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Teaching Basic Math Strategies: Solving, Number Sense, Estimation and Mental Math

By Trent Lorcher

You don't need to be Isaac Newton to understand these basic mathematical concepts. Students who understand the four basic strategies for solving math problems will excel in the classroom and on standardized tests.

Strategies for Solving Word Problems

The proliferation of standardized tests as a critical component of math assessment has led to an increase in the importance of word problems. Because word problems require real world application of mathematical computations, they are the preferred method for assessing student achievement. Of all math teaching strategies, this one may be the most important. Use these tips to facilitate student mastery of word problems:

  • Teach math vocabulary. Standardized tests/word problems are primarily reading tests with subject specific vocabulary. It, therefore, behooves the teacher of math to emphasize frequently used math terms: sum, difference, equals, equation, for example.
  • Teach students to write word problems. Students who learn math in isolation have difficulty applying it outside the classroom. As you teach standard math concepts, create meaningful context. Teach students to find quantifiable situations from life and across the curriculum. Teach them to create word problems based on these situations.


  1. There are six periods in a day. Instruct students to write a math word problem figuring out when the day is half over.
  2. In the short story "The Devil and Tom Walker," Tom Walker charges 4% interest per month on his loans. Instruct students to create a word problem that requires figuring out the yearly interest rate.
  3. The local team is losing 57-49. Instruct students to create a word problem that requires figuring the number of 3-point field goals the team would need to take the lead.

Number Sense

Math Genius 

The valedictorian at my high school had a perfect grade point average but couldn't figure out how to wash a dog without flooding the upstairs, how to mail a package without getting it returned, or how to organize a simple shopping trip to get dinner. She had no common sense. The math wizard equivalent exists. He or she may be able to solve complex equations, yet sometimes comes up with answers that are so far off, it demonstrates a clear lack of number sense.

Without number sense, students are unable to judge whether their answer is reasonable. Teaching math strategies, therefore, must include teaching number sense:

  • Teach numbers in context.
  • Visualize quantities.
  • Recognize relationships
  • Quantify findings in newspapers and textbooks.


  1. 16 ounces of butter would be too much for a slice of toast.
  2. An average person is about six feet tall.
  3. 1 trillion dollars is $100 bills stacked seven feet high over an entire football field.
  4. A baseball field is bigger than a tennis court.


In our haste to teach students problem solving skills and mathematical computations, we neglect one of the more important math concepts, how to estimate. Estimation is more than having a student round up or round down. Estimation is a real life skill that students fail to develop because they are focused on 100% accuracy--necessary for sending a man to the moon or calculating the correct angle for making sure the new office building on Main and 5th doesn't collapse, but unnecessary when figuring out approximate times or tabulating the approximate cost of groceries.

Try this mini-lesson to help students develop this critical skill:

  1. Flash a math problem on the board or projector screen.
  2. Force students to write the answer without any written computations.
  3. Create a reasonable range of acceptable answers.


Mental Math

student thinking 

Sometimes we get so caught up in teaching math, we forget that students have their own strategies. Children find their own ways to solve problems that sometimes differ from the way we teach them.

Teaching Tips:

  1. When going over tests, quizzes or homework, ask individual students how they came up with the correct answer.
  2. Remind students that some strategies are better than others and that a strategy that works for one student may not work for another.
  3. This strategy can be applied across the curriculum.