During our Expressions unit, we spent time making sure students didn't fall for the 'less than trap.' That is, students need to recognize that 'five less than...' means to take 5 away from the starting amount. following from the progress made during Expressions, one of the goals of today's Think about It Problem is to encourage students to read carefully (see INM.pdf). The key point I want to come out of this problem is that translating the expressions from words to numbers and symbols makes it easier to determine if the equations are equivalent.
I expect that some students will write about the Commutative Property when answering this problem. Subtraction is not commutative, so the order of the terms matters. Other students will reason about the differences. As of yet, they don't know how to perform the operations with integers. But, they know that 12-10=2, and can reason that 10-12 would give a negative answer. Therefore, the expressions can't be the same.
After the Think about It, this lesson provides students the opportunity to continue to practice translating from verbal expressions to numeric expressions and equations (INM.pdf). The lesson begins with guided examples before the class moves into partner practice.
In Problem 1, students should end up with n + 8 = 5. I ask students, "Does this seem right?" Some will want to argue that this can't be correct, because 'nothing' plus 8 will give us a sum of 5. I remind them that we are not working to find the solutions to our equations today. I ask them if they have any ideas, though, about the value of n. Students predict that n must be a negative value, if we're going to add 8 and end up with 5.
Problem 3 is a good place to talk about using fractions or decimals. I have students use both to represent this example, so that they have a reference when they are working independently.
The Partner Practice problem set allows pairs to decide how much of a challenge they want to tackle. Note that there are not enough 1-point problems for students to earn all 20 needed points...so every group will need to pick out some more involved problems to solve.
As I circulate around the room, I am checking for the following issues:
Here are some questions that I plan to ask students during Partner Practice:
Before we move into Independent Practice, students complete the final check for understanding on their own. I pull a popscicle stick and have that student explain his/her thinking. I then open it up for feedback from the group around what they like about the organization of the student work and what can be improved.
Students work on their own on the Independent Practice problems. As I circulate, I am looking to be sure that students are annotating their problems. The common errors that will come up are students confusing the order of the terms for 'less than,' 'greater than,' 'fewer than,' etc.
I do have some students who struggle with the language in these lessons. My struggling readers have a word bank to use as a resource when they encounter a word like 'quotient.'
Not every student will finish this problem set. The problems do get more complex as students get further along, so that my faster workers are challenged more as they get towards the end of the problem set.
As a closing to this lesson, I ask students to turn and talk with their partner. They summarize the steps they should take when translating a verbal expression into an equation. I ask for volunteers to share out with the class. I ask students to share out any 'tricky' things that they should look out for when working on these translations.
Students then work on the Exit Ticket. Students who translate quickly will have the chance to practice solving for the variable.