The Importance of “Number Sense”

The Importance of “Number Sense”

September 10, 2015
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Teaching problem solving strategies is as important as teaching computation. I like to call problem solving, creative thinking, as I believe that give the process a more positive spin. Kids are less intimidated by the word, creative thinking, than they are a problem solving as that implies that there is a “problem”. Students need to learn to interpret what they are reading and draw out information. This can be difficult for some students. I have found that students’ frustration with working on “story problems” has been where to start and what information do you need. Each month I am tacking a different problem solving strategy this month it is working backwards.

Working Backwards: Problem Solving Strategies


Working backwards is sometimes the best strategy and one of the most difficult for students to understand. I was one of those that didn’t understand this strategy because rarely did I read all the information. I saw numbers, key words and started putting things together but not always correctly. Also being dyslexic it was hard enough reading the information let alone interpreting it and then working backwards and apply inverse operations.

forward backwards



When introducing the different types of problem solving strategies; looking for patterns, make a list, draw a picture, guess and check, and working backwards, working backwards can sometimes be a fun one to start first. Giving the students a trick about reading through all the directions is unintimidating and proves a point in an amusing way.

Do you remember the problem where you ask students to read all the directions before starting and then the last question says don’t do the work just sign your name at the top? These worksheets are a great way to get students to read all the directions take in all the information and then work from there.

problem solving working backwards worksheet
problem solving working backwards worksheet



After doing these worksheets apply working backwards to math. Our first goal in any problem is to read the whole problem. Is there an answer provided? Does the question have key words like equal to, amount left is, leaving ___? Once you have established that there is an answer to the problem we need to start working backwards which also means using the inverse operation.

In mathematics we are also developing the idea of inverse operation, using the opposite operation than the one given.

This is a great math way to show how that works. Can you solve this problem?

problem solving working backwards





Students see the operation given, but it is the reverse operation that will give them the correct answer in the shape. Have students create their own.

problem solving working backwards


Here’s story problem students can try.

problem solving working backwards mango exercise


Don’t tell them what strategy to use, let them figure that out and discuss the different options.



One night the King couldn't sleep, so he went down into the Royal kitchen, where he found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes.

Later that same night, the Queen was hungry and couldn't sleep. She, too, found the mangoes and took 1/5 of what the King had left.

Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes.

Even later, his brother, the second Prince, ate 1/3 of what was then left.

Finally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants.

How many mangoes were originally in the bowl?



Try out these lesson and let us know what you think. MANGO Math Crates provide great games and activities that make students enjoy and understand math. We adhere to NCTM and Common State Standards.

problem solving working backwards



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