Partial Product Multiplication vs Vectors and Planes

Partial Products Multiplication helps students learn and practice the partial products multiplication method step by step. The app gives students a visual way to multiply numbers by breaking the problem into smaller partial products. The partial products are then added to find the final answer. Students can solve randomly generated problems or enter their own multiplication problems. The Partial Products Method: In the partial products method, each place value is multiplied separately. For example, in 39 × 24, the partial products are 36, 120, 180, and 600. These are then added together to get the final answer: 936. Teacher endorsements: “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.” — R. Zeni, Ecole Sandy Hill Elementary, Abbotsford, BC, Canada “There are students who see my examples who still need some guidance, and after using your app have said, ‘Now I get it.’ The feature of selecting possible solutions in each step helps some of my students who are still building their multiplication facts.” — Z. R. Prowell, Highlands Elementary, Edina, Minnesota, USA Easy to Use: The numbers are aligned automatically so students can focus on solving each step. After the student solves each partial product, the correct answer moves into the right place. If the student presses the wrong button, the answer appears above the keyboard but does not move. Features: - Step-by-step partial products multiplication practice - Each number can have 2–3 digits - Randomly generated or manually entered problems - Current operation can be hidden - Operands of the current operation can be highlighted - Customizable interface colors - Adjustable animation speed Other iDevBooks Math Apps: Other iDevBooks math apps include Column Addition, Long Multiplication, Long Division, Column Subtraction, Visual Multiplication Table, 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.

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.