  # Number and Operations

Grade Level: 7 Names of Developers: Mary Beth Feldmann, Barbara Purdon
Leanne Adkins, Leanna Banks, and Kara Pendleton

 Topic Dates Taught Dates Assessed Understand numbers, ways of representing numbers, relationships among numbers, and number systems The student should be able to:• develop number sense for pi as one example of an irrational number. • understand and use ratios and proportions to represent quantitative relationships. • develop an understanding of large numbers (billions) & recognize and appropriately use exponential , scientific, and calculator notation. • compute percentages of numbers and compare, order, estimate, and determine equivalent relationships among fractions, decimals, and percentages. Understand meanings of operations and how they relate to one another The student should be able to:• extend understanding of operations (=, -, +, x, ÷) to include percents and integers. • explain and apply properties such as the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals . • understand the meaning and effects of whole number exponents (squaring) to simplify computations and solve problems. • develop understanding of the meaning and effects of operations with decimals, integers, fractions, and percents (including percents greater than 100% and less than 1%.) Compute fluently and make reasonable estimates The student should be able to:• add, subtract, multiply and divide rational numbers (fractions, decimals, percents, integers) both concretely and symbolically (mental, paper and pencil, calculators) to solve problems. • develop proportional thinking and explain methods such as rates, scaling, and similarity to solve problems involving proportion.

Grade Level: 8 Names of Developers: Mary Beth Feldmann, Barbara Purdon
LeanneAdkins, Leanna Banks, and Kara Pendleton

 Topic Dates Taught Dates Assessed Understand numbers, ways of representing numbers, relationships among numbers, and number systems The student should be able to:• compare and order rational and irrational numbers and find their approximate location on a number line. • represent numbers and operations in a variety of equivalent forms using models, diagrams, and symbols (number lines, 10 by 10 grids, rectangular arrays, number sentences.) • understand and apply how whole numbers, natural numbers, integers, fractions, decimals, percents, and irrational numbers ( square roots and pi) relate to each other (e.g. convert between forms of rational numbers, compare, order.) • develop an understanding of estimation of the size of rational numbers. Understand meanings of operations and how they relate to one another The student should be able to:• determine the inverse relationship between addition and subtraction , multiplication and division, and squaring and taking the square root of a number . • work flexibly with decimals, integers, fractions, and percents (including percents greater than 100% and less than 1%) to solve problems. • use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to show relationships and justify steps in problem solving. Compute fluently and make reasonable estimates The student should be able to:• use percentages and proportions in consumer applications (e.g., simple interest, percentages of increase or decrease, discounts, unit pricing, and sale pricing.) • develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results. • develop and analyze algorithms for computing with fractions , decimals, and integers and develop fluency in their use.
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