NZL123 - ODD + EVEN = ODD or does it?

ODD + EVEN = ODD

Or does it?

In todays world of fake news we are told many things; it is important for our students to learn to question, to think critically and have the skills to explore ideas, conjectures, statements and be able to convince themselves and others as to whether the ideas are true or not.

From the NZ Curriculum:
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to..... do the things listed in the bullet points

Open questions like this give the opportunity for free thought and for teachers to see a snapshot into students thinking.

Responses may give the opportunity for critical thinking in deciding which ones might be more useful in a mathematics context

Answers may also throw up some interesting ideas for future lessons

An extension to the pattern on the left could be 8, 16, 32 follow the rule 6 does not

ODD + EVEN = ODD .... Explore

Choose 1 odd number and 1 even number between 2 and 10
Draw or build ( make a model) of each
Try drawing a different way
Share your pictures and models : what do you notice ?
Put them together ADD - draw/build
Explore this process with different pairs of numbers What do you notice?

Recording my thinking

Take a piece of blank paper.

Fold in half and half again
[half of half gives 1 quarter]

Fold folded corner in, then open

I use this format for lots of things to help see the links between different representations and it gives an opportunity to talk about shape and fractions.

Put the "topic" in the centre & decide what goes in each corner.
I always start with picture and words at the top and vary the bottom depending on the context

For our ODD & EVEN investigation we could use our folded paper like this

Top Left : Draw Pictures
Record the pattern in pictures - here i have explored ways to draw ODD numbers and then chose the triangle-house-rocket model to work with as I could see a recurring pattern.

Top Right: Write words

Here I have thought about different ways i could describe what i saw in my pattern

Bottom Right: Start recording in symbols - you may get to the generalisation of 2k + 1 for ODD numbers

Bottom left: Choose what goes here - in this case i chose EVEN numbers

Always true? Sometimes true ? Never true ?

Always sometimes never questions are a great way to engage learners in discussion as they explore the concepts and highlight misconceptions

Using what you have done sort the cards into 3 piles and be ready to justify your decisions.

Do in groups of two or three

From Nrich : Download cards

Always Sometimes never Set 1

Always Sometimes never Set 2

Scaffolds:

Printable shapes if children get stuck from nrich.
Another useful tool might be the Numicon shapes

Extension:

Take 3 numbers, 2 odd and 1 even maybe and explore as to whether the statements still hold true ?

Work in a similar way as above, draw, add, notice, record

Other number patterns to explore

Click this link and you will resources for exploring Pascals triangle & Perfect Numbers and other things