Granny's egg problems continue!
Granny finally wrote us back after returning from her vacation in Florida. She was still having problems with her eggs and asked us for help.
(Setting the context)
(Working on it)
Our team was eager to help Granny. Group 1 played with eggs and a carton that had been cut down to hold 10 as granny had instructed. Once partners had considered different ways to make 10 with their coloured eggs they recorded their thinking. Below are some examples of this.
A few of these solutions were then brought back to the members of Group 1 to share the thinking. This group is quite comfortable subitizing numbers and are now being challenged to think about part part whole and in some cases hierarchical inclusion of numbers. We began the challenge by having CB come to the SMARTboard and show us one way to make 10 with coloured dots on a ten frame. She made the colours "in a pattern" (blue, pink, blue, pink) and then explained that there were 5 on the top and 5 on the bottom which makes 10, which everyone in this group easily recognized.
Here are some additional conversations, based on the work students did following the introduction of granny's letter and our initial conversation:
First student work sample shared.
MJ - LK what are you thinking?
LK - The bottom is different because 5 blues are at the top and 2 blues are at the bottom and 3 reds are at the bottom.
MJ - So is that 10?
LK - Yes.
MJ - How do you know that?
LK - It just looks different.
MJ - Help us to understand how that's 10
LK - 5 plus 4 plus 1 more equals 10.
MJ - Does anybody see a different way to tell granny?
KB - 7 blues and 3 reds make 10.
MJ - How do you know there are 7 blues?
KB - Cause I counted in my brain when Liam was talking.
MJ - How did you count?
KB - 1, 2, 3, 4, 5, 6, 7.
MJ - Anybody else...what did you see?
EA - 4 and 6 makes 10.
MJ - Can you come and circle the 4 and the 6 you are talking about? (She circles 2 on top and 2 on bottom together as the group of 4, then 3 on top and 3 on bottom together as group of 6).
Second student work sample shared.
MJ - What would you tell granny about this one?
LF - 4 and 2. (He circles 2 on top and 2 on bottom together as group of 4 and then circles the next 2 yellow together as a group of 2 working left to right across the ten frame.)
MJ - And what's 4 and 2 more?
LF - 6. Then 1 more .... (top green)
MJ - Is how many?
LF - 7 and 3 more (3 remaining green) is 10.
MJ - Did anybody see it a different way?
CL - 2 and 2 makes 4 (green dots) then 6 more (yellow dots) makes 10 (working from right to left).
LF - He almost like copied me!
Third student work sample shared.
MJ - EA come and share your thinking.
EA - 7 and 3.
MJ - Makes how many?
EA - 10.
MJ - How do you know that's 7 (blues dots).
EA - Because 5 and one more makes 6 and one more makes 7.
MJ - So you actually went with the friendly 5 and then counted on.
MJ - Are there any more ideas to share with granny?
BG adds a final thought to this last work sample discussion.
BG - 3 and 2 more makes 5 (working across top row) and 3 more makes 7 and 2 more makes 10. (working across bottom row)
MJ - You said 3 and 2 makes 5 and 3 more makes 7 and 2 more makes 10. (I write an open number line as I re-voice what he said.)
(LK has thumb down as BG talks)
LK - 3 and 2 more makes 5 and then 6 , 7, 8, and then 9 and 10.
MJ - What do you think BG. LK says 3 and 2 more makes 5 and....
LK - 3 more makes 8 and then 2 more makes 10
BG - I agree.
MJ - What did LK say?
BG - 3 and 2 more makes 5 and 3 more makes 8 and 2 more makes 10.
MJ - Can you show us here (on SMARTboard) what you are thinking.
Some really great strategies were shared here. We can't wait to hear what granny thinks.
Groups 2 and 3 work to help granny too!
Group 2 had the same challenge working with the smaller carton of 10, using 2 colours of eggs. The focus was on orally sharing their thinking. This group is developing strategies of thinking beyond 1 to 1 tagging and counting, with a focus on explaining thinking by subitizing and cardinality.
Group 3 worked with the same egg carton of 10 using 2 colours of eggs, but their challenge was to simply figure out how many eggs were in the carton. (This group is still working on 1 to 1 tagging and counting consistency, subitizing to 10, cardinality). Each time the number of eggs was changed and partners worked together to figure out how many, how do you know, do you agree with what your partner said. It is interesting with this group to listen to them help each other with strategies.
AP - 3 on top and 4 on the bottom makes 7.
VP - AP can you...what you say?
AP - 3 on top and 4 on bottom makes 7.
1, 2, 3, 4, 5, 6, 7. Five and two more makes......
VP - 7
AP - no 4
VP - 1, 2, 3, 4, 5, 6, 7. Seven AP!
AP - 5 on top, 1 on bottom makes 7 (she then touches next egg and adds 1 more) 8.
VP - AP go back. AP you say first 7 now you say 8. Count slowly AP!
Here is another conversation captured with a pair from group 3:
MJ - LW how many?
LW - 1, 2, 3, 4, 5, 6, 7, 8. Eight.
MJ - How many?
LW - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Ten.
MJ - I'm confused. First you said 8. Now you said 10. BP how many?
BP - 4 on top, 5 on bottom. That's 9 and one more makes 10.
MJ - So how many?
BP - 9
MJ - LW what do you think?
LW - 1, 2, 3, 4, 5, 6, 7, 8, 9. (She slows down her tagging and counting this time.) Nine.
MJ - Hey how many did you say BG?
BG - 9
MJ - How many LW?
LW - 9
An interesting reflection on my part with this exercise is some students noticed the colours and based their explanations on how many of each colour. Others organized the eggs by colour but still relied on talking about what they see by subitizing number formations (similiar to dot plate formations) regardless of colour placement.