Common Core State Standards for Mathematics: Coherence

Grade 5

Essential Questions

• How and why were the Common Core State Standards developed and by whom?

• What are the 3 shifts in math instruction in the CCSS?

• Why the need for Coherence?

• How is Coherence reflected in the classroom?

• What are the next steps in implementing Coherence?

Overview of the Common Core State Standards

Rationale for CCSS

• Declining US competitiveness with other developed countries

• NAEP performance that is largely flat over the past 40 years in 8th grade

• Slight improvement on NAEP performance at the 4th grade level

• Slight decline on NAEP performance at the high school level

• High rates of college remediation

Background of CCSS

• Initiated by the National Governor’s Association (NGA) and Council of Chief State School Officers (CCSSO) with the following design principles:

• Result in College and Career Readiness

• Based on solid research and practice evidence

• Fewer, higher (greater DOK), and clearer standards

College Math Professors Feel HS Students Today are Not Prepared for

College Math

What The Disconnect Means for Students

• Nationwide, many students in two-year and four-year

colleges need remediation in math.

• Remedial classes lower the odds of finishing the degree or program.

• Need to set the agenda in high school math to prepare more students for postsecondary education and training.

The Common Core State Standards

Require Three Instructional Shifts in Mathematics

• Focus: Focus strongly where the standards focus.

• Coherence: Think across grades and link to major

topics.

• Rigor: In major topics, pursue conceptual

understanding, procedural skill and fluency, and

application.

Shift 2: Coherence

The Standards are designed around coherent progressions from grade to

grade. Principals and teachers carefully connect the learning across grades so

that students can build new understanding onto foundations built in previous years. Teachers can begin to

count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an

extension of previous learning.

William McCallum on Coherence

Coherence: Think Across GradesExample:

Fractions“The coherence and sequential nature of

mathematics dictate the foundational skills that are necessary for the

learning of algebra. The most important

foundational skill not presently developed

appears to be proficiency with fractions (including decimals, percents, and negative fractions). The

teaching of fractions must be acknowledged as

critically important and improved before an increase in student

achievement in algebra can be expected.”

Final Report of the NMA Panel, 2008

12

CCSS Fraction Progression

Coherence: Think Across Grades

Coherence: Link to Major Topics Within Grades

Engaging with the shifts: Coherence Cards

In front of you lie a set of colored cards and a large poster. Each colored set of cards represents one theme, such as number lines or properties of operations, and each card has an individual standard printed on it. Your goal as a team is to correctly place the cards within each grade in an accurate progression. The only parameters are that no two of the same color cards will appear in the same grade, and that there will not necessarily be one card in each grade for each progression.

Examples of Opportunities for Connections among Standards,

Clusters or Domains

Directions: Solve the following problem. Think about how the problem connects to the standard and how it looks different than what we currently do in the classroom.

5.NF.4 & 5.NF.5 The work that students do in multiplying fractions extends their understanding of the operation of multiplication. For example, to multiply a/b x q (where q is a whole number or a fraction), students can interpret a/b x q as meaning a parts of a partition of q into b equal parts. This interpretation of the product leads to a product that is less than, equal to or greater than q depending on whether a/b < 1, a/b = 1 or a/b > 1, respectively.

Examples of Major Within-Grade Dependencies

Convert like measurement units within a given measurement system (5.MD.1) depends on

students’ abilities to apply and extend previous understandings of multiplication and division to

multiply and divide fractions. (5.NF.3)Directions: Solve the following problem. Think about how the problem connects to the standard and how it looks different than what we currently do in the classroom.

a. Five brothers are going to take turns watching their family's new puppy. How much time will each brother spend watching the puppy in a single day if they all watch him for an equal length of time? Write your answer -Using only hours -Using a whole number of hours and a whole number of minutes -Using only minutes

b. Mrs. Hinojosa had 75 feet of ribbon. If each of the 18 students in her class gets an equal length of ribbon, how long will each piece be? Write your answer -Using only feet -Using a whole number of feet and a whole number of inches -Using only inches

c. Wesley walked 11 miles in 4 hours. If he walked the same distance every hour, how far did he walk in one hour? Write your answer -Using only miles -Using a whole number of miles and a whole number of feet -Using only feet

Math ShiftsWhat is this shift?

Why this shift?Opportunities Challenges

2. Coherence: Think across grades

Group Discussion