Real Numbers Week 1 Topic 1

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, 0.333333… Real Numbers Set of all irrational and rational numbers

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…}

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}

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

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}

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

Real Numbers Which of the following is an irrational number? a. √5 7 3.78

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

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

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 82 = 64; 92 = 81; 102 = 100; 112 = 121; 122 = 144; 132 = 169

Number Properties Week 1 topic 2

Number Properties Number Properties Rap Math Properties

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

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

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

Number Properties

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

Number Properties

Number Properties This is the Closure Property

Number Properties

Number Properties

Number Properties

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

Number Properties

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

Integers and Absolute Values Week 1 Topic 3

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

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

Order of Operations Week 1 Topic 4

Order of Operations Order of Operations Rap Order of ops rap 2

Order of Operations

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

Order of Operations

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

Order of Operations

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.

Scientific Notation Week 1 Topic 5

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 106 + 1.5 x 106 = (3.72 + 1.5) x 106 = 5.22 x 106

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

Scientific Notation

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

Scientific Notation

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

Scientific Notation

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