## Math Doubles Plus Fun Time

Monday, May 7th, 2012

If you teach math, or want to enrich your children’s understanding of numbers, here is a set of activities that children will enjoy while learning a lot.

You may have heard about Multiple Intelligence Theory. One thing it tells us is that we evolved to have intelligence not only in verbal and mathematical learning, which are the main focuses in our schools, but in a number of different areas. That’s why some of us learn better through music, or nature, or art, or bodily movement.

This activity is a kinesthetic (movement-based) way to teach some important number facts. I’ve found that it increases math fact retention in everyone who plays it. One reason might be because it’s more engaging and fun than paper-and-pencil or verbal learning. Who learns well when they’re bored?

I made this project because I teach using Singapore Math, which is the best way I’ve found to teach math. However, the materials don’t focus on teaching basic facts; these are left to the teacher and/or supplementary programs. So I use lots of different activities and resources for teaching the facts; this is one of them.

Learning Objectives
After playing these games, students will be able to remember their basic addition doubles facts and squares (powers of two).

For this set of activities, you will need:

• Number mat OR sidewalk chalk
• (We’ll go into how to make the number mat in another step.)
• Space

### Step 1 Outdoor Number Mats

If you have access to asphalt, sidewalk chalk, and decent weather, this is a great activity to get your students outdoors and enjoying learning their math facts.

Just draw your chosen number grid according to the layout in the PDF file, and print and cut out the cards. Instructions for playing the games come in step 3.

### Step 2 Indoor Number Mat

This step shows you how to make the Indoor Number Mat. This is a versatile tool to have in your classroom; keep it around for bad weather, and your students may even want to pull it out during recess! You may get some great ideas from them for how to use it.

For this project, you will need:

• Large piece of fabric, Tyvek, or something else convenient (it could be a good way to recycle canvas used for a stage set). I think the minimum size is about 4′ x 5′.
• Fabric paint or acrylic
• Duct tape or ribbon

The first thing I did with my fabric was to fold it in half and see how to split it in twelfths. This was easy given the fold lines in my fabric. If you don’t have this, simply fold twice horizontally, and bring two folds to the middle to make your three. (See diagram.)

Now use your line-making option to “draw” lines along those folds. I used thinnish strips of duct tape for the vertical lines and the remaining fatter strips for the horizontal ones.

Next, paint the numbers according to the layout inside the boxes in the Grids PDF.

I chose to use the full length of my fabric and use the top half for squares, leaving the bottom half for addition doubles. I needed to do this partly because I was in a hurry at first and painted just by squeezing acrylic paint directly onto the fabric, so it bled through to the other side. I had planned to use the other side for something else, but that’s no longer possible. If you are more careful, though, or use fabric paint, you can use one side of a smaller piece for the addition and the other side for multiplication.

If you are using a fabric board, I recommend the children play on it with their shoes off.

### Step 3 Games to Play

There are so many possible games to play with these boards. Here are a few I discovered on the first day I tried them with my students.

Doubles Fun Plus or Times Jump
Note: The idea for the addition doubles jump game comes from Adrian Bruce, an Australian teacher with an awesome website, but all extensions, photos, files, and multiplication-related activities are mine.

1. Children line up.
2. Cards are shuffled. Each child picks a card and tries to solve the problem. If successful, child jumps to the number on the board.
3. Card is returned to the bottom of the pile, and another children gets to try.
4. Play continues until all children have been on the board and have had a chance to solve at least two problems.

If you are working with a small group of children just learning these facts, have them retry problems they missed until they know them automatically. Not over and over again in a row so that it’s boring, but they won’t mind doing another problem and repeating one they missed a few times because they are having too much fun, in my experience.

Doubles Fun Around the World Hopscotch
The idea of this game is to say the equations in order (e.g. “3 x 3 is 9, 4 x 4 is 16, etc.”) while hopping on the successive solutions. Teacher should model how to do this.

I think it’s important in this game that the student says the full equation aloud. This reinforces the equation in their automatic systems. I noticed that directly after the game, my students were using what they had practiced to solve problems.

For young children, once they have practiced with the equations, have them try counting by twos and jumping on the numbers in order.

Discussion Time
This isn’t a game, but an important part of developing the students’ metacognition (higher-level thinking) about these computations. Ask:

• What do you notice?
• How can these facts help us figure out a problem?
• For example, if we know what 7 x 7 is, how can we use that to figure out 7 x 8?
• Do you notice any patterns?
• Where are the doubles the same in addition and multiplication, and where are they different?
• With young children, explore odd and even numbers on the addition mat, and then flip it over and have them identify odd and even numbers on the multiplication mat.

Allow the children to explore the concepts. It will make math a lot more meaningful to them.

This project was originally published on Instructables.com. It is all my original work.

## Fostering Creativity in Math

Friday, February 11th, 2011

We hear plenty of talk about teaching and reinforcing basic skills in math. Yes, these are very important, but computation skills aren’t what lead to breakthroughs and new discoveries; new ways of thinking do, right?

This young woman exemplifies real creativity in mathematical thinking. I find this so inspiring. Investigating mathematical principles through art: what a concept!

## Tips for Times Tables and Dividing

Monday, December 6th, 2010

Teachers in my math workshops like me to share some multiplication and factoring tips I teach my students. These help with number sense as well. I hope they can be useful for you too.

Tips for Multiplying Whole Numbers

• Times 2: Double the number. If multiplying by 2, the result will always be even.
• Times 3: Triple the number. Products alternate odd and even (3, 6, 9, 12, etc.).
• Times 4: Double the number twice. The result will always be even.
• Times 5: The result must have a 5 or a 0 in the ones place.
• Times 6: Triple the number and double it, in whichever order is easiest.
• Times 7: These must be memorized. (Please add a comment below if you know a trick for these!)
• Times 8: Double the number once, double it again, and double it a third time. The result will always be even.
• Times 9: Two tricks here for multiplying single digits by 9. 1) The fingers trick: see http://www.multiplication.com/lesson10_nines_fingers.htm.
• 2) Take the number you are multiplying by 9, for example 7. The tens digit will be one less than the multiplier (6, in this example). The ones digit will be whatever it takes for the two digits to add up to 9. In this example, 6 + 3 = 9, so the answer is 63.
• Times 10: The concept here is that when multiplying by 10, it increases by one place value. So 1 x 10 is 10, 10 x 10 is 100, etc. Thus you append a 0 to the number, increases the value by one place. The result will always be even.
• Times 11: For 1-9, the result is always that both digits will be the same as the multiplier, for example, 3 x 11 = 33. For two-digit numbers 10-19, there is a cool trick. The first digit will be the same as the first digit of the multiplier; the second digit will be the two multiplier digits added together; and the last digit will be the second digit of the multiplier. For example: 11 x 18 = 198, 11 x 13 = 143, etc. Just sandwich in the sum of the multiplier’s digits between the multiplier’s digits to get your product!
• Times 12: Same as the 6 trick, but double the result.

Tips for Dividing or Factoring Whole Numbers

If you are trying to check to see if a number is divisible by another number, or can be factored by that number, or has a common factor with another number, these tips can be helpful.

• Divisible by 2: Any even number.
• Divisible by 3: Add up the digits as if they are all ones. If the sum is divisible by 3, the number is divisible by 3.
• Examples: 143 -> 1+4+3 -> 8, so not factorable by 3. 144 -> 1+4+4 -> 9, so factorable by 9
• Divisible by 4: If an even number is still even when you cut it in half, it is divisible by 4.
• Divisible by 5: Any number ending in 5 or 0.
• Divisible by 6: Any even number that fits the 3 rule.
• Divisible by 7: Memorize these.
• Divisible by 8: If an even number is still even when you cut it in half, and in half again, it is divisible by 8.
• Divisible by 9: Same as 3 rule, except the sum of the digits must be a multiple of 9.
• Divisible by 10: Any number ending in 0.
• Divisible by 11: See the Times 11 rule and reverse it.
• Divisible by 12: Any number that fits both the 3 rule and the 4 rule.

I also recommend Greg Tang’s book The Best Of Times, which is full of multiplication tricks like these, but in a fun, picture book format that children will enjoy experiencing.

A great video showing how to fill in a times table chart, and learn the facts while you are doing so, can be found here:
http://mathplayground.com/howto_learnmultfacts.html

If you have learners who struggle to learn their multiplication facts because they have trouble memorizing or can’t learn through these tips, or are just kinesthetic learners, try playing games where children toss a ball back and forth while skip counting with different tables. If they don’t know the tables at all, they can use a chart on the wall for reference while they are learning. Like with any skill, practice and repetition will eventually lead to mastery.

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