Overview: The overview statement is intended to provide a summary of themes in this unit. This unit builds on understandings of using the four operations with rational numbers (integers, fractions, and decimals) and applies the operations as multi-step strategies to construct and solve problems based on expressions, equations, and inequalities. The unit focuses on using variables to represent quantities in algebraic expressions, equations, and inequalities; and it relies on properties of operations to calculate and estimate with rational numbers in any form. Teacher Notes: The information in this component provides additional insights which will help educators in the planning process for this unit. Students should be well-grounded in knowledge of addition, subtraction, multiplication, and division of rational numbers. Students should have prior knowledge of properties of operations for whole numbers and be able to extend them to rational numbers. Students should have had opportunities to experiment with mental computation and estimation strategies. Enduring Understandings: Enduring understandings go beyond discrete facts or skills. They focus on larger concepts, principles, or processes. They are transferable and apply to new situations within or beyond the subject. At the completion of this unit on the use of properties of operations to generate equivalent expressions, the student will understand that: Algebraic solutions can be compared to arithmetic solutions to identify the sequence of operations used in each approach. Mathematical properties numbers reveal appropriate methods to manipulate values in algebraic expressions, equations, and inequalities. Variables can be used to represent any number from a domain (input value). Tables and graphs are useful for visually documenting relationships between numbers in given expressions, equations, and inequalities. Essential Question(s): A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourages re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations. What is the role of order of operations when simplifying numerical and algebraic expressions, equations, and inequalities?
How do operations on rational numbers serve as a foundation for creating numerical and algebraic expressions, equations, and inequalities? What is the limit on the number of different ways equivalent numerical and algebraic expressions, equations, and inequalities can be written? Can an expression, equation, or inequality be written to represent every real-life and mathematical problem? Content Emphases by Clusters in 7: According to the Partnership for the Assessment of Readiness for College and Careers (PARCC), some clusters require greater emphasis than others. The table below shows PARCC’s relative emphasis for each cluster. Prioritization does not imply neglect or exclusion of material. Clear priorities are intended to ensure that the relative importance of content is properly attended to. Note that the prioritization is in terms of cluster headings. Key: ■ Clusters  Supporting Clusters  Additional Clusters Ratios and Proportional Reasoning ■Analyze proportional relationships and use them to real-world and mathematical problems. The Number System ■ Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Expressions and Equations ■ Use properties of operations to generate equivalent expressions. ■ Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Geometry  Draw, construct, and describe geometrical figures and describe the relationships between them.  Solve real-life and mathematical problems involving angle measure, area surface area, and volume. Statistics and Probability  Use random sampling to draw inferences about a population.  Draw informal comparative inferences about two populations.  Investigate chance processes and develop, use, and evaluate probability models.
Vertical Alignment: Vertical curriculum alignment provides two pieces of information: A description of prior learning that should support the learning of the concepts in this unit A description of how the concepts studied in this unit will support the learning of additional mathematics Key Advances from Previous Grades: In grades K-5, students have been writing numerical equations and simple equations involving one operation with a variable. In 6, they start the systematic study of equations and inequalities, as well as methods to solve them. Grade 6 students also have used equations in two variables to express relationships between two quantities that vary together. In grade 7, students build on earlier work with order of operations, and start to simplify general linear expressions with rational coefficients. Also in grade 7, students must understand the rules for multiplying negative numbers. By grade 7, students begin to realize that integers, and positive and negative fractions and decimals all belong to a single system of rational numbers. They rely more strongly on their ability to use mental computation and estimation to assess the reasonableness of their solutions. Additional Mathematics: Students will use addition, subtraction, multiplication, and division of rational numbers: in grade 8 when expanding their knowledge in rational to irrational numbers in 8 when they include the properties of radicals and integer exponents, with special attention to 0 as an exponent in grade 8 as they understand the connections between proportional relationships, lines, and linear equations in grade 8 as they move towards an understanding of functions in algebra and geometry when they expand into real numbers and beyond Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the overarching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from outside the cluster. Overarching Unit Standards Supporting Standards within the Cluster Instructional Connections outside the Cluster 7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically; apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; N/A 7.EE.A.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.A.2: Understand that rewriting an expression in different forms in a problem