Transcript Multiplication and division - Pacific Lutheran University

Multiplication and division
October 22-27
Multiplication
• Within your group develop a strategy for
multiplication of integers using manipulatives or
drawing pictures. You are not allowed to use the
standard algorithm. Apply the strategy to the
following problems or explain why it can’t be
done:
–
–
–
–
45
10  15
12  15
123  14
Discussion
• Which properties of multiplication and
place value did you use?
• How does your algorithm relate to the
standard algorithm?
• How will you teach multiplication to kids?
• Look at the Lattice algorithm. Why does it
work? What do you think about it?
Models for multiplication
• Repeated addition
• Rectangular array
• Cartesian product
• Note: these are also different ways to
define multiplication.
Properties of multiplication
• Closure
• Commutative
• Associative
• Identity
How does this relate to addition? How are
addition and multiplication related?
Distributive property
• Use blocks or a picture to explain to a
student why 35 x 67 is not equal to
30 x 60 + 5 x 7.
• Work on “Understanding the Standard
Multiplication Algorithm.”
Strategies
• We will watch videos of children solving
multiplication problems. Write down your
thoughts in the handout I will provide.
Division
• Think about how you can use
manipulatives to divide. Use base 10
blocks to divide 432 by 3.
• Look at scaffolding. What do you think
about this as a strategy?
• Work on “Mental Division.” Which
properties of multiplication and division are
you using?
Defining division
• Missing factor approach: a/b = c if and
only if a = bc.
Contexts for division
• Repeated subtraction/measurement
• Partitioning
Properties of division
• Which properties does division share with
multiplication?
• How is division related to subtraction?
Children’s strategies
• We will look at some videos of children
doing division problems. Jot down your
thoughts in the handout that I will provide.
Long division
• Long division is very complicated. Let us
spend some time looking at what is really
going on here. For example, let’s say we
are dividing 461 by 3. When we say “3
goes into 4 once,” what are we really
saying? When we “pull down the 6,” what
is going on? Try to use blocks to help you
make sense of the algorithm. How do we
regroup here?
WASL problems
• The sum of two whole numbers is 63. The difference
between the numbers is less than 10. Find as many
solutions as you can.
• Jeff has less than 30 marbles. When he puts them in
piles of 3 he has no marbles left over. When he puts
them in piles of 2 he has 1 left. When he puts them in
piles of 5 he has 1 left. How many does he have?
• Willard Van Winkle (distant cousin of Rip) woke up
slowly and looked around. "These things don't exist," he
said, "wait a minute. ..." Suddenly a voice said, "No, wait
6,000,000 minutes!" And so it was - Willard had in fact
been asleep for 6,000,000 minutes, having fallen asleep
on January 1, 1990 at 8 PM. What time did Willard wake
up?