Tuesday, January 8, 2013

Mathematics Curriculum Frameworks - resource guide

This recently updated guide (available at: http://www.doe.mass.edu/mcas/alt/resources.html) is intended for the MCAS Alt audience but has rich uses for all teachers of mathematics looking for scaffolding and entry points in instruction.  From the guide:
"Introduction The 2012 version of the Resource Guide to the 2011 Massachusetts Curriculum Frameworks for Students with Disabilities (“the 2012 Resource Guide”) incorporates the Common Core State Standards for Mathematics, plus unique mathematics standards approved for Massachusetts students into a guide for instructing students with disabilities who are performing below the expectations for their grade-level peers. While the curriculum framework defines the concepts, skills, and content that should be taught and learned by all students in each grade, the Resource Guide also identifies “entry points” for each standard that allow educators to teach the skills needed for students who are performing below grade-level expectations to approach the grade level standard. It is especially suited for instructing students with significant disabilities who take the MCAS Alternate Assessment (MCAS-Alt) because it aligns less complex skills and content with grade-level subject matter, and allows students to progress along a continuum as they approach grade-level complexity."

The guide outlines entry points ranging from less to more complex for each of the K-8 content standard cluster headings.  If you are not familiar with the term "cluster heading" here is what they look like for Grade 7 Mathematics (page 60 of http://www.doe.mass.edu/frameworks/math/0311.pdf) 
with DOMAINS and 8 CLUSTER HEADINGS 
Ratios and Proportional Relationships 
  • Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
  • Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations
  • Use properties of operations to generate equivalent expressions.
  • Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry
  • Draw, construct and describe geometrical figures and describe the relationships between them.
  • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability
  • Use random sampling to draw inferences about a population.
  • Draw informal comparative inferences about two populations.
  • Investigate chance processes and develop, use, and evaluate probability models.

The resource guide first shows the cluster and standards as written: (e.g. page 92 of the guide)
Grade 7
Cluster
Standards as written
Use properties of operations to generate equivalent expressions.
7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Then outlines possible entry points, which can be looked to for content/instruction modifications and/or differentiation (e.g. page 93 of the guide).
Possible ENTRY POINTS to Learning Standard(s)


                        Less Complex                                             More Complex


     The student will:
     The student will:
     The student will:
Use properties of operations to generate equivalent expressions.
¨       Solve expressions involving addition and subtraction with positive and negative whole numbers, fractions, and decimals (e.g., (1/4 + 1/2) - 1/8)
¨       Solve expressions involving addition and subtraction with positive and negative whole numbers, fractions, and decimals with letters representing unknown numbers given the value of the unknown number (e.g., (x + 1/2) - 1/8 = 5/8)

See entry points for earlier grades in this or a related cluster that are challenging and use age-appropriate materials


¨       Solve expressions involving multiplication with positive and negative whole numbers, fractions, and decimals (e.g., (.56 - .28) + .73)
¨       Solve expressions involving multiplication with numbers and with letters representing unknown numbers given the value of the unknown number (e.g., (.56 - y) + .73 = 1.01)
¨       Demonstrate the commutative property of addition using manipulatives, tables, charts, and measurement models
¨       Demonstrate the commutative property of multiplication using manipulatives, tables, charts, and area models
¨       Demonstrate the associative property of addition using manipulatives, charts, and measurement models
¨       Demonstrate the associative property of multiplication using manipulatives, tables, charts, and area models
¨       Solve expressions involving one or more operations with positive and negative whole numbers, fractions, and decimals (e.g., 4 (6 - .42) + 7.3)
¨       Solve expressions involving one or more operations with numbers and with letters representing unknown numbers given the value of the unknown number (e.g., 4 (6 - .42) + w = 29.62)
¨       Match the commutative property of addition with numerical expressions (e.g., which two expressions show the commutative property of addition: 21 + 9 = 9 + 21, 10 + 2 + 1 = 1 + 2 + 10, 13 + 3 = 16, 4 + 7 = 4 + 3 + 4?)
¨       Match the commutative property of multiplication with numerical expressions (e.g., which two expressions show the commutative property of multiplication: 11 x 5 = 5 x 11, 4 x 5 x 6 = 6 x 5 x 4, 12 x 3 = 36, 9 x 5 = 45 x 1?)
¨       Match the associative property of addition with numerical expressions that exemplify the property (e.g., (96 + 56) + 44 = 96 + (56 + 44))



Please share past, present or future uses of this guide with me via comments on this blog or email ngordon@doe.mass.edu

2 comments:

  1. What a great resource for all teachers. Thank you for highlighting it. We'll start using it at our school as we continue to align to the new standards.

    ReplyDelete
  2. Let me know how it goes! If you are willing perhaps even share some examples?

    ReplyDelete