1. Lesson 1.1
Pattern: orderly and predictable way (rule) that items appear. Could be numbers, letters, images, figures.
Describe the rule and name next value:
1, 2, 3, 4,…
80, 70, 60, …
¼, ½, 1, …
2, ½, 1/8, …

2. Lesson 1.2 Warning 23 is not equal to 2 × 3!!!
Power: a way of writing repeated multiplication
23 = 2 × 2 × 2 = 8
Base: the factor (number being multiplied) of the Power (23).
Exponent: the number of times the Factor of the Power is being multiplied (23).
Warning 23 is not equal to 2 × 3!!!

3. Lesson 1.3 Scientific Notation
c x 10n, where 1≤c<10 and n is a whole number that is the number of decimal places.
120 = 1.2 x 102 = 1.2 x 100 = 120

4. Lesson 1.3 Scientific Notation
Distance to Moon: 357,000 km
3.57 × 105 km
Human Hair Diameter km
2.54 × 10-8 km

5. Lesson 1.4
Order of operations: The rules we follow to correctly evaluate an expression:
Evaluate expression in grouping symbols.
Evaluate powers.
Multiply and divide from left to right
Add and subtract from left to right.

6. Lesson 1.4
You buy a guitar for $40 and then pay $10 dollars for each of 5 lessons. What is the total cost?
$55
$90
$240
None of the above

7. Lesson 1.5 Properties of Numbers
Commutative (addition or multiplication)
Order of addition can change
Order of multiplication can change
Associative (addition or multiplication)
Grouping of addition can change
Grouping of multiplication can change
Not to addition and multiplication.
3 × ≠ 7 × 6 + 3
Not to subtraction or division

8. Lesson 1.5 Properties of Numbers
Identity Property (addition and multiplication)
Addition: any number plus zero is the number
Multiplication: any number times one is the number
Distributive Property:
a(b + c) = ab + ac
a(b – c) = ab – ac

9. Lesson 1.6
Variable: a letter used to represent one or more numbers (a, b, …z)
Variable expression: numbers, variables and operations (7 + x).
Evaluate: substitute values (numbers) for variables in a variable expression, and simplify the expression: evaluate 7 + x, where x = 3 is = 10

10. Lesson 1.6 Ways of showing multiplication with variables. 5 × f 5f

11. Lesson 1.6 Other ways of showing division with variables. 4 ÷ b b ÷ 5

12. Lesson 1.7 Turning words into math operations: Addition Subtraction
Multiplication
Division

13. Order always matters in subtraction and division.
Lesson 1.7
Remember:
Order always matters in subtraction and division.

14. 1.8 Simplifying Expressions
Simplify: to create an equivalent expression with the fewest number of terms.
Take the expression 4x - 3x + 2x2 + 1
Terms: a number, variable or product of numbers and variable separated by + or – signs: 4x, 3x, 2x2, 1
Like terms: terms that have the same variable part: 4x, 3x
Coefficient: number part of the product of a number and a variable: 4 for 4x, 3 for 3x, 2 for 2x2.
Constant: a term with a number, but no variable: 1
Simplify: x + 2x2 + 1

15. 1.8 Simplifying Expressions
Remember:
Variable with no number in front of it has a coefficient of 1.
Ex: 3x – x = 3x – 1x = 2x

16. Lesson 1.9
Equation: a mathematical sentence formed by setting two expressions equal or balanced.
Solution: a number that you can substitute for a variable to make an equation true.
Solving an equation: finding all the solutions of an equation
2 + 2 = – n = 1
3n = ÷ 2 = n

17. 1.10 Solving Addition and Subtraction Equations
Inverse operation: an operation that undoes another operation.
Addition is the inverse of subtraction.
Subtraction is the inverse of addition.
Multiplication is the inverse of division.
Division is the inverse of multiplication.
Equivalent Equations: Equations that have the same solution.
Do inverse operations on both sides of the equal sign!

18. 1.10 Solving Addition and Subtraction Equations
Subtraction Property of Equality: subtracting the same number from each side of an equation produces an equivalent equation.
x + 7 = -10
– 7 = – 7
x = -17
Check: = -10 → -10 = -10
Addition Property of Equality: adding the same number to each side of an equation produces an equivalent equation.
-9 = y - 12
= y –
3 = y
Check: -9 = 3 – 12 → -9 = -9

19. 1.10 Solving Addition and Subtraction Equations
P 50: 1-7: Use +/- Properties of Equality and show all work, including check.
Do inverse operations on both sides of the equal sign!

20. 1.11 Solving Equations by Multiplying or Dividing
Division Property of Equality: dividing each side of an equation by the same non-zero number produces an equivalent equation.
3x = 15
3x/3 = 15/3
x = 5
Check: 3(5) = 15 → 15 = 15
Multiplication Property of Equality: multiplying each side of an equation by the same non-zero number produces an equivalent equation.
y/2 = .75
2 × y/2 = 2 × .75
y = 1.5
Check: 1.5/2 = → .75 = .75