# Dispatch Monday 2/25/13 3

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Dispatch Monday 2/25/13 3𝐚𝐛 𝟐𝒂 16x2 – 40x + 25 – 0.5 (m – 5)2 Simplify

Standard: 14.0 Solving Quadratic Equations by Completing the Square
Do you remember…. What are the properties of a square? Standard: 14.0 Have students read the objective 1. Ask students what are the other two ways for solving quadratic equations

CONCEPT TASK These are examples of the Algebra Tiles and each one represents an area.Give studets a minute to play with them.

x 1 1 x A = x2 x x x2 CONCEPT TASK COPY ME!!!
These are examples of the Algebra Tiles and each one represents an area. What does this blue one represent? Its x2; why?We don’t know the length of this square or the width of this square correct? What do we use to represent an unknown? A variable. Terefore this side is equal to x and this one x because of the property of a square and therefore x times x equals x2. Notice that the length of the green rectangle is also x because it’s the same length of this square x x2 COPY ME!!!

Represent the Expression:
x2 + 3x + 6

WORK WITH YOUR PARTNERS
CONCEPT TASK x2 + 4x + 4 2x2 + 3x – 4 WORK WITH YOUR PARTNERS Go over the terminology; Go over the exampleNow with your partners I want you to represent each expression. Make a sketch on the graph paper provided Have someone pass graph paper. At this time gives me time to pass out papers while going around and answering questions. Give them 3 minutes and then have three group of students represent what they got. – 3x2 + 3x – 4

CONCEPT TASK x2 + 4x + 4 Throughout these representations, ask a student to raise up their squares so everyone can see. Then ask a student if they agree or disagree.

CONCEPT TASK 2x2 + 3x – 4 Im going to mess up on purpose

CONCEPT TASK 2x2 + 3x – 4 Im going to mess up on purpose

CONCEPT TASK – 2x2 – 3x + 4

CONCEPT TASK – 2x2 – 3x + 4

CONCEPT TASK Using ONLY the Algebra tiles below, create a square.
Tell students to arrange the tiles in such so that they begin to form a square. Remind students what a square is. Furhtermore, ask a student what is the topic for today? Completing the square. So therefore their square that they will be completing is not perfect so they need to figure out what they need to add. Ask students how many 1-unit tiles will be needed in order to complete the square

What do you do to complete the square x2 + 2x + ___
CONCEPT TASK What do you do to complete the square x2 + 2x + ___ After notice that the students are finished…Ask them what expression is represented here? x2 + 2x. Then ask them how they arranged the square. Call three distinct groups to come up and draw them in the board Then have them tell you how many one unit squares they had to add in order to complete the square. They should tell you 1. Then show them the next slide. Tell them to refer to their worksheet.

CONCEPT TASK How many 1-unit tiles do you need to add to complete the
square? x2 + 2x + ____ Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square.

CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____ 1 Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square.

CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____ 1 x + 1 x + 1 x + 1 Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square. x + 1

Number of 1-tiles needed to be added to complete the square
Completing the Square Expression Number of 1-tiles needed to be added to complete the square What is the Area of your Square? A. x2 + 2x + ? (x + ____ )2 B. x2 + 4x + ? C. x2 – 6x + ? D. x2 + 8x + ?

What do you do to complete the square x2 + 4x + ___
CONCEPT TASK What do you do to complete the square x2 + 4x + ___ Tell students to arrange the tiles in such so that they begin to form a square. Ask students how many 1-unit tiles will be needed in order to complete the square

What do you do to complete the square x2 + 8x + ___
CONCEPT TASK What do you do to complete the square x2 + 8x + ___ Tell students to arrange the tiles in such so that they begin to form a square. Ask students how many 1-unit tiles will be needed in order to complete the square

What do you do to complete the square x2 – 6x + ______
CONCEPT TASK What do you do to complete the square x2 – 6x + ______ This is when I will jump in, and discuss the discovery that the students should have made!!!! Have students guide me.

CONCEPT TASK Now arrange your tiles to make a perfect square
Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square.

CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x2 - 6x + ______ 9 Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square.

CONCEPT TASK x - 3 x - 3 x - 3 Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square. x - 3

CONCEPT TASK Area= l ● w A = (x-3)(x-3) A=(x - 3)2 x - 3 x - 3 x - 3
Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square. x - 3

CONCEPT TASK x2 - 6x + 9 = (x - 3)2
Lead them to the discussion of what is a square-all sides are equalWe need to determine what to add to this expression to complete the square. We can figure this out by rearranging our tiles to complete the square; We have a square like figure but its missing but its ok because we need to complete the square. How many small squares do we need to add to complete the square.

Number of 1-tiles needed to be added to complete the square
THINK PAIR SHARE Completing the Square Expression Number of 1-tiles needed to be added to complete the square What is the Area of your Square? A. x2 + 2x + ?  1 (x + 1 )2 B. x2 + 4x + ?  4  (x + 2)2 C. x2 – 6x + ?  9  (x – 3)2 D. x2 + 8x + ?  16  (x + 4)2 What is the relationship between the values in Column 2 and 3 and the coefficient of the linear term? What were the steps you took in order to complete the square?

Let’s try without algebra tiles
Find the missing value. s2 -16s _ = -8 Step 1: Divide b by 2 Step 2: Square the result of step 1 (-82 ) = 64 Step 3: Add the result to the original expression s2 -16s + 64 Step 4: Factor (x )2

COMPLETE THE SQUARE x2 + 22x + ___= (x + ___ )2 x2 – 16x + ___= (x – ___ )2 x2 + 12x + ___= (x + ___ )2

COMPLETE THE SQUARE x2 + 5x + ___= (x + ___ )2 g2 + 11g + ___= p2 – 9p + ___=

COMPLETE THE SQUARE m2 – 1.8m + ___= (x – ___ )2 y2 + 𝟓 𝟔 y+ ___= x2 – 𝟑 𝟖 x + ___=

CONCEPT TASK JOURNAL: Your best friend was absent today. Write your friend a letter explaining how to complete the square using algebra tiles and how to do it without using algebra tiles

Daily Practice Skills Practice Pg 59 7-12 Pg 735 Lesson 9-3 7-12
COMPLETE THE SQUARE Daily Practice Skills Practice Pg Pg 735 Lesson 9-3 7-12

Dispatch Tuesday /26/13 Find the value of c that makes the trinomial a perfect square. (Use Algebra Tiles and solve Algebraically) 1. x2 – 10x + c 1. Ask student what this is an expression or an equation? Why? What type of expression is this? Ask why

VISUALLY x - 5 Area= l ● w A = (x-5)(x-5) A=(x - 5)2 x - 5 x - 5 x - 5

ALGEBRAICALLY Find the missing value. x2 –10x + _____ (– 52 ) = 25
−𝟏𝟎 𝟐 = – 5 Step 1: Divide b by 2 Step 2: Square the result of step 1 (– 52 ) = 25 Step 3: Add the result to the original expression x2 – 10x + 25 (x – 5)2 Step 4: Factor (x )2

Dispatch Thursday 2/28/13 x = – 4 and 6 16 (m – 4)2
Solve the Equation. Find the value of c that makes the trinomial a perfect square . 1. x2 – 2x + 1 = 25 x = – 4 and 6 3. x2 + 8x + c Square Root Problem; Complete the Square problem and refer to the diagram proposed; and perfect square problem!!! Division Problem Factor 16 2. m2 – 8m + 16 (m – 4)2

Standard: 14.0 Solving Quadratic Equations by Completing the Square
Do you remember…. What are the other methods for solving quadratic equations? Standard: 14.0 Have students read the objective 1. Ask students what are the other two ways for solving quadratic equations

CONCEPT TASK These are examples of the Algebra Tiles and each one represents an area.Give studets a minute to play with them tell them to be creative to create an animal

CONCEPT TASK x 1 1 x A = x2 x These are examples of the Algebra Tiles and each one represents an area. What does this blue one represent? Its x2; why?We don’t know the length of this square or the width of this square correct? What do we use to represent an unknown? A variable. Terefore this side is equal to x and this one x because of the property of a square and therefore x times x equals x2. Notice that the length of the green rectangle is also x because it’s the same length of this square x x2

1. x – 5 = 2 x – = Have them work on this problem; discover how it is done

1. x – 5 = 2 x – = Why do I have to add the same amount of tiles to both sides? What will happen if I do not add the tiles to both sides of the equation?

1. x – 5 = 2 x – = Why do the red tiles and the tan tiles cancel out?

1. x – 5 = 2 x = Why do the red tiles and the tan tiles cancel out?

YOUR TURN 1. x + 6 = – 4 2. 2x – 4 = – 8 3. x2 + 4x = 2
Ask students that now I want them to represent and solve these equations using the Algebra tiles. I want them to separate their Cornell Notes into 2 sections and call it Visually and Algebraically. Solve them both ways and that I want them to write each step on how they solved the problem. Model a problem in the whiteboard. Then have a student reiterate the directions for me. and that I want them to coWhat is the difference between the last problem and the previous problems? Do you think we are going to solve it differently or the same? 3. x2 + 4x = 2

1. x + 6 = – 4 x = – 2 Make a mistake in purpose and ask them why do they disagree with my answer? Can you explain to me the right process to reach the correct answer? Ask a gifted student, how do you think my brother got this answer?turn to the partner. Partner A and B

1. 2x – 4 = – 8 x = Make a mistake in purpose and ask them why do they disagree with my answer? Can you explain to me the right process to reach the correct answer? Ask a gifted student, What were the mistakes that my brother made? how do you think my brother got this answer?

x2 + 4x = 5 Ask the students, what is the biggest difference between number one and two as compared to number three? Refer back to the activity. Awhat did you discover, how…take that in mind to make this discovery

Turn to partner…get right answer and wrong answer; how can you check

x + 2 x + 2 Ask them if this is a perfect square, and how do they know? They should refer back to the Area of a square and labeling all sides x + 2

Whats my goal here? Turn to partner; order of operation; inverse operation
x2 + 4x = 9 (x + 2) = 9

(x + 2)2 = 9 Step 2: Take the square root of each side to cancel the square. (m + 2)2 = 9 Choral response; give me the steps….then a TURN TO PARTNER; then write it down!!! Step 3: Solve One-Step Equation. m + 2 = ±𝟑 m = – 2 ± 𝟑 Step 4: Split Up

Think Pair Share m = – 2 ± 𝟑 m= – 2 + 3 m= – 2 – 3 m= 1 m= – 5 Challenge: Is there a faster method to complete the square without using Algebra Tiles? Write in complete sentences

YOUR TURN Solve the equation using completing the square. Represent your answer both Visually with Algebra Tiles and Algebraically. x2 + 6x = 2 Go ahead and review this concept quickly q2 – 2q = 16

1. x2 + 4x + 3 = 0

x2 + 4x + 3 = 0 Ask the students, what is the biggest difference between number one and two as compared to number three? Refer back to the activity. Awhat did you discover, how…take that in mind to make this discovery

x2 + 4x + 3 = 0 Is this a perfect square? How do you know its not a perfect square? Therefore it did not work so we need to get rid of it make a perfect square?

x2 + 4x + 3 = 0 Is this a perfect square? How do you know its not a perfect square? Therefore it did not work so we need to get rid of it make a perfect square?

x2 + 4x + 3 = 0 Is this a perfect square? How do you know its not a perfect square? Therefore it did not work so we need to get rid of it make a perfect square?

x2 + 4x + 3 = 0 Is this a perfect square? How do you know its not a perfect square? Therefore it did not work so we need to get rid of it make a perfect square? (x + 2)2 =

(x + 2)2 = 1 Step 2: Take the square root of each side to cancel the square. (x + 2)2 = 1 Choral response; give me the steps….then a TURN TO PARTNER; then write it down!!! Step 3: Solve One-Step Equation. x + 2 = ±𝟏 x = – 2 ±𝟏 Step 4: Split Up

Think Pair Share x = – 2 ±𝟏 x= – 2 + 1 x= – 2 - 1 x= -1 x= – 3

YOUR TURN x2 – 4x – 5 = 0 x2 – 14x + 30 = 6 x2 + 14x + 49 = 10

Daily Practice I want you to create your own Completing the Square Problem. Make sure you represent it using Algebra Tiles and algebraically. Make a key and be ready to share the problem with your partners tomorrow. Study Guide and Intervention Pg 118 #1-18 ODD (Skip 11)

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