College and Career Readiness Conference Summer 2014 THE IMPORTANCE OF COHERENT LESSONS IN ELEMENTARY MATHEMATICS 1

RIGOR  Reduce Side Chatter  Involve Yourself in the Process  Give Your Thoughts & Ideas  Open Your Mind on how You Can Change Instruction  Remember to Silence Electronic Devices 2

Focus Coherence Rigor 1. Conceptual Understanding 2. Procedural Skill 3. Modeling/Application 3

TODAY’S OUTCOME Participants will: Explore in depth the “shift” of COHERENCE and its impact on mathematics content, instruction, and assessment of the Maryland CCR Standards in mathematics. 4

Coherence comes from the verb to cohere, which means: To stick together in a way that resists separation; To be logically linked and naturally related. Think of Rice Krispies Treats… 5

We want our mathematics curriculum to have coherence… related concepts that stick together in a way that is obvious, understandable, connected, and reliable… for teachers and students alike! 6

A purposeful placement of standards to create logical sequences of content topics that bridge across the grades, as well as across standards within each grade. 7

CONTENT 8

Grade 3 Grade 4 Grade 5 Meaning of Fractions Fractions on Number Line Equivalent Fractions Comparing Fractions Equivalent Fractions Add/Subtract Fractions Multiplication fraction by whole number Decimals Add/Subtract Fractions Comparing Fractions Multi/Divide Fractions Multiplication as scaling 9

WHICH GRADE ?  In your group, read the topics/concepts listed.  Identify the grade level for these topics/concepts.  Place the group of concepts in the correct grade level. 10

Grades 1 and 2  Partition shapes (circles and rectangles  Describe the shares using words halves, fourths, quarters Grade 3 :  Fractions as a Number- Unit Fractions  Representing Fractions on a Number Line  Equivalent Fractions  Comparing Fractions Grade 4  Equivalent Fractions  Comparing Fractions  Adding and Subtracting Fractions  Multiplying a fraction by a whole number  Decimals Grade 5  Adding and Subtracting Fractions  Multiplying and Dividing Fractions  Multiplying as Scaling 11

Reocurring Concepts  Teaching fraction concepts using unit fractions  Representing fractions on the number line  Importance of identifying the whole  Describing the parts of the whole 12

In the following task from Illustrative Mathematics, complete the following steps: 1.Complete the task. 2.List all of the mathematics concepts/skills you used. 3.Reflect - What do you notice about this task’s reliance on COHERENCE? 13

Explaining Fraction Equivalence with Pictures 14

Grades 1 and 2  Partition shapes (circles and rectangles  Describe the shares using words halves, fourths, quarters Grade 3 :  Fractions as a Number- Unit Fractions  Representing Fractions on a Number Line  Equivalent Fractions  Comparing Fractions Grade 4  Equivalent Fractions  Comparing Fractions  Adding and Subtracting Fractions  Multiplying a fraction by a whole number  Decimals Grade 5  Adding and Subtracting Fractions  Multiplying and Dividing Fractions  Multiplying as Scaling 15

Reflection and Discussion How is understanding Grade- To- Grade Coherence helpful for planning and teaching daily lessons ? 16

Grade 4from Domain to Domain OA.AUse the four operations with whole numbers to solve problems NF.ABuild fractions from unit fractions by applying and extending previous understanding of operations of whole numbers. Extend the understanding of fraction equivalence and ordering Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models… MD.ASolve problems involving measurement and conversions of measurement from a larger to smaller unit. (use four operations to solve problems including problems involving fractions and decimals 17

Mrs. Russell’s Problem “ Mrs. Russell wants us to have ribbons on each corner of our garden identifying the various crops. She determined 2/3 of a yard was the perfect length for each ribbon. Since ribbon is sold by the yard, how much should be purchased for all four corners ? “ Create a representation to justify your thinking. Teacher Amy Spies Voulusia County, FL The Teaching Channel Lesson 18

fractions-by-whole-numbers-lesson 19

Watch the video “Multiplying Fractions By Whole Numbers”. Use the note taking form to record evidence of within-grade coherence and any between grade coherence. Reflect- What do you notice about this lessons’ reliance on COHERENCE? 20

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PARCC-Summative Assessment  Performance-Based Assessment (PBA) administered after approximately 75% of the school year..  End-of-Year Assessment (EOY) administered after approximately 90% of the school year. 22

PARCC - Reflect and Discuss  What evidence of coherence did you find? Grade to Grade Coherence Within Grade Coherence  Which Standards for Mathematical Practice are assessed in this task?  What does this mean for instruction in your classroom? 23

COHERENCE- PARCC ASSESSMENT Mr. Edmund’s Pencil Box 24

PARCC - Reflect and Discuss  What evidence of coherence did you find? Grade to Grade Coherence Within Grade Coherence  Which Standards for Mathematical Practice are assessed in this task?  What does this mean for instruction in your classroom? 25

In reality, the “key” to making the Shift of Coherence a success rests on the shoulders of curriculum writers and classroom teachers. Instruction must take advantage of every opportunity to build connections between topics both within a grade and from grade to grade. 26

Reliable Resources  Illustrative Math Bill McCullum, CCSS lead writer Sample Lessons that illustrate specific standards.  Achieve The Core Jason Zimba, CCSS lead writer Multiple Resources Lesson Plans, Assessments, Professional Development courses, Grade at a Glance  PARCC Information about PARCC Assessments Sample Lessons Practice Tests 27

What are the muddiest points? Record any question you still have after today’s presentation on your post-it note. Please provide your name and address. Stick your post-it on the front wall as you leave today. Thank you! 28