As students enter they begin the Warm Up on the screen. They are asked to make zero using the numbers 1, 2, 3, & 4 exactly one time each. This is a type of problem they have seen before in earlier lessons (see 4 Fours; FoursChart). They have to make a target number using only the numbers provided and any combination of operations that they can make work. These challenges are a fun and creative way to practice order of operations.
As they are working on the Warm Up, I circulate and check last night's homework. As they finish, I show them the next challenge:
Make all the numbers 1-5 using 1, 2, 3, and 4 exactly once in an expression.
As an incentive to work diligently, I let the students know they are getting a head start on tonight's homework.
When we go over the Warm Up, I will begin by asking the class how they made zero. As students volunteer expressions, I have the class check each expression to confirm that it is a true statement. If one is wrong, I try to help the students take the stance that the idea was correct, but it was written incorrectly on paper. I will say something like, "Try to figure out what the creator of the expression wanted us to do with the numbers. See if you can fix the expression so that it works." In many cases, the expressions can be corrected by using parentheses to change the order of operations in the expression.
For practice, my students work one problem at a time in their math family groups. While they are working on a problem, I circulate to help and survey student progress. After all of the students have had enough time to simplify an expression, I ask them to hold up their white boards to show me at the count of three. This allows me to quickly review everyone's work and provide feedback. It also encourages participation.
I plan to use the following problems:
3(5 + 9)
4(10 + 10 + 2)
(30 + 5)5
2(7 + x)
3(4n + 1)
(3 + c)5
3(2x - 3)
In the first few problems students may try following the order of operations and doing the addition inside parentheses first, but, I expect someone in each group will remind their peers that I broke up the number on purpose to make the multiplication easier. I will reinforce this when we go over each one by pointing out how ugly and "unfriendly" the multiplication is in 3(14), etc. When we go over the answers, I may ask students to volunteer ideas for how else they may have chosen to break up the 14.
When they first raise up their boards they may have different answers because I didn't ask them necessarily for a final answer. This is because they have not worked with like terms yet and don't know that they can't combine variables and constants until a later lesson (to change or not to change). I might see 3(5)+3(9) or I might see 42 for a final answer. If students are stuck on the third example, (30 + 5)5, I remind them that, "I am just distributing the candy from the back door."
The last four expressions all include a variable. I expect of my students will try to combine the terms. If this occurs, I will choose a value for x and ask students to evaluate both the initial and the final expressions. I want them to realize that the expressions now produce two different outputs from the same input. We'll discuss their ideas about what is happening. I'll ask, "Is this okay? What do you think?" I want to develop their intuitions about operations with algebraic expressions. Usually, students agree that it is not okay if the two expressions produce two different answers. At this point, I am satisfied with this understanding, and we will agree on a correct way to simplify the expression.