Factor Strings
Focused Instruction
Establishing purpose
Learning purpose
 Understand the concepts of factor, multiple, prime
 Understand numbers in terms of relations to other numbers.
Success criteria
 I can identify the factors of a number.
 I can express a number as the product of primes.
 I can identify prime numbers
Language purpose
 Factor,
 Multiple, Product
 Prime, Composite
 Multiplicative identity.
Social purpose
 Exploring
 Organising data
 Knowing when we have finished
 Mathematical wondering
Modelling or demonstrating
Display the chart on the screen. https://drive.google.com/a/maths4eal.net/file/d/1Q6QsznGi9zIdViqrEZ7CO2T6IOZo3U8M/view?usp=drivesdk
Thinking aloud

What do I notice about this chart?

There’s a line connecting 15 and 32.

There’s a line connecting 5, 2, 16 and 3.

I wonder what they have in common?

(Try adding them…

Try multiplying…?

Ah! They both have a product of 480!

I wonder if I can find any other strings with a product of 480.
Guided Instruction
Teacher: answering questions, prompts, cues and direct explanations Conducted in small, purposeful, groups. Ideal time for differentiated engagement between teacher and student. Use “Enabling prompts” from “Participating in the Inquiry” here: https://drive.google.com/drive/folders/1BgqPMiuACNxicbFTVFf67mt_v_e4Iona
Collaborative Learning
(Meaningful collaborative group work)
Students to work in groups of 3 finding factor strings.
Once all groups have found at least two strings, begin asking students to record ones found on the whiteboard.
Thinking aloud
 When this gets messy and hard to find, pause the class.
 Discuss how we can structure our data better:
 perhaps by length, and ascending order of factor.
 Model good mathematical thinking with “I wonder…” statements:
 I wonder what the shortest string is?
 I wonder what the longest string is?
 How will we know?
 I wonder how many strings there are?
Independent Learning
(Teacher’s role: feedback)
Students move on to individual work. Students can be extended with the prompts:
 What are all the factor pairs for 480? What are all the factors strings that have 3 factors? How do you know you have found them all? What about factor strings that are 4, 5 or 6 numbers long?
Wrap up

When we have found the longest string, how do we know?

What’s true about these factors.

Introduce the idea of the fundamental theorem of arithmetic (in appropriate language):
Any positive integer can be uniquely expressed as the product of primes.
Watch the video
Consolidation
Create Frayer Models of the vocabulary.