MATHEMATICS → Mathematics Content Understanding

From Arrays to the Distributive Property (MT201)


Description
COURSE: FROM ARRAYS TO THE DISTRIBUTIVE PROPERTY

This self-paced, research-based, practical course is for teachers seeking to deepen their understanding of multiplying and dividing using multiplicative thinking and the distributive property, and their capacity to explicitly teach their students to multiply and divide.
This course will be available for 30 days after purchase. This course provides 3 hours of Professional Learning.

This course will answer the questions:
What are the 2 ways to divide?
How can we see arrays additively and multiplicatively?
What is the distributive property?
What is fluency and how can our students become fluent?
What about algorithms?
And a bonus part - How could we differentiate our teaching of multiplication and division?

The 2 ways to divide are quotitive ('groups of ...') and partitive ("... equal groups)'. Partitive division is useful when dividing by whole numbers, and quotitive division is useful when dividing by fractions.

Arrays in mathematics are equal rows. Arrays may be seen additively (repeated addition) or multiplicatively (partitioned into parts). Seeing arrays multiplicatively links to area, and is a visual representation of the distributive property.

The distributive property means we make our multiplication (and division because division is just multiplication by a fraction) simpler, by distributing it over addition. The distributive property is the most important property a child will ever learn - it is the basis of a large portion of future mathematics learning.

Fluency is knowing how a number can be composed and decomposed, and using that information to be flexible and efficient with solving problems - not rote memorisation. Developing fluency in 'tables' using the distributive property allows children to learn so much more than just the 'tables'.

Multiplicative Thinking involves using mathematical meta-language to explain, and working conceptually with, relative magnitude, as ‘times bigger / times smaller’, ‘times as many / times more / times fewer’.

This course includes the following Educational Standards for Teachers (Australia):
Standard 1 - Know students and how they learn
1.2.2 Structure teaching programs using research and collegial advice about how students learn.
Standard 2 - Know the content and how to teach it
2.1.2 Apply knowledge of the content and teaching strategies of the teaching area to develop engaging teaching activities.
Standard 3 - Plan for and implement effective teaching and learning
3.3.2 Select and use relevant teaching strategies to develop knowledge, skills, problem-solving, and critical and creative thinking.
3.6.2 Evaluate personal teaching and learning programs using evidence, including feedback from students and student assessment data, to inform planning.
Standard 4 - Create and maintain supportive and safe learning environments
4.1.2 Establish and implement inclusive and positive interactions to engage and support all students in classroom activities.
Standard 6 - Engage in Professional learning
6.2.2 Participate in learning to update knowledge and practice targeted to professional needs and school and/or system priorities.

Content
  • PART A: RESEARCH-BASE
  • Research-base
  • Assessment Research-base
  • PART B: 2 WAYS TO DIVIDE
  • A-DP 2 Ways to Divide.mp4
  • PART C: ADDITIVE AND MULTIPLICATIVE ARRAYS
  • Additive and Multiplicative Arrays
  • PART D: DISTRIBUTIVE PROPERTY, ALGORITHMS, FLUENCY
  • Distributive Property, Algorithms, Fluency
  • BONUS PART: DIFFERENTIATION
  • Bonus Part: Differentiation
  • A LEARNING PLACE A TEACHING PLACE
  • Further resources: A LEARNING PLACE A TEACHING PLACE
Completion rules
  • All units must be completed
  • Leads to a certification with a duration: Forever