How do you learn your multiplication facts? What makes them stick? or float away? Here are my suggestions:
- Understand what multiplication is
- Represent it lots of different ways
- Find patterns
- Practice till you know the facts
UNDERSTAND WHAT MULTIPLICATION IS
Children who do not really understand the concept they are memorizing will not be likely to retain it for long. **
Chants and songs. Take important facts about multiplication and make up songs and chants to repeat. Example:
Is sweeping the nation
It’s the fastest way yet
To add equal sets
Start with real world examples. Multiplication can be very helpful in everyday life. ** Look for examples of equal groups or sets and create experiences around these. Don’t try to “teach’ multiplication yet. Use these as unforgettable experiences that you can refer to later. Examples:
Celebrate. Help children plan a party. Get them to decide: How many children will be there? What do we want all of them to have? One drink? One napkin? One small plate? Three cookies? Two balloons? Five stickers? Help them make a record of how many things that need to be bought, gathered or made.
Buy and sell. Make or package little products to sell to each other or other people. Use real or fake money. Keep records of how many products are sold and how much money is made.
REPRESENT IT LOTS OF DIFFERENT WAYS
2D Blocks. Make sets/groups of identical shapes. Ex: Put 3 equilateral triangles together to make a larger triangle (or 4 squares together to make a larger square). Make several. Add up all the small triangles or squares. Write as a multiplication sentence.
3D Blocks. Create cubes other sold shapes with blocks. Disassemble and count all the blocks. Put them back together. Write multiplication sentences to represent height, length and depth; e.g., 4 x 2 x 3 = 24.
Graph paper. Use 1” graph paper. Give children beans to place on paper to make rectangles and squares. Say or write how many columns and how many rows.
3 x 4 = 15
Give children any size graph paper to cut into squares and rectangles and color or decorate. Glue on contrasting paper and write the math symbols below.
Read. Read stories that involve multiplication. Ex: The Doorbell Rang by Pat Hutchins, which is actually about fair shares/division, but can be used to represent multiplication also.
Write. Create your own stories that involve multiplication.
Act out. Act out original and textbook examples of word problems involving multiplication.
Draw. Draw pictures to illustrate written and symbolic problems involving multiplication.
Place value. Roll a die. Represent that number on a place value chart. Roll the die and again and multiply times the first number. Create the new number on the chart.
Tables. Make several copies of the multiplication tables. On one, color all the numbers that are multiples of 2. On another table, color all the multiples of five. On others color in tens, threes, squares, etc. Look for patterns in the 5’s, 10’s and 9’s time tables. Find numbers that are the same but in different tables and color them; e.g., “24” is in the 2’s, 3’s, 4’s, 6’s, 8’s and 12’s. Look for other patterns.
PRACTICE TILL YOU KNOW THE FACTS
Flash cards. When you are getting close to memorizing all the tables, use flash cards to test yourself and a partner. If you get a fact right, leave it out of the deck. When you have conquered the deck, wait a day and try all the flashcards again. *
Chant or rap. Make a rhythm and chant one of the tables. Easiest are usually: 2’s, 5’s, 10’s, squares. Tape record and playback. Also do while jumping on a trampoline or skipping rope.
Tables. On a multiplication table, color in all the multiplication facts you know. Each week color in more of the table to show the facts you know.
Post. Put (just) the hardest facts for you to remember in a place where you’ll see them everyday. Every time you see them, say them aloud and concentrate on remembering them. (7 x 8 = 56 in the bathroom?)** You may fool yourself that you know your facts if you do not focus on the hardest ones.
Snake game. Draw a long “snake” onto the inside of a manila folder. Divide into many segments. Roll two dice. Multiply the numbers and move a marker that many number of segments. The first one to the end wins.
Function Machine. Cut a hole in a manila folder and put it on a desk to partially cover a child who is the “machine.” Other children will take turns giving the machine a small number of dried beans or paper clips. The machine will multiply by a secret number (e.g., “2”) and will give that number of beans or paper clips back to the child. The goal is to guess the secret multiplier the machine is using.
Self test. Set a timer for 10 minutes and write down as many facts as you can (or use a worksheet from the Internet or your teacher. Afterward, concentrate on the ones you missed. *
Play against the calculator. Compete with a friend. One of you will use a calculator and the other no props to do a worksheet. See who can finish first. Then change roles and repeat.
Interleave. Mix in problems that call for addition, subtraction and other math functions when you practice. This technique has been shown to be much more effective than concentrating on “blocked practice” with just one function (i.e., multiplication) alone. *
Take a test with written problems. Begin by working on the hardest problem but stop if you feel you are getting nowhere and switch to an easier one. This will give the subconscious brain time to work on the hard problem. When you come back to it, it should be easier to solve. *
Teach others. Let your child teach you or someone else about multiplication or how to play one of the games or do one of the activities.**
*Ideas inspired by “Learning How to Learn,” a Coursera course on the Internet from the University of California at San Diego, taught by Barbara Oakley and Terrence Sejnowskii. **Other ideas in the course that I had already been using.