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 “Cornell Notes” will be distributed.
Students are instructed to complete the heading and copy the pink AIM off the white board on their paper. The notes are filled out as follows:
“When you distribute a negative number, it is like turning the lights on and off.
On = positive
Off = negative”
We review how to distribute the negative sign into each addend. I use the lights on/off metaphor to display the switching of the signs in each addend. By showing work this way, students will make use of the structure of the distribution to justify each addend (MP7).
– (5 + 2)
= (–1) * 5 + (–1) * 2 “the opposite of on 5 is off 5 (–5), the opposite of on 2 is off 2 (–2)”
= –5 + (–2)
– [ 6 + (–2) ]
= (–1) * 6 + (–1) * (–2)
= –6 + 2
– [ (–6) + (–4) ]
= (–1) * (–6) + (–1) * (–4)
= 6 + 4
If students finish early (nearly half of them do) they are instructed to complete the 4 examples on these notes and raise their hand when they are finished so that I could check their answers. This allowed me to work one-on-one with many students, giving them individual, on the spot feedback for their work and answers. Many of them only needed to simplify the operations in their final answers. For example, they would stop here:
– ( x + 4 )
– x + – 4
With a highlighter, I would show them the signs that needed to be simplified.
This was also a good time to check in with students about their accuracy and attention to detail (MP6) when writing their answers. For example, in example c:
–2 ( t – 5 )
= –2t + 10
The letter t and the + sign must be written in a distinct way to correctly portray the algebraic expression. Many students either drop the sign or the letter. This is a good time to remind them about this habit.
After reviewing the 4 examples as a class, students are asked to choose a partner and line up along one of the aisles of the room. After approving the pair, I assign students a problem from the task and ask them to display the work and answer on the white board, the black board or using pieces of chart paper displayed around the room (see attached pictures). After the pair is finished with their assigned problem, they are to return to their seats and complete the rest of the problems given on their worksheet.
As I walk around the room monitoring groups I ask them to show as many steps as possible, including the multiplication step for each addend. Students are also asked to show their work using arrows or boxes to display the distribution.
Once there are 10 minutes left of class, students are instructed to return to their desks for review of the answers.
When reviewing the answers, I begin reviewing #11 and #12 by asking students to consider what is being distributed. For question #11, is it the term 9x, is it –9x, or something else? Many students falsely think the variable term is being distributed. This is a great time to be proactive about a common error.