GRADES 7, 8, AND 9 BIG IDEAS

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1 Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for base ten. Introduce proportion. Introduce equivalent ratios and rates. Introductory Introduce exponents and the use of exponents Introduce terms squared and cubed Introduce scientific notation Introducing GCF and LCM Introducing integers including comparing and ordering integers Introduce developing different representations for percent Recalling Recall renaming fractions and decimals Extending Extend the use of fractions Extend the divisibility rules for 3, 4, 6, and 9. Extend factors and multiples to include GCF and LCM Extend representing integers, including the zero property, concretely, pictorially, and symbolically. Introduce irrational numbers and their relationship to the real number system Introduce solution notation for inequations Introduce how to organize information into a matrix and matrix notation. Introduce solution sets for inequalities graphically, symbolically, and graphically Extend the concept of square root to principle square root. Extend the understanding of real numbers to include irrational numbers. 11/11/04 1

2 Table 2: Strand B: BIG IDEAS: MATH: Operations Introduce operations on positive and negative rational numbers Introduce problem solving with proportions Introduce operations on polynomials (add, subtract, scalar multiplication). Introduce operations with proportions using a variety of methods. Introduce adding and subtracting variables concretely, pictorially, and symbolically to solve simple algebraic problems. Introduce addition and subtraction of polynomial expressions concretely and pictorially. Introduce scalar multiplication of polynomial expressions concretely, pictorially, and symbolically. Introductory Introduce all operations of integers, concretely, pictorially, and symbolically Introduce mental math and estimation to sum, difference and multiplication with fractions and fraction sense Introduce order of operations Introduce the variable, operations with variables, and like and unlike terms Introduction of addition, subtraction, and scalar multiplication on matrices Introduce the laws of exponents for integral exponents Introduce operations with positive and negative numbers to all rational numbers. Introduce factoring of algebraic expressions concretely, pictorially, and symbolically. Introduce multiplication of polynomials using area models. Recalling Recall the meaning of positive, negative and zero exponents. Recall the properties of operations with all real numbers Extending Extend mental math and estimation strategies for integers and decimals. Extend the operations with rational numbers include decimal and fractional forms. Extend scientific notation to include operation on numbers in scientific notation. 11/11/04 2

3 Extend decimal operations Extend estimating, determining and solving percent problems Extend percent to involve creating and solving problems that involve the use of percent. Extend all operations with fractions concretely, pictorially, and symbolically. Extend problem solving to include fractions in meaningful contexts. Extend Extend addition and subtraction of polynomial expressions to include symbolic. 11/11/04 3

4 Table 3: Strand C: BIG IDEAS: MATH: PATTERNS Introduce slope Introduce solving simple linear equations algebraically Introduce the interpretation of linear and nonlinear data and their graphs including broken-line and curved graphs. Introduce solving a system of equations using graphs and tables of values. Introduce solving algebraic equations concretely, pictorially, and symbolically. Introduce creating and solving problems involving linear equations. Introductory Introduce the use of variables Introduce multiple ways of representing linear relations Introducing like and unlike terms of operations Introduce the difference between algebraic expressions and algebraic equations. Introduce the graphs of linear equations and their properties. Introducing solving one- and twostep linear equations using concrete materials and diagrams. Recalling Continue patterning, concretely, pictorially, and symbolically using constants, variables, algebraic expressions and equations to make predictions. Extending Extend the use of variables Extend graphing to include finding the point of intersection. Introduce parabolic and other nonlinear equations. Introduce the slope y-intercept equation of the line. Recall the meaning of slope and y intercept. Extend the understanding of linear equations and their graphs to include y-intercepts and slopes and using this information to find slope. Extend solving equations to include inequations. 11/11/04 4

5 Table 4: Strand D: BIG IDEAS: MATH: MEASUREMENT Introduce area of a circle Introduce area of composite figures Introduce volume and surface are of a right prism, cylinder, and composite 3-D figures Introduce Pythagorean theorem, modeling it, and applying it. Introductory Introduce the circumference of a circle. Introduce rate as applied in daily life situations in numerous forms. Introduce the concept of pi. Introduce constructing and analyzing graphs of rates to show how change in one quantity affects a related quantity. Introduce the connection between slope and rate Introduce ratios and proportions in similar triangles Recalling Recall the idea of slope as a comparison and formalize its connection to linear relationship and symbolic notations Extending Extend the concept of rate Extend perimeter and area to include composite figures. Extend volume and surface area to pyramids, cones, and spheres. Extend the concept of slope to include the calculation of slope given two points. Extend the ideas of ratios and proportions to include properties of congruent triangles. 11/11/04 5

6 Table 5: Strand E: BIG IDEAS: MATH: GEOMETRY Introduce transformations on 3-D shapes Introduce angle properties and diagonals of polygons Introductory Introduce transformational geometry and formalize the language. Introduce the use of transformations and applications. Introduce and explore properties of triangles and angles. Recalling Recall the construction of 3-D shapes using map plans and isometric dot paper. Extending Extend the idea of what makes a triangle. Extend the concepts of tessellations. Extend the concept of representing 3-D solids. Extend angles and parallel line relationship Extend isometric and orthogonal drawings to include uniqueness Extend dilatations to analyse all its properties. Introduce the conditions that produce unique triangles and investigate their properties. Introduce the properties of similar and congruent triangles and using them in problem solving situations Introduce mapping notation to represent transformations of geometric figures. 11/11/04 6

7 Table 6: Strand F: BIG IDEAS: MATH: DATA MANAGEMENT Introduce box and whisker plots Introduce the concept of randomness and its applications. Introductory Formalize biased and unbiased sampling Introduce the distinction between biased and unbiased data. Introduce the term measures of central tendency (mean, median, and mode) and how they are affected by fluctuations in data. Introduce terminology range, outliers, gaps and clusters and uses them to draw inferences and make predictions. Introduce inferential statistics Introduce curves of best fit for nonlinear data Recalling Recall and continue data analysis Extending Extend appropriate data display Extend drawing inferences and making predictions based on data Extend the knowledge of the effects of outlier gaps, clusters, etc. Extend mean, median, and mode to include the effect of variation in data. Extend scatter plots to introduce line of best fit Extend understanding of data display to include decisionmaking. Extend line of best fit for nonlinear data 11/11/04 7

8 Table 7: Strand G: BIG IDEAS: MATH: PROBABILITY Introductory Introduce tree diagrams for the outcomes of two independent events. Introduce the area model for the outcomes of two independent events. Recalling Extending Extend simulations to solve problems Extend probability for students to understand that probability can be represented in multiple forms. Extend probability to include single and complimentary events Introduce the prediction of dependent and independent events Extend theoretical probability to include dependent and independent events (with or without replacement) Extend the concepts of tree diagrams. 11/11/04 8

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