CTP Mathematics CCSSM Alignment Study
ERB is pleased to announce that we engaged WestEd in an alignment study of the CTP mathematics items to the Common Core State Standards for Mathematics (CCSSM). WestEd, a national educational organization, has been a leader in moving research into practice through research and development programs; by providing training and technical assistance; and by working with policymakers and practitioners at state and local levels to carry out school improvement and innovative change efforts. WestEd is at the forefront of providing alignment services for states, districts, and several nonprofit organizations including ACT and College Board. WestEd also serves as the Project Management Partner for the multistate Smarter Balanced Consortium.
CCSSM Alignment Results
We received strong alignment results for the CTP mathematics items:
 98% of the CTP mathematics items were found to align at either a strong or a partial degree to the CCSSM.
 Over 70% of the CTP mathematics items were strongly aligned to the CCSSM.
 55% of the CTP mathematics items were rated at DOK 2 (described below).
Criteria Used to Align the CTP Mathematics Items to the CCSSM
WestEd content experts analyzed the correspondence between the CTP mathematics items and the CCSSM in grades 112. They rated the degree of match between the items and the CCSSM and also rated the cognitive complexity of the prompts.
Degree of Match Criteria
 Strong: The item assesses a fundamental skill or concept as explicitly stated in the standard.
 Partial: The item addresses the standard at a lower level of complexity or does not cover the full intent of the standard.
 None: The item does not address any of the content of the standard.
Depth of Knowledge (DOK) Using Webb’s Scale for Mathematics
 Level 1: includes recalling information such as a fact, definition, term, or a simple procedure.
 Level 2: includes engaging in mental processing that requires using more than one step to solve a problem.
 Level 3: requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels.
 Level 4: requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.
In Detail: CTP Mathematics Items Aligned to the following CCSSM
The ERB mathematics item pool consists of 2,384 items in an online environment, and 247 paperbased items. The items are organized within files identified as Algebra, Math Levels 110, Quantitative Reasoning (QR) and Math.
The CCSSM includes both content and process standards. The content standards include the mathematical knowledge and skills students should learn; the process standards (or practices) specify the mathematical ways of thinking students should develop while learning mathematics content.
Findings show that the CTP items cover a number of different CCSSM standards across a range of different grade levels (Grade 1HS). Table 1 in Appendix A on pages 45 shows a sample of the results for the online bank, including Algebra, Math, Levels 110, and Quantitative Reasoning 310; and for the paperbased bank, including Quantitative Reasoning, Math and Algebra.
The CCSSM practices describe the nature of the learning experiences, thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics. The eight CCSSM mathematical practices include:
1.Making sense of problems and persevering in solving them.
2.Reasoning abstractly and quantitatively.
3.Constructing viable arguments and critiquing the reasoning of others.
4.Modeling with mathematics
5.Using appropriate tools strategically.
6.Attending to precision.
7.Looking for and making use of structure.
8.Looking for and expressing regularity in repeated reasons.
Table 2 in Appendix B on page 6 shows the number of CTP items aligned to the CCSSM practices.
Findings for the alignment of CTP items to the CCSSM practices show:
 46% of the items align to Practice 6—Attending to precision and to Practice 7—Looking for and making use of structure
 23% of the items align to Practice 2—Reasoning abstractly and quantitatively and Practice 1—Making sense of problems and persevere in solving them
 4% of the items address Practice 8—Looking for and expressing regularity in repeated reasons and Practice 4—Modeling with mathematics
What does this mean for my school?
 The alignment of the ERB CTP mathematics items to the CCSS is a very valuable resource for teachers. It provides teachers with flexibility in how and when they assess their students, as well as assessing a particular standard.
 The findings of this study provide guidelines for ERB to bring the CTP mathematics items into full alignment with the CCSS and beyond by 2015. All CCSS mathematics content standards and practices will be represented.
 ERB looks forward to collaborating with our member schools as we enhance our CTP mathematical services. ERB has partnered with top national experts in assessment design and currently plans to launch a formative complement to our CTP Mathematics using Khan Academy as a next step instructional component. The details of this formative solution will be outlined over the next few months with an expected project launch date of fall 2014.
APPENDIX A
Table 1: Highest Percent of CCSSM Grade Level Standards in CTB Levels.
Findings show that the items in all CTP levels align to many different CCSSM standards. For example, in Level 1 (below), four items (7%) align to the same standard; the remaining items align to different standards. The CTP paperbased items are highlighted in light grey.
CCSS Grade Levels

% of CCSS  CCSS CODE 
CCSS Standard  

Algebra  Grades 5HS  11%  7.EE.4  Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 
Level 1  Grades 16  7%  1.G.1  Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size). 
Level 2  Grades 18  9%  3.OA.3  Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 
Level 3  Grades 28  10%  3.OA.3  Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 
Level 4  Grades 18  6%  4.OA.3  Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. 
Level 5  Grades 18  8%  7.EE.4  Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 
Level 6  Grades 2HS  6%  6.SP.5.c  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 
Level 7  Grades 1HS  6%  6.RP.3c  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 
Level 8  Grades 3HS  5%  6.SP.5.c  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 
Level 9  Grades 3HS  8%  6.SP.5.c  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 
Level 10  Grades 3HS  4%  6.G.1  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real world math problems. 
QR3  Grades 18  11%  4.OA.5  Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 
QR4  Grades 18  8%  4.OA.5  Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 
QR5  Grades 28  7%  4.OA.5  Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 
QR6  Grades 2HS  7%  4.MD.3  Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 
QR7  Grades 28  7%  6.EE.2  Write, read, and evaluate expressions in which letters stand for numbers. 
QR8  Grades 38  7%  6.G.1  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 
QR9  Grades 3HS  11%  7.EE.4  Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 
QR10  Grades 4HS  13%  7.SP.7  Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies. 
QR  Grades 1HS  11%  4.OA.5  Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 
Math  Grades 1HS  4%  8.G.7  Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. 
Algebra  Grades 8HS  1%  8.NSS  Know that numbers that are not rational are called irrational. 
APPENDIX B
Table 2 below shows the coding of CTP items to the eight CCSSM practices. The CTP paperbased items are highlighted in light grey.
Table 2: Number of CTP Items Aligned to the CCSS Practices
CCSS Mathematical Practices  

1  2  3  4  5  6  7  8  
Algebra  X  X  X  X  
Level 1  X  X  X  
Level 2  X  X  X  X  X  
Level 3  X  X  X  X  X  X  
Level 4  X  X  X  X  X  
Level 5  X  X  X  X  X  X  X  
Level 6  X  X  X  X  X  
Level 7  X  X  X  X  X  X  X  
Level 8  X  X  X  X  X  X  
Level 9  X  X  X  X  X  X  
Level 10  X  X  X  X  
QR3  X  X  X  X  
QR4  X  X  X  X  
QR5  X  X  X  X  
QR6  X  X  X  X  
QR7  X  X  X  X  X  X  X  
QR8  X  X  X  X  X  X  X  
QR9  X  X  X  X  X  X  
QR10  X  X  X  X  
QR  X  X  X  
Math  X  X  X  
Algebra 
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