Algebra 1. Standard 11 Operations of Expressions. Categories Combining Expressions Multiply Expressions Multiple Operations Function Knowledge

Transcription

1 Algebra 1 Standard 11 Operations of Expressions Categories Combining Expressions Multiply Expressions Multiple Operations Function Knowledge Summative Assessment Date: Wednesday, February 13 th Page 1

2 Operations of Expressions Learning Targets Combining Expressions How did I Learning Target do on the HW? 1 I can interpret the parts of an expression (term, coefficient) I can combine multiple expressions by adding like terms. 3 I can combine multiple expressions by subtracting like term (remembering to distribute the negative). 4 I can apply combining expressions to perimeter problems. Learning Target Multiply Expressions 5 I can interpret the parts of an expression (factors, terms within the factor, coefficient). 6 I can use rules of exponents to multiply terms. 7 I can use distributive property to multiply expressions. 8 I can apply multiplying expressions to area problems. Learning Target Multiple Operations 9 I can interpret the parts of an expression. 10 I can apply order of operations to simplify expressions. 11 I can explain the difference between expressions like 5 and 5. 1 I can apply these ideas to area problems. Learning Target Function Knowledge 13 I can describe the effects of operations on function and know what type of function the outcome will become. 14 I can use given functions and operations to create new functions. 15 I understand the structure of a function in order to rewrite it as the product of different functions. How did I do on the HW? How did I do on the HW? How did I do on the HW? How did I do on the class check? How did I do on the class check? How did I do on the class check? How did I do on the class check? Do I need to practice more? Do I need to practice more? Do I need to practice more? Do I need to practice more? Page

3 Operations of Expressions DAY 1 Notes Combining Expressions (p3-5) TODAY S PLAN By the end of the lesson, students are expected to be able to do the following: 1. Identify the parts of a polynomial expression. Add and subtract polynomial expressions by combining like terms 3. Demonstrate Function knowledge (involves classification of functions) 4. Apply these processes to problems involving Perimeter Parts of a Polynomial Expression Example 1: 4x 6x + + What is the leading coefficient? What is the constant term? How many terms are there? What is the degree of the expression? What type of function is this? Example : 7.5 x What is the leading coefficient? 3 What is the constant term? How many terms are there? What is the degree of the expression? What type of function is this? Example 3: 6 What is the leading coefficient? What is the constant term? How many terms are there? What is the degree of the expression? What type of function is this? Page 3

4 Add and/or Subtract Polynomial Expressions Example 4: ( 7x ) ( x 6) + + What type of function is the first expression? What type of function is the second expression? What type of function is the answer? Example 5: ( 3x 5) ( 1.5 3x) What type of function is the first expression? What type of function is the second expression? What type of function is the answer? Example 6: ( x x 4) ( 3x 5x 3) What type of function is the first expression? What type of function is the second expression? What type of function is the answer? Example 7: ( x 3x 1) ( x 5 x ) + + What type of function is the first expression? What type of function is the second expression? What type of function is the answer? What did you have to do differently because you were subtracting? Example 8: (.5x 15) ( 3x 8) + What type of function is the first expression? What type of function is the second expression? What type of function is the answer? Page 4

5 Function Knowledge Use the previous page s examples and your own thinking to answer the following questions. A. What type of function can result from combining two linear functions? Give an example. B. What type of function can result from combining two quadratic functions? Give an example. C. What type of function can result from combining a linear function and a quadratic function? Give an example. D. What happens to the degree of an expression if you add or subtract a constant function to it? Perimeter Problems Example 9: Write a single expression for the perimeter of the figure given. Example 10: Write a single expression for the perimeter of the figure given. Page 5

6 Operations of Expressions DAY 1 Homework Combining Expressions (p6-7) Use your book to do p. 557/ 6-8, 17-6, 30, 31 and p. 69/ 1,, and 4 on this sheet or on a piece of loose leaf paper if you prefer. You must show all work. DO NOT JUST WRITE DOWN THE ANSWERS. Homework continues on the next page. There is also more work space. Page 6

7 Homework continued: 1. Give an example of two linear functions added together that result in a linear function with no constant term.. Give an example of two linear functions added together that result in a constant function. 3. True or False A linear function added to a quadratic function always results in a quadratic function? Give an example to support your answer. 4. Give an example of two quadratic functions that combine to give you a quadratic function. 5. What is the maximum number of terms a quadratic expression can have? What is the minimum number of terms? 6. Combine the expressions. ( x + 3) + ( 4x 8) ( 8x + 10) 7. Combine the expressions. ( x + 13) ( 5x 9) + ( 18x + 1) Page 7

8 Operations of Expressions DAY Notes Distribution part 1 (p8-9) Multiplying Variables ( x )( 1) ( x)( x ) ( x)( x ) 4 ( x)( x ) 3 x x x x ( x )( x ) ( x )( x ) Rule for multiplying variables with exponents: x m n x = In other words: Example Set I: Simplify the expressions. A. m 3 m B. ( y )( 3y ) 7 C. p 4 3 p D. 3 E. ( x )( 5) 13b 9b 4 F. 11x 5x 3 Example Set II: Use the distributive property to simplify the expressions. A. ( u 4u 5u ) B. 4x( 8+ x ) C. y( 7y 9y ) Page 8

9 D. 17m 3 ( 6m 3 m + 4) E. 8v 4 ( 4 7v 6 + v ) F. 9h 3 ( h 6 5h + 9h) Example Set III: Find an expression for the area of the following figures. A. B. Example Set IV: Create Functions A. Fill in the blank with an expression that after distributing, the result would be a linear expression. ( x 3) B. Fill in the blank with an expression that after distributing, the result would be a quadratic expression. ( x 3) C. Fill in the blank with an expression that after distributing, the result would be a cubic expression. ( 4x + ) D. Fill in the blank with an expression that after distributing the result would be an expression with a degree of x 5x + ( ) Page 9

10 Operations of Expressions DAY Homework Distribution part 1 (p10-11) #1-1: Simplify the expressions. 6 8y y. 8( n 6) 3. ( 10x + 1) 9x 1. ( ) ( x x 5) b + b n( 1+ 8n 7n ) 7. ( u 5.3u + 3 7u) 8. 6z ( 5z z 1) r ( n ) n r r r b ( 4 6b + 7b 3 8b 4 ) #13-15: Find and expression for the area of each figure Page 10

11 16. Fill in the blank with an expression that after distributing, the result would be a quadratic expression. 4x + 3x + ( ) 17. Fill in the blank with an expression that after distributing, the result would be an expression with a degree of 4. 4x + 3x + ( ) Review: #18-19 Use the two functions given to describe the transformations that have occurred. 18. Function 1: y = 1 ( x 4) Function : y = 3( x 4) 19. Function 1: y x+ x = 6 + Function : y = 6 + Page 11

12 Operations of Expressions DAY 3 Notes Distribution part (p1-14) Review: find the product. ( x + 4) ( 3 x) x ( 1) x x + ( x + ) x 3 Find the product. x + 3 x + 4 ( )( ) ( x 3)( x ) + ( x )( x 3) Both of those are linear linear times linear = One binomial is the other is Together they are ( a 5)( a 6a 3) + ( 3b b + 5)( b 1) * = * = Page 1

13 ( 5a 4a)( + 3a) + m ( m ) * = * = ( 3c c 7)( c c 9) + Write an expression for the area of the rectangle. Area Formula: * = Write an expression for the area of the rectangle. Write an expression for the area of the circle. Area Formula: Area Formula: Page 13

14 Write an expression for the area of the triangle. Write an expression for the area of the rectangle. Area Formula: Area Formula: Operations of Expressions DAY 3 Homework Distribution part (p14-15) 1. What type of function do you get when you multiply two linear expressions?. What type of function do you get when you multiply two quadratic expressions? 3. What type of function do you get when you multiply a linear expression and a quadratic expression? 4. Create an example of multiplying two expressions whose result is a linear expression. 5. Create an example of multiplying two expressions whose result is a quadratic expression. 6. Create an example of multiplying two expressions whose result is a cubic (degree 3) expression. Homework continues on the next page. Page 14

15 Use your book to do the following on this sheet or on a piece of loose leaf paper if you prefer. p. 565/ 9-14 all, odd (Ignore the book directions and just find the product) odd YOU MUST SHOW ALL WORK. DO NOT JUST WRITE DOWN THE ANSWERS. Page 15

16 Operations of Expressions DAY 4 Notes Multiple Operations (p16-17) Review 1) (x + 7)( x 9) ) ( x )( x 3) 3) (3x x 5)( x 1) + 4) Write an expression to model the AREA of the figure. What does squared mean? What does 5 mean? What does (6x ) mean? Example 1: (8x 3) Example : ( 7 4 x) Page 16

17 Example 3: x (3x 4) x(5x 3) + + Example 4: x(x + 5) + 3 x ( x + 4) Example 5: ( x + 1)( x + 3)(3x 4) Example 6: (x 5)( x + 4)(x 1) Example 7: Write an expression for the AREA of the shaded region. Example 8: Write an expression for the AREA of the shaded region. Page 17

18 Operations of Expressions DAY 4 Homework Multiple Operations (p18) Use this page (or your own loose leaf) to complete these problems out of your book. p. 565 #4-8 even, 18-4 even, 33-36, 41, 4; p. 57 #4-34 even YOU MUST SHOW ALL WORK. DO NOT JUST WRITE DOWN THE ANSWERS. Page 18