Transcript Kristin Numeracy Workshop 3 Addition & Subtraction

Developing
Multiplicative
Thinking
2011
.
Alison Howard and Lisa Heap
Numeracy Facilitators
Reflection on Numeracy Teaching:
Is there something new you have started doing
since the last workshop?
Used the teaching model for strategy teaching?
Introduced a new add/sub strategy?
Tried some new activities?
Used your modeling book?
Taught number knowledge as whole class, to groups and
individual practice?
• Listening to students’ thinking?
• Any other exciting ideas to share?
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Where are you now?
What are your next steps?
Objectives:
• Understand the progressive strategy stages of
multiplication & division
• Understand where basic facts in
multiplication/division “fits” with multiplicative
thinking
• Know how to use Numeracy book six and other
supportive resources to help teach multiplication
and division
• Explore problem progressions, equipment and
activities used to teach multiplication and division
strategies.
Mult Game
Basic Facts:
• Independent reading: “ Call for more times table
chants…”
• Discuss key messages in Thinking Groups
• Discuss how this will impact on your future
teaching
• Brainstorm Stage 5, 6 and 7 Multiplication Basic
Facts
• Check using your Knowledge Framework
Development of Multiplicative
Thinking
There are 6 minivans outside
the school, they are going on
a school trip. There are 5
children in each minivan.
How many children are going on the trip?
• How would a student at the different stages
solve this problem?
Mult/Div Strategy Framework
• 2/3 CA
Counts all the objects
• 4
AC
Uses skip counting
• 5
EA
Repeated addition or using known facts
• 6
AA
Derived multiplication and known facts
• 7
AM
Choosing efficiently from a range of strategies
using whole numbers
• 8
AP
Choosing efficiently from a range of strategies
using decimals and fractions
Multiplication Grid G
R e.g. Roll a three and a four: 3 x 4 or 4 x 3
Multiplication Grid G
R e.g. Roll a three and a four: 3 x 4 or 4 x 3
3x4
4x3
What is Multiplicative Thinking ?
Multiplicative thinking is not about the type of problem
you solve but how you solve it.
E.g. Although 3 x 18 is a multiplication problem, if it is solved
by adding 18 + 18 + 18 then you are not thinking
multiplicatively but are using an additive strategy.
Similarly an addition problem e.g. 27 + 54 can be solved
multiplicatively by doing (3 x 9) + (6 x 9) = 9 x 9
Refer to pages 3 - 4.
Discuss the strategies you would
use to solve the following problem:
Each carton holds 36 cans of
spaghetti
There are five cartons.
How many cans of spaghetti is
that?
Let’s look at the possibilities…
• You may have used the distributive property. This
meant that one of the factors was split additively.
• 5 x 36 = (5 x 30) + (5 x 6)
= 150 + 30
= 180
• Or…
5 x 36 =
5 x 40 = 200
200 – (5 x 4) = 180
Another strategy:
• You may have used the commutative property in
conjunction with the associative property.
5 x 36 = 36 x 5 (commutative)
= 18 x 10 (associative)
= 180
The associative property is about
grouping factors:
• So in 36 x 5, the 36 was split multiplicatively:
36 x 5 = (18 x 2 ) x 5
18 x 10 = 180
Using the Associative Property:
• There were 12 children. Each
had 33 marbles. How many
marbles are there altogether?
• Using the Associative Property,
regroup the factors to make
this an easier problem to
solve!!
Proportional Adjustment:
• Transforming the factors to create a simpler
problem.
•
•
•
•
12 x 33 becomes…
(4 x 3) x 33
4 x (3 x 33)
4 x 99 EASY!
A Multiplication Lesson:
• Watch the video and in your thinking groups
discuss the following:
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–
–
What was the key purpose of the lesson?
What stage was the lesson aimed at?
How was the key idea developed though the lesson?
What mathematical language was being developed?
When were the mathematical symbols introduces?
How did the written recording support the students
understanding?
Stage 2 - 3:
Aim: Working towards children seeing sets of
numbers as a whole unit rather than by
counting one by one.
• Building number knowledge: i.e. skip counting in
2’s, 5’s and 10’s.
Using bead strings, flip boards, body percussion,
hundreds squares, calculator constant, number
line pegs, animal strips.
• Introduce multiplication language: e.g.”groups of”,
“lots of”, “sets of”, “teams of” etc..
Getting to know Book 6:
In thinking groups explore a lesson…
• Stage 6/7 Multiplication Smorgasbord; p52
• Stage 5/6 A Little Bit more, A little bit less; p32
• Stage 4/5 Animal Arrays; p15
• Stage 3/4 Number Strips; p8
• Stage 2/3 Pre Book
Let’s look at Division:
• In your thinking groups make up a
division problem for the following:
6 x 3 = 18
The Different Types of Division:
• Division by Sharing (partitive):
18 lollies to share equally into 3 bags.
How many lollies in there in each bag?
• Division by Measuring/Grouping (quotitive):
John has 18 lollies, he puts 6 lollies into each bag.
How many bags of lollies will he have?
Pirate Crews:
• Sharing – “There are two pirates in the
crew. If they have 20 pieces of gold to
share out, how many coins will each
pirate get?”
Twenty coins shared between two pirates is ???
• Grouping -
Modelling Books:
• Share your modeling books with your thinking
group.
– What are the common features?
– What have you seen that you would like to
develop?
Using a Modelling Book:
• Helps capture students thinking and is a powerful
tool for modeling written recording.
• Is a useful record of work that both teacher and
students can refer back to during the lesson or in
future lessons.
• Helps teachers keep track of students progress by
writing names next to strategies or by attaching
the student profiles at the front of the book.
Next Time:
• We will be looking at Place Value, Fractions,
Decimals, Ratio and Proportion.
• Please bring Books 1 and 7 and SHARED LUNCH.
• Try a knowledge check and diagnostic snapshot or
recording in your modelling book or some equal
grouping/sharing.
• See you on Wednesday, 2nd November.