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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 Operational Sense:
B2.1 → Use the properties of operations to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation
Manipulating and solving equations (e.g., n + 27 = 83 or 5 x n = 45) invites students to flexibly apply inverse relationships and properties to reason about the unknown
B2.2 → Recall and demonstrate multiplication facts from 0 x 0 to 12 x 12, and related division facts
When solving m x 6 = 48 or 72 ÷ n = 8, students draw on their recall of multiplication and related division facts to verify their solution
B2.3 → Use mental math strategies to mutiply whole numbers by 0.1 and 0.01, estimate sums and differences of decimal numbers up to hundredths
Estimating whether an inequality like n + 43 > 90 is plausible encourages students to use mental strategies to judge approximate sums and differences first
B2.4 → Represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers up to hundredths
Phrasing a one-step equation or inequality as a word problem (e.g., "Add 35 to a number to get 68") gives students an opportunity to model it using tools or algorithms and reinforces addition/subtraction fluency while solving
Expectation Cluster
Expectation Cluster
C2.1 translate among words, algebraic expressions, and visual representations that describe equivalent relationships
C2.2 evaluate algebraic expressions that involve whole numbers
C2.3 solve equations that involve whole numbers up to 100 in various contexts, and verify solutions
C2.4 solve inequalities that involve one operation and whole numbers up to 50, and verify and graph the solutions
C3.1 solve problems and create computational representations of mathematical situations by writing and executing 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
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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