COMMON CORE AS S ES S MEN T COMP ARIS ON F OR MATHEMATICS G RAD E 3 J u n e 2013

\

P r ep a r ed b y: D e la w a re D e p a rtm e n t o f Ed u c atio n Accou n t a bilit y Resou r ces Wor kgr ou p 401 F eder a l St r eet , Su it e 2 Dover , DE 19901

11/27/2013 Document Control #: 2013/05/05

Common Core Assessment Comparison for Mathematics – Grade 3

Table of Contents INTRODUCTION ................................................................................................................... 1 OPERATIONS AND ALGEBRAIC THINKING (OA) ............................................................... 6 Cluster: Represent and solve problems involving multiplication and division. .................. 7 3.OA.1 – Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. ............................................................................................................... 7 3.OA.2 – Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. .......................................................................................................................................... 9 3.OA.3 – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Glossary, Table 2, of CCSS document.) .................................................................................................................. 10 3.OA.4 – Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?. .......................................................... 13

Cluster: Understand properties of multiplication and the relationship between multiplication and division. ................................................................................................. 14 3.OA.5 – Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by multiplying 3 × 5 = 15 then multiplying 15 × 2 = 30, or by multiplying 5 × 2 = 10 then multiplying 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) .................................................................................................................. 14 3.OA.6 – Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8................................................................ 15

Cluster: Multiply and divide within 100. ............................................................................ 16 3.OA.7 – Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By end of Grade 3, know from memory all products of one-digit numbers. ......................................................................................................................................... 16

Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. ........................................................................................................................ 18 3.OA.8 – Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order.) ......................................................................................................... 18 11/27/13 Document Control #: 2013/05/05

Page | i

Common Core Assessment Comparison for Mathematics – Grade 3

NUMBER AND OPERATIONS IN BASE TEN (NBT) ............................................................ 22 Cluster: Use place value understanding and properties of operations to perform multidigit arithmetic. (A range of algorithms may be used.) ..................................................... 23 3.NBT.1 – Use place value understanding to round whole numbers to the nearest 10 or 100. ..... 23 3.NBT.2 – Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.) ........................................................................................................... 24

NUMBER AND OPERATIONS—FRACTIONS (NF) ............................................................. 25 Cluster: Develop understanding of fractions as numbers. ................................................ 26 3.NF.1 – Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. .......... 26 3.NF.2 – Understand a fraction as a number on the number line; represent fractions on a number line diagram. .................................................................................................................................. 29

MEASUREMENT AND DATA (MD) .................................................................................... 32 Cluster: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. ................................................................................ 33 3.MD.1 – Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram...................................................................... 33 3.MD.2 – Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems [problems involving notions of "times as much:' see Glossary, Table 2, in CCSS document.]) ......................................................................................................................... 34

Cluster: Represent and interpret data. ............................................................................... 35 3.MD.3 – Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. ........................................................................................ 35 3.MD.4 – Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. .............................................................. 37

Cluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.............................................................................................. 39 3.MD.6 – Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). .......................................................................................................................... 39 3.MD.7 – Relate area to the operations of multiplication and addition. ........................................ 41

11/27/13 Document Control #: 2013/05/05

Page | ii

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. ........................................................... 44 3.MD.8 – Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter. ........................................................................................................................ 44

GEOMETRY (G) ................................................................................................................. 47 Cluster: Reason with shapes and their attributes. ............................................................. 48 3.G.1 – Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. ................................................................................................................................. 48 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape. ........................................................................................ 50

ANSWER KEY AND ITEM RUBRICS................................................................................... 54 Operations and Algebraic Thinking (OA)........................................................................... 55 Number and Operations in Base Ten (NBT) ...................................................................... 64 Number and Operations—Fractions (NF) ......................................................................... 65 Measurement and Data (MD) .............................................................................................. 68 Geometry............................................................................................................................... 75

PERFORMANCE TASK ....................................................................................................... 80 3.OA.8 – Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order.) ......................................................................................................... 81 3.NBT.3 – Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.) ................................................................................................................................. 81 3.MD.3 – Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. ......................................................................................... 81

11/27/13 Document Control #: 2013/05/05

Page | iii

Common Core Assessment Comparison for Mathematics – Grade 3

INTRODUCTION The purpose of this document is to illustrate the differences between the Delaware Comprehensive Assessment System (DCAS) and the expectations of the next-generation Common Core State Standard (CCSS) assessment in Mathematics. A side-by-side comparison of the current design of an operational assessment item and the expectations for the content and rigor of a next-generation Common Core mathematical item are provided for each CCSS. The samples provided are designed to help Delaware’s educators better understand the instructional shifts needed to meet the rigorous demands of the CCSS. This document does not represent the test specifications or blueprints for each grade level, for DCAS, or the next-generation assessment. For mathematics, next-generation assessment items were selected for CCSS that represent the shift in content at the new grade level. Sites used to select the next-generation assessment items include:  Smarter Balanced Assessment Consortium 

Partnership of Assessment of Readiness for College and Career



Illustrative Mathematics



Mathematics Assessment Project

Using released items from other states, a DCAS-like item, aligned to the same CCSS, was chosen. These examples emphasize the contrast in rigor between the previous Delaware standards, known as Grade-Level Expectations, and the Common Core State Standards. Section 1, DCAS-Like and Next-Generation Assessment Comparison, includes content that is in the CCSS at a different “rigor” level. The examples are organized by the CCSS. For some standards, more than one example may be given to illustrate the different components of the standard. Additionally, each example identifies the standard and is separated into two parts. Part A is an example of a DCAS-like item, and Part B is an example of a next-generation item based on CCSS. Section 2 includes at least one Performance Task that addresses multiple aspects of the CCSS (content and mathematical practices). How to Use Various Aspects of This Document  Analyze the way mathematics standards are conceptualized in each item or task.  Identify the instructional shifts that need to occur to prepare students to address these more rigorous demands. Develop a plan to implement the necessary instructional changes.  Notice how numbers (e.g., fractions instead of whole numbers) are used in the sample items.  Recognize that the sample items and tasks are only one way of assessing the standard.  Understand that the sample items and tasks do not represent a mini-version of the nextgeneration assessment.  Instruction should address “focus,” coherence,” and “rigor” of mathematics concepts.  Instruction should embed mathematical practices when teaching mathematical content.

11/27/13 Document Control #: 2013/05/05

Page | 1

Common Core Assessment Comparison for Mathematics – Grade 3

 

For grades K–5, calculators should not be used as the concepts of number sense and operations are fundamental to learning new mathematics content in grades 6–12. The next-generation assessment will be online and the scoring will be done electronically. It is important to note that students may not be asked to show their work and therefore will not be given partial credit. It is suggested when using items within this document in the classroom for formative assessments, it is good practice to have students demonstrate their methodology by showing or explaining their work.

Your feedback is welcome. Please do not hesitate to contact Katia Foret at [email protected] or Rita Fry at [email protected] with suggestions, questions, and/or concerns. * The Smarter Balanced Assessment Consortium has a 30-item practice test available for each grade level (3-8 and 11) for mathematics and ELA (including reading, writing, listening, and research). These practice tests allow students to experience items that look and function like those being developed for the Smarter Balanced assessments. The practice test also includes performance tasks and is constructed to follow a test blueprint similar to the blueprint intended for the operational test. The Smarter Balanced site is located at: http://www.smarterbalanced.org/.

11/27/13 Document Control #: 2013/05/05

Page | 2

Common Core Assessment Comparison for Mathematics – Grade 3

Priorities in Mathematics

Grade

11/27/13 Document Control #: 2013/05/05

Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2

Addition and subtraction, measurement using whole number quantities

3–5

Multiplication and division of whole numbers and fractions

6

Ratios and proportional reasoning; early expressions and equations

7

Ratios and proportional reasoning; arithmetic of rational numbers

8

Linear algebra

Page | 3

Common Core Assessment Comparison for Mathematics – Grade 3

Common Core State Standards for Mathematical Practices

Essential Processes for a Productive Math Thinker

Mathematical Practices 1. Make sense of problems and persevere in solving them

6. Attend to precision

Reasoning and Explaining

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

11/27/13 Document Control #: 2013/05/05

Student Dispositions:

Teacher Actions to Engage Students in Practices:

     

      

Have an understanding of the situation Use patience and persistence to solve problem Be able to use different strategies Use self-evaluation and redirections Communicate both verbally and written Be able to deduce what is a reasonable solution

        

Communicate with precision—orally and written Use mathematics concepts and vocabulary appropriately State meaning of symbols and use them appropriately Attend to units/labeling/tools accurately Carefully formulate explanations and defend answers Calculate accurately and efficiently Formulate and make use of definitions with others Ensure reasonableness of answers Persevere through multiple-step problems

              

Create multiple representations Interpret problems in contexts Estimate first/answer reasonable Make connections Represent symbolically Talk about problems, real-life situations Attend to units Use context to think about a problem Ask questions Use examples and counter examples Reason inductively and make plausible arguments Use objects, drawings, diagrams, and actions Develop ideas about mathematics and support their reasoning Analyze others arguments Encourage the use of mathematics vocabulary

  

Provide open-ended and rich problems Ask probing questions Model multiple problem-solving strategies through Think-Aloud Promote and value discourse Integrate cross-curricular materials Promote collaboration Probe student responses (correct or incorrect) for understanding and multiple approaches Provide scaffolding when appropriate Provide a safe environment for learning from mistakes Encourage students to think aloud Develop explicit instruction/teacher models of thinking aloud Include guided inquiry as teacher gives problem, students work together to solve problems, and debrief time for sharing and comparing strategies Use probing questions that target content of study Promote mathematical language Encourage students to identify errors when answers are wrong

      

Develop opportunities for problem-solving strategies Give time for processing and discussing Tie content areas together to help make connections Give real-world situations Demonstrate thinking aloud for students’ benefit Value invented strategies and representations More emphasis on the process instead of on the answer

    

 Create a safe environment for risk-taking and critiquing with respect  Provide complex, rigorous tasks that foster deep thinking  Provide time for student discourse  Plan effective questions and student grouping  Probe students

Page | 4

Common Core Assessment Comparison for Mathematics – Grade 3

Seeing Structure and Generalizing

Modeling and Using Tools

Mathematical Practices

Students:

Teacher(s) promote(s) by:

4. Model with mathematics

 Realize that mathematics (numbers and symbols) is used to solve/work out real-life situations  Analyze relationships to draw conclusions  Interpret mathematical results in context  Show evidence that they can use their mathematical results to think about a problem and determine if the results are reasonable—if not, go back and look for more information  Make sense of the mathematics

 Allowing time for the process to take place (model, make graphs, etc.)  Modeling desired behaviors (think alouds) and thought processes (questioning, revision, reflection/written)  Making appropriate tools available  Creating an emotionally safe environment where risk-taking is valued  Providing meaningful, real-world, authentic, performancebased tasks (non-traditional work problems)  Promoting discourse and investigations

5. Use appropriate tools strategically

 Choose the appropriate tool to solve a given problem and deepen their conceptual understanding (paper/pencil, ruler, base ten blocks, compass, protractor)  Choose the appropriate technological tool to solve a given problem and deepen their conceptual understanding (e.g., spreadsheet, geometry software, calculator, web 2.0 tools)  Compare the efficiency of different tools  Recognize the usefulness and limitations of different tools

 Maintaining knowledge of appropriate tools  Modeling effectively the tools available, their benefits, and limitations  Modeling a situation where the decision needs to be made as to which tool should be used  Comparing/contrasting effectiveness of tools  Making available and encouraging use of a variety of tools

7. Look for and make use of structure

 Look for, interpret, and identify patterns and structures  Make connections to skills and strategies previously learned to solve new problems/tasks independently and with peers  Reflect and recognize various structures in mathematics  Breakdown complex problems into simpler, more manageable chunks  “Step back” or shift perspective  Value multiple perspectives

 Being quiet and structuring opportunities for students to think aloud  Facilitating learning by using open-ended questions to assist students in exploration  Selecting tasks that allow students to discern structures or patterns to make connections  Allowing time for student discussion and processing in place of fixed rules or definitions  Fostering persistence/stamina in problem solving  Allowing time for students to practice

8. Look for and express regularity in repeated reasoning

   

 Providing rich and varied tasks that allow students to generalize relationships and methods and build on prior mathematical knowledge  Providing adequate time for exploration  Providing time for dialogue, reflection, and peer collaboration  Asking deliberate questions that enable students to reflect on their own thinking  Creating strategic and intentional check-in points during student work time

Identify patterns and make generalizations Continually evaluate reasonableness of intermediate results Maintain oversight of the process Search for and identify and use shortcuts

For classroom posters depicting the Mathematical Practices, please see: http://seancarberry.cmswiki.wikispaces.net/file/detail/1220math.docx 11/27/13 Document Control #: 2013/05/05

Page | 5

Common Core Assessment Comparison for Mathematics – Grade 3

OPERATIONS AND ALGEBRAIC THINKING (OA)

11/27/13 Document Control #: 2013/05/05

Page | 6

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Represent and solve problems involving multiplication and division. 3.OA.1 – Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. DCAS-Like

1A A zookeeper feeds a polar bear 21 fish each day for 7 days. Which number sentence should the zookeeper use to find the total number of fish he will feed the polar bear during the 7 days? A. B. C. D.

    Next-Generation

1B There is a large mural made of colored tiles at the entrance of Rena’s school. The mural is made with 48 square tiles and is 12 tiles wide. 12 tiles wide

? tiles high

Select from the numbers below and write the numbers in the boxes to show a number sentence that can be used to find how many tiles the mural is.

4

6

8

10

12

48

=

11/27/13 Document Control #: 2013/05/05

Page | 7

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.1 – Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. DCAS-Like

2A What is one way to tell how many blocks are below?

A. B. C. D. Next-Generation

2B There is a large mural made of colored tiles at the entrance of Rena’s school A part of the mural was damaged in a heavy storm as shown. The part of the mural that was not damaged is 5 tiles long and 4 tiles high. Rena wants to know how many tiles need to be replaced. Pick from the tiles below to label the model. Then, fill in the blank with the number of tiles that need to be replaced in the mural.

4

4

4

5

5

7

4

7

5

10

Part to be replaced



=4

12

tiles need to be replaced in the mural. 11/27/13 Document Control #: 2013/05/05

Page | 8

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.2 – Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. DCAS-Like

3A Cali had 65 pounds of sand. The sand was measured equally into bags. Each bag held 10 pounds of sand. How many full bags of sand did Cali have? A. B. C. D.

4 5 6 7 Next-Generation

3B A farmer has 20 apple trees that he needs to plant in his orchard. He wants to plant the trees in rows. Each row will have an equal number of trees. a. Draw pictures or diagrams to show two different ways he can plant the trees. Write a number sentence that could be used to find the number of rows for each picture. b. If he has one extra apple tree in his orchard and he still wants the trees planted in equal rows, how would this change the way he plants the trees in his orchard? Draw a picture to show how the orchard would look with the extra apple tree. Write a number sentence that could be used to find the number of rows for this picture.

11/27/13 Document Control #: 2013/05/05

Page | 9

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.3 – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Glossary, Table 2, of CCSS document.) DCAS-Like

4A Mr. Martinez divided 24 students into 8 equal groups. Each group has  students. Which number sentence is true? A. B. C. D.

    Next-Generation

4B Marcus has 36 marbles. He is putting an equal number of marbles into 4 bags. For A-D, choose Yes or No to indicate whether each number sentence could be used to find the number of marbles Marcus puts into each bag.

 

a. b. c. d.

 

11/27/13 Document Control #: 2013/05/05

 Yes

 No

 Yes

 No

 Yes

 No

 Yes

 No

Page | 10

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.3 – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Glossary, Table 2, of CCSS document.) DCAS-Like

5A Mr. Brown bought 6 towels. All the towels were the same price. The total cost was $84. How much money did each towel cost? A. B. C. D.

$11 $14 $78 $504 Next-Generation

5B a. Maria cuts 12 feet of ribbon into 3 equal pieces so she can share it with her two sisters. Use words, numbers, and/or pictures to show how long each piece is.

b. Maria has 12 feet of ribbon and wants to wrap some gifts. Each gift needs 3 feet of ribbon. Use words, numbers, and/or pictures to show how many gifts she can wrap using the ribbon.

11/27/13 Document Control #: 2013/05/05

Page | 11

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.3 – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Glossary, Table 2, of CCSS document.) DCAS-Like

6A Mr. Guzman bought 48 doughnuts packed equally into 4 boxes. Which number sentence shows how to find the number of doughnuts in each box?

   

A. B. C. D.

Next-Generation

6B a. Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend? Write an equation. Put one number in each box and one symbol in the circle to write an equation to find out how much money Juanita spent at the fair.

=

b. Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy? Write an equation. Put one number in each box and one symbol in the circle to write an equation to find out how many games Nita bought.

=

11/27/13 Document Control #: 2013/05/05

Page | 12

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.4 – Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?. DCAS-Like

7A What number belongs in the ? below to make the number sentence true?

? A. B. C. D.

6 7 8 9 Next-Generation

7B a. Fill in the blanks below with whole numbers greater than 1 that will make the number sentences true. 1.

72

2. 3. 4.

8

5. b. If the product of two whole numbers each greater than 1 is 63, what could the two whole numbers be? ______, ______

11/27/13 Document Control #: 2013/05/05

Page | 13

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5 – Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by multiplying 3 × 5 = 15 then multiplying 15 × 2 = 30, or by multiplying 5 × 2 = 10 then multiplying 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) DCAS-Like

8A Mary wrote the expression value.

. Susan wrote a different expression with the same

Which expression could be the one that Susan wrote? A. B. C. D. Next-Generation

8B For each expression in A-D, answer Yes or No if the expression is equivalent to the product of 7 and 9. a.

 Yes

 No

b. c.

 Yes  Yes

 No  No

d.

 Yes

 No

11/27/13 Document Control #: 2013/05/05

Page | 14

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.6 – Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. DCAS-Like

9A and A. B. C. D.

. What is ?

4 5 8 15 Next-Generation

9B At the garden center, Mr. Garcia is putting plant pots into boxes ready to take to market. The diameter of each plant pot is 3 inches. Each box measures 9 inches by 15 inches.

3 inches

9 inches

15 inches

a. How many pots can Mr. Garcia arrange along the side of the box that measures 15 inches? _______________ b. How many pots can Mr. Garcia arrange along the side of the box that measures 9 inches? _______________ c. How many pots will the box hold? Show how you figured this out.

11/27/13 Document Control #: 2013/05/05

_______________

Page | 15

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Multiply and divide within 100. 3.OA.7 – Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By end of Grade 3, know from memory all products of one-digit numbers. DCAS-Like

10A Which sign goes in the box to make the number sentence true?  A. B. C. D. Next-Generation

10B For the following items, choose Yes or No to show whether putting the number 7 in the box would make the equation true. a.



 Yes  No

b. c.

 

 Yes  No  Yes  No

11/27/13 Document Control #: 2013/05/05

Page | 16

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.7 – Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By end of Grade 3, know from memory all products of one-digit numbers. DCAS-Like

11A The figure below is a model for the multiplication sentence.

Which division sentence is modeled by the same figure? A. B. C. D. Next-Generation

11B For the following items, choose Yes or No if the equation is true. a.

 Yes

 No

b.

 Yes

 No

c.

 Yes

 No

d.

 Yes

 No

e.

 Yes

 No

11/27/13 Document Control #: 2013/05/05

Page | 17

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.8 – Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order.) DCAS-Like

12A Mrs. Jones has 30 students in her class. To complete a project, each student will need 2 sheets of white paper and 1 sheet of blue paper. How many total sheets of paper will Mrs. Jones need? A. B. C. D.

30 33 60 90 Next-Generation

12B A roller skating team has 10 members. Each team member has 2 skates. Each skate has 4 wheels. What is the total number of skate wheels that the team has? __________ wheels Show how you got your answer.

11/27/13 Document Control #: 2013/05/05

Page | 18

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.8 – Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order.) DCAS-Like

13A Randy had 40 pieces of candy. He wanted to share them with 7 friends. He gave each friend 4 pieces of candy. How many pieces of candy did Randy have left after he was done sharing? A. B. C. D.

12 pieces 16 pieces 18 pieces 28 pieces Next-Generation

13B Jasper used the expression feet.

to find the area of a rectangular closet floor, in square

On the grid, draw a rectangle that Jasper could have measured.

a. What is the area of the closet floor? __________ square feet 

Jasper has 200 square feet of tile. He will use some of the tile to cover the closet floor. He will only use whole tiles.

11/27/13 Document Control #: 2013/05/05

Page | 19

Common Core Assessment Comparison for Mathematics – Grade 3

b. How many square feet of tile will Jasper have left after covering the closet floor with tile? __________ square feet  Jasper wants to use some of the remaining tile to cover the floor of a kitchen. The kitchen is 12 feet long and 12 feet wide. c. Does Jasper have enough tiles to cover the kitchen floor? Circle your answer: YES

NO

Show how you got your answer. You may use drawings, mathematical expressions/equations, and words.

11/27/13 Document Control #: 2013/05/05

Page | 20

Common Core Assessment Comparison for Mathematics – Grade 3

3.OA.8 – Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order.) DCAS-Like

14A Two groups of students from Barry Elementary School were walking to the museum when it began to rain. The 6 students in Mr. Roberson’s group shared the 4 large umbrellas they had with Ms. Fray’s group of 14 students. If the same number of students were under each umbrella, how many students were under each umbrella? You may use the space below to draw a picture of the problem.

A. B. C. D.

5 10 18 21 Next-Generation

14B On Monday morning the baker baked 4 full trays of cookies to sell in his shop. Each tray had the same number of cookies on it. Here is what the trays looked like on Monday evening.

a. How many cookies did the baker sell on Monday? Show how to use multiplication equations and other operations, if needed, to show how you solved the problem. Refer to the trays of cookies in your explanation. b. Use words or equations to explain how you know your total is correct.

11/27/13 Document Control #: 2013/05/05

Page | 21

Common Core Assessment Comparison for Mathematics – Grade 3

NUMBER AND OPERATIONS IN BASE TEN (NBT)

11/27/13 Document Control #: 2013/05/05

Page | 22

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.) 3.NBT.1 – Use place value understanding to round whole numbers to the nearest 10 or 100. DCAS-Like

15A What is 1413 rounded to the nearest hundred? A. B. C. D.

1000 1400 1410 1500 Next-Generation

15B When rounding to the nearest ten: a. What is the smallest whole number that will round to 50? __________ b. What is the largest whole number that will round to 50? __________ c. How many different whole numbers will round to 50? __________ When rounding to the nearest hundred: d. What is the smallest whole number that will round to 500? __________ e. What is the largest whole number that will round to 500? __________ f. How many different whole numbers will round to 500? __________

11/27/13 Document Control #: 2013/05/05

Page | 23

Common Core Assessment Comparison for Mathematics – Grade 3

3.NBT.2 – Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.) DCAS-Like

16A Which number has a 4 in the tens place and a 4 in the hundreds place? A. B. C. D.

6424 6244 4462 6442 Next-Generation

16B The number sentence below can be solved using tens and ones. ?

tens and

?

ones.

Select one number from each column to make the number sentence true.

Tens  2  6  8  9

11/27/13 Document Control #: 2013/05/05

Ones  2  5  10  12

Page | 24

Common Core Assessment Comparison for Mathematics – Grade 3

NUMBER AND OPERATIONS—FRACTIONS (NF)

11/27/13 Document Control #: 2013/05/05

Page | 25

Common Core Assessment Comparison for Mathematics – Grade 3

Cluster: Develop understanding of fractions as numbers. 3.NF.1 – Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. DCAS-Like

17A Which two fraction models are equal? A.

B.

C.

D.

Next-Generation

17B Bryce drew this picture:

Then he said, “This shows that is greater than .” a. What was his mistake? Draw a picture that shows why

is greater than .

b. Chose True or False for each equation: 

>

 True  False






 True  False

