(1) A Learning and Teaching Resource for Equivalent Fractions 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The resources were made using the following material; glue stick, permanent marker, ruler, scissors, pencil, pencil case and bucket (used for stenciling), A3 paper, A3 cardboard, and A4 paper. Firstly, the bucket was used to stencil a circle onto the coloured pieces of paper (2 are needed as A3 is not wide enough). The two pieces of paper were cut along the line and glued together. Cardboard was added as a backing to give durability and sturdiness. Four ‘Happy Birthday’ signs were then created using the A4 paper, to place on top of the “cake”. 40 small circles and 8 larger circler were stenciled using the glue stick and pencil case, these were then cut, and drawn on using the permanent marker to create a “flower” look. The flowers and signs were then glued on, and candles were also drawn on, creating an identifiable birthday cake. The cakes were then measured and cut into fractions. Each cake has an approximate diameter of 36cm.

 

The reason for choosing a birthday cake was because it is appealing and familiar to most children from their real-world experiences. Creating a visually appealing and practical resource that will demonstrate to children the concept of equivalent fractions. The vibrant colours of the cakes also enhance the resource visually for children.

 

This resource will facilitate understanding of equivalent fractions as children can visually see that by placing for example the four quarters over the whole, there is no space left, showing that four quarters are equivalent to a whole. Thus, creating an understanding.

 

This resource demonstrates equivalence, as is it symmetrical. Each individual cake (for example, the halves) is equal, and thus can be placed on top of the whole cake or the other cakes to show their relationships. Students will use the resource by rearranging the cakes to explore equivalence and the relationship they have with the ‘whole’. Any age group can use this resource to assist them whilst learning about fractions, as the cakes are large they are able to be cut up into smaller fractions. This resource, however, is particularly useful for year two when the concept of equivalence is introduced. 

 

(2) The Purpose of the Equivalent Fractions Resource 

 

The purpose of the resource is to introduce and demonstrate the concept of equivalent fractions. The concept of equivalence is the idea that different parts of a whole can be the same as or are equal value to other parts. The students will rearrange eighths, quarters, and halves to explore their relationship to the whole and other parts.

 

The concept of equivalence is first introduced in year 2. This is supported by the following appropriate ACARA (2014) reference: Year 2, the Number and Algebra strand, Fractions and Decimals sub strand. The content description is recognise and interpret common use of halves, quarters and eighths of shapes and collections (ACMNA033), with the elaboration of recognising that sets of objects can be partitioned in different ways to demonstrate fractions (ACARA, 2014)

This reference clearly resembles the aim of the chosen resource. The aim of the resource is to demonstrate how a whole can be partitioned into different ways (i.e. whole, halves, quarters, eighths) thus, representing fractions. Hence why the resource was chosen.

 

The equivalent fractions resource would best fit into the materials language stage within the language model.

This resource allows children to demonstrate how objects can be partitioned in different ways to represent fractions, as stated in the Australian curriculum, hence why if fits into the materials language stage. This resource isn’t used in the children’s language stage as the students should have learnt in year one how to recognise and "describe one-half as one of two equal parts of a whole” (ACARA, 2014).

This resource is concrete/visual as the concept of equivalence is being introduced, allowing students to have a visual aid whilst being able to physically move the resource, creating not just a image in their head of the concept of how two halves will equal one whole or how one quarter is half of a half. Students should be able to understand the concept of equivalence by using this resource. 

 

(3) Using the Equivalent Fractions Resource to facilitate Learning (text only)

Today we are going to introduce equivalent fractions. (Holding up whole cake - green) Here we have one whole birthday cake, we need the one whole to relate all the other parts back to the whole. (Hold up halves cake – blue) Here we have two equal parts, also known as halves. (Hold up quarters cake – orange) Here we have four equal parts, also known as quarters. (Hold up eighths cake – purple) Here we have eight equal parts, also known as eighths.

 

 

 

 

 

 

 

 

 

 

Firstly we will see how many halves we need to make one whole cake; one part, 2 parts.

 

 

 

 

 

 

 

 

You can now see that there is no green left over. How many quarters will make up one whole? Lets see; 1, 2, 3, 4. 4 quarters make one whole!

 

 

 

 

 

 

 

 

 

 

How many eighths will make one whole? Lets see; 1, 2, 3, 4, 5, 6, 7, 8! There is no green left over, so therefore 8 parts or 8 eighths make one whole.

 

 

 

 

 

 

 

 

 

 

 

 

We can also use these cakes to find out how many quarters it takes to make one half; 1, 2! There is no more blue cake left, therefore, 2 quarters makes one half.

 

 

 

 

 

 

 

 

 

 

How many eighths equals one half? 1, 2, 3, 4! We can now see that 4 eighths equals 1 half. We can also see that 4 eighths equals 2 quarters. 

 

 

 

 

 

 

 

 

 

 

 

As you can see we have now demonstrated how many halves equals one whole, how many quarters equals 1 whole and how many eighths equals 1 whole. As well as how many quarters equals 1 half, and how many eighths equals one half.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(4) References

Fractions Cartoon [Image] Retrieved from http://www.livebinders.com/play/play?id=678519

 

 

Australian Curriculum Assessment and Reporting Authority (2014). Mathematics. Retrieved from: 

http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1