Transcript Document
Day Two Training
Taking Time to SelfReflect
Fact
Selection
Strategy
Practice
Knowledge
How do I
select which
facts for
students to
learn?
What
strategies
do I use to
help
students
understand
these facts?
How do I get
students to
learn these
facts once
they
understand
them?
How do I get
students to
use the
basic facts
they know?
Adapted from Basic Facts Knowledge: A Staff Tutorial.
http.nzmaths.com, 2010.
A Look Back at Day One
What to expect from today.
• Examine alternative strategies for
multiplication and division.
• Relate the concepts of multiplication &
division.
• Assess student work and identify their
misconceptions.
Fact Selection
Multiplication and Division-Grade 3-Unit 2. Georgia Department of Education. 2007. p. 26.
Mastering Math Facts
The problem with rote work comes when
it is used exclusively for teaching math
facts. Research shows that
overemphasizing memorization and
frequently administering timed tests is
actually counter-productive, (National
Research Council, 2001).
Van de Walle, J.A., & Lovin, L.H. (2006)
Teaching Student Centered Mathematics
Volume II (3-5), Boston: Pearson.
Let’s get rockin’ with
SALUTE
Materials:
a deck of ten frame cards with wild
cards removed.
three participants for each group
Student
Student
CAPTAIN
How my students think!
A muffin recipe requires 2/3 of
a cup of milk. Each recipe
makes 12 muffins. How many
muffins can be made using 6
cups of milk?
Adapted from Multiplicative Thinking. Workshop 1. Properties of
Multiplication and Division. http.nzmaths.com, 2010.
The Additive Thinker
A muffin recipe requires 2/3 of a cup of milk.
Each recipe makes 12 muffins. How many
muffins can be made using 6 cups of milk?
2
3
1
4
2
Each rectangle represents a third of a
cup of milk.
A muffin recipe requires 2/3 of a cup of milk.
Each recipe makes 12 muffins. How many
muffins can be made using 6 cups of milk?
The Multiplicative Thinker
Works with a variety of numbers such as larger
whole numbers, decimals, common fractions, etc.
Can solve a range of problems involving
multiplication and division
Can communicate math findings in a variety of
ways including words, diagrams, symbolic
expressions and written algorithms.
Multiplicative Thinking-Workshop 1. Properties of Multiplication and
Division. http.nzmaths.com, 2010.
A family has $96.00 to spend at
the Wally World adventure
park. Each ride at the park
costs $4.00 per person. How
many rides will the family be
able to enjoy while there?
Time for a Break
Additive Multiplicative
Both
Learning How Students Think
Why encourage multiplicative
strategies if additive strategies can
be used?
“The Jones family has $396.00 to
spend at the Wally World adventure
park. Rides cost $4.00. How many
rides will the family be able to
enjoy?”
Reflection Time
Writing about what
you have seen.
Why is math vocabulary so
difficult?
Students must be provided adequate
opportunities to learn this vocabulary in
meaningful ways. Learners need
experiences with constructing meaning
from context as well as from direct
teaching.
Reflection Time
Let’s Make 100
1. Use the die to generate a number.
Spin the spinner to get the multiplier.
The person closest to 100 after 5 spins
is the winner.
2. You have the option of “staying” after 3
spins.
3. Any number greater than 100 is a
bust.
Reflection Time
Multiplication in KCAS
Multiplication
23
x16
138
230
368
Errors or
Misconceptions?
Ashlock, Robert. Error Patterns in Computation: Using Error Patterns to Help
Each Student Learn-Tenth Edition, 2009. Covenant College
p.15.
What About Alternative
Strategies?
If you use it, you must
understand why it works and
be able to explain it.
John Van De Walle
Partial Products
30 x 10
30 x 9
8 x 10
8x9
38
x 19
300
270
80
+ 72
722
78
x 54
70 x 50 3500
70 x 4
280
8 x 50
400
8x4
+ 32
4212
Partial Products (Area Model)
60
2
10
600
20
8
480
16
62
x 18
600
480
20
+ 16
1116
54 x 37 =1500+350+120+28 =1998
50
4
30
1500
120
7
350
28
(2x + 5) (x + 6)
5
2x
x
6
5x
30
2x
12x
Lattice Method
3
2
7
1
6
1
3
7
1
3
3
5
5
1
9
5
5
5
37
x 95
185
3330
3515
46 × 37
4
6
3
7
46 × 37 = 1702
4
1
1
6
2
1
2
2
0
2
7
4
8
7
8
3
2
476
x 8
354
268
3808
476
x 38
354
268
121
218
18088
times 8
times 3
CHINESE METHOD OF MULTIPLICATION
12
400
140
CHINESE METHOD OF MULTIPLICATION 23 x 24 =
400
140
12
552
31 x 43=
Reflection Time
Lies my teacher told me…
To multiply by ten just add a zero
to the end of the whole number.
The product is always larger.
5 x 10 =
.5 x 10=
3245 x 10=
3.245 x 10=
10 x 2 =
10 x .02=
So What About Division?
How many of our students understand
dividing a number by 3 is the same as
multiplying the number by 1/3?
169 ÷ 14 =
To begin thinking about division, solve
this problem using a strategy other than
the conventional division algorithm. You
may use symbols, diagrams, words, etc.
Be prepared to show your strategy
Hedges, Huinker and Steinmeyer. Unpacking Division to Build
Teachers’ Mathematical Knowledge, Teaching Children
Mathematics, November 2004, p. 4-8.
Hedges, Huinker and Steinmeyer. Unpacking Division to Build
Teachers’ Mathematical Knowledge, Teaching Children
Mathematics, November 2004, p. 4-8.
KCAS
CONNECTION
Primary Resources: Maths: Multiplication and
Division.www.primaryresources.co.uk.maths.mathsC2.htm
The Confusion of
Division
24 ÷ 6 =
• How many times can 6 be subtracted
from 24?
• 24 divided into 6 equal groups.
• 24 divided into equal groups of size 6.
• What number times 6 gives the product
of 24?
The symbolism of division
24 ÷ 6
24/6
24
6 24
6
Division Vocabulary
Quotient
Divisor
THE PARTITIVE PROBLEM
Partitive
Example 1: Write a word
problem to represent this
model of division?
THE MEASUREMENT PROBLEM
Measurement
Example 2: Write a word
problem to represent this
model of division?
Multiplicative Thinking-Workshop 2. Properties of Multiplication and
Division. http.nzmaths.com, 2010.
The standard algorithm
Reflection Time
Forgiveness Method
21
12 252
- 120
132
- 120
12
- 12
0
10
10
1
21
Issic Leung, Departing from the Traditional Long
Division Algorithm: An Experimental Study. Hong Kong
Institute of Education, 2006.
Change it UP!!!!
1. Deal each player five cards. The remaining cards are
placed face down on the center of the table.
2. Player one places a card face up on the table reads the
division problem and provides the quotient. The next
player must place a card with the same quotient on the
first card. If the player cannot match, he/she may place
a “Math Wizard” card on top and then a card with a
different quotient.
3. If the player in unable to make either move, he/she
must draw from the deck until a match is made.
4. The first player to use all of his/her cards is the winner.
Lies my teacher told me…
Division is about “fair sharing”.
35 ÷ 8 =
The Remainder
Can be discarded.
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.
1. Landon bought 80 piece bag of bubble
gum to share with his five person
soccer team. How many pieces did
each player receive?
2. Brittany is making 7 foot jump ropes for
the school team. She has a 25 foot
piece of rope. How many can she
make?
3. The ferry can hold 8 cars. How many
trips will it need to make to carry 25
cars across the river?
Near Facts…
Find the largest factor without
going over the target number
Partial Quotients
18 R 25
26 493
- 260
233
- 130
103
- 78
25
10
5
3
18
The Remainder Game
1. To begin the game, both players place their token on
START.
2. Player one spins the spinner and divides the number
beneath his/her marker by the number on the
spinner. If there is a remainder, he/she is allowed to
move his/her token as many spaces as the remainder
indicates. If the division does not result in a
remainder, he/she must leave his/her marker where it
is.
3. The play alternates between the two players (a new
spin must occur each time) until some reaches
HOME.
Lies my teacher told me…
Any number divided by zero is zero!
6÷0=
How many times can 0 be subtracted from 6?
How many 0 equal groups are there in six?
What does six divided into equal groups of 0
look like?
What number times 0 gives you 6?
Reflection Time