Posts Tagged "fill in the gap"

What’s the Difference? Comprehensive vs. Supplemental Materials

20150327 21st wordleRecently, Learning List’s reviewers were confronted with an interesting question: How do we characterize materials as comprehensive or supplemental? Generally speaking, we understood that a comprehensive product would address all, or nearly all, of the standards for a particular grade and subject area, and a supplemental product would focus on a particular set of standards. However, our reviewers found that some materials that were designed to for supplemental instruction (e.g., test preparation resources) addressed nearly all of the standards for a given course. This prompted us to examine our thinking about what the labels “comprehensive” and “supplemental” mean in terms of instructional materials.

To clarify our understanding, we looked to how some states and districts define these terms. For example, California defines comprehensive, or “basic”, instructional materials to be “instructional materials that are designed for use by pupils as a principal learning resource and that meet in organization and content the basic requirements of the intended course (Educ. Code § 60010.a). In California, supplementary materials are materials that provide more complete coverage of a subject in a course, address diverse learning needs, and support the use of technology in the classroom (Educ. Code § 60010.l). Similarly, Carroll County Public Schools in Maryland defines comprehensive materials as “the primary source of instruction for students in a course” (emphasis in the original) and supplemental materials as “those items used to extend and support instruction and address the needs of all learners.”

Both definitions of comprehensive materials clarify that a comprehensive material is one that supports instruction for a course’s full curriculum and is provided for all students. Such materials would include broad, deep discussions of content; remediation and enrichment activities; formative and summative assessments; as well as teacher resources. Although neither definition specifies that a comprehensive resource must address 100% of the standards for a course, it seems reasonable that a “principal learning resource” or a “primary source of instruction” would need to be highly aligned to standards. Both definitions of supplemental materials indicate that supplemental resources are not designed to be the sole instructional resource for a course. Instead, supplementary materials complement, enrich, or extend the content of comprehensive resources. It seems reasonable that supplemental products will vary in terms of their alignment to standards. Some products may focus on a narrow set of standards, while others, such as test preparation resources, may provide a brief review of all standards.

[Source: Learning List]

[Source: Learning List]

Learning List’s Fill in the Gap™  tool helps educators identify supplemental materials that will extend content and address gaps in comprehensive resources. For each product in Learning List’s database that is not 100% aligned to standards, the Fill in the Gap tool suggests other products that address the missing standards. Suggested products may include both comprehensive and supplemental materials that address the missing standards. This allows educators identify the particular product or combination of products that meets the needs of their students.

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Which Products Are Least Aligned to CCSS Mathematics Standards?

[Source: Education Week]

[Source: Education Week]

Last week, Education Week hosted a webinar addressing the mathematics standards that were most challenging for students to master. The webinar identified broad groups of standards in measurement, modeling with mathematics, fractions, and statistics and explained how these concepts build on one another. The presentation illustrated a trajectory in which elementary students who did not master early concepts continued to struggle with more advanced concepts in later grades. For example, students who did not master concepts such as length in elementary school also struggled with line graphs and coordinate grids in middle school.

[Video courtesy of]

[Video courtesy of]

This analysis prompted Learning List to think about the Common Core mathematics products we’ve reviewed. In particular, we wondered which mathematics standards were least aligned in the products we’ve reviewed. We analyzed our data to identify the CCSSM standards that were not addressed in at least half (50%) of the products for which we’ve verified CCSS alignment.

Our analysis did not identify any standards at grades K-5 for which 50% or more of products were not aligned. Individual products were not aligned to some standards, but no one standard in any grade level was consistently not aligned in 50% or more of the products.

At the middle school level, our analysis identified two standards that 50% or more of products did not address:

  • At grade 6, we have reviewed 12 products; 58.3% of these products did not address CSCCM 6.SP.5: Summarize numerical data sets in relation to their context.
  • At grade 8, we have reviewed 12 products ; 50% of these products did not address CCSSM 8.G.5: Use formal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

At the high school level, we identified four standards for Algebra I and three standards for Algebra II that were not addressed by 50% of products:

  • For Algebra I, of the eight products we have reviewed:
    • 50% did not address CCSSM A-REI.4: Solve quadratic equations in one variable.
    • 50% did not address CCSSM F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    • 50% did not address CCSSM F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    • 50% did not address CCSSM F-LE.1: Distinguish between functions that can be modeled with linear functions and with exponential functions.
  • For Algebra II, of the four products we have reviewed:
    • 50% were not aligned to CCSSM A-SSE.1: Interpret expressions that represent quantity in terms of its context.
    • 50% were not aligned to CCSSM A-REI.11: Explain why the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/ or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
    • 50% were not aligned to CCSSM F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

The results of our analysis indicate that publishers have greater difficulty meeting the CCSSM in high school algebra courses.  If a specific instructional material does not align to 100% of the CCSM standards, Learning List has a key feature, Fill-in-the Gap™,  that identifies other products that align to the remaining standards. If needed, this enables educators to use at least two instructional materials that, in the aggregate, would align to 100% of the CCSM standards.

In a subsequent post, we will examine our TEKS data to identify the least aligned mathematics standards in the products we’ve reviewed. We welcome your comments or questions about this topic; please send comment/question to

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April 2021