Area Models for Multiplicative Reasoning

GOT QUESTIONS? Consider attending one of my Multiplication Matters Workshops. Ask me.

Multiplication is not “just repeated addition”. We must stop allowing students to believe this to be true. Multiplication is an operation in its own right. It moves directionally and involves units of units. Multiplicative thinking requires proportional reasoning and is not likely to develop once students have convinced themselves that multiplication is just adding.!!!

Read, reflect, consider the implications…. If repeated addition was good enough, would we not expect more of kids to have mastered multiplication???

I was working from several different powerpoints for the session. I do not believe we got through everything but here is one of the slide shows that might help remind you of some of the ideas… SWATCA Multiply

 I believe we played with some BERCS cards to puzzle our way into distribution…

bercs cards title    What’s the distribution equation?

Pink Distribute

8(5+3) = (8×5)+(8×3)

 

Multiplication and division are inverse operations.

If you can multiply, then use it to divide.

2 digit puzzles

7200 ÷ 90 = ?     90 x ? = 7200

bercs cards title

Division is multiplication

Division is multiplication

Division is not “just” repeated subtraction. I would never leave a student with this kind of strategy. It is inefficient and will be of no help when students move to integers, rational numbers and algebra.

 Do not encourage it as a strategy, bike againdespite what textbooks might show. All this work and he makes a mistake when he counts how many times he removed 3 so he gives a wrong answer.

This is really inefficient. The groups or sets of 3 should trigger thinking multiplication. Three times ten is 30. There’s a good start.

Three times 5 is 15, there’s a different start. The subtraction involved in dividing needs to be applied efficently.

 

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