This idea comes from Cheesemonkey's post ... read it here! Thank you for sharing.
I am drowning in grading. Giving feedback is a must! This process is great for simplifying peer to peer feedback as well as teacher feedback.
To break up the monotony of working in desks, I brought in beach towels - 10 of them ... to create "islands" ... oases of math learning! On each island there is a group whiteboard, 3 markers, 3 calculators, and necessary handouts (could be done without any but I'll explain why they were helpful).
As students entered they set their bags aside, brought only their math notebooks with them, selected an island and had a seat. I required no more than 3 people to an island. I had a few islands with just 2 people.
I gave each team an index card ... students put their names on it.
Then I gave instructions ... our topic of the day is solving systems using matrices. The first half of class was practicing solving 2 x 2 matrices by hand, the second half of the day was practicing solving 3 x 3 matrices by calculator. (We have 90 minutes ... every other day ... rotating schedule).
I projected 3 systems on the board. In groups students solved each system using matrices ... clearly outlining the determinant, inverse matrix, and matrix multiplication. As groups finished a problem I checked it and hole-punched their index card. When punched, students immediately moved on to the next problem. Groups had to rotate who did the writing and who coached.
As students finished the 3 systems that were projected, they moved to a handout with word problems - practicing the same skill but first finding the equations. So having the handout served as a differentiation tool ... students who worked quickly through the projected problems could move forward.
Students clamored for their hole punches! Amazing. Free. Simple!
About half way through we switched gears so that students could learn how to solve systems of equations using their calculators. To get a hole punch every member of the team had to have the answer on his/her calculator.
Teams earned about 12 - 16 hole punches in the class period. BUT much more than that ... every student was coached in how to solve the problems of the day. Every student got feedback. Every student had support for the parts they found difficult.
And the energy was high. The conversations totally about math. And they clamored for their hole punches! Amazing. Free. Simple!
Are you using Cramer's rule for the 3x3 inverse ?
No, we don't teach Cramer's rule. We use our TI calculators for all matrices other than the 2 x 2. And for the 2 x 2 we teach only the inverse method of solving. It's short introductory unit ... just 4 lessons.Delete
Good ! Cramer's rule belongs in the dustbin (trash can) of history.Delete
The row operations on the matrix and the unit matrix together is so much easier, and that is how the calculator will be doing it (well, I hope so !). But you know this already.
Seems to want me to be anonymous
Love the Island Study! This is definitely going on my "to try" list.ReplyDelete
It was definitely fun ... but more than that it was great math ... lots of math dialogue, peer to peer feedback, and much practice!Delete