Fifth Grade

Algebra

Standard 5-3: The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts.

The indicators for this standard are grouped by the following major concepts:

• Patterns, Relationships, and Functions
• Representations, Properties, and Proportional Reasoning
• Change in Various Contexts

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follows.

Patterns, Relationships, and Functions

Indicators

5-3.2 Analyze patterns and functions with words, tables, and graphs.

 Fourth grade students focused on analyzing numeric, nonnumeric, and repeating patterns involving all operations and decimal patterns through hundredths. Fifth grade students are analyzing patterns and functions with words, tables, and graphs. Students should recognize the connections between these three representations which will lay the foundation for the understanding of functions in middle school. When students analyze functions in fifth grade they should look for patterns within the function. For example: Teachers could use an input/output table, function machine, etc. This is the first time that students are required to use function rules to make generalizations.

Teacher Note: This is the first time students are exposed to the word “function”.

Representations, Properties, and Proportional Reasoning

Indicators

5-3.1 Represent numeric, algebraic, and geometric patterns in words, symbols, algebraic expressions, and algebraic equations.

5-3.3 Match tables, graphs, expressions, equations, and verbal descriptions of the same problem situation.

5-3.4 Identify applications of commutative, associative, and distributive properties with whole numbers.

Fourth grade students used variables to represent an unknown quantity and to write a mathematical expression and equations in symbolic form. They had experience analyzing numeric, nonnumeric, and repeating patterns. Fifth grade students for the first time will represent numeric, algebraic, and geometric patterns using words, symbols, algebraic expressions and algebraic equations. The focus for new learning is on algebraic and geometric patterns. Geometric patterns could include triangular numbers and square numbers. Algebraic patterns include patterns with variables as well as numbers.

Fifth grade students should be able to make associations of tables, graphs, expression, equations, and verbal descriptions of the same problem situation. For example: Teachers could represent several problem situations using tables, graphs, expressions, and equations and cut them into “pieces”. Students could match the tables, graphs, expressions, and equations that represented the same problem situation. Students should be able to verbally explain the matched pieces.

Students as far back as first grade were exposed to the concept of commutativity when working with basic facts for addition and subtraction. In fifth grade, students will identify applications of commutative, associative, and distributive properties with whole numbers. For example: Given 3+4 = 7 and 4+3 = 7 which property does this represent?

Change in Various Contexts

Indicators

5-3.5 Analyze situations that show change over time.

Fourth grade students illustrated situations that show change over time as increasing, decreasing, or varying. Students in fifth grade are expected to analyze situations that show change over time. In other words, they should examine situations that show increasing, decreasing, or varying change over time and describe the relationship between time and the change. Students should be provided with multiple opportunities to analyze real world situations and describe the change that occurs.

Teacher Note: Great connections can be made here with science.