STANDARD 4.3: Mathematics

Mathematics

Mission: Through mathematics, students communicate, make connections, reason, and represent the world quantitatively in order to pose and solve problems.

Standard 4.3 Patterns and Algebra
All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

Big Idea Algebra provides language through which we communicate the patterns in mathematics.
4.3 A. Patterns
Descriptive Statement: Algebra provides the language through which we communicate the patterns in mathematics. From the earliest age, students should be encouraged to investigate the patterns that they find in numbers, shapes, and expressions, and by doing so, to make mathematical discoveries. They should have opportunities to analyze, extend, and create a variety of patterns and to use pattern-based thinking to understand and represent mathematical and other real-world phenomena.
Essential Questions	Enduring Understandings
- How can change be best represented mathematically? (4.5C1; 4.5F1; 4.5F2; 4.5F3; 4.5F4) - How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? (4.5C1)	- The symbolic language of algebra is used to communicate and generalize the patterns in mathematics. - Algebraic representation can be used to generalize patterns and relationships.
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Recognize, describe, extend, and create patterns. · Descriptions using words and number sentences/expressions · Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11, . . . or 800, 400, 200, . . .)
4.3 B. Functions and Relationships
Descriptive Statement: The function concept is one of the most fundamental unifying ideas of modern mathematics. Student begin their study of functions in the primary grades, as they observe and study patterns. As students grow and their ability to abstract matures, students form rules, display information in a table or chart, and write equations which express the relationships they have observed. In high school, they use the more formal language of algebra to describe these relationships.
Essential Questions	Enduring Understandings
- How are patterns of change related to the behavior of functions? (4.5F1; 4.5F2; 4.5F3; 4.5F4)	- Patterns and relationships can be represented graphically, numerically, symbolically, or verbally. (4.5E1)
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Use concrete and pictorial models to explore the basic concept of a function. · Input/output tables, T-charts
4.3 C. Modeling
Descriptive Statement: The function concept is one of the most fundamental unifying ideas of modern mathematics. Student begin their study of functions in the primary grades, as they observe and study patterns. As students grow and their ability to abstract matures, students form rules, display information in a table or chart, and write equations which express the relationships they have observed. In high school, they use the more formal language of algebra to describe these relationships.
Essential Questions	Enduring Understandings
- How are mathematical models used to describe physical relationships? (4.5E2) - How are physical models used to clarify mathematical relationships? (4.5E3)	- Mathematical models can be used to describe and quantify physical relationships. (4.5E2) - Physical models can be used to clarify mathematical relationships. (4.5E3)
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Recognize and describe change in quantities. · Graphs representing change over time (e.g., temperature, height)
2. Construct and solve simple open sentences involving addition or subtraction (e.g., 3 + 6 = __, n = 15 – 3, 3 + __ = 3, 16 – c = 7).	Sample Assessment Items: • MC: Kamala bought a box of crayons for 29¢. She also bought a coloring book for 65¢. Which number sentence shows how much money Kamala spent on the crayons and coloring book? a. 65¢ - 29¢ = ___ b. ___ + 29¢ = 65¢ * c. 29¢ + 65¢ = ___ d. 65¢ - ___ = 29¢ • MC: What does the p equal in 3 + p = 15 ? a. 3 b. 5 * c. 12 d. 18
4.3 D. Procedures
Descriptive Statement: Techniques for manipulating algebraic expressions - procedures - remain important, especially for students who may continue their study of mathematics in a calculus program. Utilization of algebraic procedures includes understanding and applying properties of numbers and operations, using symbols and variables appropriately, working with expressions, equations, and inequalities, and solving equations and inequalities.
Essential Questions	Enduring Understandings
- What makes an algebraic algorithm both effective and efficient? (4.5D1)	- Algebraic and numeric procedures are interconnected and build on one another to produce a coherent whole. - Reasoning and/or proof can be used to verify or refute conjectures or theorems in algebra. (4.5D1; 4.5D3; 4.5D4; 4.5D5)
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Understand and apply the properties of operations and numbers. · Commutative (e.g., 3 x 7 = 7 x 3) · Identity element for multiplication is 1 (e.g., 1 x 8 = 8) · Any number multiplied by zero is zero	Instructional/Assessment Focus: • While recognizing that 3x7 and 7x3 yield the same answer, grade 3 students would not necessarily be expected to label that as the commutative property.
2. Understand and use the concepts of equals, less than, and greater than to describe relations between numbers. · Symbols ( = , < , > )

Link to Standard 4.3 Grade K-2

Link to Standard 4.3 Grade 4

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