# Wall of numbers

A number of walls (even number triangle , number pyramid or number tower ) is a didactic means for learning the basics of addition . An ordinary number wall is pyramid-shaped, and each cell is equal to the sum of the two below. Frequent modifications are the multiplication wall and the subtraction wall.

An ordinary number wall with 4 basic cells

## Basic principle

 a + 2b + c a + b b + c a b c

The usual number wall is built so that each cell is the sum of the two lower ones. A wall of numbers can theoretically be any size.

Accordingly, in a wall of four rows with a, b, c, d in the base row (in this order) at the top:

${\ displaystyle a + 3b + 3c + d}$

and for six rows with a, b, c, d, e, f in the back row at the top:

${\ displaystyle a + 5b + 10c + 10d + 5e + f}$

In general, one can derive a formula for the value in the top depending on the values ​​in the basic series with binomial coefficients as factors.

## Number walls in mathematics didactics

The wall of numbers is an operative form of exercise with which different degrees of difficulty can be realized. It is often used in the 1st to 4th grade. Depending on how the values ​​are entered in the cells, the person who solves the wall of numbers has to use different operations. When the basic series is completely filled, only addition is used; if the values ​​are distributed, knowledge of subtraction is also required. These basic math skills and competencies are practiced in this way.

## literature

• Günter Krauthausen: Wall of numbers in the second school year - a substantial exercise format, in: Grundschulunterricht, Volume 42, Issue 10, 1995, pp. 5–9.
• Petra Scherer: Substantielle task formats - cross-year examples for mathematics lessons, 3 parts, in: Grundschulunterricht, Volume 44, 1997, Issue 1 (pp. 34-38), Issue 4 (pp. 36-38), Issue 6 (p. 54 -56).
• Rita Schurr, Elisabeth Rathgeb-Schnierer: Wall of numbers with a difference - rediscovering familiar tasks, in: Praxis Förderschule, Volume 2, Issue 2, 2007, pp. 14-18, .
• Erich Ch. Wittmann , Gerhard N. Müller: Handbook productive arithmetic exercises . tape 1 . Klett, Stuttgart 2017, ISBN 978-3-12-200926-7 , pp. 119-122 .

## Individual evidence

1. A. Delius: Walls of numbers. (PDF) In: lehrerfortbildung-bw.de. State Academy for Further Education and Personnel Development in Schools, May 19, 2010, accessed on February 19, 2019 .
2. Dennis Rudolph: Number pyramid, number tower or number wall. In: gut-explained.de. Dennis Rudolph, December 18, 2017, accessed February 19, 2019 .
3. Friedhelm Padberg and Christine Benz: Didaktik der Arithmatik . 4th edition. Springer, Heidelberg 2011, ISBN 978-3-8274-1996-5 , pp. 102-103 .
4. Introduction of the wall of numbers in class 1. In: Hausarbeiten.de. 2012, accessed February 19, 2019 .
5. Dr. Maria Koth: walls of numbers. (PDF) In: mathe-online.at. Retrieved February 19, 2019 .