This document contains a lesson on introductory algebra concepts including algebraic expressions, terms, coefficients, variables, and constants. It provides examples of each concept and exercises translating sentences to algebraic expressions. Key terms for translation include added to, multiplied by, and divided by. Students are asked to rewrite sentences as algebraic expressions, such as "5 more than a number" as x + 5.

1. Algebra
Grade 9
Mrs. N. Wilson

2. Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 2

3. − 2 = 4
− 2 = 6
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 3

4. What is Algebra?
Algebra is the use of letters and
symbols to represent values.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 4

5. Algebraic Expressions
This is a
combination of
one or more
terms.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 5
Examples:
3𝑚 + 2
𝑥2 + 4𝑥 + 4
12 + 𝑏
3𝑚 + 6𝑛 − 6

6. Term
This is the name given to a number, a
variable or a number and variable
combined by multiplication or division
within an algebraic expression.
Example:
1. 𝑎 + 2 ,the terms are a and 2
2. 3𝑚 + 6𝑛 − 6 ,
the terms are 3m, 6n and -6.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 6

7. Question
What are the terms in the expressions
below?
1. 3x + 4
2. a × 2b ÷ b
3. 24z – 16z
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 7

8. Numerical Coefficient
This is the number by which a variable
is multiplied.
Example: Given 8x, the coefficient of x
is 8.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 8

9. NOTE:
If there is no coefficient before the
variable then the coefficient is
considered to be 1.
Example: Given x, the coefficient of x
is 1.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 9

10. Variable
This is an unknown value that is usually
represented using a symbol or a letter
of the alphabet.
Example: Given 9a, a is the variable of
9a.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 10

11. Constant
This is a number that cannot change its
value.
Example:
In the expression 5𝑥 + 7𝑦 − 2, the
constant is -2.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 11

12. Activity
Use the following terms to identify
each part of the expression below:
Numerical coefficient, variable and
constant
9x + 4
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 12

13. Sub-topic:Translating Sentences
into Algebraic Expression
This is to re-write a given sentence using
algebraic terms.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 13

14. Key terms to note when
translating
Operation Key terms/phrases Examples
Addition 1. Added to
2. Increased by
3. More than
4. The sum of
5. The total of
6 more than a number
Let the unknown
number be x
6 + x
Subtraction 1. Less than
2. Minus
3. Decreased by
4. Less
5. Subtracted from
34 decreased by a
number
34 - x
Division 1. Quotient of
2. Divided by
3. The ratio of
The quotient of 9 and
a certain number
9 ÷ x
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 14

15. Terms Cont'd
Operation Key terms/ phrases Examples
Multiplication 1. Multiplied by
2. Product of
3. Twice; double
4. Times
The product of 12 and
a number
12 × x or 12x
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 15

16. Now it’s your turn!
In your groups attempt to rewrite the
following sentences into expressions.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 16

17. Questions:
1. A number decreased by 11
2. 5 more than a number
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 17

18. Cont’d
3. A number divided by 7
4. The product of p and q.
5. 4 times the sum of 1 and a number d
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 18

19. Worded question
Yuri is 8 years old. Raymond is two-
and-a-half times as old as your. Write
an algebraic expression for Raymond's
age?
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 19

20. Individual Work!
1. 7 subtracted from x
2. The quotient of x divided by 7
3. If Martin’s m kilograms, represent
his mass after he gains 7 kilograms.
4. Stacey is x years younger than her
sister who is 15 years older. Express
Stacey’s age algebraically.
Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 20

21. Tuesday, May 8,
2018
Mrs. Nembhard-Wilson 21