Creating Effective Math Problems

 What Makes a Good Math Problem?

This week in class we continued to talk about creating math problems and what characteristics contribute to an effective problem. Some of these characteristics we discussed include:

• The problem is relevant to the students
• There are multiple approaches and methods to solving the problem
• Students can use various manipulatives
• Wide base where everyone can join in
• The problem uses soft language 
• The problem creates discussion
• Students have the option to work together and collaborate
• There is a "high ceiling", which means that there is the potential to increase difficulty and challenge students

Wrapping up Joel's Cat Food Problem

We wrapped Joel's Cat Food problem this week with a Math Congress. In large groups, we were asked to discuss the different approaches we used to solve Joel's Cat Food problem. A few students were assigned leader roles where they explained how their group solved the problem and made sure that every student in the group understood the approach. After our group discussed three different approaches to solving the problem, we went on a Gallery Walk where we got to see how other groups solved the problem. Here are some pictures of the different approaches that students took. Our group discussed how some of the other approaches were more visually geared and how our approaches could seem difficult to understand for some students. One aspect of the solutions that all of us determined to be important was that the information given was shown. Knowing that Bob's store sells 12 cans for $15 and Maria's store sells 20 cans for $23 was shown on almost every piece of chart paper. Even though this information was provided on the slideshow, most students found it helpful to re-write this information on the chart paper.

Proportional Thinking

We continued the lesson by discussing the concept of proportional thinking and how we think about proportions on a daily basis. Proportional Thinking is the ability to compare quantities multiplicatively and ties into our previous lessons on Ratios and Fractions. Some of the ways we think proportionately can be as obvious as baking or as subtle as thinking about how much gas you need to get from Point A to Point B. Fractions and Ratios is not a foreign concept and plays an important role within life, so it is extremely important that students learn about proportions and how to compare them.

Integers, Gizmos, and CLIPS

We wrapped up the class this week by discussing integers. One of the biggest problems with integers is trying to apply "rules" that students have learned to a problem where the rule does not apply. There are many different ways to develop an understanding of integer size and operations and creating rules can limit a students understanding of how integers work. Gizmos is a website we discussed briefly discussed in class that can help students understand integers. Gizmos are interactive math and science simulations that help students understand concepts that they struggle with. There are several Gizmos that are aimed towards Integers that allow students to develop their own understanding as opposed to a definition created through rules. The term "integers" may be foreign to students, but the actual concept is more understood than a student might think. The Critical Learning Paths Supports website, or CLIPS, is an educational website that provides students with videos and activities to help understand math. One of the areas it focuses on is integers and how integers are embedded in daily tasks. Outside temperature will usually determine how someone dresses. When students are told this, they begin to understand how integers can be thought of as a whole numbers. This website allows students to explore the concept of integers and see how integers are present in their daily routine.