Use of Bar Models to Represent px = q
Lesson 15 of 23
Objective: SWBAT show what they know about algebraic vocabulary and solving two step equations on Quiz #8. SWBAT draw bar models to represent word problems in the form px = y, where p is a fraction.
Do Now - Quiz
Students enter silently. Quizzes are on their desks and they are to begin as soon as possible. They are allowed to spread out and sit at empty tables and are given the option to use cardboard dividers and noise canceling head phones. Instructions on the board notify students that they will only have 30 minutes to complete this quiz (a timer will be displayed) and that there are available optional “bonus” questions. Incorrectly answered problems will not be held against them. At the end of the quiz, all students will be asked to turn in their quizzes, bonus questions, and Class Notes will be distributed.
On this assessment I am still checking in on vocabulary to continue helping smaller groups of students who still struggle in this area. The results to the first 5 questions will inform my decision for groups to see during our "remediation block" during the week. The remaining questions aim to assess student understanding of solving two step equations. As this unit comes to a close, this data will let me know which skills students need to practice before they take their unit test in two weeks. This data also helps inform what additional material I should add to our class website where students can find helpful worksheets, videos and other resources.
Students are instructed to complete the heading and copy the second AIM off the whiteboard into their class notes.
"KWBAT draw bar models to represent word problems
in the form px = y, where p is a fraction"
The discussion about bar models begins with the notion that the “bars” or smaller rectangles that make up a “bar” represent equivalent quantities. I make sure to check for understanding of the word “quantity”, a given number. In the first example, equations with whole numbers, the term 3x is considered a quantity, just as the variable alone, x, is a separate quantity. The quantity of “12” is equivalent to the quantity of the “product” of 3 and x. This is a great opportunity to spiral through basic vocabulary. Students can be asked to recall the definition of quantity, equivalent, product, term, variable, etc. When we get to example 2, we read it as “three fourths of a number, y, is 16”. Reading the equation this way instead of simply, “three fourths y equal 16” will facilitate the application of this strategy to word problems like example 3. Students can write the equation for this problem by first stating the answer to the question, “what does this word problem ask us to find?”, “three fifths of 50”. Students often have difficulty identifying the operation that needs to be used to find the answer to this question. The issue is not knowing the operation, but instead, understanding the conceptual idea of a fractional part of a group. By teaching students the strategy of using bar models, I hope to clarify this misunderstanding. Students are also in use of MP4 through their use of bars and rectangles to represent and compare quantities and real world problems. Please see attached document for images of bar models for each example in the class notes.
Before I end this class notes section of class, I ask students about their opinion of the statistics used in the third example. Some students ask if the statistic is real and I reveal that it is. Other students say they think it’s a larger number than expected while some also state that they are surprised by that number. I like to encourage discussions of this nature so that my students can begin to think about the perceptions out there regarding students of color, students like them.
Task + Closing
During the "task" section, students work in groups of 4 to draw bar models for each problem on the back of the "class notes". I ask each group to copy their work on quadrille chart paper to display in the classroom. Some of these students papers display the bar models correctly and some don't.
Ten minutes before the end of class, I ask all students to choose one groups' displayed work and determine if there are any errors by filling out a simple evaluation form. This means I have to ensure every group has at least 4 other students evaluating, rather than letting it turn into a popularity contest. Each form must be left by the displayed work for the original student creators to return and collect before they leave class. This activity enables students to practice MP3. Again, I have to make sure to circulate as much as possible to ensure evaluations forms are being filled out correctly. I also tell students that if they do not agree with the feedback given on any of the forms the MUST ask about that form during remediation or study hall, rather than assuming that their peer is wrong. By asking students to come see me, we are reviewing the information over and over in different ways. If we determine that the "student evaluator" was in fact mistaken when giving any feedback, the student who put up the work is then responsible for looping back to the student evaluator to explain why their work IS correct.