Modeling Mixed Numbers

We have been working diligently on our fraction unit despite all the recent snow days we have experienced!  One recent lesson was adding two fractions with the result an improper fraction.  We needed to change our improper fractions into a mixed number.  My students really struggled with this lesson and I needed to find a way to help them visualize how the two fractions would form a mixed number.

After some thought I decided to create a worksheet with pictures that were rectangular arrays.  My colleague  suggested that the students color each portion of the fraction with a different color to help them visualize how the mixed number is made.

Here is a picture of the original sheet I created.  At the time it was quicker to hand write the sheet than to use the computer and make it look good.

Students were much more successful with the assignment once they could visualize how the mixed number was created by the two different colors on their worksheet.  I was very happy to see how well they did on the assignment.  The addition of color helped them to cement the concept of the mixed numbers.

Hope everyone is enjoying their Sunday afternoon.

Equivalent Fractions

We started our fraction unit a week late due to a rare four days off for snow.  We don't get much snow in Eastern North Carolina so just 2-3 inches caused students to have off for four days!

We began the week by discussing whether or not 1/4 and 2/8 were the same.  We used paper folding to determine if they were the same number.  During our next lesson we used a Meaningful Math Task created by our district curriculum specialist.  The task was:

My students sit with a partner throughout the day, partners are grouped according to abilities so that students can learn from one another and get support as needed.   The lesson began by displaying the Math Task on the SmartBoard and students were given fraction bars to assist them in visualizing how to determine which person had the best plan for sharing the brownies.  The math talk was very interesting and diverse.  Just from listening to the students talk with their partners it was clear who had a grasp of the concept and who would need additional support.   Several students struggled with the fact that denominators were not the same or that there were more pieces in the brownies that were cut in sixths and twelfths.  
I heard one of my students clearly tell his partner that the fractions were all the same because the fraction bars all lined up so therefore they had to be the same or equivalent.  Here are pictures of how the students worked out the problem with their partners.

Students spent about 10 minutes working with their partner to determine if the fractions were equivalent.  We then discussed how many brownies each person would get for each of the three plans listed in the task.  This discussion allowed us to generate a list of equivalent fractions and students recorded these in their math journals.  

This was a great way to introduce students to the concept of equivalent fractions.  The use of the fraction bars gave students the opportunity to visualize what the pieces of brownies would look like. Allowing students to begin with a concrete representation before moving to a pictorial and eventually abstract representation is the best way to engage students in math concepts that can be very difficult to comprehend.  

We ended the week by playing a great game called Take Away game with smartie candies.  The students enjoyed the game.  

Hope you enjoy this activity with your students.

Great Math Resource

Great resource from North Carolina Department of Instruction.

I had forgot about this great resource until I went searching for a game I wanted to use for place value.  NCDPI has a great site with math resources.  Although the resource is not specifically based on Common Core there are some great games, etc. that will work for grades 3-5.  Check out the resources at:  http://mathlearnnc.sharpschool.com/cms/One.aspx?pageId=5051238

All of them are available as a PDF file so you can save them for future use.  Each week features specific objectives and has some sort of game or activity to reinforce the objective.  

Hope you find it helpful!