a story of units

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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

A Story of UnitsBetty Chin


N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Units

Standards for Mathematical Practices

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1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of

others.4. Model with mathematics.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.



Framework

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Review of Module Structure

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Module Overview

Topic

L1 L2 L3

Topic

L4 L5

Topic

L6 L7 L8



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Homework

Exit Ticket

Debrief

Problem Set

Application

Fluency

Concept

Development



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Balanced, Rigorous Instruction



Key Points

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• Modules Overviews and Topic Openers provide essential information about the instructional path of the module and are key tools in planning for successful implementation.

• Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Standards to life.

• The Exit Ticket is an essential piece of the Student Debrief and provides daily formative assessment.

• Opportunities to nurture the Standards for Mathematical Practice are embedded throughout the lesson.



A Story of UnitsFluency in Practice



Implementation of a Fluency Routine

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Fluency activities serve a variety of purposes:• Maintenance: Staying sharp on previously learned skills

• Preparation: Targeted practice for the current lesson

• Anticipation: Building skills to prepare students for the in-depth work of future lessons

In fluency work, all students are actively engaged with familiar content. This provides a daily opportunity for continuous improvement and individual success.



Required Fluencies

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K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication



Fluency Exercises in A Story of Units

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Three general categories of fluency work support student learning in A Story of Units:

• Counting Exercises• Choral and White Board Exchanges • Sprints



Key Foundational Skills in A Story of Units Module 1

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• K – Counting to 5, counting consecutively, and recognizing numerals

• 1 – Counting a set of objects or pictures and assigning a numeral, and counting on in a number sequence

• 2 – Adding and subtracting units such as tens and centimeters, and using rulers to count, add, and subtract

• 3 – Group counting (skip counting) to lay the foundation for understanding multiplication as repeated addition

• 4 – Multiplying and dividing by 10, and decomposing numbers into units

• 5 – Renaming decimals in various place value units (3.14 = 3 ones 14 hundredths = 31 tenths 4 hundredths = 314

hundredths)



Differentiation in Fluency Practice

Some possibilities for adapting fluency exercises include:

• Modeling with visual tools

• Adapting the length and pace of exercise

• Using content from lower or higher grades

• Varying between independent, partner, small group, and whole class activities

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A Story of UnitsApplication and Concept Development in Practice



Application Problems

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• Application involves using relevant conceptual understandings and appropriate strategies even when not prompted to do so.

• Time allotted to application varies, but is commonly 10-20 minutes of the lesson.

• The Read, Draw, Write (RDW) process is modeled and encouraged through daily problem solving.



Concept Development

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• Constitutes the major portion of instruction and generally comprises at least 20 minutes of the total lesson time.

• Builds toward new learning through intentional sequencing within the lesson and across the module.

• Often utilizes the deliberate progression from concrete to pictorial to abstract, which compliments and supports an increasingly complex understanding of concepts.

• Accompanied by thoughtfully sequenced problem sets and reproducible student sheets.



Differentiation in Application Problems and Concept Development

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Student Needs Solution to Address the Challenge Multiple Means of….?

Fine motor difficulties Application Problem: Use materials and take a picture

Representation

English Language Learners

Application Problem: Work with a partner Action & Expression

Students struggling with visual focusing

Concept Development: Paper or card stock to help focus on embedded numbers

Engagement

Students who do not have mastery of subitizing

Concept Development: “How many did you count? Repeat that total. (Repeat several times, helping them to focus on seeing the quantity.)”

Action & Expression

Students who do not have consistent 1:1 correspondence

Concept Development: “Grab and lift the objects from the carton as you count.”

Action & Expression



A Story of UnitsStudent Debrief in Practice



Another Look at Problem Sets

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• Generally embedded within the Concept Development.

• May be completed independently or with teacher guidance, and are reviewed in class as part of the Student Debrief.

• Provide an opportunity for students to apply understanding(s) from the lesson.

• Directions introducing the Problem Set give guidance about how to differentiate



Another Look at Problem Sets

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The Student Debrief

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• Includes sample dialogue or suggested lists of questions to invite the reflection and active processing of the totality of the lesson experience.

• Encourages students to articulate the focus of the lesson and the learning that has occurred.

• Promotes mathematical conversation with and among students.

• Allows student work to be shared and analyzed.• Closes the lesson with daily informal assessment known as

Exit Tickets.



Differentiation in the Student Debrief

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• Have students restate their learning for the day. Ask for a different representation in the restatement. Would you restate that answer in a different way or show me by using a diagram?

• Encourage students to explain their reasoning both orally and in writing.

• Let students use pictures and gestures to calculate and explain.

a story of units

Documents

story of unitsstandards

story of unitsreview

entire story

story of unitsbetty

component of rigor

examples of rigor

coherence session

curriculum overview