Tag Archives: 5th Grade

Reversing the Number Talk

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I am a huge fan of number talks and use Sherry Parrish’s book at least two to three times a week to conduct a number talk with my students.  Sometimes I pose just one problem for students to solve mentally and discuss strategies while making connections between them or I do a string of problems targeting a specific strategy.  Recently, I have been focusing on partial products and using friendly numbers as strategies to multiply. I noticed that as the string went along, they wanted to try and predict what the final problem (or “the hard problem” as my students would say) in the string would be. I started taking a few predictions each time and the conversation was really intriguing to me.

For example, the other day, the string was:

5 x 10

5 x 50

10 x 50

15 x 50

15 x 49

As they predicted the final problem, they actually made a more difficult prediction than the ending problem, 15 x 49. They predicted problems such as 15 x 47, 30 x 51 and 15 x 52.  Their reasonings were targeting the strategy of using friendly numbers without me having to outwardly say it.

So I thought it would be interesting (and fun) to go in the opposite direction and give them the last problem of a string  to see if they could develop the string of three problems that would come before it.  I gave them “36 x 19” and they ran with it.  Here are some ideas i captured from the journals:

Photo Oct 09, 12 50 16 PM Photo Oct 09, 12 51 15 PM Photo Oct 09, 12 52 40 PM

This is a great formative assessment for me to see their thought process through our multiplication problems. Definitely adding it to my list of favorite activities!

~Kristin

Number Talks by Sherry Parrish: http://store.mathsolutions.com/product-info.php?Number-Talks-pid270.html

Meaningful Math Conversations…

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I am a true believer that content coaching is a necessity in the improvement and sustainability of math instruction, however we all know that finding time to even use the restroom during the course of the school day is close to impossible! So how do we find time for these important conversations to happen and more importantly, we need to be fortunate enough to have a position in our school that does just that, coach.

Last week, my class was working on finding fraction/percent equivalents using a 10 x 10 grid.  They did great with the fourths and eighths, but then we hit 1/3!  As I walked around and talked to the students, I saw a range of strategies: shading one out of every 3 squares, shading one out of every 3 rows, then squares, and some just knew that three 33’s was as close as they could get with whole numbers and had just shaded 33. No matter which strategy they chose, the “leftover box” was leaving many perplexed.

After quite a bit of struggling with what to do with this leftover box and some happy to just settle at 1/3 = 33%, Nancy (our math specialist, former 3rd grade teacher, and partner in crime with all things math) came into the room.  She helped me by chatting with a group about their thoughts on what do with this 100th box. Class, unfortunately, had to wrap up to go to lunch, and I wasn’t comfortable that some students had had sufficient time to think about it, so I left the class with that leftover box as food for thought that night.

Over lunch, Nancy and I were talking about what she had heard from the students and she made the statement, “It is amazing how they don’t make connections to all of the sharing brownie work we did in 3rd grade when trying to count off by 3’s in the grid..” For those who use Investigations, you will  know the exact lessons to which she is referencing, for those who don’t you can probably infer the context 🙂 We discussed the difference of the contexts for students, the array work they do in 4th grade and then tried to figure how to make that connection for my afternoon class. Tall job for the 15 minutes left of lunch, AKA speed eating.

I typically start my class with some type of number talk, so we sketched out a number talk that focused on the brownie problems of years past. Lunch ended and when the class came in the classroom, they headed to the carpet for a number talk.

I did the following sequence of problems, sharing strategies as we went:

How can four people share one brownie?

How can four people share 6 brownies?

How can four people share a pan of 21 brownies?

They did an amazing job and were very confident in their strategies and I definitely put them into a “fraction state of mind.” We then went into finding our percentages and even the strategies for finding the percents equivalent to fourths and eighths seemed smoother and then when we hit 1/3 and that leftover box was much less mysterious.  There were still a few who struggled but I definitely could see more perseverance and entry points at problem solving. They seemed to make a connection to the brownie problems at the beginning of the lesson.

This entire rambling of my thoughts really boils down to one thought….Improving instruction is about finding time to have those meaningful math conversations. Had I not had that conversation with Nancy and changed my number talk for the second group, the lesson was going to have the same fate as the first.  That conversation helped me make math connections that I could then make my students. Would I have loved to have more time to think out this lesson and retry it the next day, of course, but did Nancy and I improve it…absolutely!

~Kristin

Fraction Talk

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It has been forever since I have blogged, and although I have been so inspired from many things I read this summer, nothing inspires me like talking to my 5th graders!

As we begin our venture into fractions, I have to first give some props to my 4th grade teachers. I have never heard so many “Yeah, fractions” and “I love fractions!” ever.  I attribute this to a lot of hard work and dedication by Nancy (math specialist), the fourth grade teachers, and the Marilyn Burns’ Do the Math fraction units.

Yesterday in class, to get a feel for what my students know about fractions, we did a “Show What You Know” with problems involving writing, comparing, and adding fractions. They seemed very comfortable with writing fractions, comparing fractions using benchmarks, and finding fraction of a group.

Then we get to the problem asking students if the expression 2/3 > 2/6 is True or False. As they shared their reasonings, I heard many anticipated strategies such as “2/6 is equivalent to 1/3 so 2/3 is bigger than 1/3” and “The pieces are bigger in 2/3 and you have the same amount of each so it has to be more.”

As the conversation was coming to an end, one student raises her hand and sets my wheels spinning.  She said “I know that if I just subtract the numerator from the denominator, whichever fraction has the the smallest difference is the larger fraction. But it only works when the numerators are the same.” Huh. I asked her why she thought that worked and she said she didn’t know but proclaimed it would work every time.  I told her we would think through that one and revisit it soon because I needed time to think it through. Being the thoughtful student she is, I had this work from her by the end of the day:

IMG_2186 IMG_2187I was proud she gave examples and tested even and odd numbers to be sure that didn’t effect the outcome.

So my next question for myself (and anyone else who is reading and feels like offering some advice) was what to do with this…

Nancy and I sat and talked about why this works…here are some points to our discussion:

– When you subtract the numerator from denominator you could finding the fractional piece the fraction is from a whole, assuming you put it back over the denominator.

– But since the denominators are different this would not give you a piece of information that would make this “trick” valuable.

– As the denominator gets larger and the numerator stays the same the fraction gets smaller.

– So the bigger the difference between the numerator and denominator, the smaller the fraction.

– Does it work with improper fractions? Yes.

– Is it worth revisiting in class yet because some students may pick up the “trick” and not be ready for the reasoning behind why it works.

– But isn’t it really simple? 3/4, 3/5, 3/6, 3/7…and so on…the difference of the numerator and denominator is getting greater, so the fraction is getting smaller.

So in closing I have no answer of what to do with this information. I am thinking I will revisit it with the student alone because she is anxious for why this works. I may save it for the rest until I have a better grasp on where they are with their understanding of numerator/denominator relationships, but am I being too cautious? I just don’t want “tricks” to be used because they are easier for some students than the reasoning piece.

Would love any thoughts!

-Kristin