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):
- 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?
- 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?
I love the patterns found within your second option. OA.7 lends itself to SO MUCH discussion, I’d be interested to see what your first graders have to say! Using reasoning only, can they determine that the first option is false? Can they also see that the third option is true, again without doing any computation? I also like the numbers you’ve chosen for the 2nd and 4th problems, increasing one addend while decreasing the second will result in the same value. What would this look like on the number line? The 2nd problem might lead to an interesting discussion of 10, which could propel you into some discussions surrounding the equations on your blue post-it. Looking forward to seeing how your talk evolves!
Wording possibility for your exit ticket: write your own problem that would fit in with the ones we just did.
I think I am going to try the second talk with my kids as a starter today. I am going to see if they recognize the false statement, and how they found the error. I am also interested in how they will react to the true statements, that is, will they believe them to be false at first glance. My children see one item and immediately assume to same actions will apply to all of the problems in a set. I am trying to get them to read each problem, find things they recognize, and identify which strategy they will use to solve. Your second number talk will allow me to see this in action.
Are your first graders comfortable with the meaning of the equal sign? Many at this age have the misunderstanding that the equal sign means the answer follows. Your first set might be difficult if they haven’t been exposed to multiple problem types or if they don’t have a strong understanding of the part part whole relationship. Your second set has good concepts, it allows kids to think about both sides computationally as well as relationally. Some kids may only see past the equal sign and say false because 9+1 does not equal 9. They may not even notice the + 3 at the end. A lot will depend upon the experiences they have already encountered in their classroom.
I am anxious to hear how it goes!
As Denise questioned above, I’m not sure where these first graders are at with their understanding of the meaning of the equal sign–the first string would allow you an opportunity to see if students see the equal sign as only operational/indicating an answer or relational/indicating “the same value as”. Kids need a relational understanding of the equal sign in order to analyze the equations in the second string of equations.
Back to the first string–If the kids don’t have much experience with missing addends/subtrahends/minuends, then I would expect counting on to be a common strategy. I would also expect an answer of 1 for the second equation–I think some kids (and some adults) would see the 5 and the 4, see that the equation calls for subtraction, and subtract 5 – 4 to get 1.
I’m curious to see which string you selected, and how the Number Talk went!
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Thank you all SO much for your feedback! I ended up going with the 1st set of problems today and I completely should have changed the order of the problems! Great news is the equal sign was not an issue at all, it was more the placement of the missing number. I think if the ? in the 5=?-4 had been where the 4 was and the 9 was given, they would have gotten that easily. I had so much fun and cannot wait until the video is released from Teaching Channel bc the convo was AMAZING!
Thanks you so much for this blog. I tried the first number string and the students gave great strategies. I changed the numbers because of the students conversations. I used
9 + 5= ?, 8 + ? = 12, 15 = ? + 7, 9 = ? – 4
9 + 5 = ? one student decomposed 5 to 4 +1 and couple others used 10 + 5 -1,
8 + ? = 12, students used 10 + 2 + 2,
15 = ? + 7 students double and added 1 (I put this one in because I want to see if they could figure out the ? after the = sign before I moved to subtraction.) All the addition problems were no problem.
9 = ? – 4 was a different story. Many of the students believed the ? was 5. One student said 13. After a couple of explanation half the class believed it was 13 but still half believed it was 5. The teacher said a group of boys spent 10 minutes trying to convince each other of their different answers.