Answer to Question #285665 in Algebra for ZAN

Question

Patterns can be represented in different ways. Mention and describe five ways of representing patterns. Use examples to explain your description. 

Answer 1

Solution:

A number line in mathematics in used in a variety of purposes. In some cases, it can be used in representing numbers on a line like rulers, timelines, measuring scales among others. All the mentioned examples are of a number line. Therefore, a number line can either take any form ranging from curved to a straight line.

Showing a maths pattern using a number line, we can link the numbers with counting. Creating that a pattern that will skip counting. Then representation of the pattern on a number line in a way that it keeps on repeating. For instance, 1, 2, 3, 4, 5, 6, 7, 8, 9... The above number line shows a pattern with equal distance on a number line that is useful to students to skip counting. The pattern here is adding 1, 1, 1, 1, 1, 1, 1, 1 starting from 1. Similarly, you can create a pattern of a number line with unequal distancing for example 2, 5, 10, 17, 26.... and so on. The pattern here is adding 3, 5, 7, 9 starting from 2. The only key is to be able to identify the pattern in any given numbers. Students apply the knowledge of a number line to discover patterns in number sequences and other mathematical order of operations. All the above examples are changing patterns. Repeating patterns take a form of like 1, 2, 3, 1, 2, 3.

A number grid is crucial to learners as it helps them to get a clear understanding of numbers and how they work. Also, is a tool which assists learners to be able to count and solve mathematical problems which they can't solve by themselves. Number grids can be used to explore number patterns. For example, children can start at zero and count by 2s. If they color each box as they go, they will have colored all the even numbers. If they start at one and count by 2s they will color all the odd numbers. If they count by 5s, starting at zero, they will color numbers with 0 or 5 in the ones place. They can be used as a counting tool as shown below.

Mathematical table: The standard form of a mathematical table puts the independent value in the first column and the dependent value in the second column. In math, the independent value is the variable being manipulated. The dependent value is the variable that is affected by changes in the independent value.

In this case, the independent value is the number of tables in a row—that changes with the size of the room. The dependent value is the number of chairs, which increases or decreases depending on how many tables are used.

So let’s start filling out the chart. A one-table row will need 6 chairs — 2 on each side, plus the additional chair at each of the two ends. Put a second table end to end with the first, and Kim will need 4 chairs for each side of the row, plus 2 more for ends of the row, for a total of 10 chairs. A third table added to the row will require 4 more chairs, 2 on each side. That brings the total to 14. A fourth table means another 4 chairs, or 18 altogether.

Graph:

Another way to study and predict patterns is with graphs. Let’s look again at the table we made above figure out how many chairs are needed.

The values in a table can be written as ordered pairs, which can then be plotted as points on a graph. Remember, the independent value is the x-coordinate and the dependent value is the y-coordinate. The ordered pairs represented by Kim’s tables and chairs are: (1,6), (2,10), (3,14), (4,18).    

These points can now be graphed on a coordinate plane.

Other patterns: Some specific patters are:

• Arithmetic Sequence.
• Geometric Sequence.
• Square Numbers.
• Cube Numbers.
• Triangular Numbers.
• Fibonacci Numbers.