Fly on the Math Teacher's Wall Blog Hop



I'm joining in with some great math teachers in the Fly on the Math Teacher's Wall blog hop! We are going to squash the mathematical misconceptions some teachers and students have on the topic of FRACTIONS! I know Fractions is a huge topic right now, I am being asked questions about fractions on my blog, my fractions products are being purchased on Teachers Pay Teachers and ideas are being pinned on Pinterest. So this is perfect timing. There are 18 blogs to hop through, so enjoy and I hope all your questions are answered!

Having just taught Foundation (Kindergarten), we investigated fractions on a basic level, what is a whole, what is a half, what is a quarter and what does this mean? We wanted the children to understand that half meant "break into 2" and quarter meant "break into 4". Because the children really couldn't go wrong here, I am reflecting back on the 2013 school year when I taught 3rd and 4th Grade.

There were two misconceptions the children had.

The big number always goes on the bottom.

and

The bigger the bottom number, the bigger the fraction. 

Perhaps you are sitting there reading this and thinking, my class had that same problem! Well lucky for you I am going to talk to through some activities I have found help children understand both these concepts.

The big number always goes on the bottom. 

You may have questioned before whether you really need to teach the concept of "numerator" and "denominator" to children. I always do, as I believe it helps the children understand what a fraction is. And with a mother who was a High School Maths teacher, she always said to me Primary/Elementary Teachers should be teaching the "proper" names for Maths concepts. I always teach the denominator as being the number "Down Under".

The important thing is that we teach children that the bottom number is the total number of equal parts that make up the whole in the fraction and is not always the bigger of the two numbers even if they can't remember the proper name for it.

To make connections to this concept, we had a brainstorm to do with 1/2 constantly reflecting on the parts and total number of parts in the whole.


I constantly have the children draw the fraction as well as write the fraction. If they do this, they will record the denominator being how many equal parts there are in the whole shape and the numerator as being how many parts are shaded, or taken away etc. Pictorial representations can show so much! 

Children with a beginning knowledge of fractions will always automatically put the bigger of the two numbers on the bottom. This is true when children are dealing with Grade 3 and 4 Maths, but what happens when they are then introduced to improper fractions? 

We all know using food is a great way to demonstrate fractions. Bring in two of something; cakes, oranges, apples, pizza, chocolate blocks etc. something that you can cut up. Work with the children to  cut each cake into 4 parts. Then collect 6 of the parts - put the line and the denominator in (4), then ask them what number should go on top? This concept will challenge many children, so let them discuss and teach you what they understand. 

The bigger the bottom number, the bigger the fraction.

The other misconception I have found many children to have is that they just assume that the bigger the number on the bottom is, the bigger the fraction. So for example:

3/8 would be bigger than 1/2 (because the 8 is larger than the 2, right?) WRONG!

The easiest way I have found to teach this concept is to create a number line in the classroom. Place a big 0 at one end of the classroom and place a 1 at the other end of the classroom. Give children a card each with different fractions. Ask them to position themselves in the correct location on the number line. This activity can easily take 20 minutes (even if you only have 10 children putting themselves on the number line) due to the discussion you can have with the children and what they can teach you about their understanding. For example when a child with 1/8 stands up, have the discussion about how many parts does the number line have to be separated into? 8. Then at how many parts does the child need to stand at? 1. Repeat this with multiple fractions.

If children understand the basic concept behind the number line, you might make things more complicated by giving children equivalent fractions. This activity is all about discussion!


After the class discussion, children can then draw a number line in their book and place different fractions on the number line. Ask the children to write about what they learnt today as a reflection. 

The next blog for you to hop to is Mr Elementary Math. Enjoy!


4 comments

  1. Great post Alison! I love your that you said we should teach children the correct names from the start, not only does it become more familiar to them as time moves on but it also increases their vocab :)
    Thanks!

    Tania
    Mrs Poultney's Ponderings

    ReplyDelete
  2. Great ideas for squishing these big misconceptions!

    Tara
    The Math Maniac

    ReplyDelete
  3. Great post! You know I love number lines.

    Greg
    Mr Elementary Math

    ReplyDelete
  4. Great post. I love having the kids make number lines to compare numbers.
    Daisy Fryer at Not Your Mother's Math Class

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