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MATHEMATICS ACHIEVEMENT ACADEMY: PROBLEM SOLVING AND DISCOURSE, GRADE 3

Day 1: Problem Solving

Academy Celebrations

Share a student success story based on a Mathematics Achievement Academy activity,

strategy, or tool.

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Welcome!

• Intended outcomes

• Learning intentions and success criteria

Resources and Materials

Texas Gatewayhttp://www.texasgateway.org/

• Mathematics TEKS: Supporting Information• Vertical Alignment Charts

Norms

1

1 12

2 2

3

3 3

Participation Discourse Mathematics

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Participation

Discourse Mathematics

Norms

Academic Vocabulary

Heuristic

Problem-Solving Model: • Analyzing given information• Formulating a plan• Determining a solution• Justifying the solution • Evaluating the problem-solving process and

the reasonableness of the solutionMathematics TEKS 3(1)(B)

Academy Pre-Assessment

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Problem Solving

Problem Solving in Everyday Life

Problem Solving in Mathematics

Problem Solving

What is problem solving?

Proficient Problem Solvers

What actions are completed by proficient problem solvers?

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Students who can both develop and carry out a plan to solve a mathematical problem are exhibiting knowledge that is much deeper and more useful than simply carrying out a computation. Unless students can solve problems, the facts, the concepts, and procedures they know are of little use.

NCTM, 2000, p. 182

Proficient Problem Solvers

What is Problem Solving?

3(1)(B) The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

What is a heuristic?

What is Problem Solving?

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Kamika’s Party

• What are heuristics for problem solving?

• What are heuristics for solving this problem?

What is Problem Solving?

Kamika’s Party

What actions of a proficient problem solver do you see reflected in each of these work samples?

What is Problem Solving?

Connecting to aProblem-Solving Model

3(1)(B) The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

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Connecting to aProblem-Solving Model

Students are expected to use this process in a grade-appropriate manner when solving problems that can be considered difficult relative to mathematic maturity.

TEA, 2018

Connecting to aProblem-Solving Model

Rotating Trios

0

1

2

0 2

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Analyzing Given Information

What does it mean to analyze given information?

How might a proficient problem solver analyze given information?

Formulating a Plan or Strategy

What does it mean to formulate a plan or strategy?

How might a proficient problem solver formulate a plan or strategy?

Determining the Solution

What does it mean to determine a solution?

How might a proficient problem solver determine a solution?

How might proficient problem solvers determine if a solution is reasonable?

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Justifying the Solution and Evaluating the Problem-Solving Process

What does it mean to justify a solution and evaluate a problem-solving process?

How might a proficient problem solver justify a solution and evaluate a problem-solving process?

Connecting to the Problem-Solving Model

Break

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Justifying Versus Explaining

Justifying Versus Explaining

Justifying Explaining

Why? What?

Justifying Versus Explaining

Card C

I know that of a whole is less than of the same whole

because the numerators are the same. The pieces are

smaller for since the denominator is larger than the

denominator for . A larger denominator results in smaller

partitions.

2

4

2

62

4

2

6

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Card E Card F

To multiply 56 x 9, I solved a simpler problem of 60 x 9, which is 540. Since I had 4 extra groups of 9, I needed to subtract 36 from my original product, which gave me 504.

To subtract 743-528, I first added two to each number. Then I subtracted the new numbers, 745-530. This helped me because I didn’t have to regroup to solve the new problem.

Justifying Versus Explaining

Applying the Problem-Solving Model to Grade 3 Mathematics Content

How might a proficient grade 3 problem solver solve the problem using the problem-solving model as a heuristic?

What additional ways might a proficient grade 3 problem solver solve the problem?

What justification has been provided? What would you add?

Applying the Problem-Solving Model to Grade 3 Mathematics Content

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Where do you see evidence of a problem-solving model?

What evidence is not visible? Why might some components not be visible?

Applying the Problem-Solving Model to Grade 3 Mathematics Content

How might teachers model the use of metacognitive questions to support students’ growth in problem-solving proficiency?

Applying the Problem-Solving Model to Grade 3 Mathematics Content

Applying the Problem-Solving Model to Other Mathematics Content

What common characteristics do you notice?

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Exercise Versus Problem

An exercise asks a student to practice a familiar skill.

A problem involves the application of previously learned mathematical skills, concepts, and/or procedures to a situation where a solution process is not immediately apparent.

Exercise Versus Problem

Online Professional Learning

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Online Professional Learning

Exit Ticket: Success Criteria