Multiplicative Thinking - PLD meeting notes

Today's PLD for maths focused on Mulitplicative Thinking.  It was hands on learning, beginning with a puzzle of the key progressions of mult/div.  Starting from emergent, teachers had to arrange stages with number problems and explanations. 

It was really pleasing to see the content knowledge come out and the key questions being asked by teachers to Sue regarding identifying whether students are at certain levels using OTJs.  Teachers were reflecting on previous lessons and problems they have used and discussed where students strategies fitted on the progressions we'd just laid out.

Discussion moved to proportional thinking...WOW!  The example that Sue started with was 54x27...she then talked about thirding the problem e.g: 6x9 (54) + 3x9 (27) = 9(3+6)x9=81....and 12x33 go to doubling and halving e.g: 4x99=400-4=396....and then 14x6 doubled and halved is 7x12=84.  And these are examples of how proportional thinkers think!  I'm going to make a conscious effort to try a few of these...my mind was buzzing.

Students need to construct and coordinate three aspects of multiplicative situations:

• Groups of equal size
• The number of groups
• The total amount

Set language before symbols and then use things like arrays and games to develop understanding. Use materials to give students visual representation of what a strategy looks like.  E.g modelling skip counting by putting counter in cups - 1 cup has 2, another has 2 which make four, another has 2 which makes six...2, 4, 6, 8 etc.  You could introduce pairs to connect to counting in two and groups of two.  When putting materials in groups think about ways to define a group e.g: ladies birds on a leaf, or sheep in a pen etc.  It's important to for students to see groups in array so that they can see for example 6 groups of 5, but also 5 groups of 6.

Good maths story books are 'One Hundred Hungry Ants" by Elinor J Pinczes, and "Pete the Cat"...these can also be accessed on Youtube.

We looked at solving the problem:  A farmer has 8 paddocks and 296 sheep.  How many sheep will go evenly into each paddock.  We looked at:

• Rounding and Compensating  320 / 8 = 40  40 - (24 / 8) =   40 - 3 = 37
• Place Value   240 / 8 = 30  56 / 8 = 7   30+7=37
• Proportional adjustment   296 / 8 =    148 / 4 =    74 / 2 = 37
• Reversibility   8 x 30 = 240   8 x 7 = 56