MthEd 377 Lesson Plan



MthEd 377 Lesson Plan

Cover Sheet

|Name: Becky Vandermark |Date: 10-7-05 |

|Section Title: Solving Equations with Variables on Both Sides |

|Big Mathematical Idea: |

| |

|Given an equation with the same variable on both sides of the equal sign you can use basic operations to solve for the variable, the |

|solution can be found by following different orders of steps, and there is usually a “best” set of steps. |

|Why is this topic important? |

| |

|As students move on into higher math courses they will run into many situations where they have to solve an equation, usually much |

|more complex than the ones in this lesson, it is important for them to get comfortable with manipulating equations. |

|How does this lesson fit in to the overall unit? (i.e., How does this lesson build on the previous lessons and how do subsequent |

|lessons build on it?) |

| |

|This lesson is more or less a direct result of the previous lessons, in the lessons before this one, students learn how to solve |

|equations with one variable. This lesson is an extension of those that looks at a special case when you have the same variable on |

|both sides of the equation. The lesson that follows takes a step toward a more complicates idea, being, when you have more than one |

|variable in an equation how do you solve for a specific one. Without the knowledge gained in this and previous lessons about |

|manipulating equations doing the next lesson would be quite difficult. |

| |

|Grading rubric (for Keith’s use) |

| |

|5 The Big Mathematical Idea addresses core mathematical concepts and is clearly articulated |

|5 Description of the importance of the topic is well thought out and relevant |

|5 There is a clear, insightful discussion of how this lesson fits in to the mathematical content of the overall unit |

|5 Lesson sequence is well thought out and detailed |

|5 Students' thinking is anticipated with forethought and detail |

|5 Reactions to students' thinking is mathematically oriented, insightful and detailed |

|10 3-5 reflection paragraphs demonstrate thoughtful |10 Met with Dr. Leatham and made appropriate revisions based on this |

|reflection and are clearly articulated |discussion |

| |30 3-5 page reflection paper demonstrates thoughtful reflection and |

| |is clearly articulated |

|Lesson Sequence: Learning activities, tasks |Time |Anticipated Student Thinking |Your response to student |Formative Assessment, |

|and key questions (what you will do and say,| |and Responses |responses and thinking |Miscellaneous things to |

|what you will ask the students to do) | | | |remember |

|Launching the Lesson |

|What we are going to do today is similar to | |The word “term” might bring up |I will explain what a term | |

|what we have done the last couple of days | |some questions because we may |is, and right an example | |

|but now there will be more terms. What do | |not have used it yet. |equation on the board and | |

|you think I mean when I say that there are | | |point out the “terms.” | |

|more terms? | | | | |

| | | | | |

|Remember when you do operations on one side | | | | |

|of the equation that you have to keep things| | | | |

|equal on the other side. | | | | |

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|Orchestrating the Task |

|Have students break up into groups. Handout| |I think that some students |I will talk through with them| |

|the worksheet, and go through the | |might have a hard time |how to get started, possibly | |

|instructions. They can use the model to try| |articulating what it is that |go through how to word one | |

|to solve the equations, but try to think | |they are doing to the equation |step with them, and then | |

|about how to do it without. | |in order to solve it. |encourage them to talk out | |

| | | |the way to word the rest with| |

|Look for differences in the way that the | |The word problems might also |each other. | |

|groups solve the equations, especially #3, | |cause some confusion. The | | |

|how they go about manipulating them and how | |students may not be sure how to| | |

|they describe what they are doing. | |go about writing an equation | | |

| | |with the given information. | | |

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|Facilitating the Discussion |

|Did you notice anything interesting about | |I’m sure that someone will |At this point we can have a | |

|the solution to any of the problems? | |bring up problem # 2, which has|small discussion about what | |

| | |no solution. |it means to have “no | |

|Have a couple of groups who have solved | | |solution.” That being, that | |

|equation #3 slightly differently present | | |there are no values of x that| |

|their solutions and how they got them. | |I think that some of the |make the equation true. | |

| | |students might take issue with | | |

|Discuss the differences in the way that the | |the idea that you don’t have to|Try and have the students | |

|groups went about solving the equations. | |do things in a specific order, |discuss why this might be | |

|Ask if the students can see other ways that | |or that the variable can be |true, guide the discussion, | |

|the equations could be worked out. | |moved to either side of the |redirect, or reword when | |

| | |equation, and the answer will |necessary. | |

|If all of the groups solve #3 the same look | |still be the same. | | |

|at the page of other possible ways to solve | | | | |

|and write the equation on the board and ask | | | | |

|the students how they would continue if this| | | | |

|step (write first step) were done first. | | | | |

|Debriefing the Lesson |

|What did we notice about how we got to the | |There are different ways that | | |

|solutions to these equations? Were some | |the solution can be found. | | |

|ways better than others? When I say that | | | | |

|some ways are better what do you think I | |Better means faster. | | |

|mean? | |Better means not as much | | |

| | |writing. |All of these ideas are | |

| | |Better means that you don’t |correct and I’m sure that | |

| | |have to do as much difficult |there are many other things | |

| | |arithmetic. |that using the best order of | |

| | | |steps will simplify. | |

| | | | | |

Task

Explain, using sentences, what you have to do to solve each equation, and then solve it. You can use the model to help you if you would like. Have each member of your group be the “explainer” for one of the problems.

1. 3 – 4x = 2x + 5

2. 4(x – 2) = 4x

3. 8y – 20 = 4(-3y +10)

4. Three angles are supplementary, the difference of two of the angles whose measures are (4x – 10), and (2x + 15) is equal to the measure of the third angle, x. Find the angles.

5. One half of a number increased by 16 is four less than two thirds of the number. Find the number.

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