1. Algebra: Equations & Patterns
Math 6

2. Expressions & Equations
Equations, Patterns, & Graphs
Expressions & Equations

3. Expressions & Equations
Numbers and operations (+, -, x, ÷ ,) grouped together that show the value of something
2 × 3
3 + 5 – 7 x 2 ÷ 10
It is one side of an equation

4. Expressions & Equations
A mathematical statement that tells that two sides are equal.
It will include an equals sign "=“.
2 + 5 = 7
1 + 6 = 2 + 5
Solve the following =

5. Expressions & Equations
An equations says: “The value of the expression on the left (2 + 5) is equal to the value of the expression on the right (7)”
An equation is a statement "this equals that“
Think of it like a scale

6. Expressions & Equations

7. Expressions & Equations
Variable:
A variable is a symbol for a number we don't know yet.
It is usually a letter like x or y.
Variables on their own (without a number next to them) actually have a hidden 1
x is really means 1(x)
ex. How many students will be absent tomorrow?

8. Expressions & Equations
Algebraic Equation:
A mathematical statement that tells that two sides are equal.
It will include a variable.
The variable must be “solved”
is also like a scale
x + 2 = 6
4x − 7 = 5

9. Expressions & Equations

10. Expressions & Equations
Find the missing number to make the equations true:
8 x  = 112
show “HOW” you solved it

11. Expressions & Equations
What strategy did you use?
112 ÷ 8 = 14
This method is called: Inverse Operations
An operation that undoes another operation (the opposite)

12. Expressions & Equations
Examples
4 + 7 = 11 / 11 – 7 = 4 (11 – 4 = 7)
6 x 3 = 18 / 18 ÷ 3 = 6 (18 ÷ 6 = 3)

13. Expressions & Equations
You Try
216 = 48 + 
216 – 48 = 168

14. Expressions & Equations
Algebra Method (solve for x)
x ÷ 6 = 144
The variable x is not alone on one side . It has a ÷ 6 beside it. To find out what the value of x is we need to “isolate the variable”

15. Expressions & Equations
Algebra Method (solve for x)
Step 1:
Perform the inverse operation to both sides, which means to multiply 6 from both sides.
x ÷ 6 = 144
x x 6

16. Expressions & Equations
Algebra Method (solve for x)
Step 2:
Solve
x ÷ 6 = 144
x x 6
x = 864

17. Expressions & Equations
Algebra Method (solve for x)
Step 3:
Check
x = 864
864 ÷ 6 = 144

18. Expressions & Equations
You Try:
x + 2 = 3
x = 1
1 + 2 = 3

19. Expressions & Equations
You Try:
x - 2 = 3
+ 2 = +2
x = 5
5 - 2 = 3

20. Expressions & Equations
You Try:
2x = 8
÷ 2 = ÷ 2
x = 4
2 (4) = 8

21. Expressions & Equations
You Try:
x ÷ 2 = 8
*2 = *2
x = 16
16 ÷ 2 = 8

22. Expressions & Equations
Translating Phrases:
Addition: increased by, more than, sum of
Subtraction: decreased by, difference, less than
Multiplication: multiplied by, product of
Division: per, quotient of, groups of

23. Patterns, Graphs, & Equations

24. Patterns Function Machine:
Input
Output
Patterns
Function Machine:
Shows the relationship between input & output values
The input column is a variable number (changes)
The middle line represents a mathematical “rule”
The output is the result of the “rule”. It is dependent on the variable number

25. Patterns Function Machine
Input
Output 1 2 3 4
Patterns
Function Machine
The input column is a variable number (changes)
What is the pattern?
Start at 1 add 1 each time

26. Patterns Function Machine
Input
Output 1 2 3 4
Patterns
Function Machine
The middle line represents a mathematical “rule”
In this case the rule is “+8”

27. Patterns Function Machine
Input
Output 1 9 2 10 3 11 4 12
Patterns
Function Machine
The output is the result of the “rule”. It is dependent on the variable number
What is the pattern?
Start at 9 add 1 each time

28. Patterns
You Try: The rule is multiply by 5
Input
Output 1 2 3 4

29. Patterns 1 5 2 10 3 15 4 20 You Try: The rule is multiply by 5 Input
Output 1 5 2 10 3 15 4 20

30. Input
Output 1 9 2 10 3 11 4 12
Patterns
We can use the input pattern and the output pattern to solve the “rule” between the 2 columns.
Write the input pattern: start at 1 add 1
Write the output pattern: start at 9 add 1

31. Patterns The rule can have more than one operation.
Input
Output 2 10 4 14 6 18 8 22
Patterns
The rule can have more than one operation.
This rule is multiply by 2, then add 6.
Algebra expression: 2x +6

32. Patterns You Try: Write the input pattern: Write the output pattern:
Write the algebra expression:

33. Patterns 2 4 6 8 10 You Try: multiply by six, then add one Input
Output 2 4 6 8 10

34. Patterns
You Try: multiply by six, then add one
Input
Output 2 13 4 25 6 37 8 49 10 61

35. Patterns You Try: Write the input pattern: start at 2 add 2 each time
Write the output pattern:
start at 13 add 12 each time
Write the algebra expression:
6x + 1

36. Patterns You Try: Write the input pattern: Write the output pattern:
Write the algebra expression:

37. Patterns 30 60 90 120 150 You Try: divide by 3 then subtract 2 Input
Output 30 60 90
120
150

38. Patterns
You Try: divide by 3 then subtract 2
Input
Output 30 8 60 18 90 28
120 38
150 48

39. Patterns 𝑥 3 −2 You Try: Write the input pattern:
start at 30 add 30 each time
Write the output pattern:
start at 8 add 10 each time
Write the algebra expression:
𝑥 3 −2

40. Input
Output 1 2 5 3 9 4 13 17
Patterns
We can use the input pattern and the output pattern to solve the “rule”
Write the input pattern: start at 1 add 1 each time
Write the output pattern: start at 1 add 4 each time

41. Input
Output 1 2 5 3 9 4 13 17
Patterns
Since the output pattern increase by 4, that is a clue about the operation. (repeated addition)
This suggests that the input numbers are multiplied by 4.
1 x 4 ≠ 1
2 x 4 ≠ 5

42. Patterns Think…If you have 4 how do you turn it into a 1?
Input
Output 1 2 5 3 9 4 13 17
Patterns
Think…If you have 4 how do you turn it into a 1?
(divide by 1)?
Think…I you have 8 how do I turn it into a 5?

43. Patterns Multiply the input by 4. Then subtract 3.
Output 1 2 5 3 9 4 13 17
Patterns
Multiply the input by 4. Then subtract 3.
algebra expression: 4x – 3 =
Test for 5
4 * 5 = = 17

44. Patterns
Step 1:
Find the output pattern.

45. Patterns
Step 2:
Multiply the INPUT numbers by the gap.

46. Patterns
Step 3:
What must you do to each number in the second column?

47. Patterns Step 4: Write a rule for the T-table:
Multiply by 3 then add 2
Write an expression
3x + 2

48. Patterns You Try: Write the input pattern: Write the output pattern:
Write the algebra expression:

49. Patterns
Input
Output 1 7 2 14 3 21 4 28

50. Patterns You Try: Write the input pattern: start at 1 add 1 each time
Write the output pattern:
start at 7 add 7 each time
Write the algebra expression: 7x

51. Patterns You Try: Write the input pattern: Write the output pattern:
Write the algebra expression:

52. Patterns
Input
Output 1 9 2 14 3 19 4 24

53. Patterns You Try: Write the input pattern: start at 1 add 1 each time
Write the output pattern:
start at 9 add 5 each time
Write the algebra expression:
5x + 4

54. Patterns Use a pattern to solve a problem
Dara works at a fishing camp in the Yukon.
Dara earns $25 a day, plus $8 for each fishing net she repairs.
On Saturday, Dara repaired nine nets.
How much money did she earn?

55. Patterns Strategy: What is the variable?
Dara earns $25 /day. If she doesn’t fix any nets she still gets $25.
She gets $8 per every net she fixes.
The variable is “how many nets she fixes”
8n + 25 =

56. Patterns
Input
Output 1 33 2 41 3 49 4 57