Submitted by: Heather Cummans
Endorsed by: Don Descy Mankato State University

Date: May 14, 1997

Grade Level(s): 4, 5

Subject(s):

• Mathematics/Arithmetic

Description:

The purpose of this lesson is to teach students how to work mentally with numbers, as to nurture number sense, and create a foundation and enthusiasm for mathematics. This is a fun and interactive way for students to learn and helps to create a feeling of accomplishment.

Goal(s):

Students will understand some ways in which to compute mathematics problems mentally.

Objectives:

The students will be able to:

1. mentally figure out the answers to problems without the use of paper, pencils or calculators

2. explain how they came up with the answer given

Background Information:

This activity can be used with students of all ages, however, I feel that students at the fourth-fifith grade levels could handle the concept of mental mathematics more readily. The lesson teaches them ways in which to work out math problems in their heads, without the use of any materials.

Concepts:

The students will be able to:

1. think before they start computing

2. utilize their minds instead of manipulating tools

Materials:

Chalkboard and chalk

Procedure:

1. Open the lesson with the following statement: "Students, today we are going to do some mental math, so put away your pencils and get ready to have some fun!"

2. Ask the question: "Does anyone know what mental mathematics is?" Hold a discussion and accept all answers.

3. The teacher will then use four activities to introduce the concept of mental math, which are: Give Me a Date, Raise me a Number, Multiplication Shortcut, and Numbered Square.

4. Give Me a Date is simply asking the students to come up with as many operations possible for a given date. The teacher will ask the students to give him/her any date that they would like and will write it on the board. Underneath each number, the teacher will place a box to record the operations the students generate as a class.

5. Raise Me a Number will begin by the teacher handing out basic playing cards to a group of two students. The cards will include the King, Ace, 1,2,3,4,5,6,7,8, and 9. The teacher will ask several math questions as the students take turns holding up the cards that show the answers to the problems given. (King=0, Ace=1)

6. Multiplication Shortcut is an activity to encourage the use of shortcuts while figuring out math problems mentally. The teacher will select a student to come to the board. The student will wait until the teacher gives the problem to write on the board, and then has 30 seconds to answer the problem.

The questions will start out easy, using the strategy given before the activity. The problems will only involve numbers ending in five, with the number being multiplied by itself (15*15, 25*25, 35*35, 45*45, etc.).

Here is an example of how the shortcut can be used for this problem:

15*15=?

All answers for 15*15, 25*25, 35*35, and others that continue this pattern will automatically end in the number 25.

So, 15*15= _25

To find the digit that comes before the 25, start with the first number in the problem: 15. Increase the tens place by one; that gives you 2. Then take the number 2 and multiply that by the tens place in the second number (1).

2*1=2; 2 will be the number that is placed before the 25.

15*15=225.

This same procedure can be applied to 25*25=? The answer will end in 25. To find the digit that comes before the 25, start with the first number in the problem: 25. Increase the tens place by one; that gives you 3. Then take the number 3 and multiply that by the tens place in the second number (2).

3*2=6; 6 will be the number that is placed before the 25.

25*25=625.

7. Numbered Square is simply drawing a square and writing six numbers on the board. The numbers should be placed on, in, around, and under the square, so that the students will have to explain the numbers asked for.

Example: The teacher says, "In and Above"; the students' response would be to find the numbers that are in the square and above it, and then add, subtract or multiply them (whichever operation is specified before the question is asked). The student would be expected to say the problem correctly.

Example:"5 plus 9 equals 14".

Assessment:

1. The teacher will be listening to the students' responses and monitoring facial expressions and questions carefully, jotting down notes for each student.

2. The teacher will ask the students the following questions:

A. Why do you think that it is important to learn how to do math mentally?

B. How do we use mental math in our everyday lives?

C. Ask for student suggestions on other ways in which we could compute math mentally.

D. Ask if they followed the instructions, and if they understood the concept behind the activities. Useful Internet Resource:
* Squaring Two-Digit Numbers Ending in 5
"http://mathforum.org/library/drmath/view/57994.html