Please be sure to sign-in. Sign-in sheets are at each table.

1
Welcome

• Please be sure to sign-in. Sign-in sheets are at
  each table.
• Please do not rearrange seating.

2
Housekeeping

• Please turn your cell phones to courtesy mode.
• We would like you to be an active participant in
  our session today.
• You will need a pen or pencil. Materials can be
  found on your table.
• Breaks
• Parking Lot

3
Making Meaning of Multiplication and Division
Situations

• 3-5 Math Teacher Leader Training

4
Modeling Word Problems
Work the 5 problems using either cubes or
counters. Do not work with others yet.
5

• Christopher is playing a video game. He has
  collected 8 magic jelly beans. If an extra life
  costs 2 jelly beans, how many extra lives can
  Christopher buy?

6

• Lila has 10 cookies. She wants to share her
  cookies with 3 friends. How many cookies will
  each person get if Lila and her friends each get
  the same amount of cookies?

7

• Ms. Lees class is going to the zoo. There are
  24 children in Ms. Lees class and 7 children can
  fit in one car. How many cars will Ms. Lee need
  to take her class to the zoo?

8

• Martha bought 6 t-shirts at Wal-mart. She has 3
  children. She would like to divide the t-shirts
  equally among her children. How many t-shirts
  does each child get?

9

• Alberts cabbage patch has 4 rows of cabbage. In
  each row, there are 5 heads of cabbage. How many
  heads of cabbage does Albert have in all?

10
What to do with Whats Leftover?

• Read the following pages from Teaching Student
  Centered Mathematics
• K-3 TSCM pages 81-82
• 3-5 TSCM pages 61 - 62

11
Remainders

• In the absence of a context, a remainder can be
  dealt with in only two ways
• It can remain a quantity left over.
• It can be partitioned into fractions.

12
Remainders

• In real contexts, remainders sometimes have three
  additional effects on answers
• The remainder is discarded, leaving a smaller
  whole-number answer.
• The remainder can force the answer to the next
  highest whole number.
• The answer is rounded to the nearest whole number
  for an approximate result.

13
What to do with Whats Leftover?

• Write a corresponding word problem that goes with
  the number sentence, 46 4.
• Write problems with the answers 11, 12, 11 ½ ,
  and 2.

14
Progression of Development Strategy Types

• Direct Modeling
• Counting Strategies
• Derived Facts/Number Facts

15
Direct Modeling
Direct Modeling - Student acts out the situation
using manipulatives or diagrams. Children act
out the problem. They are very literal. They
model every number and work the problem in
chronological order.
16
Direct Modeling
Example Ms. Jenkins bought 7 boxes of cupcakes.
There were 4 cupcakes in each box. How many
cupcakes did Ms. Jenkins buy? Student counts out
one set of 4 blocks, then another set of 4
blocks, then a third set and a fourth set, a
fifth , a sixth, and a seventh. After she has
finished making 7 groups with 4 blocks in each
set, she counts all the blocks and says, 28.
She bought 28 cupcakes
17
Counting Strategies
Counting strategies show that a student can hold
some portion of the problem in their head. There
still may be manipulatives and drawings used for
part of the problem. Counting strategies for
multiplication often involve some type of skip
counting which is used to keep track of counts
rather than to represent objects in the problem.
18
Counting Strategies
Example Ms. Jenkins bought 7 boxes of cupcakes.
There were 4 cupcakes in each box. How many
cupcakes did Ms. Jenkins buy? Jamie counts, 4
pause, 8, 12, 16, 20, 24, 28. She bought 28
cupcakes. As Jamie counts, he extends a finger
with each count. When he has extended seven
fingers, he stops counting and gives the answer.
19
Derived Facts/Number Facts
Students show knowledge of number facts during
problem solving. Does not have to be the fact
that is in the problem.
20
Derived Facts/Number Facts
Example There are 7 peaches in each box. How
many peaches are there in 6 boxes.
Rudy answers 42, almost immediately.
Teacher How do you know there were 42?
Rudy Because I know that 5 sevens is 35, so 1
more seven is 42.
21
Using Number Sense to Help

• 7 x 8
• What are some derived facts kids might use to
  solve this problem?

• What strategies would students need to have
  before they can use the derived facts for this
  problem?

22
Problem Type Card Sort

• Sort the problems so those that would be directly
  modeled in a similar way are together.

23
Multiplication and Division

• Read pages 33 38 in Cognitively Guided
  Instruction.

24
Problem Type Card Re-Sort

• After Reading , resort the problem set into
  three groups.
• After sorting the problem set into groups define
  each group.
• Each group of cards should be assigned a problem
  type.
• Write a definition for each problem type.

25
Multiplication
Multiplication problems give the number of groups
and the number of objects in each group. The
unknown is the total number of objects.
26
Multiplication Problems
A. Chih had 5 bags of candy with 7 pieces of
candy in each bag. How many pieces of candy did
Chih have? c. Brenda raises puppies. Each
mother dog had 4 puppies. She has 3 mother dogs.
How many puppies were there?
27
Measurement Division
Measurement Division problems give the total
number of objects and the number of objects in
each group. The number of groups is the unknown
28
Measurement Division Problems
D. Maria has 17 fish. If 3 fish can be put into
1 fishbowl, how many bowls does she need to hold
her fish? E. Lee collects stamps. He has 45
stamps. If he sticks 9 stamps on each page, how
many pages would he fill with stamps? G. 19
children are going to the circus. 5 children can
ride in each car. How many cars are needed so
that all the children can go to the circus?
29
Partitive Division
Partitive Division problems give the total number
of objects and the number of groups. The number
of objects in each group is the unknown.
30
Partitive Division Problems
B. At Sallys birthday party there were 15
children and 3 blankets. If the same number of
children sat on each blanket, how many children
sat on each blanket? F. Mr. Wong has 4
children. He wants his children to share 12
marbles so that they each get the same amount.
How many marbles should Mr. Wong give each child?
31
Guess the Problem Type
32
Mary has 7 marbles in each of her 3 jars. How
many marbles does she have all?
33
Problem Type

• Multiplication

34
Hannah had some bags of candy. There are 4
pieces in each bag. If there are 36 total
pieces, how many bags does Hannah have?
35
Problem Type

• Measurement
• Division

36
Ethan collects cars. He has 6 boxes to put them
in. He has 54 cars and wants to put the same
number of cars in each box. How many cars will go
in each box?
37
Problem Type

• Partitive Division

38
Kathy has 24 cookies. She puts 6 on each plate.
How many plates will she need?
39
Problem Type

• Measurement
• Division

40
Leo bought 6 gumballs. Each gumball costs 12
cents. How much money did Leo spend on gumballs?
41
Problem Type

• Multiplication

42
Mr. Gomez has 12 cupcakes. He wants to put the
cupcakes into 4 boxes so theres the same number
in each box. How many cupcakes can go in each
box?
43
Problem Type

• Partitive Division

44
There was an ant parade walking across a table.
They walked 7 inches, stopped and then continued
walking. They did this 4 times. How far did the
ant parade walk?
45
Problem Type

• Multiplication

46
Area and Array Problems

• Read pages 49-52 in Cognitively Guided
  Instruction.
• As you read think about the following question
  Why is it important to introduce students to
  Array and Area problems?

47
How Does this Fit with Common Core?
48
Create your own problems using the poems in your
packet for inspiration.
49
Next Steps

• Redeliver to grade level teachers by November 9.

50
Multiplicative Comparison

• Read the following pages from Teaching Student
  Centered Mathematics
• K-3 page 79.
• 3-5 pages 59 - 60.

51
Team Time

• Plan with your school level team.
• Decide how you are going to redeliver to grade
  level groups. You may want to consider the
  following
• Will it be afterschool or during planning times?
• Will it be school-wide or by grade level?
• Be prepared to share your tentative plans.

52
Closing