Mitchell District High School

MPM 1D Principles of Mathematics

Unit 2: Algebra Unit Goals:

1) can simplify algebraic expressions.

2) I can add and subtract polynomial expression.

3) I can solve linear equations.

4) I can use algebra to solve word problems.

# Topic Goal Questions to Ask About

1 Like Terms and Distributive Law

I can recognize like terms and I can simplify by using distributive law.

2 Adding and Subtracting Polynomials

I can add and subtract polynomial expressions.

3 Solving Equations I can solve one and two step equations.

4 Multi-step Equations

I can solve multi-step equations.

5 Equations

with Rational Coefficients

I can solve equations that contain rational coefficients.

6 Introduction to Word Problems

I can translate English into mathematical expressions and can write "let" statements.

7 Solving Algebraic Word Problems

I can solve word problems using algebra.

8 Rearranging Equations

I can to rearrange formulas.

2.1.notebook

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September 13, 2013

Unit Title­ AlgebraGoals for the Unit:1. Simplify algebraic expressions2. Add and subtract polynomial expression3. Solve linear equations4. Use algebra to solve word problems

Goal: I can recognize like­terms and I can simplify by using distributive law

Like Terms and Distributive Law

                       share the exact same variables and each of those variables must have the exact same exponent.

example: Group the following like terms together.

­8

5x2

5xy4yx

­8xy5

­8x

2. Explain why 5xyz, 8yzx, and ­12yzx are like terms

­ when multiplying, the order of the variables do not matter

Terminology and Notation

3 x2 y

­ called a term­ held together through multiplication

coefficient  variables

Like terms

5x 4y2

4x2 4x

y2

5 x 3 x 2

3 x 2 x 5

2 x 3 x 5

2.1

2.1.notebook

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September 13, 2013

Distributive Law2(3+5)                                          2(3+5)

p. 300    #9­45 odd

Examples: Simplify

1.   

2.

Examples: Simplify

1.   2 ( x + 3) 2.   ­4 ( 3x ­ 5)

3.   2x( 3x ­ 5)

4.   ­3x2 ( x5 ­ 2x + 7 )

2.2 AddSubPoly.notebook

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Goal ­ I can add and subtract polynomial expressions.

Adding and Subtracting Polynomials

Polynomials are mathematical expressions.  They don't have equal signs.

eg.2x3x ­ 57x3 ­ x2 + 10

monomialbinomial

trinomial

When we are adding or subtracting polynomials, it is almost the same as collecting like­terms.

2.2

1 term2 terms

3 terms

Examples: Adding

2.2 AddSubPoly.notebook

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Subtracting

­ add the opposite.­ when you remove the brackets "change" the sign of ALL terms in the polynomial you are subtracting

Examples: Simplify

Page 309 #21­27

Page 311 #21­26

2.3Solve1and2Step.notebook

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GoalI can solve one and two step equations

Solving Equations

Expression:

A mathematical phrase made up of numbers and  variables connected by operators.

Examples: 2x + 5y ­ 6 + 4x

3(x+2) ­ 2(5x+1)

All you can do with expressions is SIMPLIFY!!!!!

Equation:

A statement setting two mathematical phrases equal to each other.

Examples: 2x + 5 = ­6 + 4

3(x + 2 ) = ­2(5x + 1)

Inverse Operations:

WHAT you do to one side of the  equal sign you must do to the  other side!

2.3

2.3Solve1and2Step.notebook

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Solve the following:

2.3Solve1and2Step.notebook

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P. 353 #3­18

P. 348 #15­32

2.4multi.notebook

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Multi­step Equations

Possible steps:1. Get rid of brackets (distributive law, adding and subtracting    

like terms...)

2. Simplify each side of the equal sign

3. Add and subtract to get variables to ONE side"        "              ' to get constants (numbers) to the other side.

4. Multiply or divide to get 1x = 

Examples:  Solve

Goal ­ I can solve multi­step equations.

2.4

2.4multi.notebook

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3. 3[2x ­ 5(2x + 1) ­ 4] = 2[4 ­ 2(x + 1)]

Page 353 #27­40

Page 355 #33­39

Worksheet

2.5rationals.notebook

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Rational Coefficients

Steps:

1.  Find a common factor for the denominators2. Multiply EACH term in the equation by the common denominator.3. This should cancel the denominators and you can solve like 

normal.

Examples:   Solve

Goal ­ I can solve equations that contain rational coefficients

2.5

2.5rationals.notebook

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Worksheets

2.6wordtrans.notebook

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GoalI can translate English into mathematical expressions and can write "let" statements.

Introductions to Word Problems

The following is a list of words that we associate with particular operations.

Add Subtract

Multiply Divide

plus positive

sum moreless

minus

take away negative

difference

timesproduct

doubletriple

of­half, third, quarter,.....

per

quotient

Examples:Create an algebraic expression for the following. DO NOT SOLVE. (simplify please)

1. The sum of three consecutive integers.

2. Fifteen minus one half of the sum of a number and ten

3. The sum of two numbers is 40.  3 times a number minus 4 times the second number.

2.7wordEquations.notebook

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Goal:  I can solve word problems using algebra

Solving Algebraic Word Problems

Steps:

1. Identify key words (numbers, operations, variables,......)2. Draw a diagram (if it will help)3. Identify how many unknowns there are and develop a "LET" 

statement for each4. Create an algebraic equation5. Solve the equation6. REFLECT on the answer

Examples:

1. The difference between two integers is 17.  Nine  times the smaller number is 69 more than three times the larger number.  Determine the numbers.

2.7wordEquations.notebook

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2.Hailey has 50 coins in her piggy bank consisting of quarters and dimes. After adding them up, she finds that she has $8.00. Determine how many quarters and dimes she has.

2.8RearrangeFormula.notebook

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Goal ­ I can to rearrange formulas

Rearranging Equations

In math, we often ask you to demonstrate your algebra skills. These same skills can be used in other courses, specifically SCIENCE!

Examples :  The equation for density is  D = MV

Solve for the following variables.

a) m b) V

2. Solve the following equation for the indicated variables v2 = v1 + at

a) v1 b)  a

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3. solve for r in V= πr2h3

4. Solve for h in  SA=2πr2 + 2πrh