## Sunday, February 24, 2013

### Interactive Notebooks: Data Analysis

It was nice to follow our unit on fractions with a unit on data analysis and graphing.  It gave ALL of our brains a nice little break!  Our 4th grade teachers really did an excellent job of teaching our kids all about bar graphs, line graphs, and data landmarks.  In Ohio in 5th grade, we move toward more complicated graphs such as double line graphs, double bar graphs, and circle graphs, as well as being able to look at a set of data and decide which graph would best show that data.  Going into this unit, I knew I didn't want to just show my students a bunch of graphs and have them analyze them.  I wanted to get them really involved and care about their data, which meant that we had a LOT of data to collect!  We began with a survey:

 Each student got to pick their survey question and had to survey 20 people

Next, we created a frequency chart to organize the data we collected.  Because we just finished our unit on fractions, we were able to change our totals into fractions, then percents.  This allowed us to display our data in a bar graph as well as a circle graph.  To create the circle graph, we colored a strip of centimeter grid paper in the same fashion we colored our bar graph.  For example: in the picture below, Allison colored 12 squares purple because 12 people voted for math as their favorite subject (YAY!!!!), 6 squares pink for science, and so on.  We cut the strip out and taped the ends together to create a circle, and made our circle graph based on the outer edge of the circle.  That way, the regions in the circle graph were accurate.  It also gave us a great visual for how to create a circle graph.   The result is below:

Next, we moved into double line graphs.  I had assigned one student to be in charge of taking the morning temperature and afternoon temperature everyday for a week.  Then, we organized our data into a chart. Next, I asked my students what they could tell from the data.  It was difficult for them to come to any definitive conclusions because it was difficult to visualize how the temperature changed from morning to afternoon and day to day.  So, of course, we plotted our data onto a line graph.  Once all the data was in a line graph,  the students were really able to see what happened to our temperature from day to day.  Some conclusions they made were:
"It is more likely to be warmer in the afternoon than the morning."
"The sun doesn't have time to warm up the earth at 8 a.m. in February, but by 3 p.m. it had a chance to warm everything up."
"Ohio weather is really unpredictable, Ms. McHugh!"

Welcome to Ohio, kids!  Allison's notebook is below:

Next, we collected data on 4th graders who wrote with their left/right hand and 5th graders who wrote with their left/right hand so that we could create a double bar graph.  I left them in charge of coming up with a title, labels  and a scale.  They also dictated how they wanted their chart to look.  Each class had a slightly different title and slightly different charts, but their bar graphs were spot on!  We also decided that while a scale of 10 wasn't optimal, it was our best choice for the size of the grid paper.  The students concluded that the data would probably be pretty similar if we asked the 2nd and 3rd graders too, since the 4th and 5th were so similar.  Poor lefties!

We created foldables to show the definitions of our data landmarks.  I let them use a glossary but asked them to use their own words that would make sense to them and create an example.  They really know these well!  (Thanks 4th grade teachers!!!!!)   We will wrap up our unit on graphing with a project this week.  Thanks to Friday's snow day, we had to push it back.  Stay tuned!

### Fun With Fractions

Fractions! It's always that time of year that requires the most focus and stamina out of my students.  I really get to see their true colors and get to see just how far I can push them.  We started with a pretty basic understanding of what fractions really are.  We busted out the fraction squares and explored how they worked and what they showed us.  This really helped, not only for my lower kids, but for my higher kids too.  My high kids love to be able to show me they know the numbers, but I also like to see that they really understand what's happening, and what better way than through the use of models?

 Allison was kind enough to let me borrow her notebook.  These fraction bars gave us a great visual to start our unit on fractions!
We really utilized our interactive math notebooks during our fraction unit.  Because this is my first year with notebooks, I haven't done a stellar job implementing the traditional left page/right page setup of notebooks.  That's something I plan to tweak for next year.  You'll notice that in the pics :) Anyway, back to fractions.  We began by using our fraction squares to find equivalent fractions.  In fact, we used fraction squares for just about everything before moving into the numbers of the problems.  Once we had the models down, we talked about what was actually happening with the fractions.  The visuals really helped when making that transition!  Below are some of the pages we entered into our notebooks on simplifying fractions and finding equivalent fractions.
 Step 3 is KEY!  If they can't prove their work with a model, then they don't really 'get it'!  We also learned how to use prime factorization as a way to find the GCF.

 I did ask this student to go back and change what she was dividing by to look like a fraction rather than a whole number. !

 This is one of my favorite foldables.  It took us a while but it was worth it!
The fraction squares were perfect for teaching how to add and subtract fractions with unlike denominators.  It really was an 'ah-ha' moment for them when they saw that they could use other fraction pieces and replace them so that the result were squares of all the same size and color.

 Here is our foldable on adding and subtracting fractions with like and unlike denominators.

Here are some of the other things we did with fractions.  Phew....it was a long unit!

 This page was totally independent.  Up until this point, I had written up notes for them.  Starting now, they are coming up with their own notes and steps!  I think they did a pretty good job on their first try!

 Here is a sample problem adapted from a former OAA test question.  I wanted to see if they knew to change the fractions to percents and the percents to fractions.  Most got it!

 Fractions -->Decimals --> Percents foldable