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The importance of Coherent Lessons in Elementary Mathematics

Explore the importance of coherence in elementary mathematics education, focusing on logical sequences of topics and standards across grades. Discover how coherence enhances instruction and assessment. Learn practical strategies to implement coherence in your classroom.

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The importance of Coherent Lessons in Elementary Mathematics

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  1. COHERENCE The importance of Coherent Lessons in Elementary Mathematics College and Career Readiness Conference Summer 2014

  2. 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

  3. SHIFTS

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

  5. COHERENCE • 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…

  6. 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!

  7. COHERENCE 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.

  8. COHERENCE CONTENT The writers of the CCSS: • Built COHERENCE into the content standards. • Clarified and shared their vision of grade-to-grade and within-grade COHERENCEin the Progressions documents.

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

  10. 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.

  11. GRADE- TO-GRADE COHERENCE 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 • Multiplyingand Dividing Fractions • Multiplying as Scaling

  12. 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

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

  14. Explaining Fraction Equivalence with Pictures

  15. GRADE- TO-GRADE COHERENCE 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 • Multiplyingand Dividing Fractions • Multiplying as Scaling

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

  17. WITHIN-GRADE COHERENCE

  18. 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

  19. WITHIN-GRADE COHERENCE https://www.teachingchannel.org/videos/multiplying-fractions-by-whole-numbers-lesson

  20. WITHIN-GRADE COHERENCE • 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?

  21. COHERENCE In ASSESSMENT Evidence of Coherencein assessment is not tremendously different from evidence of coherencein classroom instruction.

  22. 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.

  23. 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?

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

  25. 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?

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

  27. Reliable Resources • Illustrative Math https://www.illustrativemathematics.org • Bill McCullum, CCSS lead writer • Sample Lessons that illustrate specific standards. • Achieve The Corehttp://achievethecore.org • Jason Zimba, CCSS lead writer • Multiple Resources • Lesson Plans, Assessments, Professional Development courses, Grade at a Glance • PARCC http://parcconline.org • Information about PARCC Assessments • Sample Lessons • Practice Tests

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

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