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⭐ Connecting Equations and Inequalities to Essential Key Concepts ⭐️
Exploring Equations and Inequalities offers authentic opportunities to revisit the Essential Key Concept of Decimal Operations and Patterns to Algebra:
B2.4 → Represent and solve problems involving adding and subtracting whole numbers and decimal numbers
When students solve equations such as n + 5.3 = 12.8 they are applying their understanding of decimal operations to isolate the variable
B2.7 → Represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths
Solving equations such as 2.5n = 375 allows students to reinforce their multiplication and division skills with decimals
C1.1 → Identify and describe repeating, growing, and shrinking patterns, including linear growing patterns
Students explore how solving equations like 2n + 3 = 11 reflects finding the "nth term" in a growing pattern
C1.2 → Create and translate patterns using algebraic expressions and equations
Students can write pattern rules such as "start at 4, add 5" as algebraic equations (y = 5x + 4), connecting pattern language directly to equation structure
C1.3 → Determine pattern rules and use algebraic representations to solve for unknown values in linear patterns
When students solve 3n - 2 = 10, emphasize that they're finding the input "term" of a pattern, reinforcing that equation-solving mirrors finding pattern rules
Expectation Cluster
Expectation Cluster
C2.1 add monomials with a degree of 1 that involve whole numbers, using tools
C2.2 evaluate algebraic expressions that involve whole numbers and decimal tenths
C2.3 solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions
C2.4 solve inequalities that involve two operations and whole numbers up to 100, and verify and graph the solutions
C3.1 solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves conditional statements and other control structures
C3.2 read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code
Process Expectation Focus: Reasoning and Proving, Problem Solving
Organize your observations of student learning related to the key concepts and skills for this topic:
Explore a menu of possible MathUP lessons, Building Fluency lessons, problems, explorations and games.
During this topic, pay attention to the students' ability to build relationships and communicate effectively.
How do students respond to feedback, questions or prompts from the teacher and their peers?
Do students build on each others’ thinking?
Do students use supportive ‘math talk’ language?
Models and Tools
Models and Tools
Concrete Learning Resources Tools:
algebra tiles
number lines
grid paper
Virtual Learning Resources and Tools:
Online visual practice with balancing equations:
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