## New Singapore Math® iPad apps

With new apps being added to Apple’s iTunes store all the time, I’m always on the lookout for ones that advertise themselves with the term “Singapore Math”.

Listed below are some recent additions. I paid for and personally played with all of these in order to offer my candid assessment of each.

You can find these and more Singapore Math-related apps on the Singapore Math® iPad Apps page, which is among the most frequently visited on this site.

Note: I didn’t include the online version of Discovering Mathematics textbooks as they are designed to support the books only.

Archimedes Roost – \$2.99

Kindergarten app based on Singapore Number Bonds and Montessori using parts and wholes and Montessori bead chain and strip board manipulatives. Includes addition and subtraction within 20. Fully narrated for non-readers.

Opinion? Great graphics and engaging activities.  Good number bond and missing addend problems. This is worth \$2.99.

Maths Facts – \$0.99

Four choices: Number Bonds and Fact Families practice to Ten, Addition & Subtraction to Ten. No ability to differentiate or make it more difficult. Addition & Subtraction is find the sum or difference only, no missing addends.

Opinion? Simple and minimal levels. Very basic, froze a couple of times, but only 99¢.

Let’s Count – Free

For ages 3-6, this is a very basic app with four options. Order quantities of jelly beans from least to greatest, count and label bars to ten, Count beans to ten, match numbers.

Opinion? Well, it’s free and doesn’t take up much memory.

Master addition and subtraction with math whizzes Robin and Dob. 10 levels of each, addition & subtraction, no customizing. The dog pops up when you’ve taken too long and offers help in the form of an abacus, tens and ones place value chart with apples or the problem stacked instead of horizontal. Adorable!

Opinion? While the game is simple and has minimal levels, the basic practice is solid (and adorable!).  This is worth \$2.99.

Place Value Cards Cards – \$0.99 each

A number is given and you must show it two different ways, for example if 3 tens and 6 ones is given, you could also make 36 with 2 tens and 16 ones.

• Level 1: Tens and Ones
• Level 2: Hundreds, Tens, and One
• Level 3: Thousands, Hundreds, Tens and Ones
• Level 4: Hundreds, Tens, Ones, and Tenths
• Level 5: Tens, Ones, Tenths, and Hundredths

Number Bond Cards – \$0.99 each

• Level 1: Ten Frames and
• Level 2: Number Bonds with missing whole
• Level 3: Number Bonds with missing part

Opinion? Both of these apps are very simple and have minimal levels. If your child needs this targeted practice you could spend the 99¢.

Crackers and Goo – \$2.99

Crackers and Goo uses patterns to teach children to identify patterns and see parts of wholes. Flying crackers need to be dragged down to complete the problems. Starts very basic and finishes with rounding then multiplying 898, 899, 900. Yikes! Mental math strategies are explained.

16 levels with 5 mini-levels on each

• Grades K-1: game levels 1-4
• Grades 2-3: game levels 5 – 7
• Grades 4-5: game levels 8 – 11
• Grades 5 and up: game levels 12 – 16

Opinion? Great, if repetitive, practice. Turn the volume down on the annoying music. I can’t see kids playing this for long, but it is more of a “game” than typical flash cards. I dig this app, but not sure about young students.

Visual Word Problems  – \$4.99

Designed to help 1st and 2nd grade school children to visualize, understand and solve basic addition & subtraction word problems, this is a guided, easy to use app for early learners. I really like how prompted the steps are to maneuver through the program and that the default option is to have the app read the problems aloud. The animated word problems that use actual pictures of cows, oranges and apples are fabulous. They are laid out as a definite precursor to the bar modeling that begins in grade 3.

Opinion? Worth the \$4.99, but this is not a game. If you would like your child working some basic addition & subtraction word problems, here’s your app.

Xyla and Yabu  – \$0.99

Help Xyla and Yabu trade gems back and forth by learning to add and subtract with number bonds. Use the relative sizes of number bond bars representing parts and wholes to develop number sense while solving word problems. Understand and become automatic at using tens, doubles, and other recurring patterns with numbers.

Each number bond is presented in the context of a word  problem. After mastering sums up to 20 (14 activities), kids explore similar patterns with sums up to 100 (13 activities), for 10 levels in all. There is no option to have the app read the problems aloud. In numbers to 20, there is a picture and a bar hint, in numbers to 100, just some bar hints. After the beginning levels, three possible answers are given.

Opinion? Best 99¢ you can spend on a word problem app for grades 1-2 working with parts and wholes to 100. Of course, Thinking Blocks is still free.

Math Master Bingo – Free to download, 99¢ in-app purchase for unlimited play.

Practice your four operations with Bingo. Choose the operands rang and the operation. (% is used for ÷). Answer questions until you get five in a row.Every 5 problems, it asks you to upgrade. Has two buttons on homescreen to send you to Facebook, only one for Twitter

Jingle’s Puzzle – \$1.99

For grades 3-6, the website claims this app is designed Singapore primary school’s mathematics model methods.  Good luck with that. This is a problem-solving, logic game. Sums are listed on teh left and top of an array and some of the squares are filled in. Students find the pattern and complete the grid.

Opinion? I think the words of the single reviewer say it best: “VERY confusing…Not for young child…There is NO app support. I want a refund.”

Math Olympiad – Free for first 6 problems, then \$15.99 per level to unlock.

Designed for 8-12 year olds, this app has official competition questions from the Asia Pacific Mathematical Olympiad for Primary Schools. And the 6 problems that are included are exactly the types of problems seen on the U.S. version of the Math Olympiads for Elementary & Middle Schools.

Opinion?  This might be a great purchase for Math Olympiad teams looking for new problems. The levels are less expensive than the books in the MOEMS store.

Hey Math from Singapore – Subscriptions from \$0.99

Videos and practice with multiple levels from Singapore’s #1 online learning site. Hey Math! is an official Partner of the Academy of Singapore Teachers. They also  make Factorama – which my 17 year old son loves to challenge me on.

Opinion? This is a very good iPad version of the online site. The videos are very directed and the practice is like an online worksheet.

Smartest Singapore – Free

Online learning game for Singapore primary school children. Students play in 60 second speed challenges in languages, mathematics and general knowledge. There is no way I could see to customise this app to focus on mathematics. You need to choose a Singapore primary school in order to register and there is no option for “other” or “homeschool”. If you’d like to study up on topics, there is an option. Choose from activities,  animals, food, Geography, Plants, the MRT (subway in Singapore, Singapore history & famous people or a language. you never know when the Chinese word for bricklayer may come in handy.

Opinion?  Pass. Unless you want your child deciding if a picture is of Chimgan Mountain in Uzbekistan or Global Geoparak in Hong Kong. Game portion works about 50% of the time.

Math Mastery! – Free

Secondary and Middle school topics. Supports Ace-Learning.com, who also declares itself the “leading online Mathematics E-Learning system in Singapore”. Must be a registered user of Ace Learning to use.

Math Exam Revision Kit – Free

Also by ACE-Learning Systems and so must be registered to get the full app. Secondary and Middle school topics including notes, questions with guided solutions and more practice questions.

Matholia iMath tools & Essential Practice – Free to download, paid subscription to access

For grades 1-6, Matholia is an another online mathematics learning portal providing pupils, teachers and parents with dedicated content based on the latest primary maths syllabus from the Singapore Ministry of Education – or you could get the U.S. version. Try the program free for 7 days with a code, then you must subscribe to continue. Ther are practice learn and games option available on the desktop version as well as Singapore math tools and virtual manipulatives for differentiated interaction.

Designed for students in grades 6 and up, this is an ipad version of a book of math and math puzzlers. From the Amazon description:

Mathematical Quickies & Trickies contains more than 300 non-routine problems to enhance students’ problem-solving skills…Mathematical Quickies & Trickies would appeal primarily to students and teachers looking for some fertile trick and tricky questions; mathletes preparing for local and regional contests and competitions; problem solvers longing to be challenged by questions whose obvious solutions are never the correct ones for what offhand appears to be true is false.

More Mathematical Quickies & Trickies  – \$9.99

Opinion? Cheaper than the books.

2048 SG Army  – Free

Version of 2048 in which you match tiles to earn your way through the Singapore Armed Forces

Opinion? Probably not for your typical child. I made it through the ranks to Staff Sargent through sheer luck. Stick with the regular numbers version.

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## Thoughts from NCTM session on Singapore Math + Technology

Last week I presented with Lauri Susi at the National Council of Teachers of Mathematics (NCTM) 2012 Annual Conference in Philadelphia.  Here was our session description:

470 – Technology + Singapore Strategies = Number Sense
Co-Speaker: Lauri Susi

Visual reasoning is a powerful tool for making sense of mathematics. Learn successful visual strategies and instructional methods from Singapore that allow students to develop a deeper understanding of number concepts using hands-on manipulatives and software. Walk away with strategies for guiding students’ learning that you can use tomorrow.

We displayed the above image of lions on the screen while discussing the Concrete-Pictorial-Abstract progression of understanding. A teacher raised her hand and said something along the lines of:

I don’t like that picture. There are male lions and female lions, they aren’t the same. I can’t add them together and students get confused in upper grades when they think that these can be added.

Which is such a great comment. Why? Because this illustrates one of those interesting points that isn’t always in a student textbook and as the teacher you have to be aware of it : labels matter. Yet it isn’t so obvious at a kindergarten level.

2 male lions and 3 female lions make 5 lions altogether.

Well, they’re all lions and we’re looking at a part-whole understanding of addition. Here’s another image from the kindergarten book:

2 boys and 3 girls make 5 children.

2 daisies and 2 tulips make 4 flowers.

So how does this apply to later, more advanced concepts? Consider:

• 2 ones and 3 ones make 5 ones.
• 2 tens and 3 tens make 5 tens.
• 2 tens and 3 ones make 23 ones.
• 2 dimes and 3 pennies make 5 coins and they also make 23 cents.
• 2/5 and 3/5 make 5/5
• 2/5 and 3/4 make…hmmm, we need some common terminology here.

Thanks kindergarten and first grade teachers for laying this foundation!

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## Making math masters: A brief overview of Singapore Math®

My students love math class. In fact, many will tell you math is their favorite subject. Why? They’ll tell you it’s because Singapore math is fun. I’d say it’s because once they understand how math works, they become confident in their abilities. So what exactly is Singapore math?

### Wait, math from Singapore? Isn’t that some little island in Asia?

Primary Mathematics is based on a program of study introduced by the Ministry of Education in Singapore in 1981, a time when Singapore’s students were middling in math. Fifteen years after the adoption of its new Primary Mathematics Syllabus, Singapore students led the world in global Math achievement tests (Singapore topped international rankings first in 1995, and again in 1999, 2003 and 2007).

The Singapore math success story—from mediocre to world-class in a generation—is no secret. The curriculum provides students with a solid foundation in mathematics by focusing on visual understanding, connections, number sense, mastery, and word problems.

### Concepts in Singapore Math® are taught in a concrete – pictorial – abstract sequence

Hands-on manipulatives or real life objects are used to demonstrate the concept, then students use and create pictorial representations. This interim visual step is typically missing from many curricula used in the U.S. It provides a transition from the words to an abstract algorithm. The goal is always to use the concrete and visual components  to get to a standard algorithm.

To gain number sense, students are taught to make connections between topics. While first graders will still work on “fact families”, Singapore math also uses a pictorial representation called a “Number Bond” to help students see the connections between addition and subtraction.

Fact Families:                  Number Bonds:

### Understanding numbers and operations is critical to mathematics

Singapore materials focus on place value to provide a deep knowledge of numbers. As students work with and manipulate numbers, they work towards fluency by learning and using mental math strategies.

For example:

“If I know that 7 and 3 make 10, I could solve the problem of 47 + 8 by breaking the number 8 apart into 3 and 5. Adding the 3 to 47 gives me 50, then I can easily add on 5.”

These mental math skills show flexible thinking and provide a “check” students use when the algorithm is learned. I was in a first-grade classroom last week where the teacher was talking about addition and subtraction strategies with her students. They were working with numbers like 9 + 5 and the teacher had asked the students how they got their answers:

“I counted on from 9”
“I took 5 apart to 1 and 4 and made a ten first”
“I used automaticity!”

To get to mastery, students work on focused concepts and skills. U.S. curricula are typically criticized for being “A mile wide and an inch deep”. Topics continually spiral and “It’s ok if kids don’t have their multiplication facts memorized this year, we’ll reteach them again next year.”

And next year and next year…

Not so with schools using Singapore Math®. In first grade, students will learn multiplication of twos and threes within 40. In second grade, they’ll master multiplication and division by 2,3,4,5 and 10. Each year builds on the prior foundation and extends student understanding. By the end of third-grade students will have mastered all of their multiplication tables as well as multiplying and dividing by a single digit. Yep, they will even become proficient with the dreaded “long division algorithm”.

### Understanding problem solving

Another component of mastery is the ability to take what you already know and apply it in a new context. Remember being tortured in school with story problems? The heart of the Singapore curriculum is an emphasis on problem-solving — and that means word problems. They are incorporated throughout the materials to provide context to each topic as it’s taught. The key to solving these begins with a bar model or pictorial representation of the word problem. For instance:

1)  Ginny has 40 cherry and grape gumballs in all. She has 24 cherry gumballs. How many grape gumballs does she have?

2)  Ginny has 24 gumballs. She has 3 times as many gumballs as Paul does. How many gumballs does Paul have?

3) 2/5 of the students in a class are boys and the rest are girls. There are 35 students in the class. How many boys are in the class?

4)  The ratio of the number of boys to girls in a class is 2:3. After 6 boys join the class, the ratio becomes 5:6. How many boys were in the class at first?

This is a sixth-grade problem from a unit on changing ratios. Can you see the answer? Note that the number of girls doesn’t change.

1 unit = 6 boys

4 units = 24 boys

### Mastering Math Makes Math Fun!

Singapore Math® is a great foundation for elementary math success. Working with teachers in their classrooms, I see the impact the materials have on students every day. Singapore math can help make every child in every classroom a competent and confident mathematics student.

1) Ginny has 16 grape gumballs

2) Paul has 8 gumballs

3) There are 14 boys in the class

4) There were 24 boys in the class at first

Bar Models generated from ThinkingBlocks.com

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I visited a wonderful second grade classroom last week!

Number bond, words and a place value chart for the number 152.

In the classroom, students were working on adding two-digit numbers. Some examples follow: