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Fractions

The focus of this unit is on reading and representing fractions. Grade 3 is the first time (in the Nova Scotia curriculum) students are formally introduced to fractions. Of course, kids have heard fractional language (half, quarter) all of their lives, and this unit serves to help them understand the meaning of those terms and to explore how fractions are used in practical situations.

Topics covered include:

describing everyday situations in which fractions are used.
sorting a given set of diagrams of regions into those that represent equal parts and those that do not.
identifying, modeling, and explaining the meaning of numerator and denominator.
representing a given fraction concretely and pictorially.
naming and recording the fraction represented by the shaded and non-shaded part of a given region.
comparing given fractions with the same denominator using models.

A Bit of Background

Fractions are a rather abstract concept, and it can be challenging to wrap your head around the idea that these number symbols represent part of something. In addition, we use the same fraction name to represent things that are completely different sizes. Half of a whiteboard is different than half of a credit card, and yet both are half. It is important for kids to understand that we can only call something a fraction or use fractional words accurately when we have a whole item broken entirely into exactly equal pieces, and when we can relate the pieces to the whole.

In class, we spend a great deal of time exploring equal pieces. We look at examples of pieces that are equal and also at unequal portions. We relate the idea to "fair shares" and how, in order to share something fairly, we need all of the pieces to be equal. We also talk about how we need to share the entire item, and not throw away part of it.

As much as possible, we look at fractions in the context of every day life and where we might see and use fractions. Practicing fractions skills is a great activity to do at home. It helps reinforce that fractions is not just a concept we practice at school - it has real-world applications.

Students in grade 3 need to know the terms numerator and denominator, and although remembering those exact words might happen over time as they continue to work on fractions in future years, they do need to know what the numbers in a fraction mean. The denominator tells how many equal pieces it takes to make the whole. It's total number of equal pieces that we broke the item into. We think about the denominator as the name of the pieces. In the above example, the pieces are named "fifths" because there are 5 of them. The numerator is the number of pieces that we are counting or the pieces that we are paying attention to. In the above example, if we are paying attention to the blue pieces, then 3 pieces are blue. The pieces are named fifths, so we have 3 fifths. It's important to note that the above picture also shows 2 fifths if we are asked to count the white pieces.

Some Ways to Practice at Home:

Encourage (and use) proper fractional language at home. If a pizza is being equally shared among 4 people, call the slices quarters, not halves. If you break a chocolate bar into two pieces one larger than the other, describe them as "more than half" or "less than half" to describe the pieces.
Find things that have been divided into equal pieces and practice naming the pieces. For example, my living room window has 12 equal panes, so each one is a twelfth. Also find examples where the pieces are not equal and see if your child notices.
Notice fractions in the world around you and ask your child to name them. What fraction of the cars in the parking lot are blue? What fraction of the pizza did you eat? What fraction of the Skittles are green? Just be sure that the whole has been broken into equal pieces.
Do some baking and cooking - the long way! If the recipe calls for 1 cup of something, have your child test the measuring cups by using the 1/4 cup or 1/3 cup to see how many it takes to make 1 cup.

When preparing meals, have your child help in dishing out the food. Get them to try to make equal portions (being sure to use all of the food) and then name the portions as thirds, fourths, etc.
Give instructions to make a fraction drawing. "Draw a house and colour half of it blue. It should have 5 windows, and 3/5 of the windows should have curtains."
use coloured cubes or squares of paper. Put 10 of one colour in a bag and add 10 of a different colour. Roll a die or pick a number up to 10. Randomly pull out that number of items from the bag and make a shape. Write the fractions that are represented by each colour.
Roll 2 dice and make a fraction. At this point, make sure the lesser number always goes on top, and have your child model or draw a picture of the fraction. Remember that 3/3 is a fraction and represents the whole thing!

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