1. Real Numbers
Week 1 Topic 1

2. Real Numbers Irrational Numbers Rational Numbers Real Numbers
Numbers that cannot be written as a fraction
√2, π
Rational Numbers
Numbers that can be written as a fraction
Decimals that repeat
Decimals that stop
√25, ½, 5, 0.123, …
Real Numbers
Set of all irrational and rational numbers

3. Real Numbers Integers Whole Numbers Natural Numbers
Positive and negative counting numbers (plus 0)
{…-3, -2, -1, 0, 1, 2, 3…)
Whole Numbers
Counting numbers starting at 0
{0, 1, 2, 3…}
Natural Numbers
Counting numbers starting at 1
{1, 2, 3…}

4. Real Numbers Infinite sets- not countable Finite sets- countable
Whole numbers greater than 8
{3, 4, 5 …}
Finite sets- countable
Integers between 2 and 17
{2, 5, 7, 19, 23}

5. Real Numbers Estimating the value of an irrational number
Compare perfect square values
List perfect squares close to your value
√67
√49 = 7; √64 = 8; √81 = 9
67 is between 64 and 81 so √67 is between 8 and 9
8 < √67 < 9

6. Real Numbers
Which of the following represents an infinite set of numbers?
{1/2, 1/3, ¼, 1/5}
{Negative integers}
{-3, -1, 0, 1, 3}
{Natural numbers between 5 and 20}

7. Real Numbers
Which of the following represents an infinite set of numbers?
{1/2, 1/3, ¼, 1/5}
This set has a clear start and stop, we see exactly 4 values in the set so it is countable or finite
{Negative integers}
integers go off to infinite so this set is not countable
c. {-3, -1, 0, 1, 3}
We can count the 5 values in this set.
{Natural numbers between 5 and 20}
We can list and count the values in this set. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

8. Real Numbers Which of the following is an irrational number? a. √57
3.78

9. Real Numbers Which of the following is an irrational number? a. √5
b. √9 = 3 whole numbers are rational
7 = 7/1 whole numbers are rational
3.78 = 378/100 decimals that stop are rational

10. Real Numbers
3. Between which two consecutive integers is √113 ? a. 12 and 13 b. 8 and 9 c. 10 and 11 d. 11 and 12

11. Real Numbers
3. Between which two consecutive integers is √113 ? a. 12 and 13 b. 8 and 9 c. 10 and 11 d. 11 and = 64; 92 = 81; 102 = 100; 112 = 121; 122 = 144; 132 = 169

12. Number Properties
Week 1 topic 2

13. Number Properties
Number Properties Rap
Math Properties

14. Number Properties Commutative Property Associative Property
Numbers can be added or multiplied in any order.
1 + 2 = 2 + 1
2(3) = 3(2)
Associative Property
When adding, changing the grouping doesn’t matter.
(1 + 2) + 3 = 1 + (2 + 3)
When multiplying, changing the grouping doesn’t matter.
2(3x4) = (2x3)4

15. Number Properties Identity Inverse Distributive Property
Adding 0 doesn’t change a value
Multiplying by 1 doesn’t change the value
Inverse
Adding the opposite gives you 0
Multiplying by the reciprocal gives you 1
Distributive Property
3(a + b) = 3a + 3b

16. Number Properties Closure
When you add or multiple real numbers together the answer will also be a real number.

17. Number Properties

18. Number Properties
When we multiply by 1 the number keeps its value or “identity”.

19. Number Properties

20. Number Properties
This is the Closure Property

21. Number Properties

22. Number Properties

23. Number Properties

24. Number Properties
The numbers are being regrouped so this is the associative property.

25. Number Properties

26. Number Properties
The multiplicative inverse is the reciprocal. We use it to make a number turn into 1.

27. Integers and Absolute Values
Week 1 Topic 3

28. Integers Adding two positive integers Just add.
Answer will be a positive
Adding a positive and a negative
Subtract
Answer will be the same as the larger of the two numbers
Adding two negatives
Just add
Answer will be negative

29. Absolute Value
Absolute Value is the distance a number is from zero on the number line.
|-2| = 2
|3 – 6| = |-3| = 3

30. Order of Operations
Week 1 Topic 4

31. Order of Operations
Order of Operations Rap
Order of ops rap 2

32. Order of Operations

33. Order of Operations Parenthesis 22 – 2[5 + 3(5)]
Brackets (more parenthesis) 22 – 2[5 + 15]
22 – 2[20]
Multiplication 22 – 40
Subtraction -18

34. Order of Operations

35. Order of Operations
2[7 + 5(-3)]
2[7 + (-15)]
2(-8)
-16

36. Order of Operations

37. Order of Operations 2(-48 / 4 x 3) 2(-12 x 3) 2(-36) -72
This one is tricky…we have to multiply and divide at the same time from left to right.

38. Scientific Notation
Week 1 Topic 5

39. Scientific Notation
A number written as a product of a power of 10 and a decimal number greater than or equal to 1 and less than 10.
3.72 x 106
When adding and subtracting the exponents must be the same…or we have to rewrite them in standard form first.
3.72 x x 106 = ( ) x 106 = 5.22 x 106

40. Scientific Notation Multiplying Dividing
Multiply the factors, add the exponents
Dividing
Divide the factors, subtract the exponents

41. Scientific Notation

42. Scientific Notation
Since the exponents have the same value we can add the factors 7.8 and -4.2.
(We end subtracting)
7.8 – 4.2 = 3.6
So our answer is 3.6 x 1020

43. Scientific Notation

44. Scientific Notation
5.1 / 1.7 = 3
-6 – (-4) = = -2
3 x 10-2

45. Scientific Notation

46. Scientific Notation Asia / Australia (1.72 x 107) / (3.13 x 106)
1.7 is about half as big as 3.13
1.72/3.13 ≈ .55
Subtract the exponents… 7 – 6 = 1
.55 x 101 = 5.5