Mathematics: Download Short Notes on Patterns and Relation for Basic 7. Mathematics: Download Short Notes on Patterns and Relation for Basic 7. Mathematics: Download Short Notes on Patterns and Relation for Basic 7
Welcome to the exciting world of Algebra! Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating those symbols. In Basic 7, we will focus on one of the sub-strands of Algebra, which is Patterns and Relations. In this tutorial, we will learn how to derive the rule for a set of points of a relation, draw a table of values to graph the relation in a number plane, and make predictions about subsequent elements of the relation.
Deriving the Rule for a Relation (B7.2.1.1.1)
A relation is a set of ordered pairs, where the first element of each pair is related to the second element in some way. To derive the rule for a set of points of a relation, we need to look for a pattern or relationship between the first and second elements of each pair. For example, consider the following relation:
{(1,3), (2,5), (3,7), (4,9), (5,11)}
To derive the rule for this relation, we need to look for a pattern or relationship between the first and second elements of each pair. We can see that the second element of each pair is always 2 more than the first element multiplied by 2. Therefore, the rule for this relation is:
y = 2x + 1
Drawing a Table of Values and Graphing a Relation (B7.2.1.1.1)
Once we have derived the rule for a relation, we can draw a table of values to graph the relation in a number plane. To draw a table of values, we substitute different values of x into the rule and calculate the corresponding values of y. For example, using the rule from the previous example:
| x | y |
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
| 5 | 11 |
We can now plot these points on a number plane and join them with a line to graph the relation.
Describing the Rule for a Relation (B7.2.1.1.2)
When describing the rule for a relation, we use mathematical language such as “one more”, “one less”, “one more than twice”, etc. For example, consider the following relation:
{(1,4), (2,7), (3,10), (4,13), (5,16)}
To describe the rule for this relation, we can say that the second element of each pair is “3 more than 3 times the first element”. Therefore, the rule for this relation is:
y = 3x + 1
Identifying the Relation or Rule in a Pattern/Mapping (B7.2.1.1.3)
Sometimes, we are given a pattern or mapping presented numerically or symbolically, and we need to identify the relation or rule. To do this, we need to look for a pattern or relationship between the input and output values. For example, consider the following pattern:
2 -> 5 4 -> 11 6 -> 17 8 -> 23
To identify the rule for this pattern, we can see that the output value is always 3 more than 2 times the input value. Therefore, the rule for this pattern is:
y = 2x + 3
In this tutorial, we have learned how to derive the rule for a set of points of a relation, draw a table of values to graph the relation in a number plane, describe the rule for a given relation using mathematical language, and identify the relation or rule in a pattern/mapping presented numerically or symbolically. We hope this tutorial has been helpful in understanding Patterns and Relations in
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