It’s a party! Solving Multi-step Equations A GEMS Submission for ALEX Submitted by: E. Thompson, PhD. Summer 08

Review of One-Step Equations 2x = 8 x +3 = 15 x – 5 = 20 Allow students time to solve equations / review answers. If students have difficulty, remediate before continuing with multi-step equations. Be sure you can solve each type of problem before we begin!

With Multi-Step Equations it can be hard to know where to start… With Multi-Step Equations it can be hard to know where to start…. pretend it’s a party! You are the host - a.k.a. ‘X’ In what order do people leave a party? Enemies (get rid of them to avoid trouble) Acquaintances (after mingling with everyone, they usually leave early) Friends (they hang out with the host a little longer) Family (if attending, they will stay to the end to help clean) The ‘basic premise’ of the activity (practice and examples will follow).

Who is who? Consider our one-step equations FAMILY….right beside you…and only you… until the end! 2x = 8 x +3 = 15 x – 5 = 20 FRIENDS….they are close to you…they stay longer than some people, but not as long as family Think back to the practice problems The next slide will show an acquaintance….we will save enemies for later in the lesson after we practice a few problems together.

Who are the acquaintances? Because this number mingles with all other many parts of the equation instead of giving most of its attention to the host (x), it is not a friend…it is an acquaintance. Explain that the 3 isn't just dividing the host (x) but also the -5! Because it is affecting the entire problem, and keeping us from being alone with family/friends…the acquaintance goes first.

Identify all the Party-goers FRIEND FAMILY This slide is for identification practice only. Check comprehension to this point. Let the students think about who is family/friend/acquaintance…then click for answers. The next slide will show the same problem and discuss the actual solution. ACQUAINTANCE

The equal sign is the door…who goes out the door first? The work: ACQUAINTANCE – multiply each side of the equation by 3. This slide shows the first step… Give students an opportunity to respond…click for steps until the result is shown. Remaining steps to follow The result: We still have company... lets continue….

Friends – add 5 to each side. Who is next to leave? Friends – add 5 to each side. The work: Give students an opportunity to respond…click for steps until the result is shown. The result: All that is left is family…a familiar one-step equation.

Clean up the party with a family member The work: Family – divide each side by 2 Who is family? The 2 Divide each side by 2 The party is over and ‘X’ is alone on one side of the ‘door’! The next slide will offer a practice….followed by a slide with an enemy. The result: Don’t forget to check your work with Order of Operations!

Try these problems: Steps: Identify the party-goers Eliminate party-goers in order Get x (the host) alone Check your solution Give students time to work independently or work with them as a large group. Next we will discuss ‘enemies’.

Enemies can ruin the entire party…get rid of them first! Its easy to spot an enemy…they affect everything! To solve, multiply each side by the reciprocal The student should be able to comp The work: Try to complete the problem from here….the answer is: The result: 21

Its party time! Do you know who is in your home? Family HOST Friend Enemy The Door! Write the equation on the board and let a student try to ID everything at the board. Let them ‘phone a friend’ as needed. One click will reveal all parts. Acquaintance See if you can ID the enemy, the friend, the acquaintance, a family member, the host and the door!

The more you party, the more responsible you will become! TIPS: Enemies and acquaintances are very similar…both affect the entire equation. Typically there are only enemies when you have already identified an acquaintance. Eventually, you will partiers outside the door (operations on both sides of the equal sign). Start these by using the same method to get everyone on one side.. If you find yourself (the host) in two places at once (variables on both sides of the equal sign), use the same method to regroup yourself back into the house. Students will need to be given examples of equations with radicals and exponents. This can be used to review students prior to adding trigonometric values in Algebra II w/Trig