Wednesday, June 8, 2011

Data Analysis: TV Survey

TV Survey is an open-ended problem that was designed to introduce students to this real-life application of sampling. Because TV is a part of students' daily life, this scenario is accessible to all students. And, because students often exhibit a keen sense of "fairness," they are sometimes disconcerted by the notion that a small group of people get to decide what all of us get to watch on TV.

TV Survey was also designed to address different Bloom levels so that students have to use higher-order thinking skills to analyze, synthesize and evaluate information about the sampling method.

  • Download the TV Survey open-ended assessment.
See more Mathwire Sampling Activities.

Tuesday, June 7, 2011

Problem Solving: Pattern Blocks

Pattern blocks are a familiar manipulative in most elementary classrooms.  Students learn a lot of geometry from informally interacting with pattern blocks.  These problem-solving activities were specifically designed to target important mathematical concepts using these available manipulatives.

  • In Pattern Block Symmetry students must create a pattern block design to satisy the given conditions involving line symmetry and the number of different pattern block pieces used.
  • Pattern Block Design (Grade 3) requires students to create a design to meet specified criteria.
  • Pattern Block Design (Grade 4) requires students to create a design to meet specified criteria.
  • Hexagon Dragons challenges students to use an input-output table to record dragon growth, then analyze the pattern and write a rule for dragon growth.
  • In Fir Tree, students must use an input-output table to record and analyze data, then write a rule for this growing pattern.
  • Symmetric Snowflake challenges students to use pattern blocks to complete the snowflake design so that it has line symmetry.

Thursday, June 2, 2011

Problem Solving: Fractions 2

Students sometimes find the set model of fractions harder to understand and use.  These problems were designed to help students concretely work with the set model to solve problems.

Let's look at a sample problem:

Mrs. Puglisi’s third graders visited the park nature center to see the tadpoles and 
frogs.  They counted 20 animals in the tank. 

•  3/4 of the animals had already changed to frogs.  
•  The rest  were still tadpoles. 

•  How many frogs were in the tank? 
•  How many tadpoles were in the tank? 
•  Explain how you know your answers are correct.

Concretely Solving the Problem:  

  • Students should begin by counting out 20 manipulative objects they will use to solve the problem.
  • Next, students look at the fraction 3/4.  The denominator tells us that the animals were divided into 4 groups.   NOTE:  It is often helpful to use a piece of paper that is folded into quarters so that students may sort the manipulatives evenly into each of the 4 spaces. 
  • Students deal out the manipulatives as if they were cards, placing one in each of the 4 spaces and repeating until all of the manipulatives have been distributed.  
  • Students check to make sure that each quarter has the same number of animals.
  • Now students look back at the fraction 3/4.  The denominator of 4 told students how many groups.  The numerator of 3 in this case tells students how many of the groups had already changed to frogs.  
  • Students count the total number of frogs in 3 groups.
  • The other group are still tadpoles.  Students count how many animals are still tadpoles.
  • Finally, students may use words, pictures and numbers to record their thinking and explain how they knew their answer was correct.
Extension:  After students have mastered this concrete approach to solving fraction problems using the set model, they may move to a paper-and-pencil semi-concrete solution method.
  • The student draws a square on his paper. 
  • He checks the denominator of the fraction to see how many groups are needed.  The student divides the square into that many identical parts.
  • The student then makes dots or tally marks in each section, as above, dividing the total number of objects evenly among the groups.
  • The student checks the numerator of the fraction to see how many groups he must label for his answer.

  • NOTE:  The beauty of this method is that students may easily use this approach in standardized testing situations.  It's completely portable!
  • Students may also simply draw four circles to represent the 4 groups and proceed as above.
Practice Problems:
  • Tadpoles and Frogs requires students to use fractions to figure out how many tadpoles and frogs there were in the tank.
  • Animal Shelter requires students to use fractions to figure out how many cats and dogs were available for adoption at the animal shelter.
  • Ask students to write original problems, peer solve and edit, then add to your classroom collection for future use.  

Wednesday, June 1, 2011

Problem Solving: Fractions

Problem solving activities help students develop conceptual understanding of fractions as they use appropriate fraction models to think about and solve the different tasks.  These Mathwire open-ended assessments were designed to measure students' conceptual understanding of fractions.

Pattern Block Fraction Design requires students to fill a shape with pattern blocks to create a design that meets certain requirements.   Students must also write a fraction that describes the part of the total design represented by each different color pattern block.

Fraction Game simulates a Fraction War game but students must draw a representation of each fraction and explain who won, based on the drawings.  This assessment was designed for students in an Everyday Math program.  Students may draw any representation that helps them decide which fraction is larger and explain their thinking.

Mrs. Meatball challenges students to solve pizza fraction problems pictorially.  The problems are listed on one page, but students should use lots of room to draw pictures, label and explain how they solved each problem pictorially.  NOTE:   This task was originally designed for a teacher in-service class where participants were not allowed to use any previous fraction knowledge to solve the problems.  They were instructed to use only words, pictures and numbers to solve the problems and explain their thinking.  They were not allowed to use any fraction algorithms, etc.