Student Actions

Teacher Actions

• Develop a Deep and Flexible Conceptual Understanding by developing a strategy to solve real world problems involving addition, subtraction, multiplication or division.

• Develop the Ability to Make Conjectures, Model, and Generalize by displaying and communicating solutions to real world math problems involving all four operations using models, words, graphs, tables and concrete objects in a way that others can understand thinking .

• Develop a Productive Mathematical Disposition by looking for ways to apply strategies more efficiently and choosing strategies based on the nature of the question.

• Develop the Ability to Communicate Mathematically by explaining what approach was taken in solving a real world math problem.

• Develop Strategies for Problem Solving by developing and testing more than one strategy to find solutions to addition, subtraction, multiplication, and division problems, and identify when multiple solutions to a real world problem are possible.  EX. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”

• Implement tasks that promote reasoning and problem solving by allowing students to explore real world situations with varying solution strategies.

• Pose purposeful questions that will help lead the students back on track if data or strategy seem to be unconnected or inappropriate to the inquiry.

• Pose purposeful questions about the reasonableness of their result based on the context of the problem and not tied to the operation of the problem or estimation.

• Elicit and use evidence of student thinking by asking students to model or demonstrate their chosen computational strategy.

• Support productive struggle in learning mathematics by providing a plethora of real world contexts for computations that require a variety of representations.

• Facilitate meaningful mathematical discourse by asking students to compare and contrast student solution strategies and evaluate them for understanding and efficiency.

Key Understandings

Misconceptions

• Fluently add, subtract, multiply, and divide single digit numbers.

• Use keywords to problem solve with correct operations.

• Understand inverse relationships between addition/subtraction and multiplication/division.

• Know a variety of strategies to help assess the reasonableness of results.

• Think they can solve multiplication and division problems the same way they would solve addition and subtraction problems.

• Think there is only one way to solve a problem.

• Only use "key words" to indicate which operation to use when solving a story problem.

• Have overspecialized their knowledge of multiplication or division facts and restricted it to.

• See addition and subtraction or multiplication and division as discrete and separate operations.

• Their conception of the operations do not include the fact that they are linked as inverse operations.

• Have overspecialized during the learning process so that they recognizes some multiplication and/or division situations as multiplication or division and fails to classify others appropriately

• EX. Student recognizes that a problem in which 4 children share 24 grapes is a division situation but states that a problem in which 24 cherries are distributed to children by giving 3 cherries to each child is not

• Know how to fluently use their operations but does not know when to use their operations (other than because they were told to do so, or because the computation was written as a certain operational problem)

• Think that the operation that needs to be performed (+, –, ×, ÷) are defined by the numbers in the problem.