For today, I will simply list the apps on my school-use iPad. Later, I will sort them by price. In the meantime, just check them out in the Apple App Store. Since I have an Apple device, I do not know if these apps are available in Google Play Store, but these days, most companies market their apps to both formats. I have tried all of these apps, and though some have minor bugs (freeze-ups, some levels that are too difficult, small mispronounciations of some letter sounds, etc.), most work well to help children learn to use letters and numbers to to become proficient in reading and math. If you find serious issues with any of these, please let me know so that I can remove them from the list. All games listed as "Lite" are free to try but with limited levels or skills. These require an upgrade (usually $0.99 to $2.99) to become fully functional. With these, you want to be sure your child does not have the ability to download apps without your permission.
If you have some great apps that you use at home with your child, please share and I will add them to the list to help other parents!
Shapes (Lite) - Eggroll Games
Colors (Lite) - Eggroll Games
Letter Quiz (Lite) - 22 Learn
Phonics Farm (Lite) - 22 Learn
Sight Words (Lite) - Maelstrom Interactive
Kids Phonics 1 (free with no in-app purchases or ads) - Al Bailey
Kids Phonics 2 (free with no in-app purchases or ads) - Al Bailey
Letter Tracing - ABCya.com
ABC Games - Innovative Investments Limited
Magnetic Alphabet (Lite) - Dot Next
Train Phonics CVC - Joe Scrivens
Kids Phonics 3 (free with no in-app purchases or ads) - Al Bailey
Kids Phonics 4 (free with no in-app purchases or ads) - Al Bailey
Kids Phonics 5 (free with no in-app purchases or ads) - Al Bailey
CVC Words - Innovative Investments Limited
Spell & Learn - Afflatoon Games (annoying pop-up adds every few seconds, but a good review of color and shape words)
First Grade Phonics (Lite) - Arch Square
Sight Words List - Innovative Mobile Apps
Sight Words (Lite) - Terasoft, a.s.>
Fry Words Ninja - Grasshopper Apps
Shapes Colors (Lite) - Frugoton.com
Free Preschool Pop Quiz - GrasshopperApps.com
Elmo's 123's (Lite) - Sesame Workshop
Basic Skills (Lite) - 22 Learn (I have these in both preschool and kindergarten)
Lola's Math Train (Lite) - BeiZ Ltd.
Animal Math (Lite) - Eggroll Games (This one has a $4.99 price tag to upgrade, but I really like it, so I upgraded Pre-K, K, and 1)
Pre-school Basic Skills: Fun in Space (Lite) - 22 Learn
Endless 123 (Lite) - originator (I'm not especially fond of this one, but it could be a good review for students struggling with numbers)
Math Games for Preschool and Kindergarten Kids (?Lite?) - great beginning counting
123 Genius (Lite) - Samir Bouderqa
Kindergarten Games Summer Review - Innovative INvestments Limted
Kindergarten Math - Class K12
Kindergarten Addition - I Did It Learning LLC (rather bland, but good concepts)
Rocket Math Addition Home (Lite) - Rocket Math, LLC
Math Racing Turbo - Tuti nova (for higher challenge)
Nearly everything I have found by Innovative Investments Limited is $0.99 or free and most are great quality despite the lack of sparkly appeal. I really like thier apps. 22Learn and Eggroll Games also have great stuff, but it is a little more expensive for the upgrades, so you want to lock your child's tablet to prevent purchases. I will add more apps as the year progresses. Please contact me with your favorites!
Also most of your favorite child-centered companies promote apps as well, such as Crayola & Starfall.