Category Archives: number routines

1st Gr Number String: Missing Number

Yesterday, I wrote a quick post as I was trying to decide which of two number talks I should do with a 1st grade class. I got some great feedback and went with the first one in the post! It was amazing and completely evident that the teacher, Ms. Williams, does a great job asking students to share their thinking regularly. The students were so clear in explaining their reasoning and asking questions of one another.

The first problem drew out exactly what I was hoping and more. One student shared counting on and a few students shared how they decomposed the 4 and added 2 and then 2 more. I was not expecting the use of a double, but two students used 8+8 in their reasoning. The use of their “double fact” reminded me of the solving equations conversations I have with Michael Pershan but in a much more sense-making way than I personally think about it. The students said they “knew 4 and 4 made 8 so they took 4 away and that changed the answer.” I tried to get out of them that they subtracted the 4 from the 16 as well, but it just made sense to them the 16 changed to 12 because he subtracted 4 from the 8. I am so glad I videoed this talk because I want to talk more about it after I re-watch it!

The second problem was as tricky, as I anticipated, and split the class between the answers 1 and 9. The students seemed very used to having the difference on the lefthand side of the equal sign which is great, but some still wanted to add 1 to the 4 instead of subtract the 4 from the missing number. I moved on to the final question because we were at a bit of a standstill at this point. Hindsight, I wish I did that problem last, but I had them journal about it after the talk.

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The final problem, which I wish was my first problem – what was I thinking in this order? – was great! They decomposed the 5, made 10 and talked their way through the two incorrect responses.

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I asked them to journal about the second problem when we finished. The prompt was to explain which answer, 9 or 1, they thought it was and why. Here are few examples:

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I think I would love to post the following string (all at once) on the board to start tomorrow’s lesson:

? – 4 = 5

5 = ? – 4

? + 4 = 5

5 = ? + 4

Ask what the question mark is in each one and which equations seem most similar.

Such a great day in 1st grade!

 

1st Grade Number Talk

I am planning for a number talk tomorrow with a 1st grade class. I have been playing around with two different problem strings that I would love feedback on, because I can’t make a decision!

I would particularly like feedback on:

  • What could we learn about student thinking?
  • What would you be curious to find our about their thinking at the end?
  • Do you think one would be better before the other or doesn’t it matter?

Here are the two I am playing around with (sorry, I had them written on Post-its):

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My thoughts:

  • 1st problem – Do they add to 10 and then add on? For example, 8+2=10 and since 12 is 2 more the answer is 4 or do they subtract 8 from 12?
  • 2nd problem – How do they do with the missing number on the right side of the equation? Do they visualize a 10 frame, taking 4 off of the bottom row to leave 5? Do they add 5 and 4?
  • 3rd problem – Do they decompose the 5 into 4+1 to use the 1 with the 9? Do they count on from 9?

Prompt at the end – How are these problems different? Which was your favorite to do? Why?

Second option:

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My thoughts:

  • 1st problem: Set the stage for expressions on both sides of equal sign. Notice you can’t add more to the same number and stay equal. Did we need to solve both sides to know that?
  • 2nd problem: Both equal 10 but did we need to solve both sides to know it is equal? Take one from one addend and add it to the other and still remain equal.
  • 3rd problem: Commutative property.
  • 4th problem: Now that I just wrote the commutative for problem 3, I want to switch the 8+5 on this one to 5+8 so that they might also think about taking 2 from one addend and adding it to the other.

Prompt at the end: Write two of your own equations that would fit something you noticed in our problems today. (wording is rough on that one).

Chances are I will have the opportunity to do both of them and I think they both hit on different, interesting things. I would love feedback on both and know if you think one is better before the other or if it doesn’t matter?

 

 

Number Talks vs Number Strings

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When I first saw this image, I have to admit, it didn’t match what I had been calling a Number Talk in my classroom. Having started my journey with Number Talks with Parrish’s book, I saw it as a string of problems with a specific strategy as the focus of the string that got progressively more difficult (which sounds more like a string in reading this slide). As I started creating my own and making variations to them over the past couple of years, I have simply started calling them Math Routines….it was just easier than trying to make things fit into a certain framework in my brain. After going back and forth about terminology, I started looking at these structures more in the sense of purpose than the name and I am finding it very interesting. Please keep in mind as you read, this is completely from my experience with Math Routines in the classroom and I find all of these talks so incredibly valuable!

First comparison: Single problem vs string of problems. In my experience, I think these two designs have a substantial difference in purpose. When I give one problem, I am going for one of two things: a variety of strategies to see where students are in their thinking OR connections/comparisons of multiple strategies. Personally, I like the variety of strategies before and after we have investigated different ideas that could impact their thinking. For both the students and myself, it shows growth and I can use what I find to help me in planning future routines. Connecting and comparing takes a bit longer and, for me, I don’t get as many strategies out because we focus on connecting and comparing only a few for time’s sake.

Second comparison: Difference in having a model and context. I don’t give a model or context unless a student brings one up in a explanation. If it comes from them, I go with it, if it doesn’t, I don’t write it up there. If there is a specific representation I am hoping comes up because we have been doing work with it during our math class, but doesn’t, I do have them do a quick journal response. I will ask them something such as, “How was our number talk similar to or different from our work in math class this week?” Then I can read their journals and have some students share the next day about the representation connection they made. I also have had students create contexts after we finish a number talk with a prompt such as, “Write a context that you think fits one of the problems in the string. How does the context change for another problem in the string?” For example if the string has “16 x 4” followed by “16 x 8” I am hoping to see connections between the two problems in the context.

Nothing to compare in the final piece, multiple strategies discussed in both!

In the end, students are talking math with a mathematical purpose so they are win/wins in my book, but I am curious to hear what others think around the purposes of different formats of these routines! Would love to hear other ideas so comment away!

-Kristin

Growth Patterns…the Beginning

It is finally here, our last unit of the year and I have to say I am so excited to make it to Growth Patterns! Before we did some reorganization of units due to CCSS shifts, I could never get to this unit, however now having fewer units, I finally make it to the end!

If you have never looked at this Investigations unit before, here is a brief description:

1This unit is really a beautiful culmination of all of the pattern noticings my student do all year long.

Being the end of the year, I know I am going to miss constantly having a class to try out my ideas on during the course of the summer, so I am making the most of the time I have left to test some different number routines.  After reading through this unit, two things jumped out at me that could potentially be incorporated into our number routine work before the lesson: predicting nth terms and relationships between two sets of numbers. So, I thought it may be interesting to do some counting and then think about relationships between our sets we make.

I first had a student count by 3’s four times: 3,6,9,12…. I asked the 10th term and everyone looked at me like I was crazy because this seemed too simple and said “30.” I asked how they knew and immediately thumbs went up and they all agreed that 3 x 10 = 30.I asked for another way you could get there? Next I got, “If you add one more 3 and get 15, you can just double it because it is doing the same thing all the way.” I wrote (12 + 3) x 2 = 30. Another student said, “You can double/half and do 5 x 6 = 30.” Me, “How does double/halving look here?” Silence for a minute, so I asked them to chat with a neighbor and then they came to thinking about jumps on a number line and explained that you were doing jumps twice as big so you need half as many.

Next I did the same process with 4’s: 4, 8, 12, 16 and I got much of the same as above. I asked if we could make any connections to the first set. I had an idea this one may be tough (but I had a plan for it in the next set), however I did have two students who noticed it was one more every time you counted by 4’s, so by the time you counted 10 times, you would have to add 10 to your total, 30+10=40.

The third problem, I wanted to give them the chance to make some connections to the 3 and 4 counts, so I did 12’s: 12, 24, 36, 48… Again, I got many of the above strategies, but then they made some connections to doing “3 times as many jumps of 4 in 12” and “4 times as many jumps of 3 in 12” and adjusting their 10th terms.

Because some students were really comfortable moving between the sets of numbers, others were still staying within one set of numbers in describing the 10th term, I gave them two sets to go back to their journal to reflect on: 2’s: 2, 4, 6, 8…. and 2/3’s:  2/3, 4/3, 6/3, 10/3….

I asked them to either talk about how they could arrive at the 10th term or make a connection to one of the previous sets of numbers…

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It was interesting to see their connections between the sets, but I think for next time I need to think more about either the predictions of future terms or comparing two sets, this was a bit too much at once. Next time I may have them look at sets with constant change but not starting at a multiple of that number….and then as I was typing that, I think it would be cool to come up with a set with a missing number at the end that could be varying numbers depending on how they see the pattern, then give a term after the missing number and narrow it down to which pattern it actually is….hmmmm…have to think more about this one…

-Kristin