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?
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?
Unit_7_EE_B_3_4_Problems_with_Expressions_Equations_Final.docx