1. Learning in Mathematics
Session 2
Multiplication

2. Applied Learning Discussion
Share how you used the number line with your students.
What does the artifact you brought forward and/or the observations you made indicate about the learning of your students?
5-10 min
Holli

3. What is multiplication?
Grab your phone.
Go to
Enter the code and vote!
5 min
Nadine

4. What is our purpose today?
Learning Outcome:
Recognize the leap from additive reasoning to multiplicative reasoning is significant developmentally.
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.
Focus: Concepts related to Number: Concept of multiplication.
Discuss the purpose of the presentation - 5 min
Holli

5. Nadine
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 heirarchy of knowledge more cyclical.
5 min

6. Multiplicative reasoning
Making groups
Skip counting, jumping, stretching, compressing, number line
Repeated addition
Calculating area
Creating a matrix (rectangular array)
Making rectangles
Measurement
Proportional change (rates)
Size, distance, time
Standard and non-standard units
Review the information on the slide
Holli

7. Early Multiplicative Reasoning
Subitizing (early development of understanding of arrays)
Skip counting by 2s, 5s, and 10s (early development of multiplication on the number line)
Sharing situations (equal amounts)
Sorting (money)
Patterns (repetition)
Discuss the different ways to develop early multiplicative reasoning
Apprehension towards introducing arrays to grade 1s and 2s

8. -Subitizing is recognizing the amount in an organized or disorganized array quickly
-Typically, children can recognize arrays of 4 without counting, beyond that they need practice with subitizing
-This builds the foundation for children to begin using arrays to solve multiplication problems because after they construct an array they are able to quickly see the answer.

9. Ways to Practice Subitizing
Powerpoint
Splat
Games
Refer to powerpoint of grade 1 students

10. Nadine
Multiplication can be thought of as equally sharing. An array is a great way to represent that information.
Our challenge: use an array to represent multiplication at an age appropriate level

11. Grade 6 Array Lesson
Students will learn strategies for multiplying 2 digit by 1 digit numbers... by breaking apart their arrays into easily manageable multipliers.
Review the term array and provide examples
Question - how would you use an array to multiply 2 digit by 1 digit numbers? Discuss
Watch video -
Discuss examples as a whole class
Provide examples to practice and present using whiteboards - talk and teach
Students create their own examples to present
Two digit by two digit multiplying
Discuss my apprehension doing arrays in grade 6

12. Discuss student results
Highlight Bria and Grace
Highlight Kurt

13. Multiplicative Reasoning - Applied to a Real Context
What do you notice?
How were the arrays enacted?
How were arrays shown iconically?
How were arrays shown symbolically?
Holli
Discuss the video
How are arrays enacted in real world context? (concrete)
Iconic (pictorial)
Symbolic - numbers

14. For Next Time...
Introduce your students to multiplication arrays in ways that are developmentally appropriate to your grade level.
Bring back evidence of the task you enacted, and samples of student work. What worked well? What did not work well?
Nadine