Monday, 15 April 2013

Mathematicians at work

We have been focusing on the different tools mathematicians use to make thinking visible. These include dot plates, rekenrek, quantity number line, 
5-frame/10-frame, and dominos. Our job as mathematicians is always to share our thinking: How many? What do you see? How do you know that? How can you figure that out?  We talk about "make a picture in your head" then share what that looks like with others. 

We often start our math time with brain work using one of the tools mentioned above.  Students honour the rules of our math time, allowing wait time for every brain to "think" so nobody's brain 'stops workingl'!  

Sometimes we extend these math games to continue our investigation into number sense. 

Here is a 'snapshot' of our math focus over the last week.  You will see how the documentation I got from students when they played these games helped me to decide on next steps for each group. 

We will begin with 10 Frame. 

10 frame FLASHES are one way we practice "How many", "How did you see it?" 

Here are some other ways:

1. To test out how efficient our mathematicians can be figuring out a number using a 10 frame, we played a simple game using the prompt “What would (insert a number) look like on the 10 frame?”  Students are invited to demonstrate using the 10 frame and magnets or on the SMARTboard what that number looks like. This is followed by "How many?" “How do you see it?” (Student explains his thinking.) The conversation can be turned back to the group with the prompt:
"Do you agree or disagree?" (thumb up/down/side)  
“How many do you see?” (another student to share)
“How do you see it?”
Students are encouraged to demonstrate a variety of strategies beyond one to one tagging and counting to explain how many. These strategies can then be labelled by the teacher. (e.g. 'grouping by 5', counting on, etc.)

2. We have another game our mathematicians like to play to test the efficiency of the 10 frame, using the prompts “How many?” “How do you see it?”. Students close their eyes as the teacher builds the number on the 10 frame and when eyes are opened students are encouraged to share their thinking in connection to using the 10 frame.

MJ - How many?
EA - It's 12.
MJ - How do you know it’s 12?  
EA - 5 and 5 makes 10 and 1 more makes 11 and 1 more makes 12.
MJ - So you are grouping by 5's, 5 and 5 more to make 10 and then counting on 11, 12. (I am labelling the thinking here!)

Domino (aka more 10 frame) Games!

These games are played over a number of days, each new game building on skills considered the day before. 

Please note that Day 1 Domino Cards game has been played many times previous to this and teachers may want to repeat Day 1 a few times before proceeding. 

Day 1 - Domino Cards.  This game begins with domino cards spread all around the room.  The teacher calls out a number and students must find a “picture” of that number on domino cards. Keep in mind that numbers must be manageable for all so we usually don't go beyond 10 if doing this whole group. If you want to document some students strategies I recommend using video for this game as it moves rather fast.  Some mathematicians may build the number using several cards demonstrating part/part/whole thinking (i.e. 5 and 5 make 10), others will find the quantity on a single card using grouping strategies (5 and 2 makes 7), some will continue to need to tag and count.  Students share the card(s) they have found with a partner, asking if they agree or disagree how many. Sharing can then be brought back to the whole group using the same prompts “How many?” “How do you know that?”

Day 2 -  “What’s your number?” For this game students are given a number and must find someone else in the classroom with the same number and share what the number is.  If they don’t agree then Team Jellybean mathematicians can help with suggestions (discussed and documented during prior math talk) of ways to figure out how many. 

RH - You could use the carpet. See you start at one and count till you see your number.  JS told us that last year.

Day 3 - Match the number with a picture. For this game students of similar mathematical abilities are partnered together. One is given a number and he shares what that number is with his partner. The partner has the job of finding a picture (domino) that will go with that number.  One or two partners can then be selected to present their knowledge to the group. 

Day 4Match the number with a picture (extended). The game begins by giving each student their own number.  Keep in mind that number recognition may challenge some so there may be the need to be time made to again re-visit strategies that could be used to figure out what number they have.  This time each student must find a picture to go with their number on their own.  Quite the challenge for some.  Prompts continue to be "How many?" "Find a picture to show this."  

Day 5 - A final challenge for those who are ready for it, is give them a number and then they draw their own picture to go with it! Interesting to watch mathematicians brains at work.  What strategy will they use to record?  Are they using one to one tag and count (in a line) or are they thinking about considering more efficient ways such as ten frame/domino formations?  Here are a few examples of the students recordings.  At no time did I remind them of the games we played on previous days, nor did I suggest ways to document to make it easier to know how many.  Prompts however remained constant:

How many?  
How will you show it?  
Make a picture.

Several different small group meetings followed this activity: 

For some it was a time to share efficient ways of representing how many, with peers looking at each others work (using document camera) and talking about "How many?" and "How do you know that?", sharing what strategies they saw being used to provide information.  

For another small group it was an opportunity continue to work on gaining a  greater understanding of how many and how to record their thinking (i.e. Finding a 'picture' to go with the number they recorded on their paper, then figuring out how to represent that number).

Both students in photos that follow had got part of the instruction and had found 4 different numbers and recorded them in the boxes but then got stuck, recognizing some but not all of the numbers they had recorded and overwhelmed with finding a 'picture' to go with each number.  Given a smaller number of dominos to look at and reminders from RH on a number strategy (i.e. Remember her carpet strategy to figure out how many?), both boys were able to connect that the number and the picture go together.  The number 11 was left as it was too high a number to consider at this time (as it would mean having to combine more than one domino card). 

Another small group of students were involved in playing the domino game again, using manageable numbers and simply attempting to  figure out "how many" (i.e. Documentation included watching/listening for tagging and counting, stable order, number counting, conservation). 

As a final note,  our new math problem has a group of mathematicians eagerly wanting to help granny with her egg dilemma!  It will be interesting to see if and how  the thinking from this past week will be applied to the new problem.  Stay tuned!


  1. I am always inspired by the way your documentation captures student thinking so well. You do a good job of showing the stages, and your scaffolding.
    If you plan on teaching a math workshop someday, consider me signed up.

  2. Wow I am thrilled that my documentation is so visible to you.....That is my intention and it is great to get feedback like yours to confirm that our thinking is aligned.

    Hmmm a math workshop. None planned in the near future but you never know.