Grade: 3

Purpose: To learn, memorize, and understand multiplication tables while using different strategies.

Memorization Methods:

• Understanding– Knowing and understanding what you are trying to memorize before or while memorizing it will help you recall something later.
• Mnemonics- Mnemonics are memory “tricks” or devices used for the purpose of improving memory
• Competition – Competition and rewards provide motivation to learn and remember.
• Repetition – Doing something several times over helps you implant information in your head. The more you repeat something, the less likely you are to forget it.

Note to the teacher: Your students should be slightly familiar with the concept of multiplication before beginning this lesson, but they do not have to have mastered it.  There are activities for many levels of understanding included in the lesson plan.  Feel free to choose those most appropriate for your students.  

Introduction:

Tell the class that they are going to develop special strategies for remembering multiplication tables.  Explain to them the different methods listed above and how they can improve memory.  Explain that these methods can be used beyond multiplication, even beyond math. 
Explain to the class what multiplication is.  Demonstrate the following concepts of multiplication:

It is best if the students are at least beginning to grasp the above concepts before beginning the activities below.

To begin the lesson, distribute a pre-quiz to see how many problems the children can complete in 2 minutes.  Grade the quizzes to see how many they got wrong.  Record both the number answered correctly and the number wrong at the top of the each student’s sheet. 

Activities:

1. Title:  Multiplying M & Ms    
Time: Part A - 15 min.  Part B – 5 min.
Materials:
Several small bags of M & M’s (Note - You may prefer to work with tiles, pennies, or some other object.  Each child should receive about 30-50 items.)
Paper Towels
New Sharpened Pencils
Paper (for Part B)
Instructions:
Part A -
Give each student a bag of M & M’s.  Place a paper towel on each desk.  Have the students get out of their seats and push in their chairs. 
Call out a multiplication problem (for example, “three times five.”).  When you say, “Go!”  have the students get into groups of the first number you called (three).  Then each person in the group is to take out the number of M & M’s that is the same as the second number you called (five).  As a team, they arrange the M & M’s on a nearby towel in rows & columns according to the problem. The first team to provide the correct answer and have the correct M & M display wins, and they get to eat their M & M’s.  If not using an edible item, the teacher should collect the items used by the winning group.  The point of the game is to be the first to run out of M & M’s. Continue with other multiplication problems until one student has no M & M’s left. The student must run out exactly in order to win.  If he or she doesn’t have as many M & M’s as the second number you called, he or she must wait for the next problem. If a child is unable to find a group, he or she may eat one M & M.  No one child should be without a group more than once during the entire game.  Three students may not be in the same group for two subsequent problems. 
Part B -
Have the children return to their seats with their bags of remaining M & M’s.  With their classmates at their desks, have them determine the student with the lowest number of M & M’s remaining.  These students are awarded with a brand new pencil (already sharpened) which they will use in the next step.  With what they have left, the students at the table see how many different ways they can arrange the M&M’s they have left (rows & columns or groups).  The recorder should write down the results for everyone in the group.  Have them do the same after taking one M & M away (by eating it), and again, until no M & M’s are left. The group with the greatest number of accurate and distinct combinations wins. 

2. Title: Buzz!
Time: 10-20 min.

Instructions:
Have the students stand in a circle around the room.  They are to count off, each saying the next integer, beginning with one.  However, when a student comes to a multiple of 3 (the “buzz-number”), he or she must say, “BUZZ!”  If the student does not say “Buzz!” or says “Buzz!” when he or she was not supposed to (s)he is to sit down and watch the rest of the activity.  If you wish, you can have the student return to his/her desk and write down the multiples for the “buzz-number” up to where (s)he made the mistake (or a few further).  For example – If, on the first round, a boy says “12” instead of “buzz,” have him write out the multiples of 3: 3x1=3, 3x2=6, 3x3=9, 3x4=12, 3x5=15, 3x6=18.  If the student finishes this, you may wish to have them fill out a blank multiplication table.  Once you have several out, if you have a helper, you can get another game going.  Each time after a person is “out,” you start back at one and pick a new “buzz-number.”  The winner is the last student standing. 
For the more advanced students, you can have two “buzz-numbers” at once.  For example, for each multiple of three, the student must say “buzz” and for each multiple of four, the student must say “fizz.”  For multiples of both, the student must say “buzz-fizz.”  The sequence would go: “one,” “two,” “buzz,” “fizz,”  “five, “buzz,” “seven,” “fizz,” “buzz,” “ten,” “eleven,” “buzz-fizz,” “thirteen,” etc. 

3. Title:  Tricks
Time: 5-10 min.
Instructions:
Ask the students if they know any tricks for memorizing any of the multiples.  Have them develop memory devices for any of the multiples up to 12.  Write the ideas on the chalkboard, and call on students with raised hands to share ideas.  A student might need to come up to the board to explain his or her idea to the rest of the class.  See how many they can come up with.  They should be able to develop the basic strategies for 0 (0* any number=0) and 1 (1* any number = that number) on their own.  They may also come up with a strategy for 10 (10* any number = that number with a 0 on the end …).  They are likely to find a pattern for 11’s multiplied by a 1-digit number (put the number twice in a row). They may find other patterns, such as those with multiples of 5 (5 * even number ends in 0, 5 * odd number ends in 5) or other numbers. 
Be sure they recognize that if you add the digits of the answer to any nines-multiplication problem, you always get nine.  Show them how they can use their fingers to find the answer to the multiplication tables from 1 – 9.  Hold up your fingers and count off your fingers starting with 1 on the left, stopping at the number by which you want to multiply 9.  Bend that finger down.  The number of fingers to the left is the number in the ten’s digit of the answer; the number of fingers to the right is the number in the one’s digit of the answer.  For example - 9x4 - put down your left pointer finger.  Three fingers are on the left, six fingers are on the right: 36. 
Have each student write down a list of all of the tricks they have developed as a class.

4. Title:  Tripods of Color & Flash
Time: 30 min.
Materials:
Index Cards
Scissors
Colored Markers
Instructions: Have the students work in partners to create flashcards for multiplication tables up to 12 x 12.  Have one student do the 1’s, 3’s, 5’s, 7’s, 9’s, and 11’s and the other the 2’s, 4’s, 6’s, 8’s, 10’s, and 12’s. 
To make the tripod flashcards, cut 3x5 index cards length-wise.  Fold one of the halves into three sections, so that it can fold in & out, like a brochure.  The student is to write the two numbers to be multiplied on the front flaps on the outside, and the answer in the middle on the inside.  They can fold & unfold these flaps, with either number going on top (because 3x4=4x3=12). The three numbers should be grouped together in the child’s memory. These cards can be used later when learning division.
As they make their flash cards, they should use different colored markers: one for even numbers, one for odd numbers, one for the ‘x’ sign.  As they take turns testing each other with the flashcards, ask them if they notice any patterns with the odd/even numbers -- (i.e. even x even  = even, even x odd = even, odd x odd = odd). 

5. Title:  Troublesome Numbers
Time: 5-10 mins.
Instructions: Explain to the students how they can find the answer to a multiplication problem when they get stuck, based on multiplication problems “similar.”  For example, say they cannot remember 4 x 6, but they know that 4 x 5 = 20.  Because 6 is 1 more than 5, they can simply add 4 to 20 to get 4*6.  Or, if they know 8*5 = 40, but cannot remember 8*4.  They can simply subtract 8 from 40, because 4 is 1 less than 5.  Likewise, if they can’t remember 4x9, but they know that 4x4=16 and 4x5=20.  The sum of these two products, 16+20, equals 36, the answer to 4x9.  Another example: 7x9=7x4+7x5.  Have them determine which multiplication facts are most difficult for them to memorize. Each student should write a list of his or her “Personal Problem Numbers”.  Allow them to practice using this strategy to find the answer. 

6. Title: Chalk Relay
Time: 15 mins.
Materials for each team:
          Handout - Chalkboard Relay: Multiplication Problems
          Piece of chalk
          Eraser
Instructions: Divide the class into 2-4 teams (depending on space in the room and chalkboard availability).  Choose one person to be the monitor for each team.  Have each monitor draw a large multiplication table on the chalkboard, filling out only the labels of each row and column (not the actual answer for each box).  You could also have this done ahead of time, if possible.  Or, used the attached blank multiplication table make an enlarged copies to laminate and reuse.  If 0’s and 1’s are too easy, you can have them not draw this portion of the multiplication table.  During this time, have the other group members form a line behind a certain distance from the chalkboard across from their monitor (each group’s line should begin at the same distance from the chalkboard as the others groups’).  Once each group has done this, hand out a sheet (attached) of scrambled multiplication problems to each monitor.  
This is a silent activity.  After you begin the game with, “Go!” nothing should be heard until the game is over.  To start, the first person in line for each group walks up to the chalkboard.  The monitor must point with the chalk to the box corresponding with the first problem on the multiplication sheet and then hand the chalk to the teammate, who then fills in the box with the answer to that multiplication problem and returns the chalk to the monitor.  This continues, as the monitor points to the appropriate box to the other multiplication problems in the order they are listed on the sheet.  If the monitor notices a mistake of a teammate, he or she is to erase the answer and repeat the problem with the next person in line.  If the monitor does not catch a mistake, the teacher should give a signal (a kazoo is fun, but a simple bell or even a knock on the desk would work.  Then the monitor erases the incorrect answer and gives the chalk to the next student to fill in the box with the correct answer. 
When a team has completed the sheet, the monitor sits down.  When the rest of the team notices this and sits down in the line from where they started, they have finished.  The first team to finish wins, if they have followed the rules (including being silent, going in the listed order, and keeping the line the designated distance from the chalkboard) AND their multiplication table is filled out correctly. 

7. Title: Double Die to Multiply
Time: 10 min
Materials:
2 dice for each group
pencil and paper for each student
Instructions: Students take turns rolling two dice and finding the product of the numbers.  They write down the answer and keep a running tally of their own score.  If they get the problem wrong, they must subtract the product from their score.  The student to reach 100 points first wins.  This game can also be played with large dice that go from 1-12 if you have them.  For this, you will want to increase the winning number. 

8. Title:  Working Backwards (Factoring)
Time: 5 mins
Materials:
Pencil for each student
Factorization Forms – 1 set for each team
Instructions: Give the students sheets of numbers that have many factors.  Have them write down as many multiplication combinations they can think of for each number.  For example, all the possible answers for 8 would be: 1x8, 2x4, 4x2, 8x1 (for advanced students, you can use 2x2x2 as well).  No fractions are allowed.  They are allowed to administer different numbers to members to work individually and combine answers. The group with the most correct multiples after 2 minutes wins.  (Time may be adjusted as needed.)

9.     Title: Individual Multiplication Table Race
Time: 5 min
Materials: Blank Multiplication Table & Pencil for each student
Instructions: Have the children fill out blank multiplication tables at their desks.  This can be made into a race.  The student who completes his/her table first gets a sticker.

Conclusion:  Administer a quiz with the same problems as the pre-quiz.  Allow the students to compare their results before the activities to those after the activities.  Discuss with the students which activities they found the most helpful and have them try to articulate why they thought it was the most helpful.  Which did they find was the most fun?  Was the most fun the most helpful?  You can use this quiz several times and have the students plot their progress over the school year. 

ã 2001 by Emilie Sutterlin.  Permission to copy for educational purposes is granted.  Notification of use is requested.  Please contact memory@muelly.ch.