Transcript Teaching Math Conceptually

SCASD Math Curriculum
MJ Kitt
K-6 Math/Science Coordinator
Bill Harrington
Secondary Math Coordinator
A Model for Success
Students
Parents
Teachers
Conceptual
Understanding
Skills
Problem
Solving
Elementary Math Office Goals
2008-2009
•Development of Elementary
Math Parent Handbook
•Distributed at Back-to-School Night
•Parent Informational/Workshop
Opportunities
•Dec 08 to present
Elementary Math Parent Handbook
Distributed at
Back-to-School Night
Parent Informational Workshops
12-10-08
Corl Street Informational Night
01-28-09
District PTO Meeting
02-4-09
Radio Park Information Night
02-12-09
Parent Math Luncheon
03-26-09
Easterly Parkway Parent Workshop
04-1-09
Park Forest Math Celebration Night
04-13-09
Corl Street Coffee
04-14-09
Grays Woods Parent Workshop
04-23-09
Panorama/Boalsburg The Math Zone
04-30-09
Corl Street Coffee
06-1-09
Houserville/Lemont MathWorkshop
TBA
Ferguson Township Math Workshop
09-10
District Parent Informational Night
Future Plans for
Parent Opportunities
•District Informational Parent Math Night
•Overview of K-5 math curriculum
•District elementary math goals
•Parent communication
•Math Exploration Venues
•Work study groups
•Grade level workshops
•Informal math conversations
•In-home math socials
•Breakfasts, lunches
•District Math Website
Responding to Parent Concerns
What about fact practice?
?
When are algorithms introduced?
Are students prepared for higher level mathematics?
Computational Fluency Statement
SCASD Expectations~
K:
Model with objects
1st: Addition facts to 10
Combinations of 10
2nd: Subtraction facts to 10
Addition facts to 20
3rd: Subtraction facts to 20
Multiplication facts through 5 x 9
4th: Multiplication facts through 12 x 12
5th: Multiplication and Division through 12’s
2-digit +/- (regrouping)
3rd Grade
3-digit +/- (no regrouping)
3-digit +/- (regrouping)
3-digit x 1-digit Multiplication
4th Grade 3-digit ÷ 1-digit Division
+/- of Decimals through .00
+/- of Fractions - like denominator
+/- Thousands to Hundredths
(regrouping)
4 digit x 2-digit Multiplication
5th Grade 4-digit ÷ 1-digit Division
4-digit ÷ 2-digit Division
+/- Fractions through 1/16ths
History of the District
Math Review Committees
School Year
2002-2003
2003-2004
2004-2005
2005-2006
2006-2007
2007-2008
2008-2009
Committee
Original Math Review Committee
(building representatives, chair - Susan Younkin, supervisor - Cameron Bausch)
Math Review Committee (each elementary building represented)
K-2 Math Committee (each building represented)
Grade 3 Math Committee (grade 3 teachers, 1 primary, 1 Title I)
Grade 4-5 Math Committee (grade 4-5 teachers, 1 grade 3, 1 grade 6, 1 Title I )
Extend the Vision Committee (each grade level K-6 represented)
Extend the Vision Committee (each grade level K-6 represented)
Fifth Grade Gains
2007 Gain
2008 Gain
-2.1
-0.2
-10.9
+2.6
-4.4
-7.5
Math Thi nking Test Results
School
Year
95%+
86-94%
57-85%
56%-
2008
0.5%
22.5%
56.0%
21.0%
2009
8.0%
25.0%
54.0%
13.0%
-5.1
-1.8
-1.9
-0.9
-1.6
-7.0
2006-2007
96
-2.4
+1.8
2007-2008
74
-8.8
+1.1
2008-2009
73
Title I Math Students Served
100
SCASD
PA STATE
90
80
70
08
60
50
07
40
30
20
10
0
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Grade 11
Why the 2nd Edition?
2nd Edition Investigations provides:
improved parent communication
integration of standard algorithms
additional practice opportunities
more rigorous development of the number and operations strand
more explicit suggestions for modifications and extensions
enhanced student, teacher, and parent technology components
Pennsylvania State Standards
Anchor Assessment Areas
1.
2.
3.
4.
5.
Number Systems and Operations
Measurement
Geometry
PSSA
Algebraic Concepts
Content
Data Analysis and Probability
Data Analysis
Number Systems
PSSA
Content
Algebra
Geometry
Measurement
PSSA
Content
K
What is the repeating unit of this pattern?
What comes next in this pattern?
Kindergarten
K
Activity:
Students make patterns with connecting cubes
and record with paper cube strips.
1
A
B
C
A
What color will the
10th square be?
B
C
First Grade
1
Activity:
Students will determine the color of cube “x”
given a prepared AB, AAB, or ABC cube train.
2
Activity:
Students make a building with
connecting cubes, given a certain
number of rooms per floor (ex: 3
rooms/floor). Then they determine
the total number of rooms in a
building with a certain number of
floors.
Second Grade
2
Activity:
Students create a table to represent
the ratio of # of floors to # of rooms.
Building A
Total # of Floors
Total # of Rooms
1
2
3
6
Third Grade
3
Child
Beginning #
Nightly #
Tovar
20
2
Winger
20
4
Jorad
45
3
Activity:
Students complete a table that shows how
many marbles each of 3 children has after every
5 nights if they receive a different number of
marbles each night.
Students then write a rule to determine how
many marbles each of the 3 children will have
on any given night.
3
Child
Beginning
#
Nightly #
Tovar
20
2
Winger
20
4
Jorad
45
3
What story can we
tell about Tovar and
Winger by looking
at this graph?
4
Activity:
Students look at a graph of a runner’s
speed over time and draw conclusions
about her progress based on the shape
of the graph.
Fourth Grade
a
b
c
g
d
f
e
time
•At what point is she speeding up?
•At which point has she stopped?
•At which point is she going at a slow, steady speed?
•What is she doing at d?
•What is she doing at f?
•What is she doing at c?
4
Activity:
Students create a graph and
compare the data for each
situation.
Round
Penny
Jar A
Penny Jar
B
Start with
8
0
1
10
4
2
12
8
3
14
12
4
5
6
5
Activity:
Fifth Grade
Students build a rectangular array with rows of
3 tiles and examine the relationship between
the number of rows and the number of tiles.
=3
=6
5
Activity:
Students work with the same arrangement of
tiles and consider the perimeter of the shape
as the number of rows increases.
P=
What would be the
perimeter when 10 rows
of 3 tiles are added?
P=
P=
P=
What rule would
determine the
perimeter for “n”
rows?
M
Middle
Students look at one set of
data represented in the form
of a table and compare it to
another set of data
represented in a graph.
• Which bike shop offers better
rates?
• What is the best way to
compare this data?
•What patterns can you find
and how can you use the
patterns to predict values not
included?
M
Students solve problems by
comparing tables, graphs, and
equations.
Middle
Mighty Tee charges $49 plus $1 per T-shirt.
No-Shrink Tee charges $4.50 per T-shirt.
• Which company offers the
250
better deal for 20 shirts?
• For what number of T-shirts
is the cost of the two
companies equal?
No-Shrink
200
CMighty = 49 + n
CNo-Shrink = 4.5n
150
100
Mighty
•What are the advantages to
using equations to answer
these questions? Graphs?
Tables?
50
0
0
T-Shirt Cost
10
20
30
40
50
M
Solving Equations
Middle
y = 3x + 3
y = 2x + 8
3x + 3
=
2x +
8
H
Solving System of Equations
High
Tyrel and Dalia bought some pens and pencils. Tyrel
bought 4 pens and 5 pencils, which cost him $6.71. Dalia
bought 5 pens and 3 pencils, which cost her $7.12.
Let x = the cost of a pencil
y = the cost of a pen
4x + 5y = 6.71
5x + 3y = 7.12
H
Other Functions
High
Power Functions: y = xp
H
Other Functions
High
Exponential Functions: y = P0ax
H
Other Functions
High
Logarithmic Functions: y = lnx
H
Other Functions
High
Periodic Functions:
4
Remember this?
a
b
c
g
d
f
e
time
H
High
Rate of Change
H
Rate of Change
High
Estimate the average rate of change between t=0 and
t=10. Interpret your answers in terms of water.
800 500
 30
10 0
The average rate of
change is about 30
cubic meters per week.
H
High
Rate of Change
Thank You!
MJ Kitt
K-6 Math/Science Coordinator
Bill Harrington
Secondary Math Coordinator