Singapore Math Cheat Sheet: Starting a Child Mid-Year

Wednesday, March 13th, 2013

A teacher recently asked me a question: “What do I do with the student who is strong enough in his math concepts, but he has no idea about Singapore Math approaches like number bonds, and he starts our school late in the year?”

For her and other teachers in the same boat, I’m making this “cheat sheet,” which is targeted at elementary school children who start mid-year in Math in Focus or Primary Mathematics.

1. Number Bonds

Number bonds show the ways in which numbers relate to each other. They can also be thought of as “part-whole” pictures, in which you see two or more parts that make up a whole.

To catch a child up with these, you can try one of several things.

a) Sit with the child and a laminated number bond page, and write number bonds in them. Ask the child to create number sentences (equations) from the number bonds. Then have the child fill in the missing number in a number bond with a part, or the whole, missing.

Example:

number bond graphic

Whole with two parts

Number sentences:

4 + 6 = 10

6 + 4 = 10

10 – 4 = 6

10 – 6 = 4

With practice, the child will realize that all these facts are related, and that subtraction starts with the whole minus one part, while addition is made of two parts forming a whole. I’ve found it can help students who are struggling with subtraction, especially with those problems missing the whole, for example _____ – 7 = 5. Rewriting these as a number bond can assist the child to see that the whole is what is missing, so she needs to add the two parts.

An article that explains number bonds more in depth can be found at Let’s Play Math.

b) Have the child play number bond games. One of the best I have found is called Number Bonds. It is available for both addition/subtraction and multiplication/division. See my review of these games here.

c) Play other games that involve number bonds. Addition War and Subtraction War, which are outlined in this PDF, are both fun games children love. You can customize them to this need by having the student write the problems that turn up on the cards on a laminated number bond sheet with a dry-erase marker, which will show you how much the child understands about number bonds.

2. Model Drawing

Another feature of the Singapore approach to teaching math that is new to many US teachers in model drawing for problem solving. This is a powerful visual approach, and with practice, it becomes much faster than other ways of solving word problems.

A great resource to learn about model drawing is at thesingaporemaths.com. To practice free problems using the model drawing approach, head on over to thinkingblocks.com. There are also videos on that site that explain the approach, and free iPad apps are available for four different types of word problems here.

For a new student when you don’t have much time to give one-on-one attention, set her up on Thinking Blocks to help her understand how to use this.

3. Place value

The Singapore approach places a heavy emphasis on place value. Many other programs do too, but not all, so you may find this lacking in a new student.

Again, considering that teachers may be too busy to spend a lot of one-on-one time with students, I am providing several electronic resources to teach this.

a) NLVM has some good resources for teaching place value. They require Java to run and can be used on a computer or interactive white board, or you can download their app that doesn’t require Java. Here are links to:

b) Here is an Illuminations lesson plan to play a place value card game.

c) A good iPad app for modeling with place value blocks is Number Pieces.

d) If you do have the time, make your own place value chart and use money or place value blocks to represent tens, ones, and other places your student may be learning. This will help a great deal with his number sense.

 

That wraps it up for this article, but if you have other questions, suggestions or issues, please let me know in the comments, and I’ll update the article as needed. Thanks for reading!

 

Math Doubles Plus Fun Time

Monday, May 7th, 2012


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kids on board out edit2If 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
  • Number cards: Download multiplication and/or addition card PDFs

Step 1 Outdoor Number Mats

Outdoor board

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

times board

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

clothThe 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.)

cloth with tapeNow 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.
cloth numbers
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.add board

Step 3 Games to Play

class on in board
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.
marcel jumping
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
rubyonboardThe 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.

        
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