Monday, April 7, 2014

Guest Post Lucy Ravitch: How Decimals and Fractions are Related

Hi, I'm Lucy Ravitch and I blog at!

I'm excited that All Things Upper Elementary is having me as a guest today.  I am currently a stay-at-home mom with a degree in Elementary Education and I LOVE to teach math.  I also write children books with math concepts too, but they are not yet published (believe me I've been trying--for four and a half years now).

Today I'm blogging about a concept that I feel can be confusing or unknown to fourth and fifth graders.

Decimals and Fractions can represent the same numbers!

I remember as a young kid (probably 2nd grade) thinking--Are fractions and decimals related?  My teachers are showing me fractions.  But I know 1/4 is a quarter and a quarter (coin) equals $0.25.

It wasn't until I was in fourth or fifth grade that decimals were finally introduced, but I think it could have been introduced earlier (but not every kid was or is as math inquizative as I was).

As a teacher now, Common Core puts base ten and fractions both as Numbers and Operations but does separate them (at least they are next to each other).  I want to show you a way to teach your students so they can understand how these two concepts (base ten and fractions) are related.

I have a book I've written titled Maurice's Mozzarella: A story of tenths, hundredths, and thousandths (yes, still not published) that I'll summarize the concept of the decimal place value system.  With this story you use base ten blocks, starting with the large cube (typically identified as the thousands).

You can tell your students.... Maurice (a mouse) is a master Mozzarella maker and one day he needs to make an order for a customer that will be given to 1,000 students.  One of his big balls of cheese will need to go to 10 schools, which each have 10 classes with 10 students each.  He discovers if he cuts the ball into a square block it will be much easier to divide.  He cuts the block into 10 equal slices (tenths), then each of those into 10 equal sticks (hundredths), and then the sticks get cut into 10 equal mini-cubes (thousandths).

I made a quick little video showing the base ten representation...

So, this story displays the base ten system.  But still, how does that relate to fractions?  Wait, there's more...

Now that Maurice knows how to make slices (tenths), sticks (hundreds), and mini-cubes (thousandths) he can use this strategy when he has customers come in that want to share or not have a whole block.  Students can make up their own stories and figure out their answers.  I still have to write the sequels to the book, but here are some ideas...

Triplets come into the shop and each want an equal share of one of Maurice's blocks.  They will each get 1/3 right?  Here is what it looks like when the kids show it with their base ten blocks.  Of each three pieces, one will go to each sibling...

What if one customers only wants half of a block?  1/2 equals 0.5 (and you teach the kids how to say the decimal correctly as five tenths)

Then you could try something challenging... A large family comes in and wants it divided equally for all eight members of their family.  Can your students figure out what 1/8 in decimal form is?  Here's another video in case students are stuggling...

Once your students understand how to find fractions in their decimal forms you can also show how equivelant fractions all equal the same decimal.  1/2 also equals 2/4, 3/6, 4/8, 5/10, 6/12...  They all equal the decimal 0.5 or 0.50 or 0.500 which can be simplified to 0.5.

FYI: I used the base ten papers from this site with blackline masters.  I also have a place value book reinforcing the ones through millions place.  It is a printable book on my teacher stores at TpTTN, and BST.  Additionally, I founded a Google Plus community for Elementary School Teachers (feel free to join if you want).  On Facebook you can follow my author fan page if you like : )  and if anyone has math posts they would like to share I have a weekly linky called Math activity Thursday (with a different elementary grade focus each month).

Thanks again to All Things Upper Elementary for having me as a guest!  And thank you for watching and reading!  How do you teach fractions and decimals?  Do you use any manipulatives?

1 comment:

  1. Thanks for having me! One video was missing but it still looks good. Hope your readers enjoyed it : )
    ~Lucy Kids Math Teacher


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