Applying Standards Based Constructivism:
A Two-Step Guide for Motivating Students
Student Made Word Problems

Popular Name: Student-Made Word Problems
Grade Level: 3rd Grade
Discipline: Mathematics
Standards: Students will understand mathematics and become mathematically confident
Learning Objectives:
Students will be able to:
  • Represent multiplication problems as arrays through the creation of labeled drawings
  • Solve multiplication problems using their array drawings as tools and as a way to explain their thinking
  • Create challenging, real-world, multiplication problems
EXPLORATORY PHASE:
  • Students explore what makes a good math puzzle and write up math puzzles they create or puzzles they obtained from friends and family.
  • Students use the Problem Solving Strategy Method to solve student math puzzles.
DISCOVERY PHASE:
Performance Task
  • Students create multiplication word problems for their classmates to solve.
  • Students solve student-made multiplication math problems using the problem solving strategy method. 

Student-Made Word Problems
Popular Name: Student-Made Word Problems
Grade Level: 3rd Grade
Discipline: Mathematics
Standards and Performance Indicators Context
 
MST Standard 3
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, applying mathematics in real-world settings, and solving problems through the integrated study of numbers systems, geometry, algebra, data analysis, probability, and trigonometry.  Students will:
  • Use pattern and relationships to analyze mathematical situations.
  • Justify their answers and solutions processes.
  • Add, subtract, multiply, and divide whole numbers.
  • Know single digit addition, subtraction, multiplication, and division facts.
  • Use multiple representations (simulations, manipulative materials, pictures, and diagrams) as tools to explain the operation of everyday procedures.
Core Curriculum Outline Connection
Multiply three-digit numbers by two-digit numbers.
  • Multiplication by multiples of 10.
  • Use diagrams, charts, and tables to help understand problem information.
Learning Objectives (which will become the dimensions of the assessment’s rubric.)
  • Students will be able to represent multiplication problems as arrays through the creation of labeled drawings.
  • Students will be able to solve multiplication problems using their array drawings as tools and as a way of explaining their thinking.
  • Students will be able to create challenging, real-world, multiplication problems.
EXPLORATORY PHASE
(estimated time: day one, 15 minutes; day two, 15 minutes)
  • The teacher poses a simple math puzzle.
  • In groups of two, students discuss a way to represent the problem in a drawing and to solve the problem.
  • The groups report out what they have developed.
  • This process is repeated two more times.
  • The groups then brainstorm the characteristics of a good math puzzle.  These are reported out and recorded on the board.
  • The students are given the homework assignment of writing up a “new” math puzzle. The students are told they may seek help from others, including family members.
  • The following day several of the students’ homework math puzzles are selected at random and discussed and solved using the problem-solving strategy method: (1) Make a plan, for example, a drawing; (2) solve; (3) look back.
DISCOVERY PHASE
(estimated time: one to two 60-minute classes)

Performance Task (including planned interventions and audience beyond the teacher)
  • Students will create multiplication word problems for their classmates to solve.  (The students are giving each other their problems, so this fulfills the requirements regarding audience.)
  • Students will solve the student-made multiplication problems using the problem-solving strategy method.
Task Specifications for Developing the Student-Generated Product/Process
Students will create four multiplication word problems.

Assessment of Performance Task
Dimensions of Student-Created Multiplication Problems
 Criteria for a score of
4
 Criteria for a score of
3
 Criteria for a score of
2
 Criteria for a score of
1
Degree of Difficulty of the Problem All need to think. The solutions to the all of the student-made problems require all students to think.
 Almost all need to think. The solutions to almost all of the student-made problems require all students to think.
 Some need to think. The solutions to the some of the problems require most students to think.
 Few need to think. The solutions to most of the problems don’t require much thinking. 
Within All Students’ Ability
 All can get the answer. All problems provide an opportunity for all students to get the answer.
 Some can get the answer. Only some of the problems provide an opportunity for all students to get the answer.
 Some can get the answer. The solution to some of the problems provides an opportunity for some students to get the answer.
 Only a few can get the answer. The solutions to most of the problems provide only a few students an opportunity to get the answer.
Based on Real-World Situations
 All the problems are based on real-world situations.
 Most of the problems are based on real-world situations.
 Some of the problems are based on real-world situations.
 Few of the problems are based on real-world situations.
Student’s Personal Touch
 All of the problems are clever and/or unique.
 Most of the problems are clever and/or unique.
 Some of the problems are clever and/or unique.
 Few of the problems are clever and/or unique.
Evidence of Picture
 There is a picture for every problem. All the pictures accurately show the problem.
 There is a picture for most of the problems. The pictures accurately show most of the problems.
 There is a picture for some of the problems. The pictures accurately show some of the problems.
There is a picture for only a few of the problems. Only a few of the pictures accurately show the problems.
Evidence of a Solution: The Picture
 All the multiplication is based on the pictures showing the problems.
 Most of the multiplication is based on the pictures showing the problems.
 Some of the multiplication is based on the pictures showing the problems.
Little of the multiplication is based on the pictures showing the problems.
Evidence of a Solution: The Multiplication
 All of the multiplication results in accurate solutions to the word problems.
 Most of the multiplication results in accurate solutions to the word problems.
 Some of the multiplication results in accurate solutions to the word problems.
 Only a little of the multiplication results in accurate solutions to the word problems.
Evidence of Looking Back
 Changes in pictures and in the multiplication shows that the student looked back at the solution and reworked the solution every time it is called for.
 Changes in pictures and in the multiplication shows that the student looked back at the solution and reworked the solution almost every time it is called for.
 Changes in pictures and in the multiplication shows that the student looked back at the solution and reworked the solution when it is called for.
 A change in pictures and in the multiplication shows that the student didn’t look back at the solution and/or didn’t rework the solution when it was called for.

Suggestions for the Teacher
Working in Groups versus Working Individually
  • Some students may find the performance task intimidating. This could be overcome by having the students work in pairs. If this option is used, a journal entry exercise should be added to check on individual understanding.
The Problem-Solving Strategy Method
  • There will probably be a need for spontaneous interventions regarding this method.
Selection of Appropriate Operational Method
  • This lesson doesn’t focus on the selection of the appropriate operational method. An expansion of this lesson that mixes problems that use a variety of mathematical operations may be called for.
Exemplars
  • A selection of various kinds of multiplication word problems may need to be provided to illustrate the dimensions of the rubric.