Multiplication

Bruce Moody
Are there differences between additive and multiplicative thinking. Are there differences in the brain between these. What links will we be wanting students to make? What will we track and measure students learning?
Extended concept:
3 groups of 4- Freddy the frog lesson
Is it worthwhile? Additive thinking will only work for so long.

Students move from recognising the hand clap as 5 and 5, to 2 hands and 5 fingers on one hand.
Creating an area rather than a number line. It is not sequential but simultaneous.

Reinforces the idea that multiplicative thinking is not linear and should involve area, packaging, unpackage and re-packaging.

Legs- 5 people with 2 legs each, 2 stools with 3 legs, 3 dogs with 4 legs-
Then move on to wheels. You can have two different things but refer to them in one sentence at the end.


Students can have a go at creating their own. Two referents and two quantities.
Boxes- 3 dinosaurs in 2 boxes- boxes are hiding the dinosaurs so they are out of sight. Resources
shown then hidden
Kumara- 3 kete and 3 kumara. No visible kumara and nothing to represent the kumara. Imaging
Double count- Bruce would change both the 3 is confusing. Having one number different allows
them to sort out and remember which one they are counting at a time.
Doubles are different- 3+3
This image has more to do with area


INtroduce copycat for idea of doubles- start off copying actions then change to quantity. I might hold up
3 fingers, then my friend shows up 3. If I show up 3 fingers how many fingers would we both hold up?
Move on to not modelling with equipment.
Next tell the story- I went to the beach and I picked up 5 shells. How many did we pick up?
Looking at 5 only then can say the answer is ten. Know the second set will look the same.
Ask the question backwards- My copycat friend and I went to the beach. Wemade 6 sandcastles,
how many did I make?
See two different quantities in the equation and report on those.



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