Deconstructing the 3-8 Math Multiple Choice To Differentiated Instruction

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Deconstructing the 3-8 Math Multiple Choice To Differentiated Instruction. LIASCD October 13, 2006 Dr. Lorna R. Lewis Three Village CSD lornal@3villagecsd.org 631-730-4060. Agenda. What’s a District to Do? District Item analysis AIS identification for 2006-07

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### Deconstructing the 3-8 Math Multiple Choice To Differentiated Instruction

LIASCD

October 13, 2006

Dr. Lorna R. Lewis

Three Village CSD

lornal@3villagecsd.org

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

Standard 3

Process and Content Strands

Mathematical Reasoning

Number and Numerations

Operations

Modelling

Patterns & Functions

Measurement

Uncertainty

Number Sense & Operations

Geometry

Algebra

Measurement

Statistics & Probability

From Key Ideas to Content Strands

Prekindergarten

Number Sense and Operations

Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.

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)

Major

Understanding

Strand

Performance

Indicator

Band

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 8 1/8

B 6 1/8

C 5 3/4

D 5 2/6

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

22. What is the mean (average) of the set of numbers below?

15, 39, 30, 10, 8, 39, 27

F 39

G 31

H 27

J 24

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

• Ron works from 8:45 a.m. to 3:05 p.m. How long does Ron work?

F 5 hours 40 minutes

G 6 hours 20 minutes

H 6 hours 40 minutes

J 7 hours 20 minutes

• Which equation shows the commutative property of addition?

A 6 + 3 = 9

B 6 + 3 = 6 + 3

C 6 + 3 = 3 + 6

D 6 + 3 = 5 + 4

7. Simplify the expression below.

24x2y

6xy3

A 18x3y4

B 4xy2

C 4x

y2

D 18x2y2

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 3 x 9

G 3 ÷ 9

H 9 – 3

J 9 ÷ 3

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 9s – 3

G (9 + 3)s

H 9s – 3s

J 9s – s– 3

14. Which algebraic expression represents “six less than half a number”?

F 1/2x – 6

G 6 – 1/2x

H 1/2(x – 6)

J (6 – 1/2)x

4 in.

18. What is the volume of the cylinder below?

10 in.

Volume of Cylinder = πr2h

F 80πcubic inches

G 160πcubic inches

H 400π cubic inches

J 1,600π cubic inches

[ Not drawn to scale ]

19. The circumference of the circle below is 25.12 centimeters.

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

29. A circle has a circumference that measures 18πinches. What is the radius, in inches, of the circle?

A 6

B 9

C 18

D 36

C=2πr

12

6

4

2

9

3

• 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

• 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

• Kyle writes the number sentence below.

> 1/3

Which fraction belongs in the box to make the number sentence correct?

F 1/8

G 1/6

H 1/4

J 1/2

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 7m + 20 < 150

G 7m + 20 > 150

H 20m + 7 < 150

J 20m + 7 > 150

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.

Which equation can be used to determine the number of gallons, g, of water in the pool after h hours?

F g = 600h

G g = 1,500h

H g = 1,500 + 600h

J g = 1,500h +600

• 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 0.2 meter

G 0.5 meter

H 0.625 meter

J 0.635 meter

• Laurel’s python is 2 ½ feet long. If the snake grows 1 foot longer, what will its length be in inches?

F 30 inches

G 32 inches

H 40 inches

J 42 inches

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 60%

G 70%

H 75%

J 80%

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 \$3.20

G \$12.00

H \$12.80

J \$19.20

• What is the total number of lines of symmetry that can be drawn on this rectangle?

A 1

B 2

C 3

D 4

15.The line graph below shows the growth of a tomato plant.

How much did the tomato plant grow from Week 1 to Week 4?

A 65 mm

B 70 mm

C 75 mm

D 90 mm

KEY

= 10 skateboards

• The number of skateboards sold at a store during a 3-month period is shown on the pictograph below.

SKATEBOARDS SOLD

How many skateboards were sold in April?

A 3

B 4

C 20

B 30

• Martin shaded 2/8 of the circles below.

Which fraction is equivalent to 2/8?

F 1/8

G 1/6

H 1/4

J 1/2

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 =

• 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.

What number belongs in Box A?

A 4

B 9

C 14

B 16

• 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

• What is the greatest common factor of 28, 42, 56?

F 2

G 7

H 14

J 28

1. What is the greatest common factor of 48x2 and 72x3 ?

A 12x2

B 12x3

C 24x2

D 24x3

4. What is the least common multiple of 3, 6, and 27?

F 3

G 18

H 27

J 54

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

### 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??

A 1 B 4 C 8

D 16

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

• 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?

F 8

G 12

H 16

J 32

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

• 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 1.69 X 10-8

G 16.9 X 10-7

H 16.9 x 107

J 1.69 x 108

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?

FKaren surveyed too many students.

G Karen’s survey sample was too small.

H Karen did not survey any high school students.

J Karen did not include enough bands in the survey.

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 40 + 60 + 50

G 50 + 60 + 50

H 50 + 60 + 60

J 50 + 70 + 60

23. The drawing below shows the number of students who ride three buses to Maple School.

Bus 1

62 Students

Bus 2

53 Students

Bus 3

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