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Common Core: Math
Subject: The Number System
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 In Topic B, students learn that to get the decimal expansion of a number (8.NS.A.1), they must develop a deeper understanding of the long division algorithm learned in Grades 6 and 7 (6.NS.B.2, 7.NS....

 In Topic A, students learn the notation related to roots (8.EE.A.2). The definition for irrational numbers relies on students’ understanding of rational numbers, that is, students know that rational...

 In Topic D, students think logically about multiplicative arithmetic. Students apply odd and even number properties and divisibility rules to find factors and multiples. They extend this...

 In Grades 4 and 5, students used concrete models, pictorial representations, and properties to divide whole numbers (4.NBT.6, 5.NBT.6). They became efficient in applying the standard algorithm for...

 Students develop the rules for multiplying and dividing signed numbers in Topic B. They use the properties of operations and their previous understanding of multiplication as repeated addition to...

 In Topic C, students problemsolve with rational numbers and draw upon their work from Grade 6 with expressions and equations (6.EE.A.2, 6.EE.A.3, 6.EE.A.4, 6.EE.B.5, 6.EE.B.6, 6.EE.B.7). They...

 In Topic C, students extend their understanding of the ordering of rational numbers in one dimension (on a number line) to the twodimensional space of the coordinate plane. They construct the plane...

 In Topic B, students apply their understanding of a rational number’s position on the number line (6.NS.C.6c) to order rational numbers. Students understand that when using a conventional horizontal...

 Prior to division of decimals, students will revisit all decimal operations in Topic B. Students have had extensive experience of decimal operations to the hundredths and thousandths (5.NBT.7),...

 Topic A focuses on the development of the number line in the opposite direction (to the left or below zero). Students use positive integers to locate negative integers, understanding that a number...

 In Topic A, students return to the number line to model the addition and subtraction of integers (7.NS.A.1). They use the number line and the Integer Game to demonstrate that an integer added to its...

 In Topic A, students extend their previous understanding of multiplication and division to divide fractions by fractions. They construct division stories and solve word problems involving division...

 Grade 8 Module 7: Introduction to Irrational Numbers Using Geometry Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented...

 Grade 6 Module 3: Rational Numbers Students are familiar with the number line and determining the location of positive fractions, decimals, and whole numbers from previous grades. Students extend the...

 Grade 7 Module 2: Rational Numbers In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their...

 Grade 6 Module 2: Arithmetic Operations Including Division of Fractions In Module 1, students used their existing understanding of multiplication and division as they began their study of ratios and...

 Updated Modules and Curricular Resources The tables below reflect Mathematics and English Language Arts curricular materials and resources that have been updated. As additional materials are updated...