## Exploring Fractions

#### Erika Tokich Year 3, Good Shepherd Primary School, Amaroo, ACT

Following Days 3 & 4 of Working Like A Mathematician presented by Mathematics Centre at the request of the Catholic Diocese of Canberra Goulburn, Erika planned and executed a unit on Fractions & Decimals. in this article she outlines her unit and provides examples of student assessment. You will find more inspired fraction teaching from teachers in this course at these links:

Year 3 explored fractions of whole objects, shapes and collections. My program went for 2 weeks and was based around Cookie Count and Rectangle Fractions, both of which have companion Maths300 lessons. The Rectangle Fractions lesson also has software. We used Poly Plug and Poly Plug Frame worksheets and Interactive White Board (IWB) resources. The assessment was very much based on examples we had done in class.

Our focussing activity was reading and acting out the story 'The Doorbell Rang' by Pat Hutchins. We discussed sharing things equally and discovered the more shares needed the smaller the share.

We then used red Poly Plug boards which represented 25 cookies. We shared the cookies between 2 and 5 friends. We drew a diagram of our results.

 If 2 friends were sharing they would get 12 each with one remainder, or 12 and a half each. If 5 friends were sharing they would get 5 each. We also discovered that 5/25 is the same as 1/5 The next day we put 2 trays together which made 50. A new whole. We discovered: half of 50 is 25, a fifth of 50 is 10, a tenth of 50 is 5! The students then coloured Poly Plug Frames to represent the different fractions. Next we put 4 Poly Plugs together which made 100! We discovered: half of 100 is 50, a quarter of 100 is 25.

 Click the student work for a larger image. ---> We then explored things in our room that are divided into fractions. Our bookshelf is a whole, but it is divided into 3 rows and 2 columns; 6 parts altogether. We represented the fractions of the bookshelf using Poly Plug and made arrays that showed how the bookshelf could be divided into halves and thirds. The students then drew a picture and coloured the fractions.

 The students also had the opportunity to discuss what they thought of the activities over the 2 weeks. Everybody gave the thumbs up! We also went on a fraction walk around the school. We discovered fractions everywhere. in the windows, at the bubbler, even in the gazebo roof! Our favourite was pizza fractions. We made our own pizzas which we divided into sixths. In guided rotations we used the IWB and fraction flip charts, explored fractions of money and coloured window frames. Finally, we did an assessment based on the activities we had explored over the 2 weeks. (Photos below show children working on their assessment and sample responses. Click student work to see a larger image.)

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