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Mental Math

Mental math is the main form of calculation used by most people and the simplest way of doing many calculations. Research has shown that in daily life at least 75% of all calculations are done mentally by adults. However, unfortunately due to the emphasis on written computation in many classrooms, many children believe that the correct way to calculate a simple subtraction fact such as 200-3 is to do it in the written form.

Through regular experiences with mental math children come to realize that many calculations are in fact easier to perform mentally. In addition, when using mental math children almost always use a method which they understand (unlike with written computation) and are encouraged to think actively about relationships involving the particular numbers they are dealing with.

In order to be effective Mental Math sessions should:

occur on a daily basis (5-10 minutes per day)
encourage ‘having a go’ on the part of all students
emphasize how answers were arrived at rather than only whether they are correct
Promote oral discussion
allow students to see that there are many ways to arrive at a correct answer rather than one correct way
build up a dense web of connections between numbers and number facts
emphasize active understanding and use of place value

Following are some possible activities for K-5 classrooms:

Fill the Hundreds Chart:
On day one display a Hundreds Pocket Chart with only 5-6 pockets filled with the correct numerals. Leave all other pockets blank. Select 3 numerals and 3 students. Ask each student to place his/her numeral in its correct pocket and to explain the strategy they used to help them complete this task. Repeat the above with 3 numbers and 3 students per day until all pockets are filled. Take note of students who use a count by one strategy and those who demonstrate an awareness of the base ten patterns underlying the chart. Select numbers based on your knowledge of individual student’s number sense (e.g. you may select a number immediately before or after a number that is already on the board for one child and a number that is 10 or 11 more than a placed number for another child who you feel has a good understanding of the base ten pattern).

Possible questions to involve other students:
Yesterday we had __ numbers on our number chart and today we added 3 more. How many numbers do we now have on our number chart? How do you know?
If there are __ numbers on our number chart how many more numbers do we need to add to fill our chart? Ask several students to explain the strategy used to solve this problem.
We now have ____ numbers on our number chart. If we continue to add 3 numbers every day how many more days/weeks will it take to fill our number chart? Explain your thinking.

Today’s Number is…
Select a number for the day (e.g. 8) and write it on the board or chart paper. Ask students to suggest calculations for which the number is the answer. Write students' suggestions in 4 columns (addition examples, subtraction, multiplication and division). After 8 or 10 responses, focus in on particular columns or types of responses that you would like more of. For example,"Give me some more addition examples", "Give me some ways which use three numbers", "Give me an example using parentheses" etc.

What's My Number
Select a number between 1 and 100 and write it down without revealing it to your students. Have students take turns to ask questions to which you can only answer ‘yes’ or ‘no’. Record each question and answer on chart paper. For example:

Is it greater than 30? No
Is it an even number? Yes
Is it a multiple of 3? No
Does it have a 4 in the ones place?...

After 3 or 4 questions ask, “What is the smallest number it could still be? What is the largest? Discuss why it is better to ask a question such as "Is it an odd number?" than "Is it 34?" early in the game. To ensure that all students are involved have them use individual laminated 100 charts with dry erase markers to mark off numbers after each question is asked. Keep going until the number has been named correctly. During the game you may also want to keep track of how many questions are asked before the number is named. Next time you play challenge students to guess the number with fewer questions.

'Friendly' number activities
Give a number less than 10. Students must respond with an addition fact that will make the number up to 10. For example, if today's target number is 10 and you say 6 the student must respond with "6 + 4 = 10". Vary the target number e.g. 20, 50, 100, 200, 1000 etc. to suit students' ability level.