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Deep Dive into Math Shift 3RIGOR

Understanding Rigor in the Common Core State Standards for Mathematics

Using the 2013-2014 Course Descriptions

Shift #3: RigorWhat is meant by rigor?

• The CCSSM require a balance of: Solid conceptual

understanding Procedural skill and fluency Application of skills in

problem solving situations

• Pursuit of all three requires equal intensity in time, activities, and resources.

RIGORConceptual U

nderstanding

Fluency

Application

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Today’s AgendaRigor in the CCSSM

We will...

1. Discuss and Find evidence of Rigor within the Common Core Standards

2. Look specifically at fluency and the role it plays in math instruction

3. Discuss conceptual understanding and differentiation

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What the Student Does… What the Teacher Does…

•Spends time practicing, with intensity, skills (in high volume)

•Pushes students to know basic skills at a greater level of fluency•Focuses on the listed fluencies by grade level

•Uses high quality problem sets, in high volume

Fluency: What is it? Skill in carrying out proceduresflexibly, accurately, efficiently and appropriately

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How do we address rigor while building fluency?

http://www.engageny.org/resource/nti-november-2012-rigor-breakdown-sprints-fluency-in-action

Rigor Breakdown - Sprints - Fluency in Action(6:07)

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Deep Understanding What is it? Comprehension of Mathematical

Concepts

What the Student Does… What the Teacher Does…

•Shows mastery of material at a deep level

•Articulates mathematical reasoning

•Demonstrates deep conceptual understanding of priority concepts

•Responds to student answers by eliciting student explanations and reasoning•Ensures that all students reach understanding

•Views concepts being taught as a coherent continuum instead of as isolated topics

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ApplicationWhat is it? Bringing mathematical skill and

understanding together and applying it to real-world situations and in new contexts

What the Student Does… What the Teacher Does…

•Applies math in other content areas and situations, as relevant

•Chooses the right math concept to solve a problem when not necessarily prompted to do so

•Applies math content to other content areas (i.e. science)•Provides students with real world experiences and opportunities to apply what they have learned

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Rigorous Group Discussion

1. Share examples of relevant, real-world experiences you use to make important connections to the concepts you teach.

2. How do these applications relate back to both fluency and conceptual understanding?

Rigor Addressed in the Standards• Conceptual Understanding:

3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• Procedural Skill and Fluency:5.NBT.2.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

• Application:4.MD.3.7 …Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems… 9

Rigor Requires Balance

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Conceptual Understanding +

Procedural Skill and Fluency +

Application

=RIGOR

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Evidence of Rigor in the Standardskey words within the standards

Conceptual Understanding Understand Recognize Interpret

Describe Explain UseRelate Represent IdentifyJustify Solve

Procedural Skill and FluencyFluently Fluency

ApplicationSolve Word Problem Real World Problem ApplyMathematical Problem Model(ing)

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RIGOR is a Balancing Act

RIGOR

Fluency

Application

ConceptualUnderstanding

Grade Standard Key FluencyK MACC.K.OA.1.5 Add/subtract within 51 MACC.1.OA.3.6 Add/subtract within 10

2 MACC.2.OA.2.2MACC.2.NBT.2.5

Add/subtract within 20Add/subtract within 100 (pencil and paper)

3 MACC.3.NBT.1.2MACC.3.OA.3.7

Add/subtract within 1,000Multiply/divide within 100

4MACC.4.2.4

Critical Area #1Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers

5MACC.5.NBT.2.5Critical Area #1

Multi-digit multiplicationDeveloping fluency with addition and subtraction of fractions

6 MACC.6.NS.2.2MACC.6.NS.2.3

Multi-digit divisionMulti-digit decimal operations

7 MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r

8 MACC.8.EE.3.8b Solve simple 22 systems by inspection

Key Fluencies

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Kindergarten Fluency ProgressionRepresent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations (K.OA.1.1).

Solve addition and subtraction word problems (K.OA.1.2)

Fluently add and subtract within 5 (K.OA.1.5)

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Grade 1 Fluency Progression

Add and subtract within 20 (1.OA.3).

Demonstrate fluency for addition and subtraction within 10 (1.OA.3.6).

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Grade 2 Fluency Progression

Fluently add and subtract within 20 using mental strategies (2.OA.2.2)

.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (2.NBT.2.5)

.

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Grade 3 Fluency Progression

Apply properties of operations as strategies to multiply and divide (3.OA.2.5)

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction (3.NBT.1.2).

Interpret products and quotients of whole numbers (3.OA.1.1-3.OA.1.4)

Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (3.OA.3.7).

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Grade 4 Fluency Progression

Fluently add and subtract multi-digit whole numbers using the standard algorithm (4.NBT.2.4).

Develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems (Critical Area #1).

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Grade 5 Fluency Progression

Fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.2.5).

Develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them (Critical Area #1)

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Rethinking Rigor

• Building Confidence through Problem Solving• Grades 3-5, Math, Number Fluency

https://www.teachingchannel.org/videos/building-math-confidence

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Group DiscussionWhere was the rigor?

How do you differentiate instruction in

your classroom?

What instructional shifts should occur in our classrooms?