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Notes: Standard Notation
Objective: Identify the Place Value of Digits in a Number.
Tennessee Curriculum Standards: 1.1, 1.7
Place value
Number systems - natural, whole, integers
Write Word Names for Numbers.
Assignment: Section 1.1 Exercises 1 8, 25 - 32, pages 8-10.
August 7, 2008
Bellwork: Overhead Problems
Times Tables 3s and 4s
Pretest page 2, 2 224 even.
Notes: Expanded Notation/ Adding and Subtracting
Objective: Convert Between Standard and Expanded Notation.
Write Addition Sentences for Real Life Problems.
Add Whole Numbers.
Find Perimeter.
Tennessee Curriculum Standards: 1.1, 1.5, 3.1
Write a Subtraction Sentence Corresponding to a Real Life Situation.
Write Related Subtraction and Addition Sentences.
Subtract Whole Numbers.
Expanded notation
- the number times its place value
Adding Whole Numbers
- Line up the decimals
- Add columns
- Carry over if needed
Commutative and Associative Properties
- Rearrange numbers (mentally) to make problem easy.
Perimeter add up all the sides.
Related sentences another problem using the same numbers.
Assignment: Section 1.1 Exercises 9 20, page 8.
Section 1.2 Exercises 3-66, every 3rd problem, pages 17 20, omit 15 27 and 39 51.
August 8, 2008
Bellwork: Overhead Problems
Times Tables 4s
Page 20, problems 69 72.
Notes: Subtraction and Related Sentences
Objective: Write a Subtraction Sentence Corresponding to a Real Life Situation.
Write Related Subtraction and Addition Sentences.
Subtract Whole Numbers.
Tennessee Curriculum Standards: 1.1, 1.5, 3.1
Subtraction
- Answer is called Difference
- Related sentences another subtraction or addition problems using the same numbers.
- Subtracting Whole Numbers
o Line up the decimals
o Sometimes need to borrow
Assignment: Section 1.3 Exercises 3-84, every 3rd problem, pages 26 29.
August 11, 2008
Bellwork: Overhead Problems
Times Tables 6s.
Page 29, 87 96.
Notes: Rounding, Estimating, and Order
Objective: Round Numbers to a Particular Place Value.
Estimate Sums and Differences by Rounding.
Ordering Numbers using > or < Signs.
Tennessee Curriculum Standards: 1.1, 1.3, 1.5, 1.8
Rounding rules.
- Locate the digit in that place value
- Digit to the right tells you to stay or round up.
- Change all digits to the right of this to zero
$847.25 To the nearest ten, tenth, hundred, one, thousand
Problem 1. Round 49,025.95 to the nearest one, ten, hundred, thousand, and ten thousand.
Estimate a sum
- by rounding each item to the same place value and add.
- Do not add, then round the answer!
- Add $279.99 and $179.95 by rounding to the nearest 10. Nearest 100.
Problem 2. Add 213, 888, 304, and 395 by rounding to the nearest 10
Ordering
- greater than > and less than <
- Can tell by creating a number line.
o The number to the right is always greater than the number to the left.
Read through at least one word problem.
Assignment: Section 1.4 Exercises 4 60, plus complete all word problems, pages 36 39.
August 12, 2008
Bellwork: Times Tables 8s
Page 39, 69 76.
Notes: Multiplication and Area
Objective: Multiplying Whole Numbers.
Estimate Products by Rounding.
Multiply to Find Area.
Tennessee Curriculum Standards: 1.1, 1.5, 1.8, 3.3
Factor x Factor = Product
3 x 5 means 3 groups of 5 or 5 + 5 + 5
In word problems, if you have several identical groups then multiply to find totals.
2 Soccer teams of 11 players is 2 times 11
5 decks of playing cards is 5 times 52.
A checkerboard has 8 squares per row and 8 rows. This is ?
Problem 1. If a building has 8 stories and has 12 windows per story, then how many windows total?
Properties
- Zero property
o Anything multiplied by 0 equals 0.
- Multiplicative Identity property
o Anything times 1 is itself
o A * 1 = A
- Distributive Property
o Can split up a number to make it easier to multiply
o 6 times 47 = 6 * 40 + 6 * 7
- Commutative Property
o Can change the order to make the problem easier
- Associative Property
o Can change grouping to make the problem easier
Problem 2. Use the properties to make the problems easier.
a. 3 * 72
b. 2 * 13 * 5
c. (4 * 4) * 5
Multiplying
274 * 306
Not important to line up decimals.
Find exact answer.
Multiply by factors of 10
Problem 3. Multiply 472 * 830, 8457 * 1000
Estimating
- Round the numbers first, then multiply.
- Round to nearest 10 and multiply
- Round to nearest 100 and multiply
Area
- Area of Rectangle
A = L x W
If length = 15 and width = 20 then area = 15 x 20.
Assignment: Section 1.5 Exercises 2-28 even.
every third problem, pages 47 51.
August 13, 2008
Bellwork: Times Tables 9s
Page 51, 85 94.
Notes: Multiplication and Area Part II
Objective: Multiplying Whole Numbers.
Estimate Products by Rounding.
Multiply to Find Area.
Tennessee Curriculum Standards: 1.1, 1.5, 1.8, 3.3
Review
a. 7 * 29
b. 6 * 7 * 5
c. (3 * 8) * 5
d. 158 * 503
e. 6570 * 100
Multiplying
2745 * 8463
(demonstrate)
Estimating
- Round the numbers first, then multiply.
- 356 * 648
- Round to nearest 10 and multiply
- Round to nearest 100 and multiply
Area
- Area of Rectangle
A = L x W
If length = 15 and width = 20 then area = 15 x 20.
Assignment: Section 1.5 Exercises 30 81 every third problem, omit 39 48.
August 14, 2008
Bellwork: Times Tables 11s
Page 47, 7 27 odd.
Notes: Division
Objective: Write a Division Sentence Related to a Real Life Situation.
Write Related Multiplication and Division Sentences.
Divide Whole Numbers.
Tennessee Curriculum Standards: 1.1, 1.5
Division
If you say out loud 20 divided by 5 = 4
· 20 is dividend, 5 is the divisor, 4 is the quotient.
· At least know Quotient!
· This is 20 items divided into 5 groups of 4
Problem 1. Divide 36 cars into 4 rows. How many in each row?
Related sentences
· There are two related multiplication sentences for each division problem.
· 21 / 7 = 3 3 * 7 = 21 and 7 * 3 = 21
· There are two related division sentences for each multiplication problem.
· 5 * 9 = 45 45 / 9 = 5 and 45 / 5 = 9
Problem 2. Write two related division sentences to the problem 6 * 7 = 42
Division basics
- Anything divided by 1 = itself
- Anything divided by itself = 1
- Zero divided by anything = zero.
- Cannot divide by zero. Undefined.
-
Long Division. Use remainders no decimals.
(for notes, just use these examples. The text has a good example on page 59.)
7616/7 (1088)
44847/56 (800 r47)
Assignment: Section 1.6 Exercises 1 78, pages 61 64, complete any 30 problems including at least 5 from each page.
August 15, 2008
Bellwork: Times Tables for 12s
Page 65, 81 88.
Notes: One Step Addition and Multiplication Equations
Objective: Solve Simple Equations by Trial.
Tennessee Curriculum Standards: 1.4, 1.5
Equations have an =
- Think of a balance
- A Solution is a number for the variable that makes the equation true.
- If the variable is alone, just do the calculation
o X = 7 * 8
o X = 56
- If the variable is not alone, then you must Solve for the variable.
o X + 20 = 50 means X + 20 has the same weight as 50
§ Whatever happens on one side of =, must happen on the other.
§ To get the X alone, what has to disappear?
§ To maintain balance, if we take away 20 from one side, what do we do to the other?
- Addition equations
- Solve by doing the same thing to both sides of the =
- X + 20 = 50
- -20 -20 Inverse step Must Show!
- X = 30
Problem 1. Solve for the variable.
X = 36/9
X + 12 = 25
- Subtraction Equations
- Solve by adding the # being subtracted to both sides of =
- X 8 = 8
- + 8 + 8
- X = 16
Problem 2. Solve x 24 = 15
Multiplication Equations
Solve by doing the opposite operation (division) with the exact same number.
4 X = 32
4 4 Inverse step Must Show!
X = 8
Problem 3. Solve 7X = 35
Assignment: Section 1.7 Exercises 1 12 all, 13 56 any 15, pages 70 71.
August 18, 2008
Bellwork: Times Tables for 3s.
Page 71, 59 67 odd.
Notes: Problem Solving
Objective: Apply Basic Math Operations (ASMD) to Solve Real Life Problems.
Tennessee Curriculum Standards: 1.8
Problem Solving Strategy (look at example 8, page 79)
1. Read the problem slowly and carefully.
a. Write out the information you know.
b. Determine exactly what the question is asking you to find.
i. Use a variable for unknown numbers. This will usually be the thing you are looking for.
c. Maybe draw a picture or a sketch. Label all the parts.
2. Translate the problem into an equation. Use the variable.
3. Solve the equation for the variable.
4. Check the answer to see if it makes sense.
5. Write the answer using the units of the problem.
- Demonstrate with problems from the text.
- Look at the chart on page 80
Assignment: Section 1.8 Exercises 1 58, pages 81 87.
August 19, 2008
Bellwork: Times tables for 4s
Page 87, 61 70.
Notes: Exponential Notation
Order of Operations
Parenthesis within parenthesis
Average
Objective: Write Exponential Notation for Products.
Evaluate Exponential Notation.
Simplify Expressions.
Remove Parenthesis Within Parenthesis.
Tennessee Curriculum Standards: 1.1, 1.7
Exponential Notation
3 * 3 * 3 * 3 = 34
Standard Notation is 81.
Define: Exponent, power, and base.
Powers of 10
- Multiplying/dividing
Problem 1. Write in Standard and exponential notation.
2*2*2*2*2
10*10*10*10*10*10*10*10
4*4*4
Order of Operations
PEMDAS
- If there are parenthesis within parenthesis, do inside parenthesis first.
- Using PEMDAS makes the problem EASIER!
o Do just one step at a time!
2 + 6 * 5
Problem 2. Simplify.
(8 - 3)2 6(7 - 5)2
Average
- Add all the stuff and divide by the number of thingys
Assignment: Section 1.9 Exercises 1 15 all, omit 11 and 13, 18 66 every fourth problem, omit 38, 46, 62, and 66, pages 94 96.
August 20, 2008
Bellwork: Times tables for 6s
Page 96, 69 - 78.
Notes: Review for test.
Assignment: Summary and Review, Exercises 1 65, pages 97 99.
August 21, 2008
Bellwork: Times Tables 7s.
Page 99, Exercises 58, 62, and 65.
Notes: None
Assignment: Chapter One Test, problems 1 44, pages 100 101.
A. 2 44 even
B. 1 43 odd
C. Omit 20 23
D. Extra Credit: What do you think the best movie ever made is? Minimum 4 sentences for credit.
August 22, 2008
Bellwork: Times Tables 8s.
Chapter 2 Pre-test, problems 1 32 even, page 104.
Notes: Integers
Objective: Identify Integers That Correspond to a Real Life Situation.
Find the Absolute Value of an Integer.
Find the Opposite of an Integer.
Tennessee Curriculum Standards: 1.1, 1.4
Integers are all the whole numbers and their opposites.
- These can model real life situations.
o A teacher gains 50 pounds
o A student loses 400 points on a 100 point assignment
o (make up others)
Problem 1. Make up a situation that would model a negative number.
Integers on a Number Line (Ordering)
- Numbers increase as you go left to right
- Negative infinity to positive infinity
- (show a number line -3 to 3)
- Comparing
o When comparing, the number to the left is always less, to the right is always greater.
Problem 2. Put the correct < or > sign between the integers.
-3 and -1, -100 and 5, 8 and 8, 0 and -7
Absolute value
- The distance from zero on a number line.
- Is always POSITIVE.
- |-7|
Opposites (Additive Inverses)
- The sum of opposites is always zero.
- Opposites are also called additive inverses.
Problem 3. Simplify
| 12 |, |-8|, -6 + 6, -1000 + 1000, -x + x
-(-11), find x if x = -20
Assignment: Section 2.1 Exercises 1 72 all, pages 110 - 111.
August 25, 2008
Bellwork: Times Tables 9s.
Page 112, Exercises 75 82.
Notes: Adding Integers
Objective: Add Integers.
Tennessee Curriculum Standards: 1.1, 1.4
Adding Integer Rules
- You must memorize these!
P + P = P (add)
N + N = N (add)
P + N = sign of larger number (subtract).
- Memorize these!
Problem 1. Solve.
9 + -14, 4 + 7, -5 + -12
Adding Opposites
- What is the opposite of a number?
o -7 + 7 =?
- The sum of opposites is always zero!
- Can you change around the order of added numbers?
o Yes, addition is good!
- Make the problem easier if possible (will definitely save you time today!)
Problem 2. Solve. (rearrange to make the problem easier)
15 + -42 + 8 + 23 + - 8 + -25 + 42 =
Assignment: Section 2.2 Exercises 1 34, all 36 74 even only, pages 116 117.
August 26, 2008
Bellwork: Times Tables 3s.
Page 118, Exercises 77 90, omit 79, 80, 87, and 88.
Notes: Subtracting Integers
Objective: Subtract Integers by Adding the Opposite.
Tennessee Curriculum Standards: 1.1, 1.4
Adding Integer Rules (remember?)
- You must memorize these!
P + P = P (add)
N + N = N (add)
P + N = sign of larger number (subtract).
- Memorize these!
Subtracting Integer Rules
- There are no rules
- Subtraction is BAD!
- Addition is GOOD!
Instead of subtracting Add the inverse (or the opposite).
1. Change the minus to a plus
2. Change the sign of the next number.
a. Memorize THIS too!
Problem 1. Solve.
6 15, -9 10, 5 - -3
Assignment: Section 2.3 Exercises 1 68 all, pages 122 125.
August 27, 2008
Bellwork: Times Tables 4s and 11s.
Page 125, Exercises 85 94.
Notes: Multiplying and Dividing Integers
Objective: Multiply Integers.
Divide Integers.
Tennessee Curriculum Standards: 1.1
P * P = P
N * N = P
P * N = N
Every pair of negatives cancels out.
Division same rules as multiplication.
Negative numbers to even powers = positive
Negative numbers to odd powers = negative
Negative numbers in parenthesis
(-5)2 = 25 = -5 ● -5
-52 = -25 = - 5 ● 5
Cannot divide by zero, answer is undefined.
Assignment: Section 2.4 Exercises 1 58, pages 131 132.
Section 2.5 Exercises 1 76 do five problems from each group of 10 (Example problems 1-5, 12-16, 25-29, etc), pages 136 137.
August 28, 2008
Bellwork: Times Tables 6s.
Page 138, Exercises 79 86.
Notes: Algebraic Expressions
Objective: Evaluate Algebraic Expressions by Substitution.
Use the Distributive Property.
Tennessee Curriculum Standards: 2.2, 2.4
Expressions
- Variables
- Constants
o Find 5x for x = 4
o Find A/B for A = -24 and B = 6
Problem 1. 4x/-8 + 10 for x = -6
More evaluating expressions
- Find the value of 7x2 + 25 for x = 3 and x = - 3
- (-m)2 and m2 for x = 11
The Distributive Property
Whatever is next to the parenthesis multiplies by each thing inside the parenthesis.
7(x + 5) = 7x + 7 (5)
7x + 35
The answer is called an Equivalent Expression.
-2 ( 3x + 4y + 5z)
Assignment: Section 2.6 Exercises 1 36, pages 143 145.
August 29, 2008
Bellwork: Times Tables 7s.
Page 145, 51 56.
Page 146, Exercises 77 84.
Notes: Like Terms
Objective: Combine Like Terms.
Determine the Perimeter of a Polygon.
Tennessee Curriculum Standards: 2.2, 2.4
Terms numbers and variables that are separated by + signs
Like Terms terms with the exact same variables and exponents. May have different coefficients. Can be added.
Simplify problems by adding or combining like terms
6x + 4y + 7x + 8y + 5x2
Unlike terms terms with different variables or exponents. Cannot be added.
Problem 1. Combine Like Terms
6x + 11x, -7m + 13m, 4x + 3 + 9x 15
Perimeter
Polygon closed figure with 3 or more sides.
Perimeter distance around one of these figures.
Rectangle 4 sided polygon with four right angles (90 degree angles).
Perimeter formula P = 2L + 2W
Perimeter of a square P = 4S
Problem 2. Find the perimeter of a polygon, rectangle, and a square (on overhead).
Assignment: Section 2.7 Exercises 2 52 even, pages 151 153.
September 2, 2008
Bellwork: Times Tables 8s.
Page 154, Exercises 55 66.
Notes: Solving One-Step Equations
Objective: Solve Equations Using Either the Addition or Division Principle.
Tennessee Curriculum Standards: 1.4
Finding Equivalent Equations
- Also called Solving for the Variable
- Get rid of stuff on same side of = with the variable.
Get rid of added terms by adding its opposite to both sides of =.
- Remember to change subtraction to addition
Get rid of multiplied coefficients by dividing by the same number.
Get rid of divided coefficients by multiplying by the same number.
Combining the steps Tomorrow!
- MUST SHOW THE INVERSE STEP!!!
X + 4 = -15 (Decide: Get rid of the 4)
+ -4 + -4 (This is the INVERSE STEP!)
x = -19 (Solve)
Problem 1. 23 = x - -12
42 = -6x (Decide: Get rid of the -6)
χ -6 χ -6 (This is the INVERSE STEP!)
-7 = x
Problem 2. 4x = -32
x/-5 = 3 (Decide: Get rid of the -5)
● -5 ● -5 (This is the INVERSE STEP!)
x = -15
Problem 3. 4 = x/-8
-x = 12 (Decide: Get rid of the neg sign.)
● -1 ● -1 (This is the INVERSE STEP!)
x = -12
Assignment: Section 2.8 Exercises 1 3, 13 60, pages 161 162.
September 3, 2008
Bellwork: Overhead Problems
Times Tables 9s
1. 3x =-18
2. 24 = x 9
3. -14 = x - -3
4. -7 = x/-9
5. 26 = -x
6. 16 = 10 - x
Notes: None (review for test)
Assignment: Complete the following problems
1. C + 17 = -11
2. -8L = -8
3. D/4 = -24
4. Find the perimeter of a square with 18 foot long sides.
5. Write 54,078 in expanded notation.
6. Write the word name for 34,040,703,000.
7. 43,683 + 17,009
8. 4531 759
9. 39 ● -9
10. 5986 χ 72
11. Round 2,948,738 to the nearest ten thousand.
12. Estimate the sum by rounding to the nearest thousand.
a. 98567 + 48487
13. Find the absolute value each of -73 and 59.
14. 8 (-9) 7 + 2
15. (-3) | 4 32 | - 5
16. 7x + 12 + 4x 8
17. Find x if x = -19.
18. 6 (4x 7y + 7)
19. If a = 7, b = 2, and c = 5, Find ab c
20. 42 + (-3)2 + -22
September 4, 2008
Bellwork: Overhead Problems
Times Tables 11s
1. Combine like terms
a. 4y + 9x 6y
b. 3 x + 9x + -3
c. 4(2x + 5) + 15
2. M - -7 = -13
3. 11 = M - 18
4. M/-6 = 12
5. 24 = -4M
Notes: None
Assignment: Inverse Operations Bingo.
September 5, 2008
Bellwork: Overhead Problems
Times Tables 12s
1. Combine like terms
a. -7y + 4x y 3x
b. 8 3x + 9x - 12
c. 3 + 5(3x - 7)
2. M - -12 = -1
3. 1 = M - -12
4. M/3 = -1
5. -36 = -9M
Notes: 2 Step Equations
Objective: Solve Equations that Require Both the Addition and Division Principle.
Tennessee Curriculum Standards: 1.4
Combines the skills from yesterday
Solve for the variable by getting rid of the stuff on the same side of the equals sign as the variable.
Opposite order of normal order of operations.
Get rid of added thing first.
Get rid of multiplied/ divided thing last.
3x + 7 = -17 Must get rid of the 7 and the 3 (in that order).
+ -7 + -7 Inverse Step Always get rid of added thing first.
3x = -24 Now its just a one-step! Divide by 3.
3 3 Inverse Step Opposite operation with the same #.
X = -8
Assignment: Section 2.8 Exercises 61 80, page 162.
Summary and Review Exercises 1 39, pages 163 165.
September 8, 2008
Bellwork: Overhead Problems
Times Tables 3s
1. Write 864.23 in expanded form.
2. 81.073 + 7.23 =
3. 6.05 2.9 =
4. -6x = 54
5. M/-3 = 6
6. 2x + 5 = 23
7. -4 = x/4 5
8. (-3)2
9. -52
10. 0.2 ● .36 =
11. 104
12. 80
13. -8 - -3 =
14. -8 ● -7 =
15. -3 + 8 (5 + 5)
16. Find the perimeter and area of a rectangle with a width of 7m and length 3m.
17. Estimate by rounding to the nearest 10. 87 + 42 + 117 + 3 =
18. 3 (2x + 5)
19. Write 2 related sentences. 48 χ 6 = 8
20. Write in exponential form. 3●3●3●3 x x x x x
21.