In 3rd grade the focus switches from Learn to read to Read to learn. Let me explain. Up until third grade, the child is LEARNING how to read. In third grade, the assumption is that they already know how to read, so now they can read to LEARN. If they haven't mastered reading at that point, they'll fall farther behind their peers quickly. It's for this reason that it's crucial that your toddler learn to read and stay on track with their peers.
I've bought practically every educational app there is out there to teach my daughters math, reading, their A-B-C's, tracing the letters, etc. I have enough that I could easily fill 10 pages on my iPad with it. I've deleted and put back on and experimented with a variety of them. What I've been looking for is something that engages my daughters, can progress with their progress, and give the parent (me) feedback on how they're doing. There are some apps that do this, most notably the Dora the Explorer series that teaches them to read. It provides feedback and I can check their progress, but my kids seem to get bored with it. I've also tried the Jumpstart series which teaches ABC's and math. But it's not as robust as I'd like it to be.
I came across a new suite of apps developed by Tribal Nova out of Canada. Its a suite of 9 apps called i Learn With. All are free to download. 8 of them have an in-app purchase that you pay to unlock it. The unlock varies from $1.99 to $2.99, so if you bought all of them, it'd set you back about $20 or so.
The 8 apps teach a variety of concepts: Language, Literacy, Math, Science, and Arts/Social Development. For example, the Math app teaches you how to count up to 15. In this particular game, two people are bowling, and they knock over pins. You have to count the pins that are knocked over then select the correct number. If its correct, they'll do it again. Each "game" has 3 levels, with 3 bars per level. Once you complete 3-4 of these "games" one bar will be completed. So in theory, they'd have to complete 9-12 games to complete one full level. Then they'd move on to the next one and so on. In the Math app, they have 3 sets of games - one that counts up to 6, then another up to 10, then the last is up to 15. 
If the child is having difficulty with a particular level, the algorithm of the app will recognize that and adjust the levels difficulty to match the child's progress.
In other apps, they'll learn things like what kind of clothes you wear for particular weather (this is in arts/social development) and how to follow instructions - like "tap the circle in front of the treasure chest". They learn concepts about habitat of particular animals, like does a polar bear belong in the jungle, etc. They also learn about emotions and what kind of emotion was expressed in a scenario that is shown to the child.
One reason why I love this app is because once you set up a log-in, you can track their progress across multiple devices. You get an email every time they complete a full level. I can have one child start on one iPad and then pick up where they left off on another iPad. Each child has their own profile, and you can have up to 4. But when they pick up the iPad/iPhone, you have to make sure they are logged into the correct profile or any progress they do will be credited to the wrong child.
The 9th app is a free app that aggregates all the data from the 8 other apps and ties it all together so you can see in the form of a "tree" - see here for more details.
I found their tech support to be highly responsive. They always responded within a day or two. I ran into a small bug and emailed and they explained that they were aware of it and were working on it.
The bug is as follows - if you've finished 1 or 2 bars out of the 3 bars to finish a level, and then you close the app and come back to it later, you have to start at the beginning of the level. It can be tedious to go back to the beginning even if you've finished that block already and I've had my kids getting "bored" and closing the game and then coming back again and having to do the same thing over and over again because they don't understand that they have to stay in the game to make further progress. It'd be nice if I could manually move them up block by block. They allow you to move level by level, but I want to be able to move block by block to avoid this from happening. Also every time you open the game, it'll give you an option of which level to start at - i.e. level 1, 2, or 3. It'd have been nice if they just jumped you right to where you left off rather than giving the child the option to start at level 3 when they should be at 1 or vice versa.
They say that this is perfect for toddlers aged 3 to 6. If your child spends a half hour to an hour a day, they could conceivably finish this in a few weeks. There are 23 games or lessons depending on how you look at it, with 3 levels of learning in each game. If they accomplish all 3 levels in 1 game per day, that's a little over 3 weeks.
Every time the child finishes a level, they get a "reward" and they can go over to Planet Boing! where they can make pictures and use their rewards and do fun stuff. It's a nice reward and I find that they like to do that but I always check to make sure that they're not spending too much time over there when they should be focusing on the next lesson.
This is available on the Apple App Store, Google Play, Nook apps, and Amazon app store, so you can use them on multiple platforms. I only tested this on Apple devices.
I really love this app series and hope they'll do a different series or expand this one for children ages 6-10 or something like that for my children to continue when they age out of this one. I highly recommend this to anybody who has a toddler age 3-6 - as it will help prepare your child for school.
