The 3rd grade is starting fractions this week and I could not be more excited. Fraction work 3-5 is some of my favorite stuff. Last year we tried launching with an Always, Sometimes, Never activity and quickly learned, as we listened to the students, it was not such a great idea. We did not give enough thought about what students were building on from K-2 which resulted in the majority of the cards landing in the “Sometimes” pile without much conversation. And now after hearing Kate Nowak talk about why All, Some, None makes more sense in that activity, it is definitely not something we wanted to relive this year!

We thought starting with a set of Talking Points would open the conversation up a bit more than the A/S/N, so we reworked last year’s statements. I would love any feedback on them as we try to anticipate what we will learn about students’ thinking and the ideas we can revisit as we progress through the unit. I thought it may be interesting to revisit these points after specific lessons that address these ideas.

We were thinking each statement would elicit conversation around each of the following CCSS:

**Talking Point 1**: CCSS.MATH.CONTENT.3.NF.A.3.C

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. *Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram*.

**Talking Point 2**: CCSS.MATH.CONTENT.3.NF.A.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

**Talking Point 3**: CCSS.MATH.CONTENT.3.NF.A.2.B

Represent a fraction *a*/*b* on a number line diagram by marking off a lengths 1/*b* from 0. Recognize that the resulting interval has size *a*/*b* and that its endpoint locates the number *a*/*b* on the number line.

**Talking Point 4:** CCSS.MATH.CONTENT.3.NF.A.1

Understand a fraction 1/*b* as the quantity formed by 1 part when a whole is partitioned into *b* equal parts; understand a fraction *a*/*b* as the quantity formed by *a* parts of size 1/*b*.

**Talking Point 5**: CCSS.MATH.CONTENT.3.NF.A.3.D

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

**Talking Point 6**: CCSS.MATH.CONTENT.3.NF.A.3.C Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. *Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram*.

After the activity, we have a couple of ideas for the journal prompt:

- Which talking point did your whole group agree with and why?
- Which talking point did your whole group disagree with and why?
- Which talking point were you most unsure about and why?
- Which talking point do you know you are right about and why?
- Could any of the talking points be true and false?

Would love your feedback! Wording was really hard and I am really still struggling with #4.

If you want to read more about Talking Points for different areas, you can check out these posts:

howardat58“Talking Point 4: CCSS.MATH.CONTENT.3.NF.A.1

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.”

The only talking point that refers to “a whole” is point 4.

All the others are about partitions or about numbers.

It seems to me that the idea of “a whole” or :the whole” is something that should be got rid of, either sooner or completely.

The thing about fractions is “part of”, in the sense of “half of a pizza” or “one third of the mixture”, and so on. The context is crucially important.

Another thing: Talking point 6 is “Express whole numbers as fractions…”

As I see it a fraction is again a part of, and so 6/1 is a fraction and 6 is a counting number, but we get lazy and treat the value of the fraction 6/1 as the same as the value of 6.

Writing 6/1 = 6 is very sloppy!

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Linda de BeerMy understanding is that the value of 1 and 6/6 is the same, but it looks differently. Same as the value of a $10 bill is the same as the value of 10 $1 bills or a heap of coins with the value of $10. But is sure feels different in my wallet.

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Becca KeslerHow about “Fractions tell us an amount.”? For me, this works better than “size”. It seems to cover many of the ways third-graders may have encountered fractions in their lives already, such as a half cup of flour, a part of a set of objects, or a portion of a whole such as pizza.

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mathmindsblogPost authorI like that a lot Becca. I was struggling with the word size and was shying away from “amount” because I didn’t want to send them down the path of “1 piece out of 2.” But maybe that would be a good thing to hear how they talk about it!

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Ramona PriesterI absolutely love how you addressed each standard. This seems like a great formative assessment. As for Talking Point 4, perhaps, “Fractions tell us how much of something.”

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JennaI love these! I’m disappointed that our third grade already started their fraction work! It would have been nice to frame the unit around the talking points. This reminds me of Marilyn Burns’ introduction to multiplication of fractions — the discussion of the statements’ validity, followed by the use of the statements as a thread running through the unit. http://mathsolutions.com/wp-content/uploads/Introducing_Multiplication_of_Fractions_A_Lesson_for_Fifth_and_Sixth_graders.pdf (this is one of my favorites!)

As for Talking Point 4…

I like the other suggestions about amount and “how much,” or how many. There’s more to the standard (3.NF.4) that this doesn’t encapsulate, too, about composition: “understand a fraction a/b as the quantity formed by a parts of size 1/b.” I guess this concept is also a part of Talking Point 6, about combining fractions…? Here’s my attempt to get at both the idea of building from a unit fractions and also generating fractions that are equivalent to whole numbers: “Fractions can be combined to make other fractions or whole numbers.” Still feels a little off. (I can tell you have already been so deliberate with your word choice!) I can’t help but think it will muddy the waters around equivalence, as combining a fraction to make another fraction feels more like using 1/4 pieces to make 3/4, and not that 3/4 is equivalent to 6/8 — there’s no combining in the later.

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mathmindsblogPost authorThanks Jenna! I know, the wording is so tricky. I wonder if “Fractions can be combined to form other numbers.” would get at two thing: 1-we can add them together and 2 – another fraction is a number? What do you think about that? I also like the idea of maybe something like “We can write the same fraction in many different ways.”

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