Transcript Slide 1

Deconstructing the 3-8 Math
Multiple Choice
To Differentiated Instruction
LIASCD
October 13, 2006
Dr. Lorna R. Lewis
Three Village CSD
[email protected]
631-730-4060
Agenda
 What’s a District to Do?
 District Item analysis
 AIS identification for 2006-07
 Connecting Content Strands to Key Ideas
 State Reporting
 Parent report
 SPI
 Exploring the Questions
 How did students perform?
 What can we find out from the wrong answers?
 Constructing parallel questions
 Web resource
 Sample Tasks, Glossary, Mathematical Language
One District’s Response
 Not recommended by NYSED
 Results are very conservative but allows
district to make AIS and honors placement.
 Using Multiple Choice responses and Free
Response data
 80% Multiple Choice + 20% Free Response =
Total Score
 Level 4= 90-100
 Level 3=75-89
 Level 2=65-74
 Level 1 Below 65
School
ID
first
last
HR
MC%
FR%
Total %
M
C
F
R
Level
Arrowhead
Jenine
35
84.62%
76.92%
83.08%
22
10
3
Arrowhead
Brian
35
80.77%
69.23%
78.46%
21
9
3
Minnesauke
Alexander
407
96.15%
76.92%
92.31%
25
10
4
Minnesauke
Elizabeth
405
92.31%
69.23%
87.69%
24
9
3
Setauket
Emily
A-3
100.00%
76.92%
95.38%
26
10
4
Mount
Andrew
219
100.00%
100.00%
100.00%
26
13
4
Minnesauke
Stephanie
406
46.15%
69.23%
50.77%
12
9
1
Arrowhead
Brenda
35
61.54%
61.54%
61.54%
16
8
1
Arrowhead
Christian
39
92.31%
92.31%
92.31%
24
12
4
Arrowhead
Sara
35
88.46%
61.54%
83.08%
23
8
3
Arrowhead
Emily
39
88.46%
92.31%
89.23%
23
12
3
Cut Points :Comparison with ELA
Level 4
Level 3
Level 2 Level 1
Grade 3 100-96
95-72
71-60
Below 60
Grade4
100-94
93-67
66-50
Below 50
Grade 5 100-91
90-65
64-40
Below 40
Grade 6 100-91
90-68
67-46
Below 46
Grade 7 100-92
91-70
69-50
Below 50
Grade 8 100-94
93-75
74-50
Below 50
Standard 3
Process and Content Strands
The Five Process Strands
The Five Content
Strands
Problem Solving
Number Sense and
Operations
Reasoning and Proof
Algebra
Communication
Geometry
Connections
Measurement
Representation
Statistics and
Probability
From Key Ideas to Content Strands
 Mathematical
Reasoning
 Number and
Numerations
 Operations
 Number Sense &
Operations
 Modelling
 Patterns & Functions
 Geometry
 Algebra
 Measurement
 Uncertainty
 Measurement
 Statistics & Probability
1999 Cohort
% Mastery of Math Key Ideas
2003 Grade 8
1999 Grade 4
1999 Grade 8
56.6
Math Reasoning
78.6
71.5
80.9
81.1
Number& Numeration
57
58.8
Operations
77.4
66.57
77.8
75.9
Modelling
72
72.5
Measurement
81.9
72.25
80.4
76.8
76.5
Uncertainty
54.5
Patterns&Functions
88.9
66
0
20
40
60
80
100
Prekindergarten
Number Sense and Operations
Major
Understanding
Strand
Students will understand numbers, multiple ways of
representing numbers, relationships among numbers,
and number systems.
Band
Performance
Indicator
Number Systems PK.N.1 Count the items in a
collection and know the last
counting word tells how many
items are in the collection
(1 to 10)
Percent
2006 GRADE 6 MATH
MULTIPLE CHOICE - % CORRECT
100
95
90
85
80
75
70
65
60
55
50
45
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Item #
2006 Grade 6 Math Question
5. Jackie wants to plant 2 ½ rows of corn
in her garden. She needs 3 ¼ ounces of
seed for each row. How many total
ounces of seed should Jackie buy?
A
B
C
D
8
6
5
5
1/8
1/8
3/4
2/6
2006 Grade 6 Math Question
13.
Ben recorded the number of customers
who shopped at his pet store every day
for one week. The results are shown
below.
42, 35, 56, 29, 42, 39, 23
What is the mean number of customers who
shopped at the pet store?
A
33
B
38
C
39
D
42
2006 Grade 5 Math Question
22. What is the mean (average) of the
set of numbers below?
15, 39, 30, 10, 8, 39, 27
F
G
H
J
39
31
27
24
2006 Grade 4 Math Question
19. Jamie naps every day. He falls
asleep at 3:30 p.m. and wakes up
at 5:00 p.m. How long does
Jamie sleep?
A
2 hours 30 minutes
B
2 hours
C
1 hour 30 minutes
D
1 hour
2006 Grade 5 Math Question
12.
Ron works from 8:45 a.m. to 3:05
p.m. How long does Ron work?
F
G
H
J
5
6
6
7
hours
hours
hours
hours
40
20
40
20
minutes
minutes
minutes
minutes
2006 Grade 6 Math Question
9. Which equation shows the
commutative property of addition?
A
B
C
D
6
6
6
6
+
+
+
+
3
3
3
3
=
=
=
=
9
6+3
3+6
5+4
2006 Grade 8 Math Question
7.
Simplify the expression below.
24x2y
6xy3
A
18x3y4
C
4x
y2
B
4xy2
D
18x2
y2
2006 Grade 3 Math Question
12.
Mr. Arthur made 9 pancakes for his 3
children. All 9 pancakes were shared
equally among his 3 children. Which
expression can be used to find the
number of pancakes each child ate?
F
G
H
J
3
3
9
9
x9
÷9
–3
÷3
2006 Grade 6 Math Question
24. Sarah collects stamps and keeps them
in envelopes. She had 9 envelopes
with a certain number of stamps, S, in
each envelope. She sells 3 of the
envelopes. Which expression
represents the number of stamps
Sarah has left?
F
G
9s – 3
(9 + 3)s
H
J
9s – 3s
9s – s – 3
2006 Grade 7 Math Question
14. Which algebraic expression
represents “six less than half a
number”?
F
G
H
J
1/2x – 6
6 – 1/2x
1/2(x – 6)
(6 – 1/2)x
2006 Grade 6 Math Question
18.
What is the volume of the cylinder below?
4 in.
10 in.
Volume of Cylinder = πr2h
[ Not drawn to scale ]
F
G
H
J
80π cubic inches
160π cubic inches
400π cubic inches
1,600π cubic inches
2006 Grade 7 Math Question
19.
The circumference of the circle below is 25.12
centimeters.
Radius
C = 2πr
[Not Drawn to Scale]
Which is the best estimate for the length of the radius
of the circle?
A
3 centimeters
B
4 centimeters
C
8 centimeters
D
16 centimeters
2006 Grade 7 Math Question
29.
A circle has a circumference that measures
18π inches. What is the radius, in inches,
of the circle?
A
6
B
9
C
18
D
36
C=2πr
2006 Grade 5 Math Question
10. The triangles below are similar.
Which fraction represents the ratio of the lengths of the sides of
the small triangle to the lengths of the sides of the large triangle?
F
1/3
G
4/9
H
1/2
J
2/3
2006 Grade 3 Math Question
7. Josie plays a number game. She uses the
numbers below to make larger numbers.
3
8
9
What is the largest number Josie can make
with the 8 in the ones place?
A
398
B
839
C
938
D
983
2006 Grade 4 Math Question
12. Kyle writes the number sentence below.
> 1/3
Which fraction belongs in the box to make
the number sentence correct?
F
G
H
J
1/8
1/6
1/4
1/2
2006 Grade 8 Math Question
26. Carol wants to earn at least $150.00 for
her charity while running a race. She will
earn $20.00 for participating plus $7.00
for each mile she runs. If m represents the
number of miles she runs, which inequality
represents the money Carol wants to earn?
F
G
H
J
7m + 20
7m + 20
20m + 7
20m + 7
<
>
<
>
150
150
150
150
2006 Grade 8 Math Question
16.
Mr. Patel filled a swimming pool with water. When he
started, the pool already contained 1,500 gallons of
water. The table below shows the number of gallons of
water in the pool after filling it for h hours.
Gallons of Water in
Pool (g)
Numbers of Hours (h)
1,500
0
2,100
1
2,700
2
3,300
3
3,900
4
Which equation can be used to determine the number of
gallons, g, of water in the pool after h hours?
F
g = 600h
H
g = 1,500 + 600h
G
g = 1,500h
J
g = 1,500h +600
2006 Grade 5 Math Question
8. Tony has a ribbon that measures 0.75
meter in length. He cuts 0.125 meter
off the ribbon and gives it to a friend.
How much ribbon is left?
F
G
H
J
0.2 meter
0.5 meter
0.625 meter
0.635 meter
2006 Grade 5 Math Question
20. Laurel’s python is 2 ½ feet long. If
the snake grows 1 foot longer,
what will its length be in inches?
F
G
H
J
30
32
40
42
inches
inches
inches
inches
2006 Grade 6 Math Question
14. Mr. Jenkins wants to distribute 40
fliers. He has distributed 30 fliers so
far. What percent of the total number
of fliers has Mr. Jenkins distributed?
F
G
H
J
60%
70%
75%
80%
2006 Grade 8 Math Question
4.
A pair of sandals is on sale for 20%
off the original price. If the original
price $16.00, what is the sale
price?
F
G
H
J
$3.20
$12.00
$12.80
$19.20
2006 Grade 5 Math Question
5. What is the total number of lines of
symmetry that can be drawn on this
rectangle?
A
B
C
D
1
2
3
4
2006 Grade 5 Math Question
Height (in millimeters)
15.
The line graph below shows the growth of
a tomato plant.
Tomato Plant Growth
100
90
80
70
60
50
40
30
20
10
1
2
3
4
Week
How much did the tomato plant grow from Week 1 to Week 4?
A 65 mm
C 75 mm
B 70 mm
D 90 mm
2006 Grade 3 Math Question
25. The number of skateboards sold at a store during a
3-month period is shown on the pictograph below.
SKATEBOARDS SOLD
Month
Number of Skateboards
KEY
April
May
= 10 skateboards
June
How many skateboards were sold in April?
A3
C 20
B4
B 30
2006 Grade 4 Math Question
6. Martin shaded 2/8 of the circles
below.
Which fraction is equivalent to 2/8?
F
1/8
H
1/4
G
1/6
J
1/2
2006 Grade 4 Math Question
25. Which number sentence always
results in an answer that is an odd
number?
A even number x even number =
B even number x odd number =
C odd number x even number =
D odd number x odd number =
2006 Grade 4 Math Question
27. When the number square below is completed,
any three numbers in a line will add up to 24.
The three numbers can be added across, up,
down, or diagonally.
6
A
2
8
0
10
What number belongs in Box A?
A4
C 14
B9
B 16
2006 Grade 3 Math Question
4. Carmen writes the number sentence
below.
218 >
Which number belongs in the box to
make the number sentence correct?
F 211
G 218
H 222
I 230
2006 Grade 7 Math Question
10. What is the greatest common factor
of 28, 42, 56?
F
G
H
J
2
7
14
28
2006 Grade 8 Math Question
1.
What is the greatest common
factor of 48x2 and 72x3 ?
A
12x2
B
C
D
12x3
24x2
24x3
2006 Grade 7 Math Question
4. What is the least common multiple
of 3, 6, and 27?
F
G
H
J
3
18
27
54
2006 Grade 6 Math Question
16.
George has a one-gallon container of apple
juice. How many cups of apple juice are in the
one-gallon container??
1 gallon = 4 quarts
1 quart = 2 pints
A
1
B
4
C
8
D
16
1 pint = 2 cups
2006 Grade 7 Math Question
16. Jennifer makes fruit punch for her family. She
prepares a total of two gallons of fruit punch.
How many cups of fruit punch does she make?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
F
G
H
J
8
12
16
32
2006 Grade 7 Math Question
24.
Ellen buys 24 ounces of green beans at the
grocery store. The green beans cost $1.90
per pound. How much does she pay for the
green beans, before tax?
F
$1.90
G
$2.53
H
$2.85
J
$3.80
1 pound = 16 ounces
2006 Grade 7 Math Question
18. In the year 2000, approximately 169,000,00
personal computers were used in the United
States. What is this number expressed in
scientific notation?
F
G
H
J
1.69
16.9
16.9
1.69
X 10-8
X 10-7
x 107
x 108
2006 Grade 7 Math Question
30.
Karen surveyed students in one middle school
about their favorite band. Of the 1,156 students
in the middle school, 65 sixth-grade students
were surveyed. More than half of the 65 students
said their favorite band is Rhonda and the Gees.
Based on the survey, Karen says most middle
school students’ favorite band is Rhonda and the
Gees. Why is Karen’s statement incorrect?
F
G
H
J
Karen surveyed too many students.
Karen’s survey sample was too small.
Karen did not survey any high school
students.
Karen did not include enough bands in the
survey.
2006 Grade 3 Math Question
16.
Ian has 48 red paper clips, 61 blue
paper clips, and 53 green paper
clips. Which is the best way to
estimate the total number of Ian’s
paper clips?
F
G
H
J
40
50
50
50
+
+
+
+
60
60
60
70
+
+
+
+
50
50
60
60
2006 Grade 3 Math Question
23. The drawing below shows the number of students
who ride three buses to Maple School.
Bus 1
Bus 2
Bus 3
62 Students
53 Students
49 Students
Which is the best estimate of the total number of
students who ride the three buses?
A
140
B
150
C
160
D
170
2006 Grade 4 Math Question
16. Students at the elementary school are washing cars
to raise money for a trip. The table below shows the
amount of money they raised on each of the 5 days.
CAR WASH FUNDRAISER
Day
Money Raised
1
$54.00
2
$48.00
3
$47.00
4
$51.00
5
$49.00
Which is the best estimate of the total number of days
it will take the students to raise a total of $500.00?
F
8
G 10
H
12
J
14