Interactive Math Notebook: Factors and Multiples

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We have been busy working on determining whether one number is a factor or multiple of another number.  We started by building arrays both with tiles and on centimeter grid paper to determine a number's factors.  Becoming proficient at building arrays has really helped some of my struggling students feel successful in finding factors even when they aren't proficient in their facts or have many strong strategies to use to determine a fact.  After practicing many many times,  I gave each student a pair of die (some were six sided, some were more for my kids who are proficient in their facts and wanted a challenge!) and grid paper and instructed them to roll the die and create an array with dimensions that match the numbers on the die.  We then added this page to our notebooks.  Below is an example.  

Next, we used our Math Handbooks and its Table of Contents (oh hello, Language Arts skills! See....I'm learning how to incorporate it all!) to find the definition and examples of factor, prime number, composite number, and square number.  We used this information to create a foldable to glue into the right hand side of the page.  An example is below!

We are also learning about multiples.  After many days of discovering, discussing, and applying this knew knowledge, we finally were able to put the information into our notebooks.  I always try to wait until I feel they understand it to put it into the notebooks.  We used a hundreds chart to choose a factor, then highlighted all of its multiples.  We also used this factor to create a basic real world problem to show how to apply it to multiples.  

This student chose the factor two, and wrote the problem: A store has CDs for $2 each.  She then drew a picture to show that one CD would cost $2, two CDs would cost $4, three would cost $6, and so on.  This shows that the price of buying CDs are multiples of 2

This student chose the factor four.  His problem is about video games costing $4 each, so two would cost $8, three would be $12, and so on.  He goes on to begin to write a question associated with it!

Lastly, I really wanted to make sure we understood the difference between factors and multiples, as it can get very confusing.  We used markers to circle all the factors in a list and all the multiples associated with it.  Students were allowed to pick their own factor, or for those who are still not feeling comfortable with multiplication, were permitted to use the factor four as I did in my example.  Then, they showed an example of an array that shows one of their listed factors and multiples, as well as a non array (just to make sure they understood that an array is a rectangle and cannot have any pieces sticking off the end!!).  These last two pages might be my favorite!  

This student wrote all the problems for the number four.  He circled all of the fours to show that is the factor.  He wrote: 4 is a factor of any whole number that it divides evenly.  He also circled all the multiples to show that you can multiply any number by four to get a multiple of four.

This student did an excellent job of showing the difference between an array that four is a factor of one of its multiples, as well as a non example saying "21 is not a multiple of 4" and using his array as proof!

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!