There is some overlap among these topics, so I recommend reading the whole page. Ultimately, what are the sources of errors and of misunderstanding? What kinds of biases and erroneous preconceptions do we have? Two of my favorite historic discoveries are Einstein's discovery of relativity and Cantor's discoveries of some of the most basic rules of infinities.
When I first started teaching, I used to display lists of keywords that students could use to solve word problems. I thought this was the best idea ever. Give students something to look for when reading word problems to know when to add, subtract, multiply or divide.
Or so I thought. Cognitively Guided Instruction affiliate. I learned that students should be taught how to understand the context of a word problem not to look for keywords. This revolutionized my thinking about how I was teaching word problems. I highly recommend the book because of the videos.
It was so interesting to watch how children were solving problems and to see what was going on in their heads. You can read all about how I teach math word problems and pick up a freebie of the word problems I use in my classroom in a previous blog post. A quick google search landed me on these definitions for addition and subtraction: The total amount of two whole numbers combined.
Removing objects from a collection.
Those are the most basic definitions I could find. Keep them in mind as we explore some addition and subtraction problems. How many kids are on the playground?
Some more kids came on the playground. How many kids came on the playground? How many kids were on the playground at the beginning? All of the above problems are join problems, which means that the operation is adding, although the unknown is in different places in each problem.
Even second graders solve these type of problems, but with more difficult number combinations. When I set up students to understand the context of a problem. We act out the problem.
I emphasize that students are looking for the action of a problem and an unknown.
Students can use any strategy to find the unknown. When students can identify the action of the problem which is the operation and the unknown what they are solving for they are set for success.
How many kids are left on the playground? Some kids went home. How many kids went home? Like the Join problems, these separate problems are best learned through identifying the action and placement of the unknown.
Number lines are one of the best tools I have found for teaching word problems. Students can physically act out the math on a large number line or draw their own open number lines for larger numbers. How many could be boys and how many could be girls?I recently mentioned that I like Fill-Agree by Kadon.I managed to solve a tiny subpuzzle, and enjoyed it a lot.
The above shows the complete set of all six ways to put two dots on an L tetromino. Free math problem solver answers your algebra homework questions with step-by-step explanations.
several web pages intended for students; this seems to be the most popular one. FONTS FINALLY REPAIRED November Browser adjustments: This web page uses sub scripts, super scripts, and unicode rutadeltambor.com latter may display incorrectly on your computer if you are using an old browser and/or an old operating system.
Using the Proportion Method to Solve Percent Problems There are a variety of ways to solve percent problems, many of which can be VERY confusing. Primary Grade Challenge Math by Edward Zaccaro A very good book on problem solving with very varied word problems and strategies on how to solve problems.
Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. The free math problem solver below is a sophisticated tool that will solve any math problems you enter quickly and then show you the answer.
I recommend that you use it only to check your own work because occasionally, it might generate strange results.