Lesson Plan #1
"Whole Numbers: How to Dissect and Solve Word Problems"
"Fractions"
| Lesson Objectives | Reading Assignment | Teacher’s Notes | Homework Assignment | Quiz |
LESSON OBJECTIVES: The objectives are listed on the following pages of your textbook.
Chapter 1: page 3
LU 1-1 Reading, Writing, and Rounding Whole Numbers
LU 1-2 Adding and Subtracting Whole Numbers
LU 1-3 Multiplying and Dividing Whole Numbers
Chapter 2: page 37
LU 2-1 Types of Fractions and Conversion Procedures
LU 2-2 Addition and Subtraction of Fractions
LU 2-3 Multiplication and Division of Fractions
READING ASSIGNMENT:
Chapters 1 and 2.
Teacher’s Notes
Chapter 1
**The problem solving system given in the text is the key to an effective attack of any word problem in math. Too often we are side-tracked by the numbers and forget the goal is too solve a problem. Arithmetic is only a tool to solve problems. This procedure will be referred to throughout the course.
State the problem. (What question am I answering?)
Decide on the best method to solve the problem.
Does the answer make sense? (Did you answer the question asked?)
Evaluate the results.
I find that half of the wrong answers on quizzes and tests are because the student did not use this system.
EX: A soldier goes to the PX with $10 in his pocket and buys 4 candy bars for $.67 each.
Q 1: How much money did he spend? (Many students would automatically solve and answer "How much money would he have left over?")
In the number 895 the 8 represents eight hundred, the nine represents nine tens and the five represents five ones.
Rounding Whole Numbers.
Identify the place value of the digit you want to round.
If the digit to the right is 5 or more, increase the identified digit by 1 (round up), if the digit to the right is less than 5 do not change the identified digit.
Change all digits to the right of the identified digit to zero.
EX: 789,234
to the nearest thousand 789,000
to the nearest ten-thousand 790,000
to the nearest hundred-thousand 800,000
Learn to estimate your answer before solving the problem. This will help avoid arithmetic mistakes or hitting the wrong button on the calculator.
EX: 121 + 487 = 100 + 500 = your answer needs to be close to 600
Again estimate your answer before doing the arithmetic.
Understand that remainders are part of the divisor
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EX: 15 ÷ 7 = 7 ) 15 is 2 1/7 (2 R1 is a grade school answer)
(HINT) on the quiz for this lesson the correct answer will not be a decimal.
For posting homework questions
Multiply—keyboard command (Alt) 0215 = ×
Divide—keyboard command (Alt) 0247 = ÷
A fraction is part of a number.
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Numerator = |
Part |
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Denominator = |
Whole |
Proper fraction: The numerator is more than the denominator. 3/4
Improper fraction: The numerator is less than the denominator. 4/3
Mixed number: A whole number and a fraction. 3 ½
Reducing fractions: Divide both the numerator and the denominator by the same number. When solving fraction problems the answers should be reduced to the lowest term.
EX: 6/8 6 ÷ 2 = 3 8 ÷ 2 = 4 6/8 = 3/4
Improper fractions to Mixed Numbers: Divide the denominator (bottom number) into the numerator (top number).
EX: 21/4 21 ÷ 4 = 5 ¼
Mixed Number to Improper Fractions: Multiply the whole number by the denominator (bottom number) and add the numerator (top number). Keep the same denominator.
EX: 4 7/10 = 4 × 10 then + 7 = 47/10
LU 2-2: Addition and Subtraction of Fractions
Addition:
Find the common denominator. (you may always multiply the denominators to produce a common denominator).
Change the fractions. (you must multiply the numerator and denominator by the same number).
Add the numerators.
Reduce the answer to the lowest term.
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EX: |
a/b + c/d |
= ad + cb |
2/5 + 1/3 |
= (2×3) + (1×5) |
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bd |
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(5×3) |
5)Whole numbers may be added to the result (when dealing with mixed numbers).
Subtraction:
Find the common denominator. (you may always multiply the denominators to produce a common denominator).
Change the fractions. (you must multiply the numerator and denominator by the same number).
Borrow if needed. (when borrowing add the numerator and denominator to produce a new numerator).
Subtract the numerators.
Reduce the answer to lowest terms.
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EX: a/b – c/d = |
ad – cd |
2/3 – 1/5 = |
(2×5) – (1×3) |
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bd |
(3×5) |
Borrowing
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EX: 7 3/5 = |
7 12/20 = |
6 32/20 |
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- 2 3/4 = |
- 2 15/20 = |
- 2 15/20 |
4 17/20 |
Multiplication:
Change mixed numbers to improper fractions.
Reduce the question if possible.
Multiply straight across.
Reduce the answer to lowest terms.
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EX: 5/7 × 7/10 = |
1/1 × 1/2 = |
1/2 |
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EX: 2 3/4 × 3 3/5 = |
15/4 × 18/5 = |
3/2 × 9/1 = |
27/2 = 13 1/2 |
Division:
Change mixed numbers to improper fractions.
Invert the second number (divisor) and follow the rules for multiplication.
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EX: 7/12 ÷ 3/4 = |
7/12 × 4/3 = |
7/3 × 1/3 = |
7/9 |
Homework Assignment
Chapter 1 page 23 1-50 through 1-78 even only
Chapter 2 page 57 2-1 through 2-66 even only.
Discussion Question
Remember you must post either the work and solution for one of these problems (not already posted) or propose a superior process or correction to someone else’s solution.
You should now take the quiz for Lesson 1.
You should now take the quiz for Lesson 1.
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