- Understand the concepts of factor, multiple, prime
- Understand numbers in terms of relations to other numbers.
- I can identify the factors of a number.
- I can express a number as the product of primes.
- I can identify prime numbers
- Multiple, Product
- Prime, Composite
- Multiplicative identity.
- 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
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…
Ah! They both have a product of 480!
I wonder if I can find any other strings with a product of 480.
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
(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.
- 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?
(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?
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.