Students enter silently according to the Daily Entrance Routine. There are Do Nows and clickers at their desks. The Do Now indicates that it will be graded. Each problem in to Do Now for today is a purposeful check for understanding on topics students continue to struggle with. The common error made on problems like #1 is to subtract before distributing, like this:
1) 12 – 2 (4 + 6x )
= 10 ( 4 + 6x )
Students who answer with a letter B most likely made this mistake. Since I can keep track of which answers were entered into clickers, I will know which students are continuing to make this mistake. Yesterday, most students made this mistake and today the data shows improvement in about half of the class. This tells me that I should put another problem like this on the Do Now tomorrow.
I explain to students that they must distribute first and that it is important to consider the negative sign in front of the 2 in order to show the work correctly:
1) 12 – 2 (4 + 6x )
= 12 – 8 – 12x
= 4 – 12x
Question 2 is also purposeful. Any students continue to struggle in identifying the coefficient in front of variables that stand alone, such as the leading coefficient in this problem. About half of the students in each class answered with letter A. This is indicative of a conceptual misunderstanding of the signs in front of each term. Students are combining t and 2t to make 3t and 5 and 5 to make 10. Considering the signs, I show the work like this:
t – 5 – 2t + 5
= 1t – 5 – 2t + 5
= 1t – 2t – 5 + 5 (commutative property)
This is where students might need more scaffolding. I had to show my students that I am subtracting the coefficients:
1 – 2 = –1
And combining the constants:
–5 + 5 = 0
This results in the following step:
= 1t – 2t – 5 + 5 (commutative property)
= –1t + 0 = –1t = –t
Question three is a purposeful way to check in with students about yesterday’s lesson while also providing a good transition for today’s lesson.
Before moving on to the class notes I ask students to raise their hand if they did not get a chance to visit our website to review the answers to the HW, or if they would like to ask questions about my work. If I get more than 5 hands raised, I display the answers and allow 4 minutes of questions. Answers are attached here as well. The website is open to anyone who has the link.
Class notes are distributed. Students are asked to complete the heading and copy the aim off the board. Then, the following situation is posed, “Pretend Mr. [our 5th grade math teacher] comes in the room and says, ‘this 5th grader is bored in my class. I want him to be in a 7th grade math class today’. The 5th grader approaches you and says ‘what’s an equation’? What would you say to him/her? Write it into your class notes in the ‘Equations section’”
Two student volunteers are asked to share. I praise the use of vocabulary words such as “equal sign”, “expressions”, “variables”, “constants”, and “operations”. Then I ask students to copy the following definition off the board as well:
An equation is a mathematical sentence that uses an equal sign to show two equivalent expressions.
Next, I ask one student to read the paragraph next to “showing work when solving an equation”. When the student gets to the blanks I instruct everyone to fill them in with the words “opposite operations”. Then, I show students the proper way to show their work when solving equation. This part of the class notes is done slowly and is highly scaffolded. A student in one class shared a misunderstanding about opposite operations. This misunderstanding shed light into a common misconception. I praised the student for sharing, stating that they had just made me a better teacher. The student wanted to know, for the class notes example, why the work could not look as follows:
x – 7 = –2
The misunderstanding here is that students think they must perform the opposite operations on all constant terms in the equation. I remind students about the balance scale I used in class the previous day. In that example, in order to leave the canister alone, I had to remove two chips from the same tray. This caused the scale to unbalance. In order to re-balance the scale, I had to remove 2 chips from the other side as well. This demonstration shows how I identify the appropriate opposite operation and why I must perform the exact same operation on the opposite side of the equation.
I begin solving this equation by warning students that while this is only a one step problem that I suspect many students can “solve in their head”, I expect them to build the habit of showing their work. I write a complex multistep equation on the board and let students know that it is a type of equation we need to be ready to solve next week. Thus, building the habit of showing work neatly, step by step, is important. Review the sample student work attached here to view appropriate ways of showing work.
I end with a review of a check step. I inserted a picture of “dramatic prairie dog” to insert a fun moment into the lesson. I tell students that each year, the biggest battle I have with 7th graders, is the check step. Then I click the picture of “prairie dog” which is linked to the dramatic sound effect we all know as “dun-dun-dunnnn!” I explain that the most common excuse is “it’s too much work!” Then, I simply state that the check step will defend students against mistakes and that I cannot force them make the right choice, but in my experience, students who don’t check their work often make small mistakes which affect their scores and their grade. Finally, I run through the steps and logic for the check step. Students must first re-copy the original equation. Then, they must substitute the value attained in the solution for the variable in the equation. Lastly, they must evaluate the numerical expression that results after the substitution step and compare it to the number on the other side of the equation. If the numbers are equivalent, this means that the equation was solved correctly. If the two numbers are not equal, this shows students that the equation was not solved correctly.
Students are asked to close their binders so that I can explain the expectations for the task. They are to line up in double lines with a partner of their choice. I must approve the partner-pair and will then hand them two different task sheets. Students can sit at booths or in any part of the room their choose to complete the work.
Each sheet includes two columns of work. The left hand column has equations that must be solved, showing all steps. Students will first work independently to solve their 6 equations. Then, they will switch papers with their approved partner to complete the check steps. When they are finished, they will return the paper to their neighbor so that he/she can fix any incorrect solutions.
While students are working together, I will be walking around the room to ensure all work is being shown and to answer any specific questions students may have.
Once there are 10 minutes of class left, students will be asked to return to their original seats. They will be given 1 minute to organize their work and clip their papers into the appropriate parts of their binders. Then, they will be instructed to turn back to their class notes. In the blank space provided under “The check step”, students will be asked to write two sentences that summarize the importance of a check step. Why complete a check step? What’s the point?
At the end of 5 minutes, 2 student volunteers will be asked to share.