Intro to Algebra Unit 2 - Central Dauphin School District · Now let’s try translating verbal phrases found in word problems to help us solve. ... 6 + 4 x 3 12 - 8 + 2 – 3 2 (7

IntrotoAlgebra–Unit2

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Mon Tue Wed Thu Fri

Sept 30 1-1 Translating Expressions HW

Oct 1 1-1 Translating Expressions HW

Oct 2 1-2 Order of Operations HW



Oct 7 Review of 1-1 & 1-2 HW

Oct 8 Quiz on 1-1 & 1-2 HW

Oct 9 1-5/1-6 Properties HW



Oct 14 (In-service Day No Students)



Oct 17 1-8 Subsets of Real #s HW

Oct 18 1-8 Subsets of Real #s HW

Oct 21 4-7 Scientific Notation HW



Oct 24 Quiz on 1-8 & 4-7 HW

Oct 25 Review HW

Oct 28 Review HW

Oct 29 Unit 2 Test HW

Oct 30 HW

Oct 31 HW

Please remember these dates may be changed based on student progress. I am using my experience from previous years to predict how long each topic will take.

Test will be on October 29th, as it will only be the second test for the 1st Marking Period.


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1-1 What verbal phrases should you look for to translate these operations into algebraic expressions?


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1-1 Translating Expressions How can you translate verbal expressions to algebraic expressions

and equations? Translate Verbal Phrases into Numerical Expressions Use your graphic organizer to help you understand what operations the words indicate. ~Remember that there are many words that all mean the same operation. Examples:

1. The product of eight and seven

2. The difference of nine and three

3. The quotient of eighteen and six

4. Seven more than three

You Try: 5. The sum of seven and five

6. Eight multiplied by three

7. Three increased by nine

8. Fifteen divided by five

**The phrase that always gives the most problems is “less than” Which expression means three less than seven?

7 – 3 or 3 - 7 This often gets confused with three less seven, which means…


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Now let’s try translating verbal phrases found in word problems to help us solve. Examples:

1. Madison earns an allowance of $5 per week. She also earns $4 per hour babysitting, and usually babysits 6 hours a week. Write an expression for the total amount of money she earns in one week.

2. Hector purchased 3 CDs for $13 each and 2 cassette tapes for $9 each. Write and then evaluate an expression for the total cost of his purchase.

You Try: 3. A taxi-cab company charges a fare of $4 for the first mile and $2 for each additional

mile. Write and then evaluate an expression to find the fare for a 10-mile trip. Translate Numerical Expressions into Verbal Phrases RECALL: Match the expressions with the verbal phrases that mean the same thing.

1. 9 – 3 a. the sum of 3 and 9 2. 3 9 b. the quotient of 9 and 3 3. 9 x 3 c. 3 less than 9 4. 3 + 9 d. 9 multiplied by 3 5. 9 3 e. 3 divided by 9

Use your graphic organizer to write two different verbal phrases for each numerical expression.

6. 5 + 1

7. 8 + 6

8. 9 x 5

9. 2(4)

10. 12 3

11.

12. 8 – 7

13. 11 – 5


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Practice Problems Write a numerical expression for each verbal phrase.

1. Six minus three 2. Seven increased by two 3. Nine multiplied by five 4. Eleven more than fifteen 5. Twenty-four divided by six 6. Four less than eighteen 7. The total amount of CDs if Erika has 4 and Roberto has 5 8. The cost of 3 notebooks at $6 each

9. Find the value of six added to the product of four and eleven. 10. What is the value of sixty divided by the sum of two and ten?

11. A bag of potting soil sells for $2, and a bag of fertilizer sells for $13.

a. Write an expression for the total cost of 4 bags of soil and 2 bags of fertilizer

b. What is the total cost of the gardening supplies?

12. Miko is packing for a trip. The total weight of her luggage cannot exceed 200 pounds. She has 3 suitcases that weigh 57 pounds each and 2 sport bags that weigh 12 pounds each.

a. Write an expression for the total weight of Miko’s luggage

b. Is Miko’s luggage within the 200-pound limit? Write two different verbal phrases for each numerical expression.

13. 8 5 14. 17 4

15. 30 3 16. 12 2

17. 18. 7 3

19. 4 5 20. 12 6


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1.2 Numbers and Expressions How can you use the order of operations to evaluate expressions?

Order of Operations: MUST be used to evaluate expressions that have a combination of numbers and operations. Step 1: Step 2: Step 3: Step 4: Look at the following expressions. Tell which operation you would perform first. 6 + 4 x 3 12 - 8 + 2 – 3 2 (7 + 2) 20 2 + 3 x 4 Now let’s try evaluating some expressions…

1. 3 + 4 x 5 2. 18 3 x 2

3. 6 (2 + 9) – 3 x 8 4. 4 [(15 – 9) + 8 (2)]

5.


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You Try: 6. 6 + 8 x 2 7. 24 8 x 3

8. 5 (4 + 6) – 7 x 7 9. 3 [(18 – 6) + 2 (4)]

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Practice Problems Name the operation that should be performed first, then find the value of each expression.

1. 3 ∙ 6 4

2. 32 24 2

3. 5 8 7

4. 6 15 4

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6. 11 56 2 ∙ 7 Find the value of each expression.

7. 2 ∙ 6 8

8. 12 3 3

9. 12 3 21

10. 9 18 3

11. 8 5 6

12. 4 7 11

13.

14.


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15. 11 6 1

16. 9 7 ∙ 13

17. 56 7 2 ∙ 6

18. 75 7 8 3

19. 5 4 12 4 2

20. 9 22 17 5 1 2

21. 10 9 2 4 6 ∙ 2

Extended Thinking

22. Tell whether 2 4 3 and 2 4 3 have the same value. Explain why or why not. Explanation: ______________________________________________________________ _______________________________________________________________________ BONUS

23. Insert parentheses to make the sentence true. 5 2 ∙ 9 3 = 42


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1-5 & 1-6 Properties There are a lot of rules in mathematics that we use all the time. Some of them may seem like common sense to you. Others you may never have seen before. It is important that you know these rules.

Property Addition Multiplication Commutative (order doesn’t matter)

Rule Example

Rule Example

Associative (grouping doesn’t matter)

Rule Example

Rule Example

Distributive (give it to everything)

(follow PEMDAS)

Rule Example

Example

Examples: Name the property shown by each statement.

1. 3 7 9 7 3 9

2. ∙ 6 ∙ 5 ∙ 6 ∙ 5

3. 2 3 12 6 18

You Try: Name the property shown by each statement.

4. 3 ∙ 10 ∙ 2 3 ∙ 2 ∙ 10

5. 2 5 2 5

6. 4 4 4


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These properties can be used to help simplify algebraic expressions. Simplify- Examples:

Simplify each expression.

1. 2 7

2. 5 ∙ 9

3. 2 0

You Try:

Simplify each expression

4. 5 ∙ 3 ∙

5. 12 ∙ 18

6. ∙ 7 ∙ 1

Practice Problems Name the Property shown by each statement.

1. 7 5 5 7

2. 2 8 16 8

3. 8 ∙ 4 ∙ 13 4 ∙ 8 ∙ 13

4. 1 ∙ 4 4 ∙ 1

5. 5 ∙ 3 3 ∙ 5

6. 6 ∙ 2 ∙ 0 6 ∙ 2 ∙ 0

7. 12 ∙ 8 8 ∙ 12

8. 2 13 2 26

9. 4 5 15 4 5 15

10. 10 ∙ ∙ 10

11. 7 0 0 7

12. 4 4


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Source: http://www.math-aids.com/cgi/pdf_viewer_8.cgi?script_name=property_definition.pl&x=85&y=29


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Simplify each expression. Rewrite the problem using one of the properties we’ve learned, and identify which property you are demonstrating. Expression Rewritten Expression Property Used

13. 6+ (x+7)

14. 3 ∙ ∙ 9

15. 8 4

16. 17 9

17. 15 12

18. 7 ∙ ∙ 4

19. 6 ∙ ∙ 8

20. 3 ∙ ∙ 5

21. 25 3


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1-8 Real Number System

Word Definition Picture/Example Real Life Connection

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Irrational Numbers

Real Numbers


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Identify which subsets of the real number system for each number by placing a “+” in each column that the number belongs.

Natural Numbers

Whole Numbers

Integers Rational Number

Irrational Number

Real Number

1. − 17

2. − 2

3. 937

4. 0

5. -6.06

6. 426

7. √225

8. 4.56

9. 3.050050005...

10. 18

11. . …

12. 0.531531…

13. − 43

14. π

15. .634

Identify one thing you notice about all the numbers above:


19 22.

11. Put in order from least to greatest. 4 , 4.68, √16, 4.09, 4


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4-7 Scientific Notation

Example: You Try:

1. 12, 500, 000 = ________ x 10 4. 34, 900, 000 = ________ x 10

2. 653, 000 = ________ x 10 5. 153, 000 = ________ x 10

3. 1, 000, 000 = ________ x 10 6. 8, 000, 000 = ________ x 10

Example: You Try:

1. 1.23 10 _______________________ 3. 5.2 10 _______________________

2. 7.23 10 _______________________ 4. 1.005 10 _______________________


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Practice Problems:


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Documents

Intro to Algebra Unit 2 - Central Dauphin School District · Now let’s try translating verbal phrases found in word problems to help us solve. ... 6 + 4 x 3 12 - 8 + 2 – 3 2 (7