AREA Models encourage spatial reasoning. Students manipulate numbers in their heads. As they work, they are constantly thinking about relationships.

## Solve the puzzle. Explain your solution with inverse equations.

## 98 x ? = ?

## In order to spatialize the teaching of double digit multiplication, the teacher must fight the urge to “proceduralize” the set up. Area models are based on organizing into a rectangular space and decomposing factors to multiply in “chunks”. The order of the multiplications and additions does not matter, thanks to the commutative property.

## Practice that engages students in

PUZZLINGwill generate active involvement. We want studentsTHINKING, QUESTIONING an REASONING.

## BERCS PUZZLE CARDS engage even the most reluctant learners. The focus is SENSE MAKING that leads students to success across all the grades. Interested in more? Consider the workshop April 26 at University of Lethbridge or join me at Summer Institute 2017 .

Do you see the factors in the BUILD? Do you see steps in the diagram that you could perform mentally? What do you really need to record to “prove” your solution? What happens if you rotate the image? What happens if you re-arrange the factors?

Is (10+6) (10+7) equal to (6+10) 17? Show how you know in the model. How would the diagram change?

Describe the model for 16 x 34. How would your diagram change?## Is this true?

## (6×10)+(6×20)+(6×4)+10×30)+(10×4) = 16 x 34?

## How could you prove it visually?

### My goal is to IMMERSE students in thinking, diagramming, manipulating the parts… Spatial reasoning engages the entire brain….. puzzles keep students focused. Encourage collaboration and variety.. Move the parts, does the whole change?