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Common Core: ELA
Common Core: Math
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 Download the materials below from the July NTI session, "Innovative Systemic Approaches to Educating ELLs/Bilingual Learners."

 In Topic G, students review material covered throughout the module. Additionally, students discuss the structure of geometry as an axiomatic system.

 Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

 Simultaneous equations and their solutions are the focus of Topic D. Students begin by comparing the constant speed of two individuals to determine which has greater speed (8.EE.C.8c). Students...

 Coordinate Systems

 Objective: Construct a coordinate system on a line.

 Objective: Construct a coordinate system on a plane.

 Student Outcomes Students create systems of equations that have the same solution set as a given system. Students understand that adding a multiple of one equation to another creates a new system of...

 Student Outcomes Students solve systems of linear equations in two variables and systems of a linear and a quadratic equation in two variables. Students understand that the points at which the two...

 Objective: Use coordinate systems to solve real world problems.

 Student Outcomes Students solve linear systems in three variables algebraically.

 Student Outcomes Students determine inverse matrices using linear systems.

 Student Outcomes Students write word problems into systems of linear equations. Students solve systems of linear equations using elimination and substitution methods.

 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...

 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...

 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...

 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...

 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),...

 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...

 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 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...

 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 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...

 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...