Lesson 5 of 9
Objective: SWBAT work cooperatively to critique the work of others and attend to precision while working on order of operations.
When students enter I have wrong answers to their homework problems projected on the screen:
1) 220 2) 132 3) 2 , 48 4) 21/28 , 3/4 5) 3
6) -1 , 45 7) 26 , 16 8) 30 , 225 , 15 9) 70 , 50 , 190 10) 14
I tell the class to do three things:
- Check for any of these wrong answers in their or their partners homework
- Try to correct it
- Check with their partners to see if their solutions agree, because the answers listed are not the only possible wrong answers
If some of their answers disagree I tell them to ask each other how they did the problem to help them find their mistake. As they work I am walking around checking two problems which I have had them highlight for me (2 & 8) I am also listening to how they are "helping" each other to make sure they are not just telling them the answer.
- I am checking Number 2 to see if they remember how to break the tie. If they went out of order I tell them to check their work on problems 4 & 6 as well.
- I am checking number 8 in case they multiplied before doing exponents and also in case they multiplied by the exponent. If they made a mistake on 8 I tell them to check the other problems with exponents in them.
If a student left any problems blank I point this out and ask if there is another student close at hand who can give help on that problem. This gets gets students to start looking at each others papers. This is also the time they can ask me for help on any of the other problems they are unsure about. I like to get the other group members involved in that for two reasons:
- I can model how to help someone
- To give them the feel that they are in this together
After I have seen each student's work (usually takes about 7 minutes, but sometimes about 10-12 in the beginning of the year), I give students the correct answers. Again, I recommend that students get help on the ones they and their partners answered incorrectly.
I circulate briefly to make sure they are looking at their mistakes to find where they went wrong and correct them. Their natural response is to say "I only missed two!" or "Darn, I missed 5!" and leave it at that. Often they will see their own mistake right away, but when they don't I want them to ask each other what they did wrong and correct it.
Small Group Activity
This activity is meant to help my students learn to conduct productive cooperative discussions in math class. I show the students two Discussion posters that were created by my 8th grade class. These resources outline:
- things that promote learning during a small group discussion
- things that hinder learning during a small group discussion
I don't go through each item on these posters, but instead direct their attention to the back of the room where I have 5 blank cardstock posters displayed (cardstock so you can peel and reapply Post-it notes). Then, I tell students that today we are going to try to come up with some different things we can ask or say in a group conversation to promote the helpful things and to discourage the hurtful things.
The five posters in the back are categories of things that 8th graders thought were important in the discussions:
- sharing your own ideas
- asking others to share their ideas (because it helps when all members join in)
- listening and trying to understand each others ideas
- testing ideas (a way of disagreeing with ideas, not people)
- staying on or getting back on task
Each math family team gets a small stack of Post-it notes, each with different questions or sentence starters in addition to a couple of blank ones. The task is to decide which category (from the posters) each question or sentence belongs to post it on that poster (Guide). There are also some blank Post-its to add new ideas that a group comes up with.
Some groups will finish sorting their prompts faster than others. When this happens, I give them one or two from another group who still has several left. At this point, I have only created one Post-it prompt that really makes sense for the "getting back on task" poster. So, I will, at the right moment, point out that the poster is almost empty I ask them to try to make some suggestions with their blank post its.
There will likely be a lot of overlap or blurring of the lines between categories. One poster may contain several of the same prompt. On the other hand, one question/sentence starter may appear on several posters. We follow the sorting activity up with a group discussion of how the questions can help in each particular category.
For homework tonight, I give the class four quotes about making mistakes. Students are to choose one of the four quotes to write about. I offer this assignment because most of my students come in with a fixed mindset about making mistakes and it gets in the way of their learning. I want to teach them that mistakes are not just normal, but helpful, and necessary in growing smarter. This is a norm and an expectation that I work on and support all year long.
To bring the lesson to closure, I read each quote to them. I tell them that if one of them already sticks out to them to circle it because that might be the one they want to write about. Otherwise I tell them to take a couple of minutes left in class to try to decide which one they will write about in class. I think this draws them in enough that they will think about the quote every once in a while during their day and they will be more likely to do it.