Equivalent Fractions

Fractions are always a tricky thing to teach students and sometimes can be a hard concept for students to grasp, especially equivalent fractions. 

Again I like to teach equivalent fractions by using the concrete-pictorial-abstract approach. 

This is an activity for teaching equivalent fractions using the concrete approach to begin. In a small teacher focus group, I handed out a bunch of scrap paper to each student. 

I asked them first to fold the paper into half and shade in one half of the paper. That was easy. We left that paper alone and grabbed another sheet. I then asked the students to fold that paper into quarters. The instruction was then to shade in as many pieces of the sheet as needed to the same amount was shaded as the sheet for halves.

We repeated this activity for eighths. 

The picture on the left is the result of our little experiment. A few students soon caught on that 1/2, 2/4, and 4/8 all represent the same size and are therefore equivalent fractions. 

This was an exciting activity for me as a teacher as I didn't tell the students we were going to learn about equivalent fractions. Rather, I sat back, gave the instructions and watched the students draw their own conclusions about the paper in front of them. It was wonderful to see the "Ah-ha!" moment on their faces when they were able to make the connection. This will definitely be an activity repeated in the future.

Fractions with Smarties

Once again when teaching in maths, I love working with concrete materials!!! They allow students to work hands-on with their learning and grasp a concept more easily than just trying to understand it on paper.

To begin our unit on fractions, I had students do an investigation with Smarties. Geeze, they were excited about that!

Students were placed into groups and given a package of Smarties. They then had to find the fractions of each colour in the box. 

For example: The fraction of red Smarties in the box is 5/40. 

I gave very little instruction to the students other than telling them they needed to find the fractions of each colour. This worked well as I was able to rove around and see the different strategies students used to find their fractions. Some groups sorted all the Smarties into each colour first, while others counted the total number of Smarties first. This was definitely an exciting investigation for the children but also a good diagnostic to see who grasped the concept of fractions.

Ordering Fractions

In teaching maths, I find one of the best ways that students learn is through hands-on activities. 

"Concrete - Pictorial - Abstract" Approach to Maths 

Read this book by David Sousa to learn more about this approach. Essentially, the approach takes a unit of math and argues that students learn best by starting with working with concrete materials, moving to then using the strategy with a pictorial representation and finally moving to abstract problem.

This website has a wonderful example of this approach: http://www.loganschools.org/mathframework/CPA.pdf

The example is working with a worded problem relating to money.

Concrete: Students use play money to solve the problem.

Pictorial: Drawing out the problem with images of the money.

Abstract: Using the number operations to solve the problem.

So when I was teaching "ordering fractions with like denominators" to my class, I began with the concrete (using fraction pieces) and then moved to the pictorial (using flash cards). I combined concrete and pictorial by giving students a fraction flash card and having them arrange themselves to create a number line of fractions with the same denominator. Students were not allowed to speak to each other when arranging themselves so it ensured that the students all used their own knowledge to understand ordering of fractions. Having students move around to represent fractions is an excellent way of keeping students engaged and showing clear representations of fractions. It also allows students to stretch and have a change of pace from sitting down for an activity.

 For more information on the Concrete-Pictorial-Abstract approach, please read the following:
http://www.loganschools.org/mathframework/CPA.pdf
http://www.k8accesscenter.org/training_resources/CRA_Instructional_Approach.asp
http://fcit.usf.edu/mathvids/strategies/cra.html

Fractions K-W-L Chart

I normally don't use a K-W-L chart in maths but I decided to give it a go and achieved great success with it. After completing a pre-test, students created a K-W-L chart for fractions. It worked well after a pre-test as students were able to activate their prior knowledge and will in the What I Know section easily. They were also able to create questions and wonderings for the What I Want to Know section based on the questions they were unable to answer on the test and new vocabulary they encountered. 

Although this proved to be a simple task, it links directly to The e5 Instructional Model. This task relates to the explore component of e5 by promoting questioning, eliciting prior knowledge and having students make connections to past learning experiences. The questions and wonderings generated by students in the What I Want to Know section has now guided the sequence of our unit on fractions and become the focus of learning during this unit. 

How Many Ways Can You Represent a Fraction?!?!

At the school I work at, we set learning goals for each class based on a set of data that is analysed during our Data Professional Learning Team meetings (based on the AIZ model) . 

My new goals for maths revolves around a unit on fractions. The first goal set was to "represent simple common fraction using physical models". These goals are based on the VELS standards for the grade level. 

 An activity that worked on achieving this goal with my class was creating a thinkboard. To the left is the example I modeled with my class.

On a poster, students had to represent the fraction by showing it in fractional form, written form, a pictorial representation and finally by representing the fraction as a set using physical models.

Some students created excellent posters. The difficulty most students faced was with creating a pictorial representation. Students struggled with the concept that each piece of the fraction needs to be the same size. Some didn't use a ruler, or tried creating a picture of the fraction in a circle but not having each piece the same size. After a few tries, students finally understood the concept. 

Here is some of their work:

Progressive Brainstorm - Fractions

Learning Focus: Representing fractions in different ways

This is one of the first lesson’s we did in our unit on FRACTIONS. Students completed a pre-test and K-W-L chart on fractions the day before. To assess whether students were able to identify fractions represented in different ways, I decided to use a progressive brainstorm.

Students were placed into four mixed-ability groups and each group was given the same colour marker. Each group was given a poster with a fraction on it. They then had three minutes to write everything they knew about that fraction on the poster. This activity is also sometimes called a GRAFFITI ACTIVITY. When the three minutes finished, the posters were moved to the next group and so on, until each group had a chance to write on each poster. We then shared our posters at the end of the lesson.

The progressive brainstorm strategy works well for EAL students as they are working with their peers and are able to see different ideas on the posters as they are moved around to the groups. Hopefully the different images and visuals on the posters help them spur their own ideas to put on the posters. This activity is great to activate student’s prior knowledge of the topic.

Here are the posters from our class. Remember that when we first started the activity, I had only written the following onto the posters.

one fifth (written out in words), 1/3 represented as a circle, 1/4 represented as a set, 3/4 written as a fraction

From this activity, I was able to learn a few things about the students’ knowledge of fractions. Firstly, most of the students have not understood that each piece of the fraction needs to be an equal part of the whole. Also, I learnt that the majority of students in the class were able to recognise a common fraction based on a picture. This will help lead my sequence of activity for the next few lessons on fractions.