1. Introduction to Variables and Algebraic Expressions
Lesson 4.1.1
Teachers: This lesson is designed to be used with mini-whiteboards. See the lesson plan for directions. There are student notes provided that will let the students know when it’s time to use the boards.
Obj. 6.EE.2a

2. Number Shapes
You will be given a set of cards. Each person is responsible for one card!
You may tell your team exactly what your card has written on it, but you MAY NOT show your card to the team!
Your challenge: Work together to determine what number is being represented by each shape.
Set 1 can be used to model the task with the class. There are four puzzles in all and they increase in difficulty. The teacher may want to prepare all sets and once a team solves one version, the teacher can give the team the next version in the set.

3. Variables A variable is a letter that stands for an unknown number.
Different letters indicate different values. For example, if X = 5, then the value of Y and Z will be a number other than 5.

4. Algebraic Expressions
An Algebraic Expression is a mathematical expression built from numbers, variables, and operations.
There are no equal signs in an algebraic expression.

5. Let’s Get Started… Expressions Involving Addition
Expressions Involving Subtraction
Expressions Involving Multiplication and Division
Expressions Involving Exponents

6. Turn-and-Talk
You have 1 minute to work with a partner and jot down as many words as you can that mean addition. (Write them on your four-door foldable in your notes!)
GO!

7. Key Words for Addition ( + )
plus
sum
total
increased by
quantity of
more than
added to
Here are some key words that indicate addition.

8. When writing an algebraic expression, you assign a variable to represent the unknown number.
The variable can be any letter of your choice. The letters “x” and “n” are popular letters to use.
Let’s take some addition phrases and see what the algebraic expression looks like...

9. Translating Addition (+) Phrases into Algebraic Expressions
A number plus 3
The sum of a number and 5
The total of 6 and some number
The quantity of 19 and a number, n
A number increased by 2
n + 3
c + 5
6 + x
19 + n
p + 2
Normally, you write the expression in the order that it is
presented in the phrase.

10. If you think about it though, the expression makes sense.
“Turn Around Words”
than, from, to
PHRASE
Algebraic Expression
10 more than a number
A number added to 11
k + 10
11 + t
Emphasize the words THAN and TO.
When you see the words than, from or to, the expression is turned around from how it is written in the phrase.
If you think about it though, the expression makes sense.

11. Match the phrase to the correct expression
x plus 25
25 + x
x + 25
Mini-Whiteboard: Have the students write their answer on a mini-whiteboard. On cue have the students hold up their answers.

12. Match the phrase to the correct expression
50 increased by x
50 + x
x + 50
Mini-Whiteboard

13. The total of 17 and a number, n
Match the phrase to the correct expression
The total of 17 and a number, n
n + 17
17 + n
Mini-Whiteboard

14. Match the phrase to the correct expression
The sum of c and 7
7 + c
c + 7
Mini-Whiteboard

15. Match the phrase to the correct expression
12 more than x
x + 12
12 + x
Mini-Whiteboard Circle 10 and draw arrow to the back! Emphasize the word THAN. This is a turn-around word.
The Tricky One!

16. Moving On… Expressions Involving Addition
Expressions Involving Subtraction
Expressions Involving Multiplication and Division
Expressions Involving Exponents

17. Turn-and-Talk
You have 1 minute to work with a partner and jot down as many words as you can that mean subtraction. (Write them on your four-door foldable in your notes!)
GO!

18. Key Words for Subtraction ( - )
minus
difference
decreased by
less
less than
fewer than
subtracted from
Here are some key words that indicate subtraction.

19. Translating Subtraction ( - ) Phrases into Algebraic Expressions
A number minus 7
The difference of 3 and a number
9 less a number
A number decreased by 12
b – 7
3 – n
9 – h
x – 12

20. 6 subtracted from a number
“Turn Around Words”
than, from, to
PHRASE
Algebraic Expression
4 less than a number
A number fewer than 21
6 subtracted from a number
x – 4
21 – m
r – 6
Emphasize the words THAN and FROM.

21. Match the phrase to the correct expression
10 decreased by a number, w
10 – w
w – 10
Mini-Whiteboard

22. Match the phrase to the correct expression
The difference of 60 and p
p – 60
60 – p
Mini-Whiteboard

23. Match the phrase to the correct expression
75 less x
x – 75
75 – x
Mini-Whiteboard

24. Match the phrase to the correct expression
Subtract c from 12
c – 12
12 – c
Mini-Whiteboard Circle the “c” and draw arrow to the back. Emphasize the word FROM. It is a turn-around word!
Hmmm…One of those tricky ones again!

25. Match the phrase to the correct expression
45 less than a number, n
n – 45
45 – n
Mini-Whiteboard Circle the “c” and draw arrow to the back. Emphasize the word THAN. It is a turn-around word.
Help! Which one is it…

26. Moving On… Expressions Involving Addition
Expressions Involving Subtraction
Expressions Involving Multiplication and Division
Expressions Involving Exponents

27. Which of the following correctly represents multiplication?
Select All that Apply
6 × 8
6(8)
(6)8
(6)(8)
6•8
All choices represent a correct way to illustrate multiplication.

28. Turn-and-Talk
You have 1 minute to work with a partner and jot down as many words as you can that mean multiplication. (Write them on your four-door foldable in your notes!)
GO!

29. Key Words for Multiplication ( x )
times
product
twice; double
triple
of (when finding part of a number)
half (times )
You can take half of something by either multiplying by ½ or dividing by 2, so half will be a key word for both multiply and divide.

30. Translating Multiplication, (x), Phrases into Algebraic Expressions
There are 4 ways to write multiplication. Can you fill in the missing ways?
PHRASE
Algebraic Expression
8 times a number 8n
8 • n
8(n)
8 x n
The product of 14 and a number
14 • n
14(n)
Twice a number; double a number 2n
2 x n
Triple a number
3 • n
3(n)
A number multiplied by 6
n • 6
n x 6
Three-fourths of a number
¾ n
¾ (n)
Half a number
½ • n
½ n
Explain the “algebra way” of expressing multiplication: the number is written in front of the variable with no symbol in between. In algebra if a number is right next to a variable, 8n, it is understood to be multiplication.

31. Turn-and-Talk
You have 1 minute to work with a partner and jot down as many words as you can that mean division. (Write them on your four-door foldable in your notes!)
GO!

32. Key Words for Division ( ÷ )
quotient
divided by
half (÷ 2 )
separated into
ratio

33. True or False
These all mean the same thing.
True

34. Translating Division (÷) Phrases into Algebraic Expressions
The quotient of a number and 7 n 7
n ÷ 7
10 divided by a number 10 x
10 ÷ x
Half a number, n 2
n ÷ 2
The ratio of a number to 15 15
n ÷ 15
Explain that the “algebra way” of expressing division is with a fraction bar.

35. The product of a number and 19
Match the phrase to the correct expression
The product of a number and 19
n ÷ 19
(n)(19)
Mini-Whiteboard

36. The quotient of 60 and a number
Match the phrase to the correct expression
The quotient of 60 and a number
60 ÷ n
n ÷ 60
Mini-Whiteboard

37. Match the phrase to the correct expression
Twice a number, n
2 + n 2n
Mini-Whiteboard

38. Match the phrase to the correct expression
50 divided by x
50 ÷ x
x ÷ 50
Mini-Whiteboard

39. Match the phrase to the correct expression
A number divided by 75 75 y y 75
Mini-Whiteboard

40. Match the phrase to the correct expression
Half a number, x
𝑥 ÷ 1 2 1 2 x
Mini-Whiteboard

41. Moving On… Expressions Involving Addition
Expressions Involving Subtraction
Expressions Involving Multiplication and Division
Expressions Involving Exponents

42. Key Words for
Exponents

43. Match the phrase to the correct expression
Mini-Whiteboard

44. Match the phrase to the correct expression
A number, x, squared 2𝑥
Mini-Whiteboard

45. Match the phrase to the correct expression
A number, y, cubed
𝑦 4
Mini-Whiteboard

46. Find the turn around words…
Closure
Add Subtract Multiply Divide
sum
plus
increased by
more than
total
quantity of
added to
difference
minus
decreased by
less than
less
fewer than
subtracted from
product
times
twice
double
triple of
half
quotient
divide by
separated into
ratio
half
Go over the key words for each operation. Point to the “Add” column and have a student name the “turn around words”.
Answer: more than, added to
Point to the “Subtract” column and have a student name the “turn around words” as well.
Answer: less than, fewer than, subtracted from
Which key words indicate that the expression is turned around from how it is listed in the phrase?
Find the turn around words…