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5-A-1-1

Page history last edited by Brenda Butz 6 years, 2 months ago

5.A.1.1 Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems.

In a Nutshell

In objective 5.A.1.1, students will be able to describe patterns when given either a table or a rule. This will be applied to real-world applications where they will make predictions and generalizations based on the given information. In fourth grade, students are familiar with one step operational rules and now we will extend that to two step operational rules.

Student Actions	Teacher Actions
Develop the Ability to Make Conjectures, Model, and Generalize by using repeated reasoning to understand algorithms and create generalizations when creating and discussing patterns. Develop the Ability to Make Conjectures, Model, and Generalize by modeling problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions. Develop a positive mathematical disposition by representing and analyze patterns and functions, using words, tables, and graphs. Develop a Deep and Flexible Conceptual Understanding by interpreting and summarizing information from charts and graphs, providing appropriate detail, e.g., describe patterns Develop Strategies for Problem Solving by expressing mathematical relationships and patterns of change using invented and standard algorithms and equations. Develop the Ability to Communicate Mathematically by constructing arguments using concrete representations such as manipulatives, pictures, and drawings. They explain calculations based upon models and properties of operations and rules that generate patterns.	Pose purposeful questions to assess and advance students’ reasoning in justifying the patterns of change. Use and connect mathematical representations to translate student thinking into numeric expressions. Implement tasks that promote reasoning and problem solving which allow varied entry points through questioning that lead them to making their algebraic predictions and generalizations.
Key Understandings	Misconceptions
Use a table to describe patterns of change. Use rules with one or two operations to predict and generalize about real-world and mathematical problems. Use rules with one or two operations to describe patterns of change.	Solve problems from left to right no matter what the operations are. Think that a variable can only stand for one particular number. Think examining one set of input-output values is enough to describe a pattern or determine a rule. Think the only way to describe a pattern is using the change between outputs rather than the change from an input to its corresponding output. Think they cannot describe a pattern of change when input values are not consecutive. Think rules describing patterns of change involve only addition and subtraction.