Out of Order

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SWBAT focus on their mistakes and the mistakes of others to help improve their use of order of operations.

Big Idea

Practicing the hard parts

Warm Up

15 minutes

The day before I had taped to their desks some of the sentence starters and questions they had sorted in previous lesson. ("conversation moves" lesson earlier in this unit)

Students begin their warm up with a 3 minute silent write in response to the following prompt:

Is making mistakes in math class good or bad? Explain why you think that.

After three minutes I have students look over the table top "conversation moves" I've taped to their desks. When they've taken a brief look I now ask them to pick out 2 or three that they think might come up in their next discussion when I ask them to share the quote that they thought about for homework and their response to today's prompt. Some will start sharing right away, but I stop and remind them that right now we are just picking out 2-3 "convo moves" that we might use first. (I said sharing the quote they "thought" about because as went through the room during their silent write a few of the kids hadn't actually written).

After students share out a few of the sentence starters and questions I tell them to use these as they are sharing what they thought about the quotes they chose and their response to today's prompt. I tell them that they may not have written everything they thought, but to share those thoughts anyway.

After they have shared with their math family I ask them to spend another 3 minutes silently writing in response to the following prompt:

Describe someone's idea that was a little or a lot different from yours, or something that was said that you hadn't thought of or that surprised you.

These are then collected for me to see how their ideas about making mistakes may be shifting.

Batting Practice & Formative Assessment

35 minutes

I call this "batting practice" because we are picking out the hard parts and working on them. I refer back to their first order of operations practice homework and tell them that most of their mistakes and questions were with problems 8 and 10, so that's what we will practice in class today on white boards. I give them one problem at a time to work on. I circulate to help and encourage them to help one another. I remind them that if they think someone has made a mistake to ask them what they did so they can find where they went wrong. I also tell them that if they are stuck to ask someone what they did in order to get them started. By using the same question "what did you do" in either case it does not become a clue as to right or wrong answers. The problems we work on, one at a time are:

15 - 6(2)+ 24

36 + 2(5) - 4

A third similar to the first two that I ask a student to create for the class

2[7 - (21 + 4) / 5]

5[8 + (14 + 4) / 9]

Another similar to the last two that I ask a student to create for the class

Common confusion in the first set comes from not recognizing a(b) as multiplication. Another common source of confusion which is invisible because they usually get the answer right is that they start with a(b) not because it is multiplication, but because of the parentheses. So when I am circulating while they are working on boards I ask students why they chose to multiply first. If students don't see the multiplication I ask the other members to look on while I ask them to show what they did. Other members usually see the mistake and I ask them to explain.

A couple of things usually come up with the second set of problems. After adding inside the parentheses students add or subtract before dividing or they go "left to right" with the multiplication and don't recognize the brackets as parentheses. The first mistake is usually picked up by another student in the same way as the above set. The second mistake sometimes needs my intervention so I will ask the student to show me what they did. When they get to the point where they multiplied I highlight the brackets and ask "before you finish operations inside parentheses?" Then they understand that brackets are another type of parentheses and correct the problem.

I ask students to raise up their boards on the count of three, but usually we've caught most of the mistakes before they raise them up. It's faster later in the year when they are less worried about hearing corrective feedback publically, but right now I want them to get into the habit of participating in the activity.

We don't usually have time to work the next ones on white boards so as they are putting their boards away I act disappointed that they didn't get to see the rest and suggest that maybe they can do the next ones in their heads. So, one at a time I put them up and tell them to keep quiet until I ask them to shout it out because people are trying to juggle math in their heads:

2x3^2            2x5^2         (2x5)^2

Some of the kids don't shout out on the first one, but when they see that they could have done it they shout out the next two.


4 minutes

I give them the remainder of class to start their homework which is very similar to the one a couple of nights ago. I suggest they find the ones like those we worked on today to start with while they have access to help