Number, Number Sense and Operations



Mathematics Benchmarks & Indicators

with Ohio Achievement Test Questions

Grades 3 – 4

Includes questions from the released

2008, 2007, 2006, and 2005 Ohio Achievement Tests

and the 2005 Practice Tests

Far East Regional Partnership

for Conceptually Based Mathematics

Youngstown State University

Compiled by A. Crabtree, 2006

Revised by A. Crabtree and L. Holovatick, 2007

Revised by A. Crabtree, J. Lucas, and T. Cameron, 2008

A. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.

3-2. Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example:

a. Recognize 100 means “10 tens” as well as a single entity (1 hundred) through physical models and trading games

b. Describe the multiplicative nature of the number system; e.g., the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1.

c. Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with centimeter and decimeter strips, or gathering 1000 pop-can tabs.

d. Explain the concept of tenths and hundredths using physical such models, as metric pieces, base ten blocks, decimal squares or money.

3-3. Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, , =, ≤, ≥.

4-2. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.

4-3. Round whole numbers to a given place value.

|Grade 3 – 2005 OAT – Problem # 1 |

| | |

|Which number is shown by the blocks? |A. 153 |

|[pic] |B. 351 |

| |C. 513 |

|Grade 3 – 2005 Practice Test – Problem # 10 |

| | |

|Which number is shown by the blocks? |A. 20 |

|[pic] |B. 83 |

| |C. 137 |

|Grade 4 – 2007 Test – Problem # 40 |

| | |

|Calvin gathered data on the number of people who live in five cities. |A. Olivia |

| |B. Franklin |

|[pic] |C. Palmer |

| |D. Trinity |

|Which city has more people than St. James? | |

|Grade 4 – 2006 OAT – Problem # 17 |

| |

|Which is the same as 480,072? |

| |

|A. 400 + 80 + 70 + 2 |

|B. 4,000 + 80 + 700 + 2 |

|C. 40,000 + 80,000 + 70 + 2 |

|D. 400,000 + 80,000 + 70 + 2 |

|Grade 4 – 2006 OAT – Problem # 45 |

| | |

|The elevation of Campbell Hill is 1,565 feet. |A. 1,500 feet |

| |B. 1,550 feet |

|What is this number rounded to the nearest hundred? |C. 1,600 feet |

| |D. 2,000 feet |

|Grade 4 – 2005 Practice Test – Problem # 11 |

| |

|Four girls ran in a race. Their times are shown in the table. |

|[pic] |

|Which list shows the students’ times from least time to greatest time? |

| |

|A. 12.033; 12.03; 12.3; 12.303 |

|B. 12.03; 12.033; 12.3; 12.303 |

|C. 12.03; 12.033; 12.303; 12.3 |

|D. 12.3; 12.03; 12.033; 12.303 |

B. Recognize and generate equivalent representations for whole numbers, fractions and decimals.

3-1. Identify and generate equivalent forms of whole numbers; e.g., 36, 30+6, 9 x 4, 46-10, number of inches in a yard.

3-7. Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red.

4-1. Identify and generate equivalent forms of fractions and decimals. For example:

a. Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g. , 1/2, 5/10, “five tenths,” 0.5, shaded rectangles with half, and five tenths.

b. Understand and explain that ten tenths is the same as one whole in both fraction and decimal form.

|Grade 3 – 2006 OAT – Problem # 17 |

| | |

|Which decimal is shown by the shaded part of the figure? |A. 0.2 |

| |B. 0.3 |

|[pic] |C. 0.8 |

|Grade 3 – 2005 OAT – Problem # 45 |

| |[pic] |

|What fraction of these stars is shaded? | |

|[pic] | |

|Grade 4 – 2007 Test – Problem # 10 |

| |

|Eight students are shown. |

|[pic] |

|Write a fraction and a decimal that represents the number of students wearing hats. |

|Grade 4 – 2006 OAT – Problem # 10 |

| |

|Some fractions are less than one. Some fractions are equal to one. Some fractions are greater than one. |

| |

|Write a fraction that is equal to one. _____________________ |

| |

|Use words, pictures or numbers to show or explain why your fraction is equal to one. |

C. Represent commonly used fractions and mixed numbers using words and physical models.

3-5. Represent fractions and mixed numbers using words, numerals and physical models.

|Grade 3 – 2007 Test – Problem # 43 |

| |[pic] |

|Jack had 10 pencils. He sharpened four of his pencils. What fraction of the | |

|pencils did he sharpen? | |

D. Use models, points of reference and equivalent forms of commonly used fractions to judge the size of fractions and to compare, describe and order them.

3-3. Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, , =, ≤, ≥.

3-6. Compare and order commonly used fractions and mixed numbers using number lines, models (such as fraction circles or bars), points of reference (such as more or less than ½ ), and equivalent forms found using physical or visual models.

4-5. Use models and points of reference to compare commonly used fractions.

|Grade 3 – 2006 OAT – Problem # 27 |

| | |

|Look at the picture below. |A. 1/3 is less than 1/2 |

|[pic] |B. 1/3 is greater than 1/2 |

|Which is true? |C. 1/3 is equal to 1/2 |

|Grade 3 – 2005 Practice Test – Problem # 2 |

| | |

|Directions: Use the fraction models to answer question 2. |[pic] |

|[pic] | |

| | |

|Which set of fractions is in order from smallest to largest? | |

|Grade 4 – 2006 OAT – Problem # 39 |

| | |

|Four students shaded rectangles to represent different fractions. |[pic] |

| | |

|[pic] | |

|[pic] | |

|Which fraction is greatest? | |

|Grade 4 – 2005 Practice Test – Problem # 14 |

| |

|Heidi and James each have a bottle of juice that is the same size. Heidi drank ¼ of her juice. James drank 1/3 of his |

|juice. |

| |

|Use pictures, words or numbers to show how you know. |

E. Recognize and classify numbers as prime or composite and list factors.

4-4. Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite.

|Grade 4 – 2007 Test – Problem # 16 |

| | |

|The numbers of students in four classes are shown in the table. |A. Mr. Willard’s class |

| |B. Ms. Smith’s class |

|[pic] |C. Ms. Rose’s class |

| |D. Mr. Hiller’s class |

|Which class can be divided into equal-sized groups that contain more than one student? | |

|Grade 4 – 2006 OAT – Problem # 36 |

| | |

|Which is a prime number between 20 and 30? |A. 21 |

| |B. 23 |

| |C. 25 |

| |D. 27 |

|Grade 4 – 2005 Practice Test – Problem # 17 |

| |

|What is a prime number? ___________________________________ |

| |

|Give three examples of prime numbers. ________________________ |

F. Count money and make change using both coins and paper bills.

3-4. Count money and make change using coins and paper bills to ten dollars.

4-8. Solve problems involving counting money and making change, using both coins and paper bills.

|Grade 3 – 2007 Test – Problem # 33 |

| |

|This menu shows the prices at a Snack Bar. |

|[pic] |

|How much money will Lisa need to buy a cheeseburger, a drink and large fries? ________________ |

|[pic] |

|Show the amount Lisa spent by circling the bills and coins below. |

|[pic] |

| |

|How much money will Lisa have left if she pays with a $10 bill? ___________ |

|Grade 3 – 2005 OAT – Problem # 29 |

| |

|What coins could you receive for change if you use a $1.00 bill to pay for something that costs $0.59? |

|[pic] |

|Grade 4 – 2007 Test – Problem # 31 |

| | |

|Erik walked Mrs. Johnson’s dog each day for six days. He earned $1.25 each day. |A. $4.75 |

| |B. $6.25 |

|How much money did Erik earn? |C. $7.25 |

| |D. $7.50 |

|Grade 4 – 2006 OAT – Problem # 28 |

| | |

|Mrs. Thomas gave the store clerk $25.00 for a pair of jeans. She received $2.88 back |A. $21.12 |

|in change. |B. $22.12 |

| |C. $22.22 |

|What was the price of the jeans? |D. $23.22 |

|Grade 4 – 2006 OAT – Problem # 42 |

| |

|Gavin bought a puzzle that costs $6.35. He gave the clerk a $10 bill. |

| |

|How much change should Gavin receive? _______________________ |

| |

|Give an example of the bills and coins Gavin could receive for change. Use numbers, pictures or words to show your work.|

|Grade 4 – 2005 Practice Test – Problem # 1 |

| | |

|Camille buys a pair of shoes for $15.95. She gives the clerk $20.00. |A. $4.00 |

| |B. $4.05 |

|How much change should Camille receive? |C. $4.15 |

| |D. $5.05 |

|Grade 4 – 2005 Practice Test – Problem # 9 |

| | |

|Kimberly has $2.31 in one pocket and $1.94 in another. |A. $0.37 |

| |B. $1.37 |

|How much money does Kimberly have in both pockets? |C. $3.25 |

| |D. $4.25 |

G. Model and use commutative and associative properties for addition and multiplication.

3-11. Model and use the commutative and associative properties for addition and

multiplication.

|Grade 3 – 2006 OAT – Problem # 45 |

| | |

|Carole has 7 marbles. Ezra gives her 3 marbles. Tonya gave Carole 2 more marbles. The |A. 7 + (3 + 2) |

|total number of marbles that Carole has can be shown by (7 + 3) + 2. |B. (7 + 3) + (7 + 2) |

|This is the same as: |C. (7 + 3) + (3 + 2) |

|Grade 3 – 2005 OAT – Problem # 17 |

| | |

|The rectangular arrays show a number fact. |[pic] |

|[pic] | |

|Which number fact do they show? | |

H. Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication.

3-10. Explain and use relationships between operations, such as:

a. relate addition and subtraction as inverse operations;

b. relate multiplication and division as inverse operations;

c. relate addition to multiplication (repeated addition);

d. relate subtraction to division (repeated subtraction).

|Grade 3 – 2006 OAT – Problem # 41 |

| | |

|Which is another way of writing 6 + 6 + 6 + 6 + 6? |A. 5 x 6 |

| |B. 5 x 5 |

| |C. 6 x 4 |

I. Demonstrate fluency in multiplication facts with factors through 10 and corresponding divisions.

3-13. Demonstrate fluency in multiplication facts through 10 and corresponding division facts.

4-14. Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.

|Grade 3 – 2007 Test – Problem # 19 |

| | |

|Which has a product of 28? |A. 5 x 8 |

| |B. 6 x 6 |

| |C. 7 x 4 |

|Grade 4 – 2006 OAT – Problem # 1 |

| | |

|Ruth’s garden has 6 rows of strawberry plants. |A. 12 |

|There are 20 strawberry plants in each row. |B. 26 |

| |C. 80 |

|How many strawberry plants are in Ruth’s garden? |D. 120 |

J. Estimate the results of whole number computations using a variety of strategies, and judge the reasonableness.

2-13. Estimate the results of whole number addition and subtraction problems using front-end estimation, and judge the reasonableness of the answers. (Grade 2)

3-15. Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates.

4-9. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

|Grade 3 – 2006 OAT – Problem # 38 |

| |

|Is 300 a reasonable estimate for 726 – 192? |

| |

|Show or explain why or why not. |

|Grade 3 – 2005 OAT – Problem # 11 |

| | |

|Callie has 21 stuffed animals. Her sister has 24 stuffed animals. Which pair of |A. 10 and 20 |

|numbers could best be used to estimate the total number of stuffed animals? |B. 20 and 20 |

| |C. 30 and 30 |

|Grade 3 – 2005 Practice Test – Problem # 8 |

| | |

|Which is a reasonable estimate for the sum of 312 and 105? |A. 400 |

| |B. 500 |

| |C. 600 |

|Grade 4 – 2007 Test – Problem # 36 |

| | |

|There are about 525,600 minutes in a year. |A. 500,000 |

| |B. 525,000 |

|What is this number rounded to the nearest thousand? |C. 526,000 |

| |D. 530,000 |

|Grade 4 – 2006 OAT – Problem # 23 |

| | |

|The distance between three towns is shown. |A. 500 miles |

| |B. 600 miles |

|[pic] |C. 700 miles |

| |D. 800 miles |

|Estimate the distance from Kellogg to Fairfield. | |

K. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division of whole numbers.

3-12. Add and subtract whole numbers with and without regrouping.

3-14. Multiply and divide 2- and 3-digit numbers by a single-digit number, without remainders for division.

4-8. Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border). (Geometry and Spatial Sense)

4-6. Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as: 5 x 47 = 5 x 40 + 5 x 7 = 200+35 = 235.

4-7. Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.

4-12. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.

|Grade 3 – 2005 OAT – Problem # 15 |

|The school store sells pencils, pens and erasers. The picture shows the cost of each of these items. |

|[pic] |

|Becky bought 2 pencils, 5 pens and 2 erasers. How much money did Becky spend? |

| |

|Show or explain your answer using pictures, words or numbers. |

| |

|The next week Becky spent 85¢ in the store. Use the table below to show how she could spend exactly 85¢. |

|[pic] |

|Grade 3 – 2005 Practice Test – Problem # 13 |

| |

|In the Bean Bag Toss game a player can score the points shown. |

| |

|[pic] |

| |

|Max tossed three bean bags in the same hole and two bean bags in a second hole. |

| |

|What is the highest score that Max could receive for these five tosses? _____ |

|Show how you found your answer using pictures, words or numbers. |

| |

|Alissa also tossed five bean bags into the holes. She scored 35 points. |

|Show how Alissa could have gotten this score. |

|Grade 4 – 2007 Test – Problem # 6 |

| | |

|Aaron saved $60 to buy airplane models for his collection. The cost of each model with |A. 4 |

|tax included is $7. |B. 8 |

| |C. 9 |

|How many models can he buy? |D. 12 |

|Grade 4 – 2006 OAT – Problem # 33 |

| |

|A store sells rice in 3-pound and 5-pound bags. Jennie is responsible for packing 60 pounds of rice into the 3-pound |

|bags, 5-pound bags or a combination of 3-pound and 5-pound bags. She needs to pack all 60 pounds of rice. |

| |

|The prices for the bags of rice are shown in the chart. |

|[pic] |

|Show three ways Jennie can pack the 60 pounds of rice into bags. For each way, show the total number of bags for each |

|weight she will have packed. Show or explain your answer by using pictures, words or numbers. |

| |

|Show which of your three ways will make the most money when all the bags Jennie packs are sold. Explain your answer by |

|using pictures, words or numbers. |

L. Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers.

3-8. Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example:

a. Use conventional mathematical symbols to write equations for word problems involving multiplication.

b. Understand that, unlike addition and subtraction, the factors in multiplication and division may have different units; e.g., 3 boxes of 5 cookies each.

3-9. Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model. For example:

a. Translate contextual situations involving division into conventional mathematical symbols.

b. Explain how a remainder may impact an answer in a real-world situation; e.g., 14 cookies being shared by 4 children.

4-11. Develop and explain strategies for performing computations mentally.

4-13. Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.

4-14. Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.

|Grade 3 – 2007 Test – Problem # 10 |

| |

|Five children share 27 crayons. Each child gets the same number of crayons. |

| |

|How many crayons will each child get? |

| |

|How many crayons will be left over? |

| |

|[pic] |

|Grade 3 – 2005 OAT – Problem # 7 |

| | |

|Alicia has 90 stickers. She gives all of the stickers to 10 of her friends. Each |[pic] |

|friend gets the same number of stickers. Which number sentence shows how many stickers| |

|each friend gets? | |

|Grade 3 – 2005 OAT – Problem # 21 |

| | |

|Find the difference. 135 – 22 |A. 113 |

| |B. 132 |

| |C. 157 |

|Grade 3 – 2005 OAT – Problem # 25 |

| |

|Six children share 20 oranges. Each child gets the same number of oranges. |

| |

|[pic] |

| |

|How many oranges will each child get? |

|How many oranges will be left over? |

|Show or explain your answers using pictures, words or numbers. |

|Grade 3 – 2005 OAT – Problem # 39 |

| | |

|Martin has three boxes of erasers. Each box holds 12 erasers. How many erasers does he|A. 4 |

|have in all? |B. 15 |

| |C. 36 |

|Grade 3 – 2005 OAT – Problem # 41 |

| | |

|Mrs. Porter’s class collected 325 box tops. Mr. Smith’s class collected 234. How many |A. 559 |

|box tops were collected? |B. 569 |

| |C. 669 |

|Grade 4 – 2007 Test – Problem #46 |

| | |

|There were 1,479 people at the movie theater on Saturday and 1,753 people on Sunday. |A. 2,232 |

| |B. 3,132 |

|How many people went to the movie theater on Saturday and Sunday? |C. 3,222 |

| |D. 3,232 |

|Grade 4 – 2005 Practice Test – Problem # 5 |

| | |

|Shiloh has 823 pennies. Lester has 988 pennies. |A. 1,701 |

|How many pennies do Shiloh and Lester have together? |B. 1,711 |

| |C. 1,801 |

| |D. 1,811 |

|Grade 4 – 2005 Practice Test – Problem # 19 |

| | |

|Stamps are sold in rolls of 100 and books of 20. Zoe bought two rolls and eight books |A. 240 |

|of stamps. |B. 360 |

| |C. 960 |

|What is the total number of stamps Zoe bought? |D. 1,200 |

M. Add and subtract commonly used fractions with like denominators and decimals, using models and paper and pencil.

4-9. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

4-10. Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators.

|Grade 4 – 2006 OAT – Problem # 6 |

| | |

|One month Tony’s puppy grew 7/8 of an inch. The next month his puppy grew 5/8 of an |A. 2/8 |

|inch. |B. 35/64 |

| |C. 12/16 |

|How many inches did Tony’s puppy grow in two months? |D. 12/8 |

Mathematical Processes

A. Apply and justify the use of a variety of problem-solving strategies; e.g., make an organized list, guess and check.

B. Use an organized approach and appropriate strategies to solve multi-step problems.

C. Interpret results in the context of the problem being solved; e.g., the solution must be a whole number of buses when determining the number of buses necessary to transport students.

D. Use mathematical strategies to solve problems that relate to other curriculum areas and the real world; e.g., use a timeline to sequence events; use symmetry in artwork.

E. Link concepts to procedures and to symbolic notation; e.g., model 3 x 4 with a geometric array, represent one-third by dividing an object into three equal parts.

F. Recognize relationships among different topics within mathematics; e.g., the length of an object can be represented by a number.

G. Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation.

H. Recognize basic valid and invalid arguments, and use examples and counter examples, models, number relationships, and logic to support or refute.

I. Represent problem situations in a variety of forms (physical model, diagram, in words or symbols), and recognize when some ways of representing a problem may be more helpful than others.

J. Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language.

I. Use mathematical language to explain and justify mathematical ideas, strategies and solutions.

Multiple Choice:

|OAT – Grades 3 & 4 |

|Number, Number Sense, and Operations |

| |Grade |Test |No. |Answer |

| | |Year | | |

|A |3 |2005 |1 |A |

| |3 |2005* |10 |C |

| |4 |2007 |40 |B |

| |4 |2006 |17 |D |

| |4 |2006 |45 |C |

| |4 |2005* |11 |B |

|B |3 |2006 |17 |A |

| |3 |2005 |45 |C |

| |4 |2007 |10 |S.A. |

| |4 |2006 |10 |S.A. |

|C |3 |2007 |43 |B |

|D |3 |2006 |27 |A |

| |3 |2005* |2 |A |

| |4 |2006 |39 |B |

| |4 |2005* |14 |** |

|E |4 |2007 |16 |C |

| |4 |2006 |36 |B |

| |4 |2005* |17 |** |

|F |3 |2007 |33 |E.R. |

| |3 |2005 |29 |B |

| |4 |2007 |31 |D |

| |4 |2006 |28 |B |

| |4 |2006 |42 |S.A. |

| |4 |2005* |1 |B |

| |4 |2005* |9 |D |

|G |3 |2006 |45 |A |

| |3 |2005 |17 |A |

|H |3 |2006 |41 |A |

|I |3 |2007 |19 |C |

| |4 |2006 |1 |D |

|J |3 |2006 |38 |S.A. |

| |3 |2005 |11 |B |

| |3 |2005* |8 |A |

| |4 |2007 |36 |C |

| |4 |2006 |23 |B |

|OAT – Grades 3 & 4 |

|Number, Number Sense, and Operations |

| |Grade |Test |No. |Answer |

| | |Year | | |

|K |3 |2005 |15 |E.R. |

| |3 |2005* |13 |** |

| |4 |2007 |6 |B |

| |4 |2006 |33 |E.R. |

|L |3 |2007 |10 |S.A. |

| |3 |2005 |7 |C |

| |3 |2005 |21 |A |

| |3 |2005 |25 |S.A. |

| |3 |2005 |39 |C |

| |3 |2005 |41 |A |

| |4 |2007 |46 |D |

| |4 |2005* |5 |D |

| |4 |2005* |19 |B |

|M |4 |2006 |6 |D |

* Half-Length Practice Test

** Scoring Rubric Not Released

Short Answer & Extended Response Rubrics

Grade 3

|NNS – Benchmark L |

|2007 OAT – Grade 3 – Problem # 10 Scoring Guidelines: |

|Points |Student Response |

|2 |The focus of this task is using a variety of methods for computing with whole numbers. The response provides the |

| |correct number of crayons for each child and the correct number of crayons left over. The answers are supported with|

| |pictures, words, or numbers. |

| | |

| |Exemplar Response: |

| |• 5, 2. 27 ÷ 5 = 5 r 2 |

| |• 5, 2. 5 + 5 + 5 + 5 + 5 + 2 = 27 |

| |• 5 2/5 |

| |[pic] |

|1 |The response provides evidence of using a variety of methods for computing with whole numbers; however, the solution|

| |is incomplete or slightly flawed. |

| | |

| |Sample answer: |

| |For example, the response may: |

| |• State 5 crayons and 2 remaining crayons, but give no explanation or strategy. |

| |• Show a correct strategy but include an error that results in an incorrect number of crayons. |

|0 |The response provides no evidence of using a variety of methods for computing with whole numbers. |

| | |

| |Sample answer: |

| |For example, the response may: |

| |• State only that each child gets crayons. |

| |• Restate the information provided in the item. |

| |• Be blank or give irrelevant information. |

|NNS – Benchmark F |

|2007 OAT – Grade 3 – Problem # 33 Scoring Guidelines: |

|Points |Student Response |

|4 |The response will consist of the following: |

| |• clearly indicates $7 |

| |• uses a correct strategy |

| |• circles money consistent with the first answer |

| |• finds change consistent with the first answer |

| | |

| |Possible correct strategies: |

| |• I added the numbers in my head. |

| |• Draws the correct money for the 3 items. |

| | |

| |NOTE: Omission or incorrect placement of dollar signs will not penalize the student; however, wrong decimal |

| |placement is penalized. |

|3 |The response correctly addresses three of the four bullets. |

|2 |The response correctly addresses two of the four bullets. |

|1 |The response correctly addresses one of the four bullets. |

|0 |The response does not correctly address any of the bullets. |

|NNS – Benchmark J |

|2006 OAT – Grade 3 – Problem #38 Scoring Guidelines: |

|Points |Student Response |

|2 |Correct response is indicated as NO and a valid estimation strategy to find an estimate between 500 and 600, |

| |inclusive. |

| |Examples of correct responses: |

| |• No, because 700 – 200 = 500. |

| |• No, 726 – 192 = 534 and that’s not close to 300. |

| |• 700 – 200 = 500 (nearest hundred) |

| |• 700 –100 = 600 (front-end estimation) |

| |• 730 – 190 = 540 (nearest ten) |

| |• 725 – 200 = 525 (friendly numbers) |

|1 |Correct response is indicated as NO with no strategy or support given. OR Response is given as YES or is not given |

| |with a valid estimation strategy. The estimation strategy may have an error. |

|0 |Response does not state NO and finds an exact answer without an explanation. OR Response indicates no understanding|

| |of the concept or task. |

|NNS – Benchmark K |

|2005 OAT – Grade 3 – Problem # 15 Scoring Guidelines: |

|Points |Student Response |

|4 |The response indicates: |

| |• correct total |

| |• correct strategy or work for first part |

| |• complete table with number of items and costs |

| |• table totals 85¢ |

| | |

| |Examples of correct answers: |

| |Part A: |

| |10¢ +10¢ +15¢ +15¢ +15¢ + 15¢ +15¢ + 25¢ + 25¢ = 145¢ or 1.45 or $1.45 |

| |OR |

| |2 × 10 = 20; 5 × 15 = 75; 2 ×25 = 50; 20 + 75 +50 = 145¢ or 1.45 or $1.45 |

| |Part B: (any one of the following tables is correct) |

| |[pic] |

|3 |The response completes 3 of the 4 bullets correctly. |

|2 |The response completes 2 of the 4 bullets correctly. |

|1 |The response completes 1 of the 4 bullets correctly. |

|0 |The response completes no bullets correctly. |

|NNS – Benchmark L |

|2005 OAT – Grade 3 – Problem # 25 Scoring Guidelines: |

|Points |Student Response |

|2 |The response states each child gets 3 oranges with 2 left over and shows correct work or strategy. |

| |Examples of correct responses: |

| |• grouping 6 sets of 3 oranges |

| |• writing a description |

| |[pic] |

| |• repeated addition |

| |• numbers oranges 1 – 6 (groups of 6) |

| |• labels oranges with 6 letters (groups of 6) |

| |OR |

| |The response states that each child gets an equal amount with the correct amount left over is also correct. For |

| |example: 2 each with 8 left over or 1 each with 14 left over. |

|1 |The response states 3 oranges each with or without the remainder and no or incomplete explanation/strategy. OR The |

| |response shows a correct strategy with an arithmetic error. |

|0 |Response is incorrect or irrelevant. |

Short Answer & Extended Response Rubrics

Grade 4

|NNS – Benchmark B |

|2007 OAT – Grade 4 – Problem #10 Scoring Guidelines: |

|Points |Student Response |

|2 |The focus of this task is generating equivalent forms of fractions and decimals. The response provides a fraction |

| |and a decimal that represent the number of students wearing hats. |

| |6/8, 0.75 |

| |¾, 0.75 |

|1 |The response shows evidence of generating equivalent forms of fractions and decimals; however, the response may be |

| |incomplete or slightly flawed. |

| | |

| |1 point sample answer: |

| |For example, the response may: |

| |• Provide a correct fraction but fail to provide an appropriate decimal. |

| |• Provide a correct decimal but fail to provide an appropriate fraction. |

|0 |The response provides inadequate evidence of generating equivalent forms of fractions and decimals. The response |

| |may have major flaws or errors in reasoning. |

| | |

| |0 point sample answer: |

| |For example, the response may: |

| |• State that 0.6 of the students are wearing hats and fail to provide an appropriate fraction. |

| |• Be blank or give irrelevant information. |

| |• Restate information given in the stem. |

|NNS – Benchmark B |

|2006 OAT – Grade 4 – Problem # 10 Scoring Guidelines: |

|Points |Student Response |

|2 |The focus of this task is identifying and describing equivalent forms of fractions that are equal to one. The |

| |response provides a fraction equal to one and provides adequate support to show or explain why the fraction is equal|

| |to one. |

| |• 4/4. It is equal to one because the numerator is the number of parts and the denominator is the number of parts |

| |in all. Since they are both 4 it means you have 4 parts and there are 4 parts in all, so it’s equal to one. |

| |4/4 .[pic] |

|1 |The response shows partial evidence of identifying and describing equivalent forms of fractions that are equal to |

| |one; however, the solution is incomplete or slightly flawed. For example, the response may: |

| |• Provide a fraction equal to one, but give no or a flawed explanation of why it is equal to one. |

| |• State an appropriate explanation but does not indicate a fraction. E.g., a fraction is equal to one when the |

| |numerator is equal to the denominator. |

|0 |The response provides inadequate evidence of an understanding of identifying and describing equivalent forms of |

| |fractions that are equal to one. The response provides an explanation with major flaws and errors of reasoning. For |

| |example, the response may: |

| |• State a fraction that is not equal to one and does not provide an adequate explanation. E.g., 4/4 |

| |• Be blank or state unrelated statements. |

| |• Recopy information from the stem. |

|NNS – Benchmark K |

|2006 OAT – Grade 4 – Problem # 33 Scoring Guidelines: |

|Points |Student Response |

|4 |The focus of the task is using appropriate operations with whole numbers to solve a multi-step problem and showing |

| |three different solutions. The response provides three correct combinations of 3 and 5 pound bags that result in a |

| |total of 60 pounds AND shows which combination makes the most money with a correct strategy or work. |

| |Sample response: |

| |• She can pack: 20 3-pound bags because 3 × 20 = 60 OR 12 5-pound bags because 5 × 12 = 60 OR 10 3-pound bags and |

| |6 5-pound bags because 10 × 3 plus 6 × 5 = 60. She makes the most money when she puts all the rice into the 3 pound |

| |bags since that combination has a value of $80 and the other two combinations have a value of $72 and $76. |

| |See table below for other possible combinations and costs. |

| |[pic] |

|3 |The response provides evidence of using appropriate operations with whole numbers to solve a multi-step problem and |

| |showing three different solutions; however, the solution may contain a slight error, a flaw or a vague explanation. |

| |For example, the response may: |

| |• Show three correct combinations of bags, but incorrectly identifies the one of greatest value due to a minor |

| |calculation error. |

| |• Show three combinations, one of which is incorrect, but correctly finds the one that makes the most based on |

| |their combinations. |

|2 |The response provides partial evidence of using appropriate operations with whole numbers to solve a multi-step |

| |problem and showing three different solutions; however, the solution is incomplete and/or contains minor flaws. |

| |For example, the response may: |

| |• Only show two correct combinations and show a strategy for finding which has the greatest value with minor flaws|

| |or errors. |

|1 |The response provides minimal evidence of using appropriate operations with whole numbers to solve a multi-step |

| |problem and showing three different solutions. The response has major flaws and errors in reasoning. |

| |For example, the response may: |

| |• State that the most expensive bag would be $80. |

| |• State at least two combinations of bags equaling 60 pounds correctly. |

|0 |The response provides inadequate evidence of using appropriate operations with whole numbers to solve a multi-step |

| |problem and showing three different solutions. |

| |For example, the response may: |

| |• Show one correct combination. |

| |• State that the bags will cost any correct amount without showing work or stating if it is the most expensive or |

| |not. |

| |• Be blank or make unrelated statements. |

| |• Recopy information given in the stem. |

|NNS – Benchmark F |

|2006 OAT – Grade 4 – Problem #42 Scoring Guidelines: |

|Points |Student Response |

|2 |The focus of the task is solving problems involving counting money and making change. The response provides the |

| |amount of change AND provides a correct list of bills and coins with an adequate explanation or work. Sample Correct|

| |Responses: |

| |• Gavin gets back $3.65. He receives three $1 bills, two quarters, one dime and one nickel, and 10 – 6.35 = 3.65. |

| |• $10 - $6.35 = 3.65 is the change that Gavin gets. Gavin gets back three $1 bills, six dimes and one nickel |

| |because this makes $3.65. |

| |• $3.65 is the change |

| |[pic] |

|1 |The response shows partial evidence of solving problems involving counting money and making change; however, the |

| |solution may be incomplete or slightly flawed. For example, the response may: |

| |• State a correct amount of change, but not list a correct example of the bills and coins he could receive as |

| |change. |

| |• State an incorrect amount of change, but correctly list a combination of bills and coins that total the given |

| |amount of change. |

|0 |The response provides inadequate evidence of solving problems involving counting money and making change. The |

| |response provides an explanation with major flaws and errors of reasoning. For example, the response may: |

| |• State an incorrect amount of change and show an incorrect amount of bills and coins he could receive as change. |

| |• Be blank or state unrelated statements. |

| |• Recopy information from the stem. |

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Number, Number Sense and Operations Standard

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