Factor Strings

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

alt text

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


Create Frayer Models of the vocabulary.