1. Division
Session 3

2. Group Reflection
Introduce your students to multiplication arrays in ways that are developmentally appropriate to your grade level.
What student samples of the task did you bring? What worked well? What did not work well?
Nadine
Please share with your table groups for 2-4 minutes
Have one person from the table group ready to explain what was discussed

3. Holli - 2 minutes
-Purpose of session: Division of the inverse of multiplication. The understanding of quotative division is required to be successful within this concept.
-Review levels of representation
Enactive - physically doing with your body (similar to concrete in the pofs)
Iconic - similar to a pictorial representation
Symbolic - numerical representation of information.
Not a hierarchy of knowledge more cyclical.

4. Nadine (2 min)
-Ask the question: How are these two scenarios different?
-#1 - Asks for the number within each group already providing the number of groups- (partition)
-#2 - Asks for the number of groups already providing the number of items in each group. (quotative)
-Teachers tend to only ask division questions that reflect the first scenario (partition), given the number of groups, and asking for how many in each group. We need to balance the meaning of division in order to support learners longitudinal development. Division involving fractions, algebraic thinking, ratios, percentages.
-Why is this problematic...

5. Holli - 5 minutes
-The size of each group is 2 and then we have 5 groups
-Partitioning - the total is split into 2 groups and has 5 items in each group.
-Can you think of a problem that represents each picture so that students would think in both ways?

6. Nadine (2 min)
Quotative division works nicely for all division problems. On the previous slide the numbers worked for both ways of thinking. Whereas, partitioning does not work intuitively for students in all scenarios.

7. Division Quotative Known - How many in each group
Unknown - Number of groups
Partitioning
Known - Number of groups
Unknown - How many in each group
Read right off slide
Holli - 2 minutes

8. Division Situations
Identify whether the following questions are partitive or quotative division.
There are 50 cards. Divide the cards equally for 4 players to play a game.
Each lesson is 45 minutes. How many lessons can we have, if a day is 6 hours long?
In a university dormitory, 3 students share a room. There are 178 new students. How many rooms do we need to accommodate the new students?
3 children received 6 apples. How many apples will each child receive?
Holli (5 min)
Partitive (discrete)
Quotative (continuous)
Quotative (discrete)

9. Create a Problem Working as a group, use the chart paper provided.
Make up a story problem that would require quotative division. Construct a representation to show your thinking.
Make up a story problem that would require partitive division. Construct a representation to show your thinking.
Nadine (10 min)
VLS
Do random grouping - cards
One whiteboard marker per group

10. Next Steps For next session:
Continue to work with students on division using quotative division. Bring another division task to the next session with a sample of student work. Look for student misconceptions.
Holli (1 min)

11. Rubrics and Vocabulary
Please see the booklets on the table:
Rubrics for non-permanent learning surfaces - thank you Grande Prairie
Math grade level vocabulary - thank you to Midnapore School.
Nadine (2 min)
Place an electronic copy on the server - Woodlands Math