Two of my favorite questions to use in class are: what do you notice? and what patterns do you see? It is amazing to see the range of perception, from the most trivial matters – you used all even numbers in your examples – to very deep understanding. I have had a lot of success in adding these two questions to teaching students how exponents work when multiplying monomials, dividing monomials, and with finding the power of a power.
Since my students love to work on whiteboards, I have the students use the individual whiteboards to expand the following problems and then put the answer in exponential form. As they are doing this, I ask students to look for any patterns.
I then start with, what do you notice? followed by what patterns do you see? Most students can see that the base stays the same and the exponents are added together. At this point, students can write the generalized algorithm and do several problems without having to expand each number out.
I start the next lesson on dividing monomials the same way. Students use individual whiteboards to expand the problems out, divide out the common factors, and put the answer in exponential form.
Again, I ask students what do you notice? and what patterns do you see? before we write the general algorithm and do some examples.
By the time we get to finding a power of a power, students understand how exponents are working and this lesson is a bit easier for them to comprehend. I still ask them what do you notice? and what patterns do you see? because I want them to verbalize their thinking and understanding.
These two questions made me realize the need to allow students to start the process of understanding, rather than me giving them the needed information. They need to work out the problems on their own so they can each see what is happening. Otherwise, there is usually the same few students who see it faster than the rest and they say the answer before everyone else can process the information at their own speed. Additionally, It allows me to gauge where each student is at, rather than starting them too far ahead in the concept. Their answers can tell me if I need to back up a bit before proceeding with the lesson I have for the day. I might need to slow down and ask more (better) questions.
Today, I want to share one of my favorite games for students to play to strengthen their adding and subtracting skills with integers. It is called Spider Match.
The object of this multi-player game is to grab as many pairs of flies that add up to the number in the middle of the spider web before your opponents see the pair. The student with the most matches wins the round.
The game can be played with up to four people. So to start, I group my students according to ability and have them move their desks so that they are sitting near each other. One student is in charge of setting the game up with a password and setting it up as a private game. The person in charge then gives the password to the other students in the group so that they can enter the game. After a few rounds, I change the groups and have all the winners play each other, the second place students play each other, etc.
Usually I have students play this game while we are studying integers. However, this game would be great to use on the day before a break when it is hard to keep students focused. I hope your students enjoy the game as much as mine do.
It’s been a long time since I’ve written a post. However, the MTBos 2016 Initiative has gotten me inspired to get back into blogging. I was also encouraged by Kate Novak’s blog to write about the basic stuff. These types of posts appeal to me especially since I am more of a small projects type of teacher.
I like activities that have little preparation and get students out of their seats. Scavenger hunts fit the bill on both counts. The most recent scavenger hunt that I have done with my 8th grade pre-algebra class is Finding the Slope of Two Points on a Graph – Scavenger Hunt. All I had to do was print off the cards, laminate them so I could use them again, hang them up around my classroom, and print a copy of the recording sheet for each student.
Sure, students could just count the number of spaces up/down and to the right/left to find the slope. However, I told students that I wanted them to give me the two ordered pairs that corresponded with the points on the graph and then to find the slope by using the change in y over the change in x.
To help with organization, I printed off a 4 x 3 blank table on the back of the recording sheet so they had a spot to to complete each problem. When students got stuck, they or I could easily go box by box to see where they made a mistake.
This year I bought enough clipboards for each student. This has made a big difference in the neatness of their work. Now, instead of students using the wall or several students trying to cram their papers on one small desk, students have their own work space.
What a great way to get students to do 12 problems while being able to move about the room!