Posted by David Wetzel
Often there are times in class when students finish their work or test early. Instead of students twiddling their thumbs physically or mentally, give them a challenging math problem to solve. Problem solving in math promotes critical thinking and math reasoning skills, as students develop solutions to complex mathematical situations.
The Problem
A strategy game which takes advantage of the movements of a specific chess piece - the Knight.
Knights can only move 2 spaces forward and then 1 space to the right or left or 1 space forward and then 2 spaces right or left.
The Challenge
How can a knight in the lower left hand corner of a 5×5 grid visit each square exactly once?
The knight may not revisit a square.
The Procedures
Students can select anywhere to start on the 5 x 5 grid.
Place a 1 in the starting square.
Then place a 2 in the next square and so forth as the strategy game continues
One excellent characteristic of this game is that there are multitude of solutions. Here is one solution:
Extensions
Use different size grids, such as 8 x 8 or 6 x 6.
Additional Math Problem Solving Resources
12 Tips for Solving Word Problems
Math and Problem Solving Skills
Math Teaching Strategies that Challenge Students
Comments:
Filed Under: Math
Posted by David Wetzel
Writing in Math
Writing in math is an excellent way to determine if students’ understand or do not understand the math they are learning about.
Allowing students to explain how they solved a math problem, how they developed a formula to solve a problem, or how they applied a math concept requires critical thinking.
Students must use the minds as they formulate a logical explanation of how they solved a math problem. Because there is always the lingering idea regarding did a student solve a math problem by rote memorization of facts or does the student truly understand the math concept.
When students write how they solved the problem using sentences or a short story, their true understanding and misconceptions become readily apparent. This is why writing in math is a useful strategy for assessing understanding of math concepts.
Checklist
Using this checklist as overall guidance will help students grasp the fundamentals of how writing in math is different than other subjects.
- Clearly restate the problem.
- State the answer in a complete sentence which stands on its own.
- Clearly state the assumptions which underlie the formulas.
- Provide a paragraph which explains how the problem will be solved.
- Clearly label diagrams, tables, graphs, or other visual representations.
Writing Prompts
Often the best way to assess students’ prior knowledge and experiences with math is to provide a situation in which they must explain a math concept or math situation. The following are a few examples of writing prompts that can be used to stimulate student thinking:
- Tips I would give a friend to solve this problem are____________, ____________, and ____________.
- Where else could you use this type of problem solving?
- What other strategies could you use to solve this problem?
- The most important part of solving a problem is____________.
- You know several ways to____________(solve an equation, add fractions, etc.) Which method is your favorite? Why?
- Write instructions for a (insert grade level here) grader to follow when (adding fractions, finding percentages, calculating averages, etc.)
- Give two examples of situations in which you have used, seen or can find the concept of ____________. OUTSIDE of this classroom.
- Write a definition in your own words of a ____________.
- Compare and contrast the terms ____________.
Resources
Writing in Math
Math Problem Solving Stories and Case Studies
Comments:
Filed Under: Math
Posted by David Wetzel
Hundreds Chart
There are many ways to use a hundred chart to help students develop a better understanding of math concepts, along with making connections within and between concepts.
When students see patterns or are able to connect math concepts in different and challenging settings, they truly understand and not just memorized math facts.
In addition to developing a better understanding of math concepts, students develop long term strategies for problem solving.
Five Ways to Use a Hundred Chart
I have come up with five ways to use a hundreds chart:
- Addition and Subtraction - Use the hundred chart as a number line to do addition and subtraction. Let the students challenge each other or the class to solve number line problems. One example is to add or subtract the fives first by counting up or down and then counting left or right.
- Multiplication - Look for counting-by multiplication patterns. Colored disks or other small manipulatives work well for marking numbers. Mark the numbers you hit when you count by four. What pattern do they make? Make the counting-by six pattern, or mark the sevens, etc. You may want to print several charts so you can color in the patterns and compare them. Some questions to ask include:
- Fractions, Percent, Decimals - The hundred chart can be used to convert between fractions, decimals, and percents. “Percent” means “out of 100.” So 30% means “30 out of 100″—which is how much of the whole chart? Some questions to ask include:
- Factors & Multiples - The first player marks any number on the hundred board. His/her opponent marks a factor or multiple of that number. Players alternate, each time marking a factor or multiple of the last number played. The player who marks the last number, leaving his opponent with no move, wins the game.
- Race to 100 - Take turns rolling one or two dice and moving that many spaces on the hundreds chart. If you correctly predict your landing place before you move (without counting squares!), then you can go one extra space as a bonus. The first person to reach or pass 100 wins the game.
Other Ways to Use a Hundred Chart?
Ideas or recommendations for additional ways to use a hundred chart to help students develop a better understanding of math, along with developing problem solving skills?
Comments:
Filed Under: Math
