An Amazing Thought!

Diana opened the doors to her combined Grade 5/6 class for a lesson study with some teachers in our FOS.  She is just about to start her next unit on multiplying and dividing and wanted to get a sense of where her students were.

For the "Minds On" part of the lesson she asked them to use mental math to divide a number.  The students were each given some think time, and then used the "turn and talk" strategy to share what they were thinking with a partner.



After they had time to think and talk, a few of the students shared their answers with us.  The writing in black was their initial thinking.  However, one of the students came up with a hypothesis of how they think that they could do a "trick" that would work on all of the numbers (that was crossing off the zeros).  So the writing in red is a reflection of the class "testing" the hypothesis.

Because it is a combined grade, Diana gave both the Grade 5's and 6's the same problem, but changed the numbers to be more appropriate for the grade (93 for Grade 5, 186 for Grade 6).  The class had to solve a division problem about dividing a set number of marbles equally among 3 students.  As the students were working, all of the teachers who were observing used the assessment for learning tool to keep track of what strategies they noticed that the students were using.  The students also completed a "Star and a Wish" statement at the bottom of their work.  The "Star" was what they thought they did well on, and the "wish" was one thing that they still needed help with.  When the students were done, Diana selected three of them to share their work with the class.  She chose them based on the different strategies that they used.  As they shared their work it was put on the board and notes were made along side of it to record the thinking / learning.

Here was the first sample of work that was chosen:

Diana picked this student's work because they used the strategy of drawing the marbles (all 93 of them) and then grouped them into groups of 3.  Once they were all in groups of 3, she then counted the groups and used that number as the number of marbles each person would get.  If you notice the "wish" this student wrote it says that they "wish" to do division in a different way than just drawing pictures.  What great insight, and a great way to self regulate and identify what they need help with.

This is what we identified as the student talked:

You can see how she orally talked about what she did, and that she has a small misconception when decomposing 93 into friendly numbers. 

Here is the second example of student work:

This student really surprised us.  When they were working we all noticed that they had divided their work into three parts, and then used tens and ones to decompose 186 marbles into 3 equal groups.  This was a little more sophisticated than the previous student sample, but what we quickly learned, what that we saw on the paper wasn't exactly what the student was thinking when they solved the problem.  Here is the picture of what they told us they did:

The student started by saying that he broke the number into 6 and 180.  They then divided the 6 into 3 and got 2.  Therefore they put the two "ones" into each of the groups they had drawn.  Here is where things got AMAZING....They then said that they thought of 180 as 18 because it was an easier number to work with.  They divide the 18 / 3 and got 6.  But they knew it wouldn't be 6 ones, but 6 tens.  So they added the 60 + 2 and got 62.  Therefore they made sure that each person got 62 marbles.  They then used the 10s to represent each ten in the 60.  To double check their work, they then added up 62+62+62 and got the final answer of 186.  Everyone in the room was blown away!  The student was pretty happy when they saw this.  What was thought of (originally) as a simple answer turned out to be much more in depth.  In fact, the oral descriptive feedback that was given to this student was to put all of their thinking down on paper, just like they had described it to us. 

The third strategy was also quite a bit different than the other two:

This student's work was chosen for two main reasons.  The "main" reason being that they had used a highlighter to underline key information in the problem.  Being in Grade 6, this is a key strategy that can help students when they write the EQAO and also as they move along in their math career.  The second reason was because they had successfully used traditional long division as a way to solve the problem.  They then used multiplication as a way to double check their answer. 

After the students had each shared their work a highlights sheet was created with some tips for them to remember when they continue through the unit.  These highlights can be added to and also can be used to help co-create success criteria.

When the lesson was over all of the teacher's headed out to a break out room where we discussed some ways that we would change the lesson to make improvements upon it.  Most of our discussion was around changing the minds on to reflect division more than multiplication.  We also discussed the merits of doing a pre-assessment "cold" (like we did here) or "warm."  The morning ended by giving some descriptive feedback to several students in the group. 

Overall, we had a great professional morning together - Thank you Diana for helping to make that happen.  (The lesson plan and AfL chart is available on our wiki)