# Lesson: 10-4 Completing the Square

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### Lesson Objective

SWBAT solve quadratic equations by completing the square.

### Lesson Plan

 Teacher: Hall/Lin Course:    8th Math Date:     April 12, 2010 Objective:  -          SWBAT  graph quadratic functions Unit Title:  Quadratics 10 Objective Number: 10-4 Materials: do now, cc, packet, textbooks, notebooks, HW, EX, clickers, CALCULATORS Vocabulary: complete the square, square root, positive and negative roots Do now: Purpose of the do now:  xCumulative Review _____________ â–¡Activate Prior Knowledge â–¡Introduce Lesson â–¡Other ___________________ Total Recall / Hook: How will you transition from the Do Now into today’s objective? How will you tie your recall to the importance of today’s objective?   Mental math – quadratics review MENTAL MATH 1- What is the standard form for a quadratic equation? 2- What is the name of the shape of a quadratic graph? 3- Will the graph of y = 1.5x2 – 2 open up or open down? 4- So will its vertex be a max or a min? (min) 5 -What will be the y-intercept? (0,-2) 6 – What is the square root of 49? (7) 7- What is the other possible answer? (-7) 8- What are the two solutions to this equation x2 = 121 (11 and -11) 9- What are the two solutions to this equation 2x2 = 50? (5 and -5) 10- The equation y = x2 – 9 has two roots – what are they? (3 and -3) Agenda: Outline of your lesson DN/CC/MM (35) Lesson (25) Partners/Guided (15) IP (30) 5.      Share (5 ) 6.      Exit Ticket (5) Intro to NM   Notes: quadratic squares FOIL problems are examples of quadratic functions Fill in the four examples What is the pattern? (double the number for the middle term, square the number for the last term)   Algebra riles: Take out an x squared and six x tiles – try to arrange them in a perfect square – it’s not possible! So not every expression is a perfect square – so today we are going to learn how to MAKE something a perfect square – this is called COMPLETING THE SQUARE - what do we need to complete the square?   NOW YOU TRY -          What’s the pattern?   Example 2:  How could we solve this equation (by graphing and finding where it equals 24; guess and check) Completing the square is another tool we can use to solve this equation. We are going to make the left side a perfect square – so what do I need to add? (25) If I add 25 to this side then I also need to… So our new equation is… Now we are going to factor our perfect square – so what would it be? Now (x + 5) needs to be what? (7 or -7)  GOOD – the way we show this step is by taking the square root of both sides Now we have two different answers, so just like we did before, we split it up into two different equations to solve – how can we check? (do it – use calcs)   Now you try: Cold call for each step   Example2: Cold call for steps: So I am going to complete the square on the left side. So what do I need to add? What’s the new equation going to be? Now what? (factor) So what do I get? What happens next? (etc.) Hmmm.. we get the square root of 20 – we might want to check to see if we made a mistake – but we didn’t so… we will write our answer the best we can. And we’ll use our calculator to estimate (check with calc)   PARTNER PRACTICE (add in scaffolding and hints) Key questions to ask during GP: (Question Script) IP   Clicker – KUTA – DO NOT PROJECT (have all students move on after x minutes)   IP from packet (optional: partner check ins) Closure: How will you close the lesson?    Raffle tickets for productive IP Share answers/questions from IP What does it mean to complete the square? Why is it useful? What is important to remember when solving an equation and taking a square root? Assessment: How will you assess mastery of the objective? EXIT TICKET Homework Anticipated Challenges

Reflection: Make sure to check your state standards. Our algebra 1 students are not required to know this, so we chose to do this just as an extension.

### Lesson Resources

 10 4 packet completing the square 929 10 4 HW 310 10 4 EX 326 10 4 DN 294

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