We had our fourth meeting of our “Making Number Talks Matter” book club last night. Our focus for this meeting was on Fractions. We spoke a little bit about decimals and percents, but we spent most of our time looking at how we can support our students in developing conceptual understandings of fractions.

This blog post is meant to serve as a recap for those who were there, a fill-in for those who couldn’t make it, and a record for anyone else who is interested!

We started off our meeting with our usual conversation about how things are going in classrooms with number talks. Some participants shared their ideas for how they are keeping track of student thinking. One teacher has tested out incorporating our student self-assessment and another has been using her document camera instead of the whiteboard to record student thinking – she then has a record of strategies being used with student names attached to help inform her Number Talks planning. It is so inspiring to hear about how excited students are about participating in Number Talks. I hope you will all continue to carve out time in your class for them!

We then looked at a “Fractions on the Number Line” activity as a group. We used a double number line for this activity. We placed the benchmarks of 0, 1/2 and 1 on the top number line and then each participant had a number to place on the line. First, we had teachers talk in groups to order the numbers at their table and then one-by-one the tables came up to put their numbers on the bottom number line, re-arranging as necessary to make it make sense.

From this activity, we moved on to talking about the BIG IDEAS for fractional thinking in the new Grade 4-7 curriculum. We used this quote from the book as our jumping-off point:

…for success in high school, there is no avoiding fractions.

We talked about: what do our students struggle with in terms of fractional thinking? And: what do we want our students to understand about fractions?

Some thoughts that came up:

- We want our students to understand that the size of the piece changes depending on the size of the whole. It is possible to have a quarter that is bigger than a half if the two wholes are different.
- We want our students to understand that fractional pieces have to be the same size but not necessarily the same shape.
- We want our students to understand that fractions are numbers that exist on the number line.
- We want to help our students make connections between their existing understanding of number and their understanding of fractions.

We then looked at the BIG IDEAS from the curriculum from Grades 3 – 9: where are our students coming from in primary, and where do we want them to go in secondary? Now that all the fraction operations have been moved to Grade 8, we have the opportunity to solidify a conceptual understanding of fractions in elementary school so that students are prepared for fraction operations and linking of fractions to algebra in Grades 8 and 9.

From here, the teachers did another activity that connects a visual representation of a fraction to its place on the number line. (Activity adapted from this blog – printable download of the activity cards are available). Teachers coloured in a section of the given square and determined what fractional part they coloured. They then placed their fraction on the number line again.

As a wrap-up, we briefly reviewed the other three types of Number Talks for fractions that are described in the book: More or less (give a fraction and have students defend whether it is more or less than a half); Closer to 0, Closer to 1/2 or Closer to 1 (give a fraction and have students decide which benchmark it is closer to), and Which is Greater (give two fractions and have students defend which one is greater).

Last but not least, we had a mini “make and take” – teachers took home yarn for a double number line and a package with coloured fraction, decimal and percent cards. I will update this post with a link to the printable package as soon as I add some improper fractions and mixed numbers to it! I will also have these packages at our final meeting for people who were unable to join us this week.

Here are a few useful links that we talked about in our meeting:

- Images to use with fraction talks – shade a region of one of these and have students defend their idea of how much is shaded
- The Teacher Studio – this blog has a fabulous series of ideas for teaching fractions conceptually. Scroll down and click on the “fractions” label on the right-hand side to find all the blog posts labelled as fractions.
- Is this shape fourths? – this activity by the Teacher Studio has students defending their ideas about fractional parts. A great extension activity from your Number Talks routine.
- Printable Fraction Clothesline Cards from estimation 180 – (more clothesline cards here as well)
- Printable Fraction, Decimal and Percent Clothesline cards
- Printable Mixed Number/Improper Fraction Clothesline cards