Common Core State Standards

3-5 Mathematics

M&M Share

• Red – something about your summer• Orange – something about your family

• Brown – something you are looking forward to• Blue – a dream, a wish, or a goal

• Green – something your group should know about you• Yellow – your “favorites”

1. Carefully open your bag of M&Ms.2. Without looking, take out one M&M.3. Starting with the person wearing the most blue,

share with your group based the M&M color prompts below:

M&M Math• Sort your M&Ms by color.• Arrange your M&Ms into “bars” to visually compare amounts.• Using graph paper, create a bar graph to illustrate this

comparison.• Now discuss the following questions with your elbow partner:

– How many reds and greens do you have altogether?– Compare the two colors you have the most of. How many more

_____________ do you have?– Compare your blue and orange. Which do you have fewer (or less)

of? How many fewer (or less)?

M & M Math (continued)

•Now combine your M & M data with a partner.

•Use a “scaled “legend and graph your combined totals of M & Ms.

•Answer questions guided by teacher.

Measurement and Data – MD

Look at your MD Standards.What do you think?

What Makes These Math Standards Different? P. 3

Fewer, focused standards -- with clarity & specificity. No more “mile high and inch deep.”

Coherence – William Shmidt and Richard Houang (2002) have said that content and curricula are coherent if they are “articulated over time as a sequence of topics and performances that are logical and reflect, where appropriate, the sequential or hierarchical nature of the disciplinary content from which the subject matter derives.” In other words, what and how students are taught should reflect not only the topics that fall within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline.

Designed to equip students to be college and career ready and globally competitive.

Kendra bought trays of flowers toplant in her front yard. Each traycontained 6 flowers.Which could be the total number offlowers she bought?A. 63B. 160C. 266D. 312

5th grade math question taken from the Mississippi Curriculum Test Second Edition (MCT2) Practice Test:

Carl bikes home from school at four o’clock. It takes about a quarter of an hour. In the evening, he’s going back to school because the class is having a party. The party starts at 6 o’clock. Before the class party starts, Carl has to eat dinner. When he comes home from school, his grandmother, who is also his neighbor, calls. She wants him to bring in her post before he bikes over to the class party. She also wants him to take her dog for a walk, then to come in and have a chat. What does Carl have time to do before the party begins? Write and describe below how you have reasoned.

Question taken from the exam given at Year 5 in Sweden:

Key Advances

Focus and coherence• Focus on key topics at each grade level.• Coherent progressions across grade levels.Balance of concepts and skills• Mathematical understanding* and procedural skill are equally important.

*Mathematical Understanding = Ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular math statement is true or where a particular mathematical rule comes from.*“Processes and Proficiencies”

Mathematical practices• Foster reasoning and sense-making in mathematics. Build on NCTM process standards of

problem solving, reasoning and proof, communication, representation, and connections… AND on adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition.

*Conceptual understanding = comprehension of math concepts, operations, and relations.*Procedural Fluency = skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.*Productive Disposition = habitual inclination to see math as sensible, useful, and worthwhile.

College and career readiness• Level is ambitious but achievable.

8 Standards for Mathematical PracticeP. 6-8

1. Make sense of problems and persevere in solving them.– Use concrete objects and pictures to help solve

problems.– Check answers using a different method.– Continually ask themselves, “Does this make

sense?” and make adjustments when it doesn’t make sense.

2. Reason abstractly and quantitatively. Creating a coherent representation of the problem

and being able to explain it Attending to meaning , not just the computation

3. Construct viable arguments and critique reasoning of others. Construct arguments using concrete objects,

drawings, diagrams, and actions Listen to the arguments of others, decide

whether they make sense, and ask questions to clarify or improve arguments

4. Model with mathematics. Apply mathematics to solve problems in

everyday life (i.e., writing an addition equation to describe a situation)

5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning. Notice mathematical patterns and repetition

Design and Organization

Standards for Mathematical Content/Practices• K-8 standards presented by grade level• Organized into domains that progress over

several grades• Related objectives are “clustered” together• Grade introductions give 2–4 focal points at

each grade level

Design and Organization (P. 5)

Content standards define what students should understand and be able to do

Clusters are groups of related standards Domains are larger groups that progress across grades

Design and OrganizationGrade Level Overviews

Let’s Get Familiar with Abbreviations

CC = Counting & Cardinality (K)

OA = Operations & Algebraic Thinking

NBT = Numbers & Operations in Base TenNF = Numbers and Operations -- Fractions

MD = Measurement & Data

G = Geometry

How do we reference the standards in lesson plans?

Let’s Practice!

3. OA. 4

4.NBT. 2a

G.5.3

What are the implications for

classroom teachers?

Frequent Use of Manipulatives

Learning Takes Place in Small, Flexible

Groups

How will I provide for small group instruction?

How will I use manipulatives?

What part of the standard will I teach?

Planning for Common Core Math Lessons/Instruction

K-2 Update

K Number Core – Numbers & Operations in Base Ten – Counting & recognizing to 100, comparing within 10, counting sets to 20, joining & separating situations (combined sets), etc.

1st Number Core – Numbers & Operations in Base Ten – Adding & Subtracting whole numbers within 20 (add to, take from, put together, take-apart), compare situations to develop meaning for +/-, Add within 100, Subtract multiples of 10, Apply properties of operations as strategies to add and subtract, Determine unknowns, extend counting sequence to 120

2nd Extend Base 10 – counting in 5s, 10s, multiples of 100 and ones. Use and understand to 1000 using base 10. FLUENTLY +/- within 20

How do I unpack the standards?

• Circle verbs.• Underline nouns and noun phrases.• Bullet.

Thoughts About MultiplicationThe CORE is Building the Concept Progressively—

It’s more about the process, not the memorization, in K-2. Students need a strong number core to make sense of the patterns in multiplication and to be able to apply prior learning for new strategies.

• KINDERGARTEN: K.CC.1: Count to 100 by ones and tens.

• FIRST GRADE: • 1.NBT.2c and 1.NBT.4: Working with multiples of ten.

• SECOND GRADE: • 2.OA.3, 4: Work with equal groups to gain foundations for

multiplication

3rd-4th-5th – REFLECT ON YOUR STANDARDS

Spend the next __ minutes thinking about the standards for the grade you teach. Record the 1 you want extra discussion on (on sticky note).

OA – Operations & Algebraic ThinkingNBT – Numbers & Operations in Base TenNF – Numbers & Operations – FractionsMD – Measurement & DataG – Geometry

Final Thoughts

1. K-2 is implementing CCSS for RLA and Mathematics 2011-2012, AND 3-5 can expect implementation for 2012-2013.

2. How can 3-5 teachers “get ahead of the curve” next year?

Small Group Math Instruction Speaking/Listening/Writing About Mathematics – Strategies,

Explanation of Processes – Mathematical Understanding Focus on Fluency – of Processes and Computation Increase Problem-Solving – through experiences interesting to and

relevant to the uniqueness of your class FREQUENT (DAILY) USE OF MANIPULATIVES