Number Sense and Quantity

Students will analyze number relationships

Solve multi-step real world problems, analyzing the relationships between all four operations. For example, understand division as an unknown-factor problem in order to solve problems. Knowing that 50 x 40 = 2000 helps students determine how many boxes of cupcakes they will need in order to ship 2000 cupcakes in boxes that hold 40 cupcakes each(MGSE3.OA.6, MGSE4.OA.3)

Understand a fraction a/b as a multiple of 1/b(MGSE4.NF.4)

Explain patterns in the placement of decimal points when multiplying or dividing by powers of ten(MGSE5.NBT.2)

Compare fractions and decimals to the thousandths place. For fractions, use strategies other than cross multiplication. For example, locating the fractions on a number line or using benchmark fractions to reason about relative size. For decimals, use place value(MGSE4.NF.2;MGSE5.NBT.3,4)

Students will conceptualize positive and negative numbers (including decimals and fractions).

Explain the meaning of zero(MGSE6.NS.5)

Represent numbers on a number line(MGSE6.NS.5,6)

Explain meanings of real numbers in a real world context(MGSE6.NS.5)

Students will recognize that there are numbers that are not rational, and approximate them with rational numbers

Numbers. Find an estimated decimal expansion of an irrational number locating the approximations on a number line. For example, for ?2, show that ?2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue this pattern in order to obtain better approximations(MGSE8.NS.1,2)

Explain the results of adding and multiplying with rational and irrational numbers(MGSE9- 12.N.RN.3)

Students will apply and extend previous understanding of addition, subtraction, multiplication, and division

Find sums, differences, products, and quotients of multi-digit decimals using strategies based on place value, the properties of operations, and/or relationships between operations(MGSE5.NBT.7; MGSE6.NS.3)

Find sums, differences, products, and quotients of all forms of rational numbers, stressing the conceptual understanding of these operations(MGSE7.NS.1,2)

Interpret and solve contextual problems involving division of fractions by fractions. For example, how many 3/4-cup servings are in 2/3 of a cup of yogurt? (MGSE6.NS.1)

Illustrate and explain calculations using models and line diagrams( MGSE7.NS.1,2)

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using estimation strategies and graphing technology(MGSE7.NS.3, MGSE7.EE.3, MGSE9-12.N.Q.3)