectors of segments and angles, and perpendicular segments. 8.4.2, 8.4.3 are assessed in classroom only, not ISTEP ** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.