Lattice Multiplication vs SymPy Editor

Lattice Multiplication helps students learn and practice the lattice multiplication method step by step. The app shows each part of the lattice multiplication process visually. Students first complete the multiplication steps and then add along the diagonals. Animated numbers move into the correct places, helping students understand how the method works. Lattice multiplication is a compact visual method for multiplying larger numbers. It is algorithmically equivalent to long multiplication and is also excellent times tables practice. Students can solve randomly generated problems or enter their own multiplication problems. Wired.com: “This was one form of multiplication that I’d never done before, but the app taught me very clearly. It makes multiplying large numbers easier, and allows you to see it all visually.” Teacher endorsement: “The math apps by Esa Helttula allow students to practice and reinforce the specific computation strategies taught in class, with as much or as little scaffolding as necessary. They also provide individualized feedback to each student, with an immediacy that is not always possible through pencil and paper practice.” — Rita Zeni, Ecole Sandy Hill Elementary, Abbotsford, BC, Canada Features: - Step-by-step lattice multiplication practice - Multiplicand can have up to 5 digits - Multiplier can have up to 3 digits - Randomly generated or manually entered problems - Current operation for each step can be hidden - Operands for the current operation can be highlighted - Three visual themes: black, gray, and gold - Adjustable animation speed - Different interfaces for iPhone and iPad The Lattice Multiplication Method Lattice multiplication is algorithmically equivalent to long multiplication. A lattice (a grid) guides the calculation. All the multiplications are done first and then the additions. The method was introduced to Europe in 1202 in Fibonacci's Liber Abaci. In this groundbreaking book Fibonacci presented many algorithms for working with Arabic numerals. Ancient Indians and Chinese originally invented some of the algorithms. Fibonacci presented both the current standard long multiplication and also an originally Indian method called lattice multiplication, which is faster and more compact for working with larger numbers. Other iDevBooks Math Apps: Other iDevBooks math apps include Column Addition, Long Multiplication, Long Division, Column Subtraction, Visual Multiplication Table, Fraction Math, Partial Differences Subtraction, Partial Quotients Division, Partial Sums Addition, Decimal Rounding, and more. Feedback: New ideas to make this app better are welcome. Please visit idevbooks.com to give feedback. Privacy: This app has no ads, no in-app purchases, and does not transmit user data during operation. The app also does not contain links to other apps or to the web.

Edit mathematics the way you read it. SymPy editor draws your expression as a real formula, and every piece of it responds to touch: tap a term to select it, type over it, pull it apart, or apply any function from SymPy, the Python computer algebra system that powers it all. The whole CAS runs on your phone. No account, no ads, no tracking, no network: CPython and SymPy are packaged inside the app, everything you type stays on your device, and it all works in airplane mode. EDIT FORMULAS, NOT CODE • Tap any sub-expression (a term, an exponent, a matrix entry) and edit it in place • Type over a selection, or place a caret between terms and insert • Tap an operator to change it: turn + into a product, make an equation, or delete it • Unwrap (cos θ → θ), isolate, delete, copy and paste sub-expressions • The SymPy source line under the formula follows it, and the formula follows the line: edit whichever you prefer ALL OF SYMPY, ONE TAP AWAY • Transform menu: simplify, expand, factor, partial fractions, trig rewriting and more • A menu per type: matrices offer determinant, inverse and transpose; integrals, sums, derivatives and limits offer evaluation; equations swap sides or collect everything on the left • A search box over every SymPy function, asking for the parameters each one needs • An "unevaluated" switch builds Integral(f, x) or Determinant(M) symbolically instead of computing it • A Symbols panel for assumptions (positive, real, integer…) and matrix symbols with their shapes EVERY STEP IS REMEMBERED • The history shows each step and what changed: in red what went, in green what came • Play it as a slideshow, at the speed you choose • Save it as a self-contained web page that works offline, or as a Python script that rebuilds every step with SymPy • Keep several sessions, each with its own history, all on your device FOR STUDENTS, TEACHERS AND SCIENTISTS Complete the square in front of a class, evaluate limits and integrals, manipulate matrices and N-dimensional arrays, and export the derivation when it is done. FREE AND OPEN SOURCE BSD 3-Clause, no strings attached. Worked derivations, the source code and a browser version are at https://upabjojr.github.io/sympy-editor/ — and the same editor runs in Jupyter notebooks (pip install sympy-editor).