To Be Incorporated Throughout All Other Standards

Standard 1: Mathematical Processes -to be incorporated throughout all other standards-

GLE: Resources: GLE 0706.1.1 Use mathematical language, symbols, and definitions while developing mathematical Online games: represent numbers in equivalent forms reasoning. http://www.mathgoodies.com/puzzles2004/

Mathematical reasoning: http://teachingtoday.glencoe.com/howtoarticles/asking- questions-that-count/four-habits-of-the-mind

GLE 0706.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including Mathematical reasoning: estimation, and reasonableness of the solution. http://mathforum.org/library/drmath/view/58940.html GLE 0706.1.3 Develop independent reasoning to communicate mathematical ideas and derive http://www.purplemath.com/modules/index.htm algorithms and/or formulas. GLE 0706.1.4 Move flexibly between concrete and abstract representations of mathematical ideas in http://learner.org/channel/workshops/algebra/workshop7/lesson order to solve problems, model mathematical ideas, and communicate solution plan.html strategies. GLE 0706.1.5 Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions. GLE 0706.1.6 Read and interpret the language of mathematics and use written/oral communication to Discovering Math: The Nature and Use of Mathematics express mathematical ideas precisely. http://unitedstreaming.com (site requires membership)

GLE 0706.1.7 Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world. GLE 0706.1.8 Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts. 1st Nine Weeks:

Unit 1: Simplifying and Evaluating Expressions Est. time: 2 weeks GLEs Addressed: GLE 0706.2.2 Understand and work with properties of and operations on the system of rational numbers. GLE 0706.3.1 Recognize and generate equivalent forms for simple algebraic expressions. Prerequisite skills and knowledge: order of operations Unit Vocabulary: algebraic expressions, base, coefficient, exponent, order of operations, power, variables SPI Student Indicator Text-book Additional Resources SPI 0706.2.1 Simplify numerical expressions involving rational numbers. 1.3, 1.4 Power of Algebra-The Basic Properties pg. 14-23 (ML) (unitedstreaming.com) (site requires membership) SPI 0706.3.1 Evaluate algebraic expressions involving rational values for coefficients and/or variables. What is it? Rational Numbers http://www.eduplace.com/math/mathsteps/7/a/  0706.3.1 Perform basic operations on algebraic expressions 1.2, 1.4 (including grouping, order of operations, exponents, pg. 9-12, 18-23 (ML) BrainPops: Algebra Properties simplifying and expanding) http://www.brainpop.com/math/numbersandoperations /

Unit 2: Integers Est. time: 4 weeks GLEs Addressed: GLE 0706.2.1 Extend understanding of addition and subtraction, multiplication and division to integers. GLE 0706.2.2 Understand and work with properties of and operations on the system of rational numbers. Prerequisite skills and knowledge: addition, subtraction, multiplication, and division or whole numbers, fractions, and decimals. Unit Vocabulary: inequality, integers, opposite SPI Student Indicator Text-book Additional Resources SPI 0706.2.2 Compare rational numbers using appropriate inequality symbols.  0706.2.1 Understand that the set of rational numbers 6.1 http://www.quia.com/cb/64603.html and includes any number that can be written as a ratio of two pg. 251-254 http://www.quia.com/cb/250454.html (Integer integers in which the denominator is not zero Jeopardy) SPI 0706.2.5 Solve contextual problems that involve operations with integers.  0706.2.2 Develop and analyze algorithms and compute 6.2- 6.5 http://aaamath.com/ (loads of activities) efficiently with integers and rational numbers. pg. 257-269 and 272- 282 http://www.brainpop.com/math/ (Brainpops: Addition and Subtraction of Integers)  0706.2.3 Recognize that rational numbers satisfy the 6.6 commutative and associative laws of addition and pg. 283-287 multiplication and the distributive law.  0706.2.4 Understand that a and –a are additive inverses and 6.2 Integer Card Games: are located the same distance from zero on the number line; pg. 258-263 *red cards are negative, black cards are positive relate distance from zero to absolute value. -Go Fish (opposites and zero pairs)  0706.2.5 Understand that –(-a) =a for any number a. 6.4 -War (+, -, x) pg. 272-275 .  0706.2.6 Use the number line to demonstrate addition and 6.2, 6.4 subtraction of integers. pg. 257, 264-265

Unit 3: Equations and Inequalities Est. time: 2 weeks GLEs Addressed: GLE 0706.3.8 Use a variety of strategies to efficiently solve linear equations and inequalities. Prerequisite skills and knowledge: two-step equations Unit Vocabulary: two-step equations, coefficient, inequalities SPI Student Indicator Text-book Additional Resources SPI 0706.3.6 Solve linear equations with rational coefficients symbolically or 7.2-7.5 graphically. pg. 322-345 SPI 0706.3.8 Solve contextual problems involving two-step linear equations. 7.5 pg. 342-345 SPI 0706.3.9 Solve linear inequalities in one variable with rational coefficients symbolically or graphically.

 0706.3.14 Understand that when solving linear inequalities, 7.6 multiplication or division by a negative reverses the pg. 346-349 inequality symbol. 2nd Nine Weeks:

Unit 4: Functions Est. Time: 4 weeks GLEs Addressed: GLE 0706.1.4 Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies. GLE 0706.3.2 Understand and compare various representations of relations and functions. GLE 0706.3.3 Understand the concept of function as a rule that assigns to a given input one and only one number (the output). GLE 0706.3.4 Use function notation where f(x) represents the output that the function f assigns to the input x. GLE 0706.3.7 Use mathematical models involving linear equations to analyze real-world phenomena. Prerequisite skills and knowledge: two-step equations Unit Vocabulary: function, relation SPI Student Indicator Text-book Additional Resources SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, and words  0706.3.2 Represent and analyze mathematical situations 7.7 National Virtual Library of Manipulatives- Function using algebraic symbols. pg. 350-353 Table: SPI 0706.3.3 Given a table of inputs x and outputs, f(x), identify the function rule http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1. and continue the pattern. html  0706.3.4 Make tables of inputs x and outputs f(x) for a 7.7 variety of rules that include rational numbers (including pg. 350-353 Input/Output Function Game: negative numbers) as inputs. http://pbskids.org/cyberchase/games/functions/ SPI 0706.3.2 Determine whether a relation (represented in different ways) is a Graphing Linear Equations: (various activities) function. http://brainpop.com  0706.3.3 Identify a function from a written description, -teacher created material table, graph, rule, set of ordered pairs, and/or mapping. Definitions and types of algebraic functions/examples: SPI 0706.3.7 Translate between verbal and symbolic representation of real-world http://library.thinkquest.org/2647/algebra/functype.htm phenomena involving linear equations. Write variable expressions and equations representing 7.1 Compare Relations and Functions: textual situations. pg. 317-321 http://www.mathwarehouse.com/algebra/relation/math  0706.3.6 Understand that the graph of a linear function f is 7.7, 7.8 -function.php the set of points on a line representing the ordered pairs pg. 350-359 (x,f(x)). Lesson Plan on Linear Functions and Inequalities:  0706.3.5 Plot points to represent tables of linear function 7.7, 7.8 http://www.learner.org/channel/workshops/algebra/wo values. pg. 350-359 rkshop2/lessonplan.html Unit 5: Ratios Est. time: 5 weeks GLEs Addressed: GLE 0706.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning. GLE 0706.1.5 Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions. GLE 0706.2.3 Develop an understanding of and apply proportionality. GLE 0706.2.4 Use ratios, rates, and percents to solve single- and multi-step problems in various contexts. GLE 0706.3.5 Understand and graph proportional relationships. GLE 0706.3.6 Conceptualize the meanings of slope using various interpretations, representations, and contexts GLE 0706.4.2 Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed. Prerequisite skills and knowledge: simplifying fractions, conversion of percents to decimals to fractions Unit Vocabulary: concentration, mixture, proportion, unit rate, inverse variation, direct variation, slope SPI Student Indicator Text-book Additional Resources SPI 0706.2.6 Express the ratio between two quantities as a percent, and a percent 9.1 Lesson plan for ratios and rates: as a ratio or fraction. pg. 415-418 http://www.deltastate.edu/docs/math/S%20Thompson SPI 0706.2.7 Use ratios and proportions to solve problems. %20LP1.pdf  0706.2.7 Write number sentences to solve contextual 8.4, 9.2 problems involving ratio and percent. pg. 387-391, 420-424 Lesson plan for rates: http://www.deltastate.edu/docs/math/H%20Johnson  0706.2.8 Apply ratios, rates, proportions, and percents (such 9.4, 9.6 – 9.8 %20LP3.pdf as discounts, interest, taxes, tips, distance/rate/time, and pg. 432-435, 446-457 percent increase or decrease) Jeopardy Game: Ratio, Percent, Probability: 8.2  0706.2.10 Solving problems involving unit rates (e.g. miles http://www.quia.com/cb/95600.html per hour, words per minute) pg. 374-377  0706.4.5 Solve problems using ratio quantities: velocity -teacher created Solve Problems using ratio quantities (velocity): (measured in units such as miles per hour), density material http://www.thetech.org/education/downloads/dconline/ (measured in units such as kilograms per liter), pressure physicsRollercoasters.pdf (measured in units such as pounds per square foot), population density (measured in units such as persons per Rags to Riches Game: square mile). http://www.quia.com/rr/97979.html SPI 0706.1.1 Use proportional reasoning to solve mixture/concentration -teacher created problems. material Scale Drawings: SPI 0706.1.4 Use scales to read maps. 8.6 pg. 400-403 http://brainpop.com/artsandmusic/artconcepts/scaledra SPI 0706.3.5 Represent proportional relationships with equations, tables, and -teacher created wing graphs. material Scales and Maps Lesson: http://www.es.mq.edu.au/courses/GEOS264/maps/map ch2/scale.htm Recognize whether information given a table, graph, or formula Interactive Lesson on Blueprints and Scale: SPI 0706.1.3 suggests a directly proportional, linear, inversely proportional, or http://illuminations.nctm.org/lessondetail.aspx? other nonlinear relationship. ID=L652  0706.3.7 Distinguish proportional relationships (y/x=k or -teacher created y=kx) from other relationships including inverse material Direct and Inverse Variation: proportionality (xy=k or y=k/x) http://www.learner.org/channel/workshops/algebra/wo SPI 0706.3.4 Interpret the slope of a line as a unit rate given the graph of a rkshop7/lessonplan.html proportional relationship.  0706.3.8 Understand slope as the ratio of vertical change to 8.3 horizontal change. pg. 378-383 The Slope-Intercept form for a Linear Equation and 8.3  0706.3.9 Identify a function exhibiting a constant rate of The Slope-Intercept Form: Rate of Constant Change pg. 378-383 change as a linear function and identify the slope as a unit (Slope) and Starting Point (Y-Intercept) rate. http://www.unitedstreaming.com  0706.3.11 Relate the features of a linear equation to a table 8.3 and/or graph of the equation. pg. 378-383 Slope Hangman:  0706.3.12 Use linear equations to solve problems and -teacher created http://www.quia.com/hm/163121.html interpret the meaning of slope, m, and the y-intercept, b, in material f(x)=mx + b in terms of the context. Slope of a straight line:  0706.3.13 Given a graph that exhibits the intersection of a -teacher created http://www.purplemath.com/modules/slope.htm line and the y-axis, write a linear function in slope intercept material form: y=mx + b 3rd Nine Weeks:

Unit 6: Similar Triangles and Scale Factor Est. time: 5 weeks GLEs Addressed: GLE 0706.4.1 Understand the application of proportionality with similar triangles, GLE 0706.4.3 Understand and use scale factor to describe the relationships between length, area, and volume. GLE 0706.4.4 Understand and use ratios, derived quantities, and indirect measurements. Prerequisite skills and knowledge: ratios and proportions Unit Vocabulary: scale factor and similar triangles SPI Student Indicator Text-book Additional Resources SPI 0706.4.1 Solve contextual problems involving similar triangles. Rags to Riches: Geometry Basics Games  0706.4.2 Use similar triangles and proportionality to find 10.5, 10.6 http://www.quia.com/rr/237636.html the lengths of unknown line segments in a triangle. pg. 502-509  0706.4.4 Compare angles, sides lengths, perimeters, and 10.5, 10.6 Similar Triangles: www.brainpop.com areas of similar shapes. pg. 502-509  0706.4.1 Solve problems involving indirect measurement 10.6 pg. 506-509 Lesson Plan on Similar Triangles: such as finding the height of a building by comparing its http://www.learningpt.org/pdfs/mscLessonPlans/roush shadow with the height and shadow of a known object. 2.pdf SPI 0706.4.2 Use SSS, SAS, and AA to determine if two triangles are similar. -teacher created material Congruence and Similarity Lesson Plans: SPI 0706.4.3 Apply scale factor to solve problems involving area and volume. http://www.deltastate.edu/docs/math/R%20McCarty  0706.4.3 Understand that if the scale factor describes how 10.5 %20LP1.pdf corresponding lengths in two similar objects are related, pg. 502-505 then the square of the scale factor describes how Scale Factor Problems: corresponding areas are related, and the cube of the scale -teacher made http://www.watertown.k12.ma.us/wms/math/math_hel factor describes how corresponding volumes are related. materials p/gradeseven/stretching/scale%20factor.htm

Interactive Scale Factor Activity: http://illuminations.nctm.org/ActivityDetail.aspx? ID=176 Unit 7: Statistics and Probability Est. time: 4 weeks GLEs Addressed: GLE 0706.5.1 Collect, organize, and analyze both single- and two-variable data. GLE 0706.5.2 Select, create, and use appropriate graphical representations of data. GLE 0706.5.3 Formulate questions and design studies to collect data about a characteristic shared by two populations, or different characteristics within one population. GLE 0706.5.4 Use descriptive statistics to summarize and compare data. GLE 0706.5.5 Understand and apply basic concepts of probability. Prerequisite skills and knowledge: reading graphs Unit Vocabulary: histogram, box-and-whisker plot, stem-and-leaf plot, upper quartile, lower quartile, interquartile range SPI Student Indicator Text-book Additional Resources SPI 0706.5.1 Interpret and employ various graphs and charts to represent data. Probability Activities:  0706.5.2 Interpret and solve problems using information 3.2-3.5 http://nlvm.usu.edu/en/nav/topic_t_5.html presented in various visual forms. pg. 108-119, 122-134 SPI 0706.5.2 Select suitable graph types (such as bar graphs, histograms, line graphs, circle graphs, box-and-whisker plots, and stem-and-leaf plots) and use them to create accurate representations of given data.  0706.5.1 Create and interpret box-and-whisker plots and 3.3, 3.4 stem-and-leaf plots. pg. 116-119, 123-127  0706.5.6 Apply percentages to make and interpret 3.5, 9.5 histograms and circle graphs. pg. 130-134, 440-445 Select, create, and use appropriate graphical 3.6 representations of data. pg. 135-139 SPI 0706.5.3 Calculate and interpret the mean, median, upper quartile, lower quartile, and interquartile range of a set of data. Use descriptive statistics to summarize and compare data. 3.4 pg. 101-105 SPI 0706.5.4 Use theoretical probability to make predictions. Probability Battleship: Understand and apply basic concepts of probabiltity. 13.1 http://www.quia.com/ba/51817.html pg. 634-638  0706.5.7 Use a tree diagram or organized list to determine 13.2 Lesson Plan for tree Diagrams: all possible outcomes of a simple probability experiment. pg. 639-642 http://www.shodor.org/interactivate/lessons/TreeDiagr Use the counting principle to find the number of outcomes. 13.3 amsProb/ pg. 643-647  0706.5.4 Use proportional reasoning to make predictions 13.1 about results of experiments and simulations. pg. 634-638 GLE 0706.5.3 (see above) Collect, organize, and analyze both single- and two- -teacher made variable data. materials  0706.5.3 Predict and compare the characteristics of two -teacher made populations based on the analysis of sample data. materials  0706.5.5 Evaluate the design of an experiment. -teacher made materials 4th 9 Weeks:

Unit 8: Square Roots, Cube Roots, and Exponents Est. time: 3 weeks GLEs Addressed: GLE 0706.2.5 Understand and work with squares, cubes, square roots, and cube roots. GLE 0706.2.6 Introduce the concept of negative exponents. GLE 0706.2.7 Understand and use scientific notation. Prerequisite skills and knowledge: exponents Unit Vocabulary: cube root, square root, scientific notation, rules of rounding, degree of accuracy, significant digits SPI Student Indicator Text-book Additional Resources SPI 0706.2.3 Determine the approximate location of square/cube roots on a Exponent Game: number line. http://www.mathdork.com/games/asteroidsexp3/asteroi  0706.2.9 Efficiently compare and order rational numbers 11.1 dsexp3.html and roots or perfect squares/cubes; determine their pg. 533-537 approximate number on a number line. Lesson Plan on Exponents:  0706.2.10 Recognize that when a whole number is not a 11.1 http://www.learner.org/channel/workshops/algebra/wo perfect square, then its square root is not rational and cannot pg. 533-537 rkshop6/lessonplan.html be written as a ratio of two integers.  0706.2.11 Estimate square roots/cube roots and use 11.2 calculators to find approximations. pg. 538-544  0706.2.12 Recognize mn = m  n and ( m )2=m. -teacher created material SPI 0706.2.4 Use rational numbers and roots of perfect squares/cubes to solve -teacher created contextual problems. material GLE 0706.2.7 (see above) Scientific Notation: http://www.aaamath.com/dec71i-dec2sci.html  0706.2.13 Use the meaning of negative exponents to 2.5 represent small numbers; translate between scientific and pg. 74-78 Negative Exponents- examples: standard notation. http://www.purplemath.com/modules/exponent2.htm  0706.2.14 Express numbers in scientific notation and 2.5 pg. 74-78 recognize its importance in representing the magnitude of a Scientific Notation: number. http://www.nyu.edu/pages/mathmol/textbook/scinot.ht  0706.2.15 Report results of calculations appropriately in a 2.5 ml given context (i.e. using rules of rounding, degree of pg. 74-78 accuracy, and/or significant digits). GLE 0706.2.6 (see above) -teacher created material