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Deconstructing the 3-8 Math Multiple Choice To Differentiated Instruction

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

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  1. 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

  2. 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

  3. 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

  4. Cut Points :Comparison with ELA

  5. Standard 3 Process and Content Strands

  6. 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

  7. 1999 Cohort % Mastery of Math Key Ideas

  8. 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

  9. 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 8 1/8 B 6 1/8 C 5 3/4 D 5 2/6

  10. 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

  11. 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 39 G 31 H 27 J 24

  12. 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

  13. 2006 Grade 5 Math Question • 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

  14. 2006 Grade 6 Math Question • 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

  15. 2006 Grade 8 Math Question 7. Simplify the expression below. 24x2y 6xy3 A 18x3y4 B 4xy2 C 4x y2 D 18x2y2

  16. 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 3 x 9 G 3 ÷ 9 H 9 – 3 J 9 ÷ 3

  17. 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 9s – 3 G (9 + 3)s H 9s – 3s J 9s – s– 3

  18. 2006 Grade 7 Math Question 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

  19. 4 in. 2006 Grade 6 Math Question 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 ]

  20. 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

  21. 2006 Grade 7 Math Question 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

  22. 12 6 4 2 9 3 2006 Grade 5 Math Question • 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

  23. 2006 Grade 3 Math Question • 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

  24. 2006 Grade 4 Math Question • 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

  25. 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 7m + 20 < 150 G 7m + 20 > 150 H 20m + 7 < 150 J 20m + 7 > 150

  26. 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. 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

  27. 2006 Grade 5 Math Question • 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

  28. 2006 Grade 5 Math Question • 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

  29. 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 60% G 70% H 75% J 80%

  30. 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 $3.20 G $12.00 H $12.80 J $19.20

  31. 2006 Grade 5 Math Question • What is the total number of lines of symmetry that can be drawn on this rectangle? A 1 B 2 C 3 D 4

  32. 2006 Grade 5 Math Question 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

  33. KEY = 10 skateboards 2006 Grade 3 Math Question • 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

  34. 2006 Grade 4 Math Question • 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

  35. 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 =

  36. 2006 Grade 4 Math Question • 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

  37. 2006 Grade 3 Math Question • 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

  38. 2006 Grade 7 Math Question • What is the greatest common factor of 28, 42, 56? F 2 G 7 H 14 J 28

  39. 2006 Grade 8 Math Question 1. What is the greatest common factor of 48x2 and 72x3 ? A 12x2 B 12x3 C 24x2 D 24x3

  40. 2006 Grade 7 Math Question 4. What is the least common multiple of 3, 6, and 27? F 3 G 18 H 27 J 54

  41. 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

  42. 1 gallon = 4 quarts 1 quart = 2 pints 1 pint = 2 cups 2006 Grade 7 Math Question • 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

  43. 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

  44. 2006 Grade 7 Math Question • 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

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