ÉCOLE
INTERMÉDIAIRE FRANK ROBERTS JUNIOR HIGH
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Box 16040, Station Foxtrap, Conception Bay
South, NL, A1X 2E2
Tel: 709-834-9847 Fax: 709-834-6069
web: http://www.fris.k12.nf.ca/
Grade 7 Mathematics
Unit 7: Algebra Review
Geometric Patterns | Extending Number patterns | What is an Equation? | Equations Involving Variables | Finding the Value of a Variable
Definition: A variable is a letter or symbol that is used to represent a quantity that can vary.
Example: A series of three figures made of squares gives the following pattern.
| Figure # | 1 | 2 | 3 | 4 | n |
| # of Squares | 1 | 2 | 9 | ? | n x n |
In this case we may determine the number of squares by multiplying the figure number by itself (ex. figure 4 has 4 x 4 = 16 squares) Therefore, it is not necessary to draw figures in this pattern to determine the number of squares in any figure.
In this case we can determine the number of squares in the n'th figure by using the expression n x n.
When given a number pattern it is possible to express any number in the pattern with an algebraic expression (a mathematical expression containing a variable).
Example: Look at the number pattern 7, 14, 21, 28, 35, ...
a) What is the 20th number in the pattern?
b) Use a variable to describe any number in the pattern.
| Rank | Number | Pattern |
| First (1) | 7 | 7 x Rank = 7x 1= 7 |
| Second (2) | 14 | 7 x Rank = 7 x 2 = 14 |
| Third (3) | 21 | 7 x Rank = 7 x 3 = 21 |
| Forth (4) | 28 | 7 x Rank = 7 x 4 = 28 |
| Fifth (5) | 35 | 7 x Rank = 7 x 5 = 35 |
| Twentieth (20) | 7 x Rank = 7 x 20 = 140 | |
| Any (n) | ? | 7 x Rank= 7 x n = 7n |
Answers: a) 140 b) 7n (algebraic expression)
An equation is a mathematical statement that two expressions are equal.
Example: We say that 25 + 4 = 33 - 4 is an equation since 25 + 4 = 29 and 33 - 4 = 29.
Example: 5 less than a number is 13
Solution:
| 5 | less than | a number | is | 13 |
| n | - | 5 | = | 13 |
Note: The number 5 and the letter n appear out of order from the original statement but this is required since 13 is 5 less than a number (not the other way around).
Example: 6n = 36
Solution:
| 6 | n | = | 36 |
| Six | times a number | is | thirty-six |
Example: Given the expression 2n + 1 find the first five numbers in this pattern.
| n | 1 | 2 | 3 | 4 | 5 |
| 2n+1 | 2(1)+1= 3 | 2(2)+1=5 | 2(3)+1=7 | 9 | 11 |
Note: After determining the first three numbers in the pattern using 2n+1 we notice that the values are going up by 2 so we know that the 4'th number in the pattern is 9 and the 5'th number in the pattern is 11 without having to calculate the values.
Example: Find the value of the variable that makes each equation a true statement.
a) 18 = m +10
What number do we add to 10 to get 18?
We know that 8 + 10 = 18 therefore, m = 8
b) h x 6 = 42
What number do we multiply 6 by to get 42?
We know that 7 x 6 = 42, therefore h = 7.