Grades 7 & 8 Pre-Algebra/Course 3, TERM 1 - AUGUST/SEPTEMBER/OCTOBER Algebra Tools Solving Equations Integers Solving Multi-Step Equations and Inequalities TERM 2 NOVEMBER/DECEMBER/JANUARY Functions & Graphing Factors & Fractions/Exploring Number Patterns Rationals TERM 3- JANUARY/FEBRUARY/MARCH Proportions & Percent Exploring Real Numbers Statistics TERM 4 APRIL/MAY/JUNE Geometry Geometry/Measurement Probability 1. Revised Summer 2008
2. Term 1: Algebra Tools MA Frameworks 7.N.5 - Apply the rules of positive integer exponents to the solution of problems. Extend the Order of Operations to include positive integer exponents. 8.N.7 - Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots. 7.P.2/8.P.2 - Evaluate simple algebraic expressions for given variable values. 8.N.8 - Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements and the notion of closure of a subset of the rational numbers under an operation. Variable & Expressions translate verbal phrases Evaluating Expressions simplify expressions solve open sentences Properties Commutative, Associative and Identity Properties of Addition & Multiplication Distributive Property Multiplicative Property of Zero identify properties use to solve problems Powers & Exponents Order of Operations use to evaluate expressions algebraic expression base brackets evaluate exponent expressions factor like terms parentheses power terms variables 1-1, 1-2, 1-3, 1-4, 1-5, 1-6 1-1, 1-2, 1-3, 1-6 Revised Summer 2008
Term 1: Solving Equations MA Frameworks 7.N.6 - Use the inverse relationships of addition and subtraction, and of multiplication and division, to simplify computations and solve problems. 8.N.9 - Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. Topic Vocabulary Teacher Resources Solving Equations use inverse operations to solve solve problems using equations solve equations using inverse properties solve problems using formulas absolute value defining a variable solution inverse operations positive integers negative open sentences simplify solving the equation 1-8, 3-1, 3-2, 3-3, 3-4 1-4, 1-5, 2-9 Term 1: Integers MA Frameworks Learning Standards 7.N.4/8.N.6 - Demonstrate an understanding of absolute value. 7.N.1/8.N.1 - Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents. 7.N.7/8.N.10 - Estimate and compute with fractions (simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). 8.P.3 - Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions. Topics Computation add, subtract, multiply and divide Absolute Value Comparing & Ordering Coordinate Grid (review) Apply to Solving Equations solve equations with integer solutions Vocabulary additive inverse counters difference dividend divisor evaluate factors model product quotient repeated addition simplify solve sum zero pair Teacher Resources 2-1, 2-3, 2-4, 2-5, 2-7, 2-8 2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 3. Revised Summer 2008
4. Term 1: Solving Multi-Step Equations and Inequalities MA Frameworks 8.P.7 - Set up and solve linear Multi-step Equations defining a variable equations and inequalities with one or division by zero solve equations that involve more than 7-1, 7-2, 7-3, 7-5, 7-6, 7-7, 3- two variables, using algebraic equation one operation 6, 3-7, 1-9 methods, models, and/or graphs. inverse operations solve verbal problems by writing and open sentences solving equations solution solve equations with the variable on solving the equation 1-7 each side terms Inequalities write and solve solve inequalities by using the properties of inequalities Revised Summer 2008
Term 2: Functions and Graphing MA Frameworks Learning Standards 7.P.1/8.P.1 - Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions. 8.P.4 - Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations. 8.P.5 Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems. 8.P.6 Identify the roles of variables within an equation. 8.P.7 - Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. 7.P.6/8.P.8 Explain and analyze both quantitatively and qualitatively, using pictures, graphs, charts, or equations how a change in one variable results in a change in another variable in functional relationships. 8.P.9 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. 8.P.10 Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns. Patterns describe, extend, and create a variety of patterns Relations & Functions use tables and graphs to represent relations and functions find solutions for relations with two variables determine whether a graph represents a function find functional values write rules and equations analyze how change in one variable affects the other describe, compare, and analyze different representations represent real-world situations Graphing Linear Functions solve problems using graphs Slope calculating slope positive/negative Intercepts graph using intercepts Graphing Inequalities introduce concept boundary domain function functional notation linear equation patterns (numeric, geometric, triangular numbers, Pascal s triangle) range relation slope-intercept form solution vertical line test x-intercept y-intercept 8-1, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8, 8-9 10-1, 10-2, 10-3, 10-4, 10-5, 10-6 5. Revised Summer 2008
6. Term 2: Factors & Fractions/Exploring Number Patterns MA Frameworks Learning Standards 8.N.4 - Represent numbers in scientific Application of: base notation, and use them in calculations and Prime Factorization common multiples 4-1, 4-2, 4-4, 4-5, 4-6, 4-7, 4-8, 4- problem situations Greatest Common Factor composite number 9, 6-9 (GCF) divisible 8.N.5 - Apply number theory concepts, Equivalent Fractions exponent including prime factorization and relatively factorization Simplifying Fractions prime numbers, to the solution of problems factors Comparing & Ordering 6-1, 6-2, 6-3, 6-4, 6-7, 6-8, 6-9 monomials Least Common Multiple multiples 7.N.3 - Represent numbers in scientific (LCM) negative exponents notation (positive powers of ten only) and use Multiplying and Dividing powers that notation in problem situations Monomials prime number Negative Exponents product/quotient of powers 7.N.1/8.N.1 - Compare, order, estimate, and Scientific Notation (positive translate among integers, fractions and mixed - and negative) numbers (i.e., rational numbers), decimals, and percents Revised Summer 2008
Term 2: Rationals MA Frameworks 7.N.7/8.N.10 - Estimate and compute with fractions (simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1) 7.N.8/8.N.11 - Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. 7.N.9/8.N.12- Select and use appropriate operations addition, subtraction, multiplication, division, and positive integer exponents to solve problems with rational numbers (including negatives) Computation estimate sums, differences, products and quotients add, subtract, multiply, divide add and subtract with like/unlike denominators write fractions as terminating or repeating decimals Applications to Solving Equations solve equations that involve more than one operation solve verbal problems by writing and solving equations solve with the variable on each side Applications to Solving Inequalities bar notation compatible numbers cross-cancelling empty set/null set equivalent Inverse property of multiplication mixed number multiplicative inverse rational numbers reciprocal repeating decimal terminating decimal 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7 6-1, 6-2, 6-3, 6-4, 6-5, 6-7 7-1, 7-2, 7-3, 7-5, 7-6, 7-7 6-5, 7-1, 7-2, 7-3, 7-4, 7-8, 7-9, 7-10 7. Revised Summer 2008
Term 3: Proportions & Percent MA Frameworks 7.N.1/8.N.1 - Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents 8.N.3 - Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change 7.N.7/8.N.10 - Estimate and compute with fractions (simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1) 7.N.8/8.N.11 - Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. 8. Ratios, rates (review) write ratios as fractions in simplest form determine unit rates Percents Finding Percent greater than 100 less than 1 Percent Proportion use to write fractions as percents solve problems using percents Solving Proportions Fractions, Decimals, Percents Percent of Change Simple Interest Scale Drawings base compatible numbers cross-product estimate interest percentage principal unit rate 9-1, 9-2, 9-4, 9-5, 9-7, 9-8, 9-9, 9-10 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-8, 8-9 Revised Summer 2008
Term 3: Exploring Real Numbers MA Frameworks 8.N.2 - Define, compare, order, and apply frequently used irrational numbers, such as 2 and π 8.N.9 - Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems 8.G.4 - Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems Square Roots find and use squares and square roots solve equations by finding square roots incorporate into order of operations Real Number System identify and explain the numbers in the real number system Pythagorean Theorem explain use to find the length of the side of a right triangle and to solve problems use to solve problems hypotenuse irrational number legs perfect square radical sign real numbers Venn diagram 13-1, 13-2, 13-3, 13-4 9-1, 9-2, 9-3, 9-4, 9-5 9. Revised Summer 2008
10. Term 3: Statistics MA Frameworks Learning Standards 8.D.1 - Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling. 8.D.2 - Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-andleaf plots, box-and-whisker plots, histograms, tables, and charts. Differentiate between continuous and discrete data and ways to represent them. 7.D.1 - Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts. 7.D.2/8.D.3 - Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. Gathering data identify and choose best methods for data sampling Data gather and record using frequency table (above) display using a variety of representations o stem-and-leaf o circle graph o box-and-whisker o histogram o scatter plot o Venn diagram interpret Measures of Central Tendency range mean, median, mode apply these concepts to comparisons of data sets back-to-back stem-andleaf plot comparative graph factorials frequency table leaves outcomes outliers quartiles (upper/lower) statistics stems 10-1, 10-2, 10-3, 10-4, 6-6, 11-2 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 4-8, 12-1 Revised Summer 2008
Term 4: Geometry MA Frameworks Learning Standards 8.G.1 - Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons. 7.G.2/8.G.2 - Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. 7.G.3/8.G.3 - Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. 8.G.5 - Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures. 8.G.6 - Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations. 8.G.7 - Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces. 8.G.8 - Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings. 8.M.4 - Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement. Polygons identify and classify according to properties, number of sides, measurements of interior angles symmetry determine missing angle measurements draw using geometric tolls and current technology draw conclusions using given characteristics Congruence and Similarity define and identify examples apply to classifications of polygons and solutions to problems incorporate ratios and proportions Angles identify classify measure use geometric tools and understanding of angle relationships to determine missing angle measurement Transformations rotation reflection translation identify, describe and draw 3-D Figures identify, describe and compare represent using 2-D drawings angles acute, adjacent, alternate exterior/interior, complementary, corresponding, equiangular, obtuse, right, straight, supplementary, vertical polygons parallelogram, quadrilateral, rectangle, rhombus, square, triangle, trapezoid triangle side classification equilateral, isosceles, scalene relationships degree, edge, face, intersect, line, line segment, net, parallel, perpendicular, point, protractor, ray, skew lines, vertex, vertices measurements congruent, corresponding parts, dilation, indirect measurement, scale drawing, similar tessellation transversal 11-1, 11-2, 11-3, 11-3, 11-4, 11-5, 11-6, 11-7, 11-8, 11-9 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7, 11. Revised Summer 2008
12. Term 4: Geometry/Measurement MA Frameworks Learning Standards 8.M.2 - Given the formulas, convert from one system of measurement to another. Use technology as appropriate. 8.M.3 Demonstrate an understanding of the concepts, apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. ------------------------------------ 8.M.1 - Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. Meanings of area, perimeter, surface area, and volume. Area parallelograms trapezoids circles Surface Area rectangular prisms circular cylinders spheres altitude base circumference diameter height lateral surface pi prism radius slant height solid 12-, 12-2, 12-5, 12-6, 12-7, 12-8, 3-5, 7-4, 7-8, 1-8 11-1, 11-2, 11-3, 11-5, 11-6, 1-8 8.M.5 - Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density. Volume rectangular prisms circular cylinders spheres Revised Summer 2008
Term 4: Probability MA Frameworks 8.D.4 - Use tree diagrams, tables, organized lists, basic combinations ( fundamental counting principle ), and area models to compute probabilities for simple compound events1 Combinations Odds Independent and Dependent Events find probability compound events model situations make predictions combinations compound events dependent events experimental probability factorial independent events outcomes mutually exclusive/inclusive permutations theoretical probability 10-5, 10-6, 10-7, 10-9, 10-10 12-1, 12-3, 12-5, 12-6 Fundamental Counting Principle use to count outcomes use to make predictions and draw conclusions 13. Revised Summer 2008