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Common Core State Standards for Mathematics: Coherence

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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?

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.

CCSS Place Value Progression

K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones.

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

1.NBT.4 Add within 100 – Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten.

1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less.

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

2. NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

2.NBT.6 Add up to four two-digit numbers using strategies based on place value.

2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

K

1

2

Coherence: Link to Major Topics Within Grades

Example: Number and Operations in Base Ten 2.NBT

Use place value understanding and properties of operations to add and subtract.

Example: Measurement 2.MD

Work with time and money.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Coherence Card Activity

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 on card in each grade for each progression.

NOTE: It may be helpful to first identify the theme for each set of cards, so that you collectively understand each strand that you are working with.

Engaging with the Shift: Investigate Coherence in the Standards with Respect to Multiplication.

In the space below, copy all of the standards related to multiplication and note how coherence is evident in these standards. Note also standards that are outside of the Operations and Algebraic Thinking domain but are related to, or in support of, multiplication.

Examples of Opportunities for Connections among Standards, Clusters or Domains

Extending students’ understanding of the base-ten system is essential for future work with numbers. It is critical that students at this grade are able to compose and decompose numbers in order to add and subtract fluently.

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.

Louis wants to give $15 to help kids who need school supplies. He also wants to buy a pair of shoes for $39. If Louis gets $1 every day for his allowance, how many days will it take him to save enough money for both? Explain how you know.

Examples of Major Within-Grade Dependencies

Students must begin work with place value and properties of operations to add and subtract (2.NBT) at or near the very start of the year to allow time for understanding and fluency to develop. Note that work with time and money (2.MD) should be integrated throughout the year.

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.

Jamir has collected some pennies in a jar. Recently, he added coins other than pennies to his jar. Jamir reached his hand into the jar and pulled out this combination:

- Jamir wants to count the total value of these coins. What coin do you suggest he start with? Why would Jamir want to start counting with this coin?
- What is the total value of these coins? Write a number sentence that represents the total value of the coins.
- Jamir reached into the jar again and was surprised to pull out a different combination of coins with the same total value as before. Draw a collection of coins that Jamir could have pulled from the jar. Write a number sentence that represents the total value of the coins.

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