GRADES K – 2

ATOMIC CONFERENCE

NOVEMBER 29, 2011

Kathy St. Onge Ann Spinelli Mary Santilli Marcia Ferreira

Making Sense of The CT Mathematics Standards

(Common Core State Standards)

Intent of the Common Core

Same goals for all students

Coherence

Focus

Clarity, rigor and specificity

Opportunities for broadening the discussion about the teaching and learning of mathematics

45 states have adopted (as of December 2011)

CCSS Assessment Projects

SBAC

SMARTER Balanced Assessment Consortium 30 states

- http://www.k12.wa.us/smarter/

PARCC (Partnership for the Assessment of Readiness for College and Careers)

25 states- http://www.achieve.org/PARCC

“These Standards are not intended to be new names for old ways of doing business.”

CCSSM, p. 5

Organization of the CCSS

Standards for Mathematical Practice

Math Content StandardsDomains

Clusters

Standards

Connecting the Practices to the Content

Standards for Mathematical Practices

8 Mathematical Practices

Related to the NCTM Process Standards (2000) and the Strands of Mathematical Proficiency (Adding It Up, 2001)

The standards for mathematical practices are located in the front of the mathematics standards and within the “nature of mathematics” section at each grade level. 

The standards for mathematical practice illustrate the connection between 21st century skills and mathematical content and instruction.

The standards for mathematical practices should be considered when creating curricula, assessments, and professional development for teachers, and administrators.

Standards for Mathematical Practice

“…describe the varieties of expertise that mathematics

educators at all levels should seek to develop in their students.”

Standards forMathematical Practice

Mathematically Proficient Students Will…

Adapted from Inside Mathematics

Standards for Mathematical Practice

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

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7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning

4. Model with mathematics

5. Use appropriate tools strategically

Reasoning and explaining

Modeling and using tools

Seeing structure and generalizing

1. Make Sense of Problems and Persevere in Solving Them

Engage in problem solving on a regular basis

Foster a “productive disposition” - build success early on

Involve students in sharing solutions, methods, and reasoning

Frame the class environment to encourage student interaction and conversation – math discourse

Allow students to “struggle” with the mathematical tasks – avoid rescuing too soon to diminish the cognitive load

Emphasize equivalent representations of a given situation or mathematical relationship

2. Reason Abstractly and Quantitatively

Teach concepts in context – symbols have meaning

Base instruction on making sense and select practice that involves the application of concepts being learned

Emphasize reasoning as opposed to only learning procedures

Allow students to develop a representation of mathematical problems on a regular basis

Mathematical Problem x  x  x  x 

4

Decontextualize Represent as symbols, abstraction

Refer back to the situation   Contextualize

5       2 =?

3. Construct Viable Arguments and Critique the Reasoning of Others

Encourage interaction and conversation on a regular basis

Use problem-based activities – rich tasks Practice the language of “argument,” conjecture, and

discourse while students are engaged in mathematical tasks

Facilitate student discourse – “talk moves” * Encourage taking risks, defending solutions Have students present solutions and

ideas on a regular basis

*Classroom Discussions: Using Math Talk to Help Students Learn, 2nd edition, Grades K‐6  by Suzanne Chapin, Catherine O’Connor and Nancy Anderson, Math Solutions, 2009.

4. Model with Mathematics

Use physical objects, drawings and physical gestures to represent math situations

Encourage student verbal descriptions

Encourage representing the same situation in different ways

Guide students to see similarities in different ways to represent the same situations

Problems in everyday life…

5. Use Appropriate Tools Strategically

Provide mathematical tools in the classroom

Ensure that students know how to use the appropriate tools effectively

Discuss criteria to help make a decision as to when to use a mathematical tool

Encourage students use their rationale for using a tool in their explanation of their solution

6. Attend to Precision

Make mathematical tools available in the classroom Display and provide instruction on mathematical

vocabulary – interactive word wall Hold students accountable for using vocabulary in

discussion and written explanations Embed instruction about math symbols (7, +, =, >,) Discuss answers in terms of the context of the

problems to give students experience with the idea of a “reasonable” answer

Review processes for computational skills; include error analysis and feedback to develop accuracy and proficiency

7. Look for and Make Use of Structure

Encourage students to always look for patterns to help develop conceptual understanding

Provide opportunities for students to generalize

Use mental math to practice patterns in our number system

Provide opportunities to work on tasks that generate data that can be used to develop a generalization

Foster a class environment that values and encourages student reasoning as opposed to teacher “telling”

8. Look for and Express Regularityin Repeated Reasoning

Encourage students to always look for patterns or an opportunity to generalize about computational skills

Use mental math to practice patterns in our number system that can be used to develop more efficient computation methods

Incorporate lessons and activities that use pattern or structure to help develop conceptual understanding

Foster a class environment that values and encourages student reasoning as opposed to teacher “telling” what to notice or how to do a skill

The Leadership and Learning Center Seminar‐ “Digging Deeper into the Common Core State Standards”

Incorporating the Practice Standards…

Examine the math problems.

Think about the Mathematical Practices that students would engage in when solving the problems.

Share with someone next to you your reasoning.

Summary

All Standards for Mathematical Practice will not be demonstrated with every

math exercise given, but multiple standards should be evident in every

mathematics lesson.

Common Core State Standards K-12 Mathematics Learning Progressions

Kindergarten 1 2 3 4 5 6 7 8 HS

Counting and

Cardinality

Number and

Quantity

Number and Operations in Base Ten The Number System

Number and Operations: Fractions

Ratios and Proportional Relationships (6 and 7)

Operations and Algebraic Thinking Expressions and Equations

Algebra

Functions Functions

Geometry Geometry Geometry

Measurement and Data Statistics and Probability Statistics and

Probabilityhttp://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=1704&ContentID=83475&Content=102764

GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2Addition and subtraction, measurement using whole number quantities

3–5Multiplication and division of whole numbers and fractions

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8Linear algebra

Priorities in MathematicsPriorities in Mathematics

http://commoncoretools.wordpress.com/

Grade Required Fluency

K Add/subtract within 5

1 Add/subtract within 10

2

Add/subtract within 20

Add/subtract within 100 (pencil and paper)

3Multiply/divide within 100

Add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi-digit multiplication

6Multi-digit division

Multi-digit decimal operations

7 Solve px + q = r, p(x + q) = r

8Solve simple 22 systems by inspection

KeyKey FluenciesFluencies

http://commoncoretools.wordpress.com/

K-2

Content Standards

Grade Level Overview

Mathematics | KindergartenIn Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.(1) Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.

(2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.

A description of the key areas where instruction &  learning time should be focused. 

Critical Areas of FocusCritical Areas of Focus

Format of Pre-K-8 Standards

StandardStandard2.NBT.1 (code)2.NBT.1 (code)

Domain Domain  Grade Lev

el

Grade Lev

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2.NBT (co

de)

2.NBT (co

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ClusterCluster

Process Used to Develop Framework for District

Curriculum Work

A Frame for District Curriculum Work

ALL Standards are Important

Kindergarten UnitsCounting and Matching Numerals 0-5 with Comparing

Counting and Matching Numerals 6- 10 with Comparing

Counting and Matching Numerals 11-20

Teen Numbers (11-19) & Counting to 100

Fluency with Addition & Subtraction within 5

Exploring Addition & Subtraction within 10

Identify & Describe 2D & 3D Shapes

Compare, Analyze and Compose 2D & 3D Shapes

Measurement by Direct Comparison

FIRST GRADE

Suggested Unit Sequence Pacing

1 Fluency with Addition & Subtraction within 10 5 weeks

2 Exploring Addition & Subtraction within 20 4 weeks

3 Counting & Place Value 5 weeks

4 Exploring Addition and Subtraction within 100 5 weeks

5 Defining Attributes of 2D & 3D Shapes 2 weeks

6 Partitioning Circles & Rectangles 2 weeks

7 Measuring Length with Non-Standard Units 2 weeks

8 Time to the Hour and Half-Hour 2 weeks

Unit Planning OrganizerDevelopment of Unit Planning Organizer (in process)

Mathematical Practices

Domain & Standards Overview

Priority & Supporting CCSS

Explanations & Examples

Concepts Students Need to Know

Skills Students Need to Be Able to Do

Bloom’s Taxonomy Levels

Unit Assessment Items

Transition Guide

Transition Guide: Displaced Grade Level Concepts

Assessment

Test Mode: Administer one on oneRote Count

Teacher: Count out loud starting at 1 and count as high as you can. Record highest number student accurately counts to. Ex: Child counts from 1-15 accurately, then skips 16. Stop student

and record last correct number stated.

Kindergarten Assessment ItemsUnit 1 - Counting and Matching Numerals 0 – 5 with Comparing

Match Numerals

Preparation: In advance, teacher puts out groups of objects (ex: counters, unifix cubes or bears) and numeral cards 0-10. Objects should be arranged in groups of 3, 5, 8 and 10.

Teacher: Give students the shuffled set of numeral cards.

Count each group. Put the matching numeral card next to each set. Observe and record ( or - ) if student correctly matches all four sets.

Unit 2 - Counting and Matching Numerals 6 – 10 with Comparing

Kindergarten Assessment Items

Kindergarten Assessment Items

Unit 4 - Fluency with Addition and Subtraction within 5

There are 5 apples in a bowl. Some apples are red. Some apples are green.

•How many of each color apple could be in the bowl? ___ red apples ___ green apples

•Find a different answer. ___ red apples ___ green apples

Constructed ResponseWrite a number sentence and solve the problem. Use manipulatives (base-ten blocks, hundreds chart, number lines) or a drawing to show how to solve this problem.

Grade 1 - Assessment ItemsUnit 4 - Exploring Addition and Subtraction within 100

Mrs. Jones needs 42 cupcakes for the class picnic. She has 32 cupcakes. How many more cupcakes does she need to buy?

Mrs. Jones needs 42 cupcakes for the class picnic. She has 32 cupcakes. How many more cupcakes does she need to buy?

This is how Joe found the answer to 29 + 30 + 1 29 + 30 + 1 = 30 + 30 = 60

What did Joe do to solve the problem?

This is how Joe found the answer to 29 + 30 + 1 29 + 30 + 1 = 30 + 30 = 60

What did Joe do to solve the problem?

Multiple Choice

Grade 2 - Assessment ItemsUnit 2 - Place Value to 1,000

Circle all the statements that are equal to this number. 823

a) 8 hundreds and 23 tens b) 823 onesc) 7 hundreds, 12 tens and 3 ones d) 82 tens and 3 onese) 8 hundreds and 23 ones f) 7 hundreds and 23 tens

What is another way to show 729?

700 + 2 + 90700 + 20 + 970 + 200 + 97 + 20 + 900

Constructed Response

Grade 2 - Assessment ItemsUnit 3 - Fluency with Addition and Subtraction within 100

Solve the problem.54

- 29

Show or explain how to find the answer two different ways.

Write an equation for this problem. Solve the equation to find the answer.

The teacher is 70 inches tall. The student is 47 inches tall.

How much taller is the teacher than the student?

QUESTIONS