Posts Tagged ‘number bonds’

More Math Apps for iPad: Singapore Math and Common Core

Saturday, July 6th, 2013

It’s been a while since my last post on iPad apps, and in the meantime a lot has happened. For one thing, I have downloaded and tried quite a number of math apps. I’m going to start a round-up of some of the most useful apps as I have time.

number bondsFirst up: exciting news! The Number Bond software, that I lamented being only on Mac or PC for so long, is now ported to iOS. As far as I can tell, having downloaded only the addition/subtraction version, it’s pretty much exactly the same as the computer version.

This has its pros and cons. Pros: the familiar interface, its simplicity, and the fact that it does one thing – it teaches number bonds at different levels. Cons: In light of the outstanding, more powerful software out there, it takes advantage of very few of these features. For example, it is not adaptive, meaning the difficulty does not change with the user’s proficiency. It also does not save user data, something the better educational software is doing (as I’ll discuss later), even emailing it weekly to the parent or teacher if desired. It also has a few bugs to iron out, which I’m sure will happen soon.

So would I recommend it? Yes, as a practice tool for a child at home or as a station in the classroom – but I would love to see it get more developer attention and become more powerful.

Download Number Bonds: Addition & Subtraction to 99

Next up: AL Abacus

For anyone teaching/homeschooling with Singapore Math or a Common Core curriculum, such as Eureka Math, or working with a child with a math learning disability, you will find  that the Slavonic Abacus, or Rekenrek, is incredibly useful for teaching number sense and place value. It breaks down numbers into groups of five and ten, which are easy to manipulate mentally, not least because our hands are right in front of us since we are in the womb, with five fingers each (otherwise known as digits!). While having the concrete manipulative is ideal for sensory feedback, sometimes teachers want to project the abacus to a group, or show a demonstration to a small group. This is where the iPad version, AL Abacus, comes in.

AL Abacus to 100This app is a Slavonic Abacus with two modes. The first is the side with numbers to 100. To access this side, hold the abacus in landscape (horizontal) mode. When all the beads are to the right, it is like pressing “C” (or Clear) on a calculator. To reset all the beads, just tilt the iPad to the left – exactly like on a real abacus. Just slide single or groups of beads to the left to add, subtract, multiply, or divide within 100.

AL Abacus to 1000sThe second side is accessed by turning the iPad to portrait, or vertical, orientation. In this mode, you can work with numbers to 1000, with different columns of beads representing the different place values. This can be a very powerful, easy tool for computing whole numbers through the thousands. To reset the beads, just lift the iPad up, and the beads all fall to the bottom.

Incidentally, this second side was designed by Dr. Joan Cotter, who did her doctoral dissertation using it. Her website, with additional resources, including how to use the AL Abacus, is

This is an almost perfect representation of a physical version of the abacus. There are only two things missing, in my view: the sound of the beads clicking together, which would be great sensory feedback.

Download AL Abacus – Activities for Learning, Inc.

Since this tool is new to many people, here are some other resources besides just the iPad version.

Do you have other ideas or resources for teaching number bonds or using the Rekenrek? Post them in the comments!

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.


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 To practice free problems using the model drawing approach, head on over to 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!



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