Wednesday, March 16, 2016

Day 122: WODB, Post It Peer Feedback, & Exit Tickets on Completing Square & Quadratic Equation

Today I introduced Which One Doesn't Belong to all my students with their cover image on their web site:
I advised students how it worked, and I didn't want them to share their ideas until everyone had time and they could share in a whole class discussion after 5 minutes. Here's what student's came up with in one class:

In 5th and 6th period, for the top left two different students noticed that the number of letters in which 5, is the only letter amount that is divisible by 3 (the other's are 3 and 6 letters long)
I also liked that a student said that the squares all had the same area, but the circle didn't belong because it had a smaller area. I loved that one.

Students were given 7 minutes to finish up their posters and add some explanations. Then I showed students the following Slides about giving productive feedback:

The quality of feedback improved immensely after I told students there was a limit of 4 students per table. They got really quiet studying the posters, knowing they had their names on the post it and they had two learning goals: What do you agree with specifically on the poster and why? Also, What do you disagree with and make a suggestion or ask a question to move the learning forward.

After they had 8 minutes to do that, they read their feedback and had a chance for rebuttal. We reviewed which feedback made them switch how they categorized an equation, and that formed our class closure notes, as follows:

Students were very focused giving their peers feedback on the post its.
The most common mistake with the equation on the left was students only dividing one of the terms by 2, instead of both of them. Also, 6x=x is a common misconception when zero is not considered. It's hard for some to see that you can subtract x form both sides and divide by the coefficient of x on both sides.
This activity uncovered many misconceptions about the distributive property.
I love how the student disagreed tactfully about 2-x=x-2 being always true and they showed how substituting x=1 did not make it true.
As students left class I gave them this 3 question exit ticket to complete in a short amount of time, 2 to 5 minutes varying in classes. Here's one example of a student who had already mastered the concept and proved it:
All work clearly shown and interpreted.
Students who didn't understand the distributive property still would use the wrong order of operations and either subtract x or subtract 3 from both sides, before using the distributive property, making it a different expression:

In accelerated Markos explained the St Louis arch problem solution. Davin offered his alternative explanation. Students practicing solving quadratic equations by picking what they predicted would be the most efficient method. Then I gave them an exit ticket on completing the square and using the quadratic equation.
In this rare misconception this student substituted the x squared and x variables instead of just the coefficients: a, b, and c.
This student did add 16 to both sides, but did not add 10 to both sides to move it over. I really like the clearly shown substitution using the quadratic equation.
This student partially understands how to complete the square for x squared plus 4x. The quadratic equation below was a similar mistake another student making, computing 56 for b squared minus 4ac, instead of 64.
I like how it's clear how the student found what was added to both sides by showing (b/2)^2. The quadratic equation work is well done too.

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