In 6th grade we start the year with a little bit of geometry and decimal operations. In Minnesota, students add and subtract decimals in 5th grade and in 6th they are introduced to multiplying and dividing decimals. I made some improvements to this unit this year, and even though I wish I were better at teaching some of these concepts, I can’t ignore the fact that I did make improvements from last year. If I keep working each year to make it better, eventually I will get closer to where I want to be when it comes to teaching these things.
Our first unit is broken down into 4 parts: the coordinate plane, area, multiplying and dividing decimals, area on the coordinate plane.
The Coordinate Plane
I read Tom’s post on creating a need for the coordinate plane a couple of years ago and knew I had to try it. This is the second year that I’ve used it, and I think it is a really good way to introduce the coordinate plane to students.
After we have talked about the parts of the coordinate plane and plotting order pairs, students do this Desmos card sort.
Then we do this Desmos activity from Nathan Kraft. This is usually students’ first time using Desmos, and I love watching them go from being somewhat confused with how Desmos works at the start to absolutely LOVING Desmos about 2 slides later. 🙂
Then we start working on finding the area of figures. I use a lot of Notice/Wonder with GIFs to talk about finding the area of various shapes.
For students to get some practice finding the area of shapes, I use this worksheet. It is similar to Sara Van Der Werf’s Add ‘Em Up activity, but in worksheet form. I use this before we do area of trapezoids.
For practice on finding the area of trapezoids, I don’t do anything fancy. I have pictures of trapezoids that I tape around my room and have students walk around in groups solving the problems.
I do a few other things with compound area and estimating decimals before we start multiplying and dividing decimals.
I tried something new this year to introduce multiplying decimals. I started by putting a decimal multiplication problem on the board and had students estimate it. Then I had students multiply the two numbers and told them to forget about the decimal until the end and to use their estimation to figure out where to put the decimal. After doing one problem together, I had students do several problems in a group and told them to look for a pattern regarding where they put the decimal at the end. For the most part, students were able to see the pattern and tell me the “rule” for multiplying decimals. I realize this isn’t perfect, but it’s better than what I had been doing in the past, so I was happy about that.
Open Middle has a couple great problems for multiplying decimals.
I used the following image to start our conversation about dividing decimals.
Generally students notice that the answer stays the same. Sometimes students think that the answer of 4 each time is wrong, so we have a conversation about that. Someone usually says that you add a zero to the divisor and the dividend each time, and usually someone else in the class knows that both numbers are being multiplied by 10.
In my experience, this has lead nicely into dividing decimals, and as we continue to work on that, I reiterate that when you multiply both the divisor and dividend by 10 (or multiples of 10) the quotient remains the same.
The reason I put decimal operations in the unit with area was so that after doing both concepts, I can put them together to review both at once.
Estimate Area on the Coordinate Plane
I have always struggled to find good practice problems for students on the types of problems in the standard above. This year, I found a few pictures online and turned it into a Desmos activity.
If you use anything in your classroom that you feel would fit with this unit, I would LOVE to hear about it!