I have literally hundreds of Mathematic apps, and most of the multiplication and division apps are drill and practice, which is great for developing speed and accuracy, but *Understanding Math: Times Tables* offers something new. The drill and practice element is there, but it is the *understanding* part that is a new and welcome feature. The activities in *Understanding Math – Times Tables* are based on Jerome Bruner’s Three Modes of Representation learning theory and they explore the concepts of division and multiplication using different visual representations.

Each activity has been linked to the Common Core Standards for Mathematics.

Solve the multiplication problem by dragging across the rows and columns. 3 x 5 can be displayed as three rows of five, or five rows of three. When you answer correctly, the equation is highlighted. If you answer incorrectly, the equation briefly highlights in red, then the correct answer is shown on the board in the equation.

The *Hundreds Board* activity was the first one I tried, and I immediately wished for a “free play” mode. Lo and behold, there was one in the app already with the *Toolbox Hundreds Board*. Like the previous activity, you can drag across rows and columns to show a multiplication problem. Under the multiplication equation, the equivalent division equation is written. This is going to be very handy for homework in our house.

An equation appears and you have to solve it by tapping a combination of fingers the current number of times. For 8 x 5 you would tap five fingers on the screen eight times. When you answer correctly, balls appear on the screen that you can pop and a reward sound plays.

Tip: before you use this activity, go to your iPad’s settings and turn off *Multitasking Gestures*. I accidentally swiped myself out of the app and into others a few times before it twigged what was going on.

Drag objects into boxes to solve the equation. If the equation is 20 ÷ 2, you will see 20 objects and two boxes. As the objects are dragged into the boxes, numbers on the box keep count of how many items are in each. If you put too many in one of the boxes, the equation highlights in red and you see the correct answer. A correct answer results in a reward sound with the correct answer highlighting in white.

An equation appears at the top of the screen with a visual representation at the base of the screen. Solve the equation by writing the answer in the centre of the screen. This is a drill and practice activity and uses hand writing recognition. I had a good run with it and tried both good and fairly shocking writing to see how it would go. For the most part, the app recognised both the accurate and the slightly less-accurate writing, but occasionally I was prompted with a question mark to write again. It might be a little frustrating for children who are not that great at writing numerals, but it could also encourage them to take a little more care. (I have no screen shots of this and the next activity because I was just too slow with the screen shots!)

This is a version of the *Training* game where two players compete against each other. Choose a difficulty level, tap the sun when you are ready to start, then try to solve your equation before your opponent. The first to enter the correct answer earns a star, and the game finishes when one player has earned 5 stars. The feature I really, *really* love about this activity is that you can choose a different difficulty level for each child. This means that potentially your 7 y.o. can take on your 12 y.o. and win.

- Equations are written either in the style we use in the UK, USA, Australia (and others) or German style.
- Separate profiles can be created for each user.
- Results are tracked for each user
- You can select which tables you wish to concentrate on (which will also be handy for homework, as my children’s classes seem to concentrate on a different table each week.)

It is great to see a Mathematics app that offers something different. The activities in *Understanding Mathematics – Times Tables* have been carefully designed so that children can manipulate items in the activity to help them understand the concept of multiplication and division. I highly recommend it. I can’t wait to see what appp media offers us next.

*Understanding Math – Times Tables: Learn to fluently multiply and divide within 100 *is on sale at %50 off until the 16th November 2014.

Publisher: appp media

Price: $2.99 until 16th November

iPad and iPhone (requires iOS 4.3 or higher)

You may remember I noted that stamps/stickers can make an App more versatile, and that certainly is the case when it comes to Mathematics. In a classroom, students commonly used counters, paddle pop sticks, blocks and other manipulatives to experiment with number. Think of stamps as *onscreen or virtual manipulatives. * If you don’t have stamps, you can use different colour and painting tools to create marks or shapes.

**Representing Number** – Paint a numeral on the screen and get children to add stamps or marks to show the number.

**Place value **– Stamp an image all over the screen. You could also use painting tools to create dots or X marks. Use the painting tools to group 10s, and then write the number with text or paint tools.

**Addition and Subtraction**– illustrate simple problems with stamps or paint tools, and then use paint or text tools to write the equation. For subtraction, you can cross off each image as it is “taken away.”

**Multiplication and Division** – set up arrays to show multiplication sums, e.g. four groups of three.

**Sets and Logic** – This activity is easiest when you have a large variety of stamps. You can draw circles on the screen and then use them to sort stamps according to shape, colour, classification, initial letter sound or whichever criteria you choose.

**Shape** – Shape tools are a big bonus when exploring shape, and the more the merrier. You can also use line tools to draw straight-lined shapes, use paint tools to count corners and sides, and use stamps to sort into shape categories. With most stamp sets, you’d probably need to look at environmental shapes, for example a bicycle might go with the circles due to the wheels. You can also use shape tools to make pictures, e.g. make a person using only circles and ovals.

**Handwriting** – use different painting tools and/ or colours to repeatedly trace over patterns letters and words.

**Letters and Sounds** – similar to the Number activity above, use the text or paint tools to write a letter or sound on the screen and then use the stamps or painting tools to illustrate it. A *B* letter may have lots of pictures starting with b, while the *AT* sound may have lots of rhyming at words. You could save these pictures and put them together to create a book with an app such as Picturebook, Book Creator or Keynote.

**Simple stories** – Create a picture and then use text tools to create a caption. If you don’t have text tools, save the image and import it into Keynote or Pages and add text.

**Spelling** – write your weekly spelling words using different paint tools.

**Story writing** – Create a series of images and either add text to the image, or import the images into an app such as Picturebook or Book Creator. You could also make a slideshow using the Keynote App. I’ve written an earlier post with more writing ideas.

**Labeling Pictures **– Import a photo into the App and use text tools or painting tools to label different parts of the picture. This can be useful for making observations and reporting on experiments.

**Mapping** – import an image of a map, for example a map of the school. Students can then use painting tools to map particular areas on the map, for example the school canteen, office, playground and their classroom. They can also map different routes through the school grounds.

There are many other ways to use painting and drawing apps. If you have some different ideas, please share them with our readers in the comments section below.

- Art Apps for Every Age (onsarahsipad.wordpress.com)

Unlike other similarly themed apps (e.g. MathBlaster HyperBlast), one does not need a lot of gaming skill to play *Arithmetic Invaders*. The controls are very simple so the child can concentrate more on the real task: defending the Solar System. Sorry. I mean practising their Mathematics skills. Children need to calculate the sums shown on the alien spacecraft and then shooting the one that matches the number on their laser gun. They move the gun by tapping the right or left buttons. As they progress through the levels, children collect space pilot insignia as a reward. You can set the length of the game to 2, 3 or 5 minutes. Content covered at each level is clearly stated, although you can’t pick levels at random but must unlock each in sequence. Unlocked levels can be revisited.

The game publishers claim that the apps can help children learn some basic facts about the solar system. Hmmmm. At the end of each game, some basic information about the current planet is given, however this could be beyond the reading ability of some children and I doubt they would learn much, although the facts are interesting. The blurb on the iTunes store page also claims the apps help to develop hand and eye coordination, but that just makes me laugh as it has been one of the top arguments used by pre-teens to convince their parents to buy any computer game in the last 3 decades. It might be a true claim, but it is the Mathematics we are really interested in, and thankfully they seem to get this part right.

Here is a quick run-down of the games and the Mathematics skills covered.

Publisher: @Reks

Universal – will work on iPhone or iPad

Price: (Apart from the Explorer, which is free) each app in the series costs $1.99

**Arithmetic Invader Express: Grade K-2**

This demo of the series is free and has activities from the other four Apps in the series. Download this one to see if these are the kinds of activities that might appeal to your children.

**Arithmetic Invaders: Grade K Math Facts**

covers counting up and down (or counting on and back, as we refer to it here), and basic addition and subtraction. It seems to reinforce the content being covered in year 1 and being introduced in Prep. Please note that I’m a little limited in my review as I don’t have all of these apps.

**Arithmetic Invaders: Grade 1 Math Facts**

This app covers simple addition and subtraction of numbers in tens and ones. Addition starts of fairly basic with single digit numbers and then progresses to double-digit with trading (refered to in the app as crossing.) Subtraction also starts with single digits and then progresses to a single digit from a double-digit number with no trading. Basic multiplication and division in the forms of doubles of single digit numbers and halves of numbers under 20 are also covered. Again, this covers Mathematics concepts covered in year one and going into year 2.

**Arithmetic Invaders: Grade 2 Math Facts**

Addition and subtraction of numbers up to 50, including both regrouping and no regrouping, doubles facts,halves of numbers under 20 (reversals of doubles facts). Mostly suited to year two, however the doubles facts are taught in earlier year levels.

**Arithmetic Invaders: Grade 3 Math Facts**

All four operations are covered in this app. Unfortunately I haven’t seen it yet so am unable to review. It has only been released in the last couple of weeks and does not have a support page up. At a guess I’d say the addition and subtraction would go to 100, but watch this space.

These games can be handy little homework tools to help children recall their basic Mathematics facts with speed and accuracy. They are enjoyable to play, and are interesting enough that children will want to play them, although probably not for hours at a time. Still, for 2, 3 or 5 minute games, they seem worth the investment. I’d recommend downloading the free Express app that covers content from the other apps to see if it will be suitable for your child/ren.

- MathBlaster Hyperblast (onsarahsipad.wordpress.com)
- Evaluating Apps: Maths Drill and Practice (onsarahsipad.wordpress.com)