Numbers & Place Value vs Number Decomposition

Explore large and small numbers and discover how place value works – interactively. This is not a drill app but an open environment for exploring and experimenting. Understanding place value is one of the most important foundations in mathematics: it underpins mental and written calculation strategies, decimals and much more. HOW IT WORKS Drag the digits up and down with your finger. Go beyond 9 and watch ten items bundle into one item of the next place. Go below 0 and see how the next place is "unbundled". Swipe or tap the quantity below a digit to change it. At the bottom of the screen, choose how the quantity is shown: place value counters, base-ten (Dienes) blocks, euro money, dot fields, 3D base-ten material and more. TOOLS ON THE RIGHT - Speaker: listen to the number being read aloud. - Speech bubble with check mark: read the number aloud yourself and check whether you read it correctly. - Expand: shows, for example, 142 as 100 + 40 + 2. - Dice: roll a random new number. - Speech bubble with dots: say a number and watch it appear. - Question mark: some places are covered, the number is read aloud and you fill in the missing digits. MORE OPTIONS - Use the grey arrows to add or remove places – explore numbers up to 100 trillion. - Move the decimal point to work with decimals down to millionths. - Tap a place label (O, T, H …) to change its color. - Swipe across a digit to cover it; tap the cover to enter your answer and get feedback. - Number words above the digits in matching place colors – optionally as "Say Ten" number words (e.g. 284 = "two hundred eight ten four"). - Many settings in the app: thousands separator, place labels, speech rate, show or hide tools and representations, protect settings. - Share a setup or task with your class via QR code. - English (UK/US) and German. - Also available in the browser: zahlen.urff.app IDEAS FOR THE CLASSROOM - Number dictation: show 3,469. - Keep adding one to the ones. What happens when you go past 9? - Show 340. What happens when you take one away from the ones? What about 300? - Show 5,216 and expand it: which numbers make it up (5,000 + 200 + 10 + 6)? What about 5,316? - Listen to a number, then change one place. Can you read the new number correctly? - Tap the question mark and solve some tasks – the app counts them for you. - Why does the leading zero in 0453 disappear? Why does the zero stay in 204 or 240?

LEARN MATH – WITHOUT COUNTING Many children learn arithmetic by counting. That is tedious and often the start of later difficulties with math. This app begins exactly where true understanding develops after quantity–number correspondence: with the automation of number bonds up to 10. Children learn how numbers are structured and can solve addition and subtraction tasks safely, quickly, and from memory. No counting, no frustration, with visible success. HOW IT WORKS • Example: 8 = ? and 3 • One part is given, the other is added via drag & drop • Correct? → reward and progress • Wrong? → gentle feedback and repeat • Only fast, correct answers (under 5 seconds) count as “known by heart” MADE FOR CHILDREN – EVEN WITHOUT READING • Intuitive operation with number tiles and structured quantity images (dice, fingers, dots, and more) • Four child-friendly animal avatars: panda, dolphin, cat, dog • Each correct task colors the avatar more • Learning progress is always visible and motivating FOCUSED LEARNING INSTEAD OF A GAME APP • Reduced sounds and calm, clear visuals • No distracting effects, no flashy colors • Clear didactic structure: not a game, but a real teaching and learning app PEDAGOGICALLY SOUND – RESEARCH-BASED • Leitner learning system with spaced repetition (boxes 1–4) • Didactic reduction: only meaningful decompositions, no swapped pairs, no zero • Structured quantity images strengthen number sense and understanding • Error-oriented learning: incorrect tasks are deliberately repeated • Progress per avatar is transparent – also for parents and teachers SAFE AND AD-FREE • No ads • No in-app purchases • Works offline – ideal for on the go • One-time purchase, permanent use DOWNLOAD NOW – MAKE MATH SIMPLE With this app, your child becomes a master of number bonds: playful, visually structured, and sustainable. Ideal for preschool, first grade, or home practice – without distractions and with full focus on what matters.