Prealgebra (Grade 8) Course of Study (COS)

Transcription

1 Prealgebra (Grade 8) Course of Study (COS) s in Grade 8 are independent thinkers. They can apply prior knowledge to new situations but may need to be guided through the learning process by continuing the use of hands-on materials, mathematical discourse, and technology. These students have the ability to take ownership of their own mathematical learning and need opportunities to explore and investigate mathematical concepts. s in Grade 8 also need to be provided with instruction that includes a balance between skill development and mathematical understanding. The major focus of the eighth-grade curriculum is the integration of new and prior knowledge to solve problems dealing with all mathematical strands, with particular emphasis on algebra, geometry, and proportional reasoning. This curriculum offers a more in-depth study of algebraic concepts than in years past. Therefore, this course is subtitled Pre-Algebra. s who successfully complete the eighth grade have a thorough knowledge of the skills and concepts necessary for the study of Algebra I. High school credit may not be awarded for this course. Number and Operations s will: N1. Use various strategies and operations to solve problems involving real numbers. N1.1 Use alternative representations of rational numbers (NOT FOUND IN CURRICULUM GUIDE) Examples: models, drawings, grids, graphs N1.2 Apply GCF, LCM, and prime and composite numbers, including justification for the reasonableness of results, when working with rational numbers Example: A new music store is having a grand opening. Every 20 th customer gets a free compact disk (CD). Every 35 th customer gets a free tote bag. The first customer to receive both gifts will be the 140 th customer, because 140 is the LCM of 20 and 35. The answer (140 th ) is reasonable because it is larger than both 20 and 35. To say that the 5 th customer, which is the GCF of 20 and 35, receives the gift is not reasonable because it is smaller than 20 and 35. N1.3 Apply proportional reasoning Example: The amount of rainfall recorded for a certain town in a 24-hour period is 16 inches. Since the rain fell 2 inches every 3 hours, 24 inches of rain will fall in days if the rain continues at the same rate. N1.4 Use vocabulary associated with sets, including union and intersection N1.5 Determine whether a number is rational or irrational N1.6 Demonstrate computational fluency with operations on rational numbers N2. Simplify expressions containing natural number exponents by applying one or more of the laws of exponents. N2.1 Write numbers using scientific notation Baldwin County Public Schools Page 1 of 12

2 N3. Use order of operations to evaluate and simplify algebraic expressions. N3.1 Apply the substitution principle N3.2 Apply the properties of operations on rational numbers to evaluate and simplify algebraic expressions Algebra A1. Graph linear relations by plotting points or by using the slope and y-intercept. A1.1 Determine slopes and y-intercepts of lines A1.2 Calculate the slope of a linear relation given as a table or graph A1.3 Exhibit conceptual understanding of various uses of variables A2. Solve problems involving linear functions. A2.1 Identify functions from information in tables, sets of ordered pairs, equations, graphs, and mappings A2.2 Determine the rule that defines a function Example: Cars Washed Input (x) Money Made Output (y) 1 $ $ $ $18.00 (Rule: y = 4.5x) A2.3 Classify variables in a function as independent or dependent A2.4 Classify relations as linear or nonlinear by examining tables, graphs, or simple equations A3. Solve multistep linear equations, including equations requiring the use of the distributive property. Example: solving -3(x 5) 6x = 2 + 4x Geometry G1. Solve problems using the Pythagorean Theorem. G1.1 Apply the Triangle Inequality Theorem Example: determining if a triangle can be formed with sides of 1 inch, 2 inches, and 5 inches G1.2 Verify the Pythagorean Theorem G1.3 Apply the Pythagorean Theorem to determine if a triangle is a right triangle G1.4 Apply the Pythagorean Theorem to find the missing length of a side of a right triangle G1.5 Calculate distances on the coordinate plane using the Pythagorean Theorem Baldwin County Public Schools Page 2 of 12

3 G2. Compare quadrilaterals, triangles, and solids, using their properties and characteristics. G2.1 Develop mathematical arguments about the relationships among types of quadrilaterals and triangles G2.2 Identify angle bisectors, perpendicular bisectors, congruent angles, and congruent figures G2.3 Construct congruent and similar polygons, congruent angles, congruent segments, and parallel and perpendicular lines Measurement M1. Determine the measures of special angle pairs, including adjacent, vertical, supplementary, and complementary angles, and angles formed by parallel lines cut by a transversal. M2. Find the perimeter and area of regular and irregular plane figures. Example: If x represents the length of a side of the square, write expressions that represent the perimeter and area of the figure at x the left. M3. Determine the surface area and volume of rectangular prisms, cylinders, and pyramids. M3.1 Estimate surface area and volume of solid figures M3.2 Determine the appropriate units of measure to describe surface area and volume M3.3 Develop formulas for determining surface area and volume of rectangular prisms, cylinders, and pyramids M4. Determine the lengths of missing sides and measures of angles in similar and congruent figures. M4.1 Apply proportional reasoning M4.2 Use dilations on the coordinate plane to determine measures of similar figures M4.3 Find the ratios of the perimeters and areas of similar triangles, trapezoids, and parallelograms (NOT IN CURRICULUM GUIDE) Data Analysis and Probability D1. Interpret data from populations, using given and collected data. D1.1 Represent the data with the most appropriate graph, including box-and-whisker plot, circle graph, and scatterplot D1.2 Make predictions by estimating the line of best fit from a scatterplot D1.3 Compare data sets involving two populations D1.4 Determine the measure of center that is the most appropriate for a given situation D2. Determine the theoretical probability of an event. D2.1 Calculate the probability of complementary events and mutually exclusive events D2.2 Compare experimental and theoretical probability D2.3 Compute the probability of two independent events and two dependent events D2.4 Determine the probability of an event through simulation Example: using random numbers to find the probability of a basketball player making six baskets in six attempts if he makes 60 percent of his shots from the court and shoots 20 times during a game Baldwin County Public Schools Page 3 of 12

4 First Quarter Variables, Expressions, and Integers 1-1 N3.1 Prioritize vocabulary and substitution principle 1-2 N2 Prioritize evaluating expressions with exponents 1-3 N3 Prioritize order of operations 1-4 Prioritize comparing and ordering integers; absolute value 1-5 N1.6 Prioritize adding integers 1-6 N1.6 Prioritize subtracting integers Reference p.39 D1.4 AHSGE VII-5 Prioritize mean, median, mode and range 1-7 N1.6 Prioritize multiplying and dividing integers 1-8 Prioritize identifying and plotting points on the coordinate plane 1-8 D1.2 Prioritize problem 27 p.50 (scatterplot) 2-1 N N3.2 Reference p N N3.2 AHSGE VII-7 Solving Equations Prioritize properties Prioritize the distributive property Prioritize rate/unit rate Prioritize simplifying expressions; very important vocabulary 2-4 N3.1 Prioritize testing solutions 2-4 Review one-step equations 2-5 Review one-step equations using addition/subtraction Baldwin County Public Schools Page 4 of 12

5 2-6 Review one-step equations using multiplication/division 2-7 N1.6 Prioritize rational number operations and equations with decimals Multi-Step Equation and Inequalities 3-1 A3 3-2 N A3 3-3 A AHSGE II-1 AHSGE II-1 AHSGE II-1 AHSGE V-3 AHSGE VI-5 AHSGE V-3 AHSGE VI-5 AHSGE V-3 AHSGE VI-5 Prioritize two-step equations Prioritize equations having like terms and parentheses Prioritize Prioritize equations with variables on both sides NNoot tt aa PPr ri iioor ri iit ttyy inequalities (?) NNoot tt aa PPr ri iioor ri iit ttyy inequalities (?) NNoot tt aa PPr ri iioor ri iit ttyy multi-step inequalities (?) Second Quarter Factors, Fractions and Exponents 4-1 N1.2 Prioritize vocabulary and factoring monomials 4-2 N1.2 Prioritize problem-solving with GCF in exercises 4-3 N1.2 Prioritize simplifying variable expressions 4-4 N1.2 Prioritize variable expressions 4-5 N2 Prioritize product of powers and quotient of powers properties (See concept activity p. 193) 12-5 N2 Prioritize product of powers and quotient of powers 4-6 N2 Prioritize negative and zero exponents 4-7 N2.1 Prioritize writing numbers Baldwin County Public Schools Page 5 of 12

6 Rational Numbers and Equations 5-1 N1.5 Prioritize representing fractions as decimals and decimals as fractions; ordering rational numbers 5-2 N1.6 Prioritize algebraic problems 5-3 N1.6 Prioritize algebraic problems 5-4 N1.6 Prioritize algebraic problems in operations with scientific notation 5-5 N1.6 Prioritize algebraic problems 5-6 A3 5-7 A3 AHSGE II-1 AHSGE II-1 Prioritize fractional coefficients Prioritize examples 1 and 2 on equations NNoot tt aa PPr ri iioor ri iit ttyy inequalities Ratios and Rates 6-1 N1.3 AHSGE VII-7 Review, if necessary 6-2 N1.3 AHSGE VII-7 Prioritize problem solving 6-3 N1.3 AHSGE VII-7 Prioritize problem solving Concept Activity p. 287 G2.1 Enrichment- Investigate similar figures 6-4 G2.2 Prioritize proportional reasoning 6-5 M4 6-5 M M4.1 AHSGE VII-3 AHSGE VII-3 AHSGE VII-3 Prioritize indirect measurement Prioritize Prioritize problem solving Baldwin County Public Schools Page 6 of 12

7 Percent Review, if necessary; percents to fractions; fractions to percents Review, if necessary; problem solving with percents and proportions Review, if necessary; problem solving with percents and proportions 7-4 Review, if necessary; problem solving with percents and proportions 7-5 NNoot tt aa PPr ri iioor ri iit ttyy in regular classes A2.1 AHSGE III-1 Linear Functions Prioritize vocabulary and function tests 8-2 A1 A2 AHSGE V-1 AHSGE V-4 Prioritize finding solutions for equations in two variables; horizontal/vertical lines; solving for y See Instructional Suggestions See Instructional Suggestions 8.3 A2.3 A1.3 A1.3 A2.4 A1 A1.1 AHSGE V-1 AHSGE V-4 AHSGE V-1 AHSGE V-4 AHSGE IV-2 Resource needed to teach independent/dependent variables; Resource needed (See MathThematics, Module 7, p ) Prioritize graphing equations using x and y intercepts 8-4 A1.2 AHSGE IV-2 Prioritize calculating slope (See concept activity p. 403) 8-5 A1 AHSGE V-1 AHSGE V-4 Prioritize graphing equations using slope-intercept form 8-5 A2.2 Prioritize matching equations to graphs Baldwin County Public Schools Page 7 of 12

8 8-6 A2.2 Prioritize determining the rule; writing equations; scatterplot and line of best fit 8-6 A V-1 V-4 NNoot tt aa PPr ri iioor ri iit ttyy direct variation (p. 423) NNoot tt aa PPr ri iioor ri iit ttyy in regular classes 8-8 NNoot tt aa PPr ri iioor ri iit ttyy in regular classes 8-9 NNoot tt aa PPr ri iioor ri iit ttyy in regular classes Set Theory N1.4 Resource: Additional resources found at Third Quarter Real Numbers 9-1 N1 AHSGE VII-7 Prioritize calculations with square roots 9-2 NNoot tt aa PPr ri iioor ri iit ttyy simplifying radicals (taught in Algebra I) 9-3 G1 G1.4 AHSGE VII-2 Prioritize solving problems with the Pythagorean Theorem (substitute decimal approximations for simplified radical form) 9-3 G1.2 AHSGE VII-2 Prioritize verification of Pythagorean Theorem (See activity p. 464) 9-3 G1.3 AHSGE VII-2 Prioritize identifying right triangles (Example 3) 9-4 N1.5 Prioritize determining whether number is rational or irrational; comparing and ordering real numbers 9-5 G1.5 AHSGE IV-2 Prioritize finding distance on the coordinate plane using the Pythagorean Theorem NNoot tt aa PPr ri iioor ri iit ttyy the distance formula Baldwin County Public Schools Page 8 of 12

9 9-6 NNoot tt aa PPr ri iioor ri iit ttyy special right triangles 9-7 NNoot tt aa PPr ri iioor ri iit ttyy tangent ratios 9-8 NNoot tt aa PPr ri iioor ri iit ttyy sine/cosine ratios Review units of measure Review basic geometry vocabulary G2 Measurement, area and volume Resource: Chart p. 817 Additional resources needed Resource: Pages , , G1.1 Prioritize triangle inequality theorem and classifying triangles 10-2 G2 G2.1 Prioritize classifying polygons and types of quadrilaterals; relationships among types of quadrilaterals and triangles Reference p M M2 Review prior to teaching 10-3 Prioritize finding area of parallelograms, trapezoids and irregular figures 10-4 M2 Prioritize finding area and circumference; define chord (see MathThematics p ) Enrichment: Investigate 10-4 p. 527 reference p M3 G2 Prioritize classifying solids Prioritize finding surface area of prisms and cylinders 10-5 M3.1 M3.3 Prioritize concept activity on nets p M3 Prioritize surface area of pyramids NNoot tt aa PPr ri iioor ri iit ttyy surface area of cones Baldwin County Public Schools Page 9 of 12

10 10-7 M M3.1 Prioritize volume of prisms and cylinders Resource: See MathThematics p. 303 p for estimation of surface area and volume 10-7 M3.2 Prioritize that for area, units are squared; for volume, units are cubed 10-8 M3 Prioritize volume of pyramids NNoot tt aa PPr ri iioor ri iit ttyy volume of cones Fourth Quarter 11-1 D1 D1.1 D1.3 Data analysis, polynomials, transformations Prioritize using stem and leaf, frequency tables and histograms 11-2 D1.1 D1.3 Prioritize comparing data sets; selecting most appropriate graph; vocabulary 11-3 reference p D1.1 D1.2 D1 D1.1 Refer to section 8-6 for scatterplots Prioritize construction of bar graphs, line graphs, and circle graphs 11-3 D1.1 Prioritize functionality of each graph and choosing the appropriate graph 11-4 D1 Prioritize vocabulary of sampling :11-4 Technology activity p D1 Prioritize interpretation of data and making predictions Baldwin County Public Schools Page 10 of 12

11 6-8 Review counting principle 11-6 Prioritize problem solving 11-7 Prioritize - Distinguish between combination and permutation and compute results 6-7 D2 D2.2 AHSGE VII-6 Prioritize theoretical probability NNoot tt aa PPr ri iioor ri iit ttyy odds in favor 11-8 D2.1 AHSGE VII-6 Prioritize mutually exclusive events and complementary events 11-9 D2.4 Concept Activity p D2.3 AHSGE VII-6 Prioritize probability with independent and dependent events NOTE: Teach Chapter 12 after SAT 10 testing if time permits 4 th Quarter Angle relationships and transformations 13-1 M1 G2.2 AHSGE VII-1 Prioritize angle relationships Reference p. 410 M1 AHSGE VII-1 Prioritize parallel, perpendicular and skew lines Reference p.714 G2.2 Prioritize constructions (perpendicular bisector, congruent angle, angle bisector) 13-2 M1 Constructions G2.3 AHSGE VII-1 Prioritize angle relationships and finding missing measures, given parallel lines cut by a transversal Resources needed for constructions of congruent and similar polygons, parallel lines Baldwin County Public Schools Page 11 of 12

12 Concept activity 13-3 G2.1 Enrichment 13-3 G2.1 Prioritize finding sum of the angles of a polygon (n-2)(180) 13-4 Prioritize translating figures 13-5 Prioritize symmetry and reflections 13-6 Prioritize rotations 13-7 M4.2 Prioritize dilations; scale factor; measure of dilated figures Polynomials and nonlinear functions 12-1 N2 Review like terms; degree 12-2 N N AHSGE VI-1 AHSGE I-3 AHSGE VI-1 AHSGE I-3 AHSGE VI-1 Prioritize adding/subtracting like terms Prioritize multiplying/dividing polynomials Baldwin County Public Schools Page 12 of 12