WERKLUND SCHOOL OF EDUCATIONGALILEO EDUCATIONAL NETWORK

LEARNING IN MATHEMATICS (K-6)A CBE RESEARCH & PROFESSIONAL LEARNING SERIES

In partnership with Werklund School of Education, University of CalgarySession 4: Friday December 8, 1:00-4:00 p.m.

The agenda, working documents and other materials for each session can be accessed on Galileo’s Professional Learning website http://galileo.org/pl

Focus: Concepts related to number division (quotative) [multiplicative reasoning, connection to number systems]

Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which it is useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those ideas to what they already know.

Learning Outcome: Division is the inverse of multiplication.  The meaning of quotative/measurement is required to be successful with division.

Participant Agenda

Time Activity Learning Intentions/ Outcomes

1:00

1:05

1:45

Welcome & Overview Review document sharing

established for data collectionApplied Learning Individual reflection to prepare

for sharing (page 3) In triads, review the evidence

of learning Record a synopsis of the

conversation in the Google form

goo.gl/Aq1YiB

Principled Practice Reflect on the first column of the

table to consider how you attended to the integrity of mathematics in the division task that you enacted

Intention: Identify multiplicative reasoning and division in teachers’ contexts and examine errors students are making.Outcome: Recognize multiplicative reasoning and division begins in K. Analyzing errors can support differentiated learning designs.

2

1:55 Discuss key insights Large group discussion Intention: Building collective and

expansive understanding of multiplicative reasoning and division using an array representation.Outcome: Deepen teachers’ awareness of multiplicative reasoning and division.

2:05 Break

2:15 Connecting multiplication and division using arrays Revisit the array and area model Factoring composite numbers

with array models

Intention:  Multiplication and division are inverse.Outcome:  Extend the area and array model to understand the relationship between multiplication and division.

2:25 What is division? Division as

quotative/measurement Division with Cuisenaire blocks -

changing units to measure a set length

Language related to the quotative/measurement metaphor

Challenging the idea that "division is making numbers smaller"

Tangrams: How many times does the small triangle fit into the square?

Intentions: Partitive meaning is overrepresented in textbooks.Consolidate participants' understanding of quotative/measurement meaning of division

We need to balance the meaning of division in order to support learners' longitudinal development (division involving fraction, algebraic thinking)Distinguish discrete and continuous numbers (within the context of division)

3:10 Consolidate Understanding of Division Engage in a problem for various

division scenarios, focusing on quotative/measurement

Construct a representation to show your thinking

Revisit: “What is division” Word Cloud?www.menti.com code 70 45 2

Outcome: Create an accurate division problem with quotative/measurement meaning

3:45 For next session:1. Continue to work with students on division using measurement.

Bring another division task to the next session with a sample of

3

student work. Look for student misconceptions.2. Use the Principled Practice document to reflect on your experience

as you continue to work with division as measurement. Identify places in the table where you could provide examples to illustrate your experience.

3:504:00

Feedback Survey: link goo.gl/nTNjbGAdjourn

Individual Reflection

Please take a moment to photograph the sample(s) of student work you brought to share and upload the image(s) to your folder.

1. Describe how you introduced the idea of division using measurement to your students. What did you do? What were the students doing?

2. What errors in reasoning did your students encounter as they worked through the activity?

4

Principled PracticeReflect on the first column of the table in light of the division activity you enacted.

Guiding Principles

Domains of Practice

Attending to the

integrity of the

mathematics

Committing to the

learning & achievement

of each student

Establishing and

managing a productive learning

environment

Learning from &

systematically improving

practice

Planning math lessons

Representing mathematical ideas

Leading a whole class discussion

Assessing

5

students’ knowledge, skill, and dispositions

Connecting Multiplication and Division Using Arrays

6

What is Division?

7

8

9

10

40 12

11

12

Division as a Ratio

Division as Area

13

14

15

16

Principled PracticeGuiding

Principles

Domains of Practice

Attending to the

integrity of the

mathematics

Committing to the

learning & achievement

of each student

Establishing and

managing a productive learning

environment

Learning from &

systematically improving

practice

Planning math lessons

Representing mathematical ideas

Leading a whole class discussion

Assessing students’ knowledge, skill, and dispositions

17