1. 1. in excess 2. dwindle 3. accumulate 4. fall Tie to LO
Activating Prior Knowledge – Notes
Write an equivalent word(s) for the word.
1. in excess
2. dwindle
3. accumulate
4. fall
Tie to LO

2. Learning Objective
Today, we will transcribe and identify expressions as linear or non-linear.
CFU

3. Concept Development Review
M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development Review
– Notes #1 & 2
1. Terms are any product of an integer power of x and a constant or just a constant.
Ex x 𝟏 𝟓 x
2. Constants are fixed numbers.
Ex 𝟏 𝟓
CFU

4. Concept Development Review
M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development Review
– Notes #3
3. When a term is the product of a constant(s) and a power of x, the constant is called a coefficient.
Ex x x 𝟏 𝟓 𝒙 x
CFU

5. M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development –Notes #4
Sort these expressions into two groups – mark one set with a star.
5𝑥+3
−8x+ 7 9 −3
9−𝑥 2
4𝑥 2 −9
0.31𝑥+7−4.2𝑥 𝑥
11(𝑥+2)
− 6−𝑥 +15−9𝑥
7+𝑥 −4 +3𝑥
CFU

6. Why did you mark certain expressions with a star?
M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development –Pair Share
Why did you mark certain expressions with a star?
5𝑥+3
−8x+ 7 9 −3
9−𝑥 2
4𝑥 2 −9
0.31𝑥+7−4.2𝑥 𝑥
11(𝑥+2)
− 6−𝑥 +15−9𝑥
7+𝑥 −4 +3𝑥
CFU

7. – Notes #5 & 6 Concept Development CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development
– Notes #5 & 6
5. Linear expressions in x are a special type of expression.
6. Linear expressions are expressions that are sums of constants and products of a constant and x raised to a power of 1, which simplifies to just x.
Typo
Ex 5x (x+2) −𝟖𝐱+ 𝟕 𝟗 −𝟑
CFU

8. – Notes #7 & 8 Concept Development CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development
– Notes #7 & 8
7. Non-linear expressions are also sums of constants and products of a constant a power of x.
8. Non-linear expressions will have a power of x that is not equal to 1 or 0.
Ex 𝟒𝒙 𝟐 −𝟗 𝟕+𝒙 −𝟒 +𝟑𝒙 ( 𝒙 𝟐 ) 𝟑 +𝟏
CFU

9. Concept Development – Notes #9
M4:LSN2
Linear and Non-Linear Expressions in x
Concept Development – Notes #9
9. A linear expression in x is an expression where each term is either a constant, an x, or a product of a constant and x.
Linear example
(𝟓𝟕−𝒙)
Non-linear example
𝟐𝒙 𝟐 +𝟗𝒙+𝟓
CFU

10. Skill Development/Guided Practice – Notes #10
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Notes #10
𝟒+𝟑𝒙 𝟓
How many terms are in this expression?
How many terms are just constants, and what are they? 𝟐 𝟏 𝟒
Linear or non-linear expression in x?
How many terms have coefficients, and what are they?
Non-linear because 𝟒+𝟑𝒙 𝟓 𝟏 𝟑
CFU

11. Skill Development/Guided Practice – Notes #11
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Notes #11
𝟕𝒙+𝟗+𝟔+𝟑𝒙
⬌𝟏𝟎𝒙+𝟏𝟓
How many terms are in this expression?
How many terms are just constants, and what are they? 𝟐 𝟏 𝟏𝟓
Linear or non-linear expression in x?
How many terms have coefficients, and what are they?
Linear because
𝟏𝟎𝒙+𝟏𝟓 𝟏 𝟏𝟎
CFU

12. Skill Development/Guided Practice – Notes #12
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Notes #12
𝟓+𝟗𝒙⋅𝟕+ 𝟐𝒙 𝟗
⬌𝟓+𝟔𝟑𝒙+ 𝟐𝒙 𝟗
How many terms are in this expression?
How many terms are just constants, and what are they? 𝟑 𝟏 𝟓
Linear or non-linear expression in x?
How many terms have coefficients, and what are they?
Non-Linear because
𝟓+𝟔𝟑𝒙+ 𝟐𝒙 𝟗 𝟐
𝟔𝟑 & 𝟐
CFU

13. Skill Development/Guided Practice – Notes #13
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Notes #13
𝟗𝟒+𝒙+ 𝟒𝒙 −𝟔 −𝟐
⬌𝟗𝟐+𝒙+ 𝟒𝒙 −𝟔
How many terms are in this expression?
How many terms are just constants, and what are they? 𝟑 𝟏 𝟗𝟐
Linear or non-linear expression in x?
How many terms have coefficients, and what are they?
Non-Linear because
𝟗𝟐+𝒙+ 𝟒𝒙 −𝟔 𝟐
𝟏 & 𝟒
CFU

14. Skill Development/Guided Practice – Notes #14
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Notes #14
𝒙 𝟏 +𝟗𝒙−𝟒
⬌𝟏𝟎𝒙−𝟒
How many terms are in this expression?
How many terms are just constants, and what are they? 𝟐 𝟏 −𝟒
Linear or non-linear expression in x?
How many terms have coefficients, and what are they?
Linear because
𝟏𝟎𝒙−𝟒 𝟏 𝟏𝟎
CFU

15. 𝒙 + 𝟒𝒙 𝒙+𝟒𝒙 is linear because both terms have a power of one. CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Exercise 1
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
The sum of a number and four times the number.
𝒙 + 𝟒𝒙
Linear or non-linear expression in x?
𝒙+𝟒𝒙 is linear because both terms have a power of one.
CFU

16. 𝟓⋅𝒙 𝒐𝒓 𝟓𝒙 CFU 𝟓𝒙 is linear because the x has a power of one.
M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Exercise 2
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
The product of five and a number.
𝟓⋅𝒙 𝒐𝒓 𝟓𝒙
Linear or non-linear expression in x?
𝟓𝒙 is linear because the x has a power of one.
CFU

17. M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Exercise 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
Multiply six and the reciprocal of the quotient of a number and seven.
𝟔⋅ 𝟕 𝒙
𝟔 ∙𝟕∙𝒙 −𝟏
Linear or non-linear expression in x?
𝟒𝟐𝒙 −𝟏 is non-linear because the x has a power that isn’t zero or one.
CFU

18. M4:LSN2
Linear and Non-Linear Expressions in x
Skill Development/Guided Practice – Exercise 4
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
Twice a number subtracted from four times a number, added to 15.
𝟏𝟓+(𝟒𝒙−𝟐𝒙)
Linear or non-linear expression in x?
𝟏𝟓+(𝟒𝒙−𝟐𝒙) is linear because the x terms have powers of one.
CFU

19. Linear or non-linear expression in x?
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
5. The square of the sum of six and a number.
𝑥+6 2
Linear or non-linear expression in x?
𝒙+𝟔 𝟐 is non-linear because the expression is being raised to a power of 2.
CFU

20. 𝑥 3 𝑥 2 = 𝑥 3−2 =𝑥 𝒙 is linear because the x terms has CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
6. The cube of a positive number divided by the square of the same positive number.
𝑥 3 𝑥 2 = 𝑥 3−2 =𝑥
Linear or non-linear expression in x?
𝒙 is linear because the x terms has
a power of one.
CFU

21. 𝑥+𝑥+1+𝑥+2+𝑥+3 4𝑥+6 𝒙 is linear because the x terms has CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
7. The sum of four consecutive numbers.
𝑥+𝑥+1+𝑥+2+𝑥+3
4𝑥+6
Linear or non-linear expression in x?
𝒙 is linear because the x terms has
a power of one.
CFU

22. M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
8. Four subtracted from the reciprocal of a number.
1 𝑥 −4= 𝑥 0−1 = 𝑥 −1 −4
Linear or non-linear expression in x?
𝒙 −𝟏 −𝟒 is non-linear because the x term does not have a power of one.
CFU

23. Linear or non-linear expression in x?
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
9. Half of the product of a number multiplied by itself, three times.
1 2 ⋅𝑥∙𝑥∙𝑥= 1 2 𝑥 3
Linear or non-linear expression in x?
1 2 𝑥 3 is non-linear because the x term does not have a power of one.
CFU

24. Linear or non-linear expression in x?
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
10. The sum that shows how many pages Maria read if she read 45 pages of a book yesterday and 𝟐 𝟑 of the remaining pages today. 𝑥
Linear or non-linear expression in x?
𝑥 is linear because the x term has a power of one.
CFU

25. 𝟏𝟎+𝟐𝒙 𝟏𝟎+𝟐𝒙 is linear because the x term has a power of one. CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
11. An admission fee of $10 plus an additional $2 per game.
𝟏𝟎+𝟐𝒙
Linear or non-linear expression in x?
𝟏𝟎+𝟐𝒙 is linear because the x term has a power of one.
CFU

26. 𝟐(𝟒𝒙+𝟓) 2(4x+5) is linear because the x term has a power of one. CFU
M4:LSN2
Linear and Non-Linear Expressions in x
Independent Classwork – Module page 3
Write each of the following as a mathematical expression and state whether it is linear or non-linear.
12. Five more than four times a number, then twice that sum.
𝟐(𝟒𝒙+𝟓)
Linear or non-linear expression in x?
2(4x+5) is linear because the x term has a power of one.
CFU

27. Closure - Paper CFU 1. What did we learn today?
2. Why is this important to you?
3. How can you tell if an expression is linear or non-linear?
Write each of the following statements as a mathematic expression. State whether the expression is a linear or non-linear expression in x.
4. Seven subtracted from five times a number, the different added to nine times a number.
5. Three times a number subtracted from the
Product of fifteen and the reciprocal of a number.
6. Half of the sum of two and a number multiplied by itself three times.
CFU