Fostering Multiplicative Thinking using Array-Based Materials Young-Loveridge 2005

"IF YOU CAN'T MODEL IT.... DON'T TEACH IT!I heard myself saying this to a teacher who had commented "Why not just teach them the way to multiply fractions!" I get similar stances on the algorithms of adding, subtracting, dividing, long multiplication, cross multiplying proportions, adding zeros for x10, 100, 1000, times-flip for dividing fractions, moving decimal points, the integer rules for arithmetic, rounding and so on.

Blind application is a meaningless process. That was why all the prices in the shop had $12.50 added to them. That's why students can do fractions in class but not in the test. That is why 8+5=13 and 7x8=56 are so darned hard to remember. That is why students who get a score out of 100 in a test ask what is the percentage mark. Give students access to answers through strategies.

Attempt the understanding first by modeling. Students not trained to this approach will squirm a bit because they have to think. Teachers do the same at every level! Teach your students to look for patterns and to make a rule about those patterns. Testing of the rule and subsequent modification completes the process and secures the understanding. Share and explain your reasoning with another person (good literacy strategy).

The skill of the teacher is to create the situation whereby the student creates the correct rules and in doing so becomes a curious lifelong learner. It is very easy to give them the rule but that is not what being a teacher is all about...is it? Maintain learning though fun activities like games. Jim Hogan 2005

WHAT ARE MULTIPLICATION WORDS?

TIMES How many is three times four?4 + 4 + 4 = Three times Four

Sets ofGroups ofPackets of Rows ofColumns of

Multiply by

Arrays I use

Activities

Mathletics

NrichSome Favorites:

Numerically Equal

My New Patio

Geoboards

Tiling

Framed

Warmsnug Double Glazing

Interactive Manipulatives: Echalk, NLVM

Multi Digit Multiplication

Decimal Multiplication

National Library of Virtual Manipulatives

Integers

Fractions

Algebra

http://nzmaths.co.nz/nzc-and-standards

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