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CHANGE PROCESS Not Content

CHANGE PROCESS Not Content. Presented by Judith T. Brendel Supervisor of Mathematics and Art Pascack Valley Regional HS District jbrendel@pascack.k12.nj.us. Fun Differentiated Tasks and New Standards NJEA 2011 Convention, 1-4 p.m. room 411 FOCUS - MIDDLE SCHOOL .

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CHANGE PROCESS Not Content

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  1. CHANGE PROCESS Not Content Presented by Judith T. Brendel Supervisor of Mathematics and Art Pascack Valley Regional HS District jbrendel@pascack.k12.nj.us Fun Differentiated Tasks and New Standards NJEA 2011 Convention, 1-4 p.m. room 411 FOCUS - MIDDLE SCHOOL

  2. Use the RULER on the HANDOUT (separate sheet) • Measure a writing tool • What decisions did you need to make? • The tool should be shorter than the ruler • Should I use inches or centimeters? • Where do I begin? Where is zero? • How exact a measurement do I need? • Do I need to round? Should I round up or down? Things we shouldn’t forget

  3. HANDS ON PRACTICE ! • CONCRETE EXPERIENCES K-12 ! • SELECT THE BEST TOOL Things we shouldn’t forget

  4. Which one Doesn’t Belong and Why? B A D C ABCD monitor each Grade-5: Classify 2-D figures in a hierarchy based on properties. (Not new, but a focus.)

  5. Which one Doesn’t Belong and Why ? B 11 A. 49 D √4 C. 50 ABCD monitor each New GR.2 – Determine if a whole number is Odd or Even? (moved from grade-3) New Gr.4 – Determine whether a given whole number (1-100) is prime or composite. (moved from grade-5)

  6. Which one Doesn’t Belong and Why ? A. 3562 2653 4272.1 2714.2 1234 2143 5246 6275 ABCD monitor and challenge ALL

  7. Which one Doesn’t Belong and Why ? A. 3562 2653 6215 427.21 271.42 698.68 1234 2143 3377 5246 6275 1,1521 GR.3: Fluently add and subtract within 1000 using strategies …. 3NBT.2 GR.4: Fluently add and subtract multidigit whole numbers. 4.NBT.4 GR.5: Add, subtract, multiply, and divide decimals to hundredths … 5.NBT.7 ABCD monitor each

  8. Which one Doesn’t Belong and Why? B. 1 2/5 + 2 1/5 = 3 3/5 A. 5/4 = 5 x 1/4 C. 6 x 1/3= 6/3 D. 8 2/3 – 3 1/3 = 5 1/3 ABCD monitor each Grade-4 NEW: Understand that a fraction a/b as ‘a’ multipled by 1/b. Grade-4 NEW: Add and subtract mixed numbers with like denominators.

  9. Which one Doesn’t Belong and Why? B. 6 > 2+1 A. 5 < 6 C. 2+4 < 1+ 5 √4 > 12 + √9 ABCD monitor each See ‘A’ above: Compare 2 two-digit numbers … record results of comparisons with symbols > < = (New.Gr.1)

  10. Let’s take a quick look at the CCSS Common Core State Standards (separate packet) C = currently required + = new requirement (from a higher grade) • = new requirement (from a lower grade) N = new content (not previously required) http://www.corestandards.org/

  11. ENGAGEMENT

  12. OPERATIONS: MIXED OPERATIONS PROBLEMS (grades 5-6) • FRACTIONS, DECIMALS and PERCENTS (grades 5-6) • EQUIVALENCY, RATIOS, and PROPORTIONS (grades 7+) EAI – 1-800-770-8010 CCSS: Understand the place value system. 5.NF.1. Add and subtract fractions with unlike denominators 5.NBT.3. Read, write, and compare decimals to thousandths. 7.RP.2. Recognize and represent proportional relationships between quantities. I Have 0.125 Who has 1/3 as a % ? I HAVE WHO HAS?

  13. PORTFOLIO - Congratulations: Dear Assistant, (pg.2) Printing day is Tuesday and I need your help! The Arts section of our local paper is completing a page on all subjects covered in 7th grade. I need you to cover the math piece for me … Write a poem, song, rap, or story about order of operations. Just follow the attached rubric and you should be fine. Be creative and watch your spelling, but have fun! Standard 2: Human Growth and Devi. Teachers know and understand (2) How student learning is influenced by individual experiences, talents and prior learning …. Standard 7: Special Needs: iii. Teachers engage in activities to: (1) Apply knowledge of students’ abilities, … talents … to positively impact student learning. Portfolio: A Creative Piece

  14. 4-Mat-4 Learning Math+Fun=more learning

  15. 4-Mat-4 Algebra (handout page-10/47) Roll a die (pick from cards 1-6 or use a spinner) -Draw a picture on a coordinate plane …. -- Bring in a portion of a map and …. ---In 1990, … write an equation to model ... ----Write a poem, song or rap …. -----Make up 5 sets of order pairs. Find the …. ------ Tape 2 … sticks … use this as a ramp …. Algebra CONCEPTUAL CATEGORY: Equations and Inequalities DOMAIN: Creating Equations Standard: Create equations in 2 or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Portfolio: Choices

  16. DISTRIBUTE SmartPAL sleeves and markers Donated by EAI education SEE EACH ONE THINKING

  17. Holiday Shopping Activity – Portfolio Unit 5 • Standard 4: Instructional Planning and Strategies • Iii. Teachers engage in activities to: (4) Identify strategies to create learning experiences that make subject matter meaningful for students, address a variety of learning styles, encourage students to pursue their own interests and inquiries and help students connect their learning to personal goals. (handouts p. 4-7) Meaningful Math WHAT GRADE LEVELS? WHAT STANDARDS?

  18. Error Analysis – Portfolio Unit 1 • Standard 1: iii Teachers engage in activities to (1) Promote the development of critical thinking, problem solving and decision making skills by engaging students in formulating and testing hypotheses according to the methods of inquiry and standards of evidence within the discipline. • Algebra 01.a Number Sense and Operations: Use properties of number systems within the set of real numbers to verify or refute conjectures or justify reasoning and to classify, order and compare real numbers. Meaningful Math

  19. Unit 1 – Error Analysis (handout page-8) Basic Algebra (collab) Problem 1: Simplifying radicals Problem 2: Comparing fractions Portfolio: Error Analysis

  20. Unit 1 – Error Analysis (handout p.9) Basic Algebra (collab) Problem 4: Graph the fraction on a number line Problem 5: Add Fractions; combine integers Portfolio: Error Analysis

  21. Equation Tic Tac Toe (handout p.11) • What standards are met here? 1 2 3 4 5 6 7 8 9 Math+Fun=more learning Use your SMART PALS

  22. Equation Tic Tac Toe (handout p.11) • What standards are met here? -3/2 7 1/4 0=0 0=-28 -1 7/11 1/4 31/7 10 2 3/11 Math+Fun=more learning Use your SMART PALS

  23. 2. 4 x 2/3 = Use your SMART PALS Change the Question not Textbook See #2 above: NEW grade-5: Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; … (5.NF.5.b)

  24. Change the Question not the Textbook Use your SMART PALS

  25. Change the Homework Question

  26. Change the Homework Question Use your SMART PALS

  27. Change the Homework Question

  28. Change the Homework Question

  29. RANGE PROBLEMS (calculators helpful) (handout pages 15-16) What are the rules? 4 2 8 3 5 7 CHALLENGE all at the same time

  30. Play the game: Graphing Linear Equations • Play the game: Graph Systems of Equations (handouts pages 17-18) MATCH-the-GRAPH

  31. Play the game: Geometric Shapes on a Grid MATCH-the-GRAPH

  32. 21ST CENTURY ASSEMBLY LINE (everyone participates) Do One Step – Pass it On! • 2x + 22 – 2(4 + 2x) = 10x – 2(14) • 3x – 14 + (3)2 = 10x 2(x-10) • [5 + 14 ÷ 2 – 10 + (2 x 52)] ÷ 4 • Draw and label a diagram of …. 5.0A.1. New to grade-5;moved from grade-6: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents 6.EE.2 Write expressions that record operations with numbers and with letters standing for numbers. 21st Century Assembly Line

  33. MY CALCULATOR is BROKEN (handout p.24) • Pretend the [2] key is broken … Find • Pretend the [4] key is broken … Find BROKEN KEYS

  34. Individual, Pair, Group Activity (handout page-25) CUT THE CAKE

  35. 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. MATHEMATICAL PRACTICES p.26

  36. FIND THE PERIMETER (handout p.26a) individual or pair activity Algebra Tiles Black = “x” yellow = “1”) UNDERSTAND PERIMETER

  37. FIND THE AREA: Draw 3-4 different rectangles that have a perimeter of 30. Record the area of each. (Use whole numbers only.) • Which shapes have the largest & smallest area? • What do you observe? (handout p.27) AREA with PERIMETER

  38. FIND THE PERIMETER: Draw 4-5 different rectangles that have a area of 36. Record the perimeter of each. (Use whole numbers only.) • Which shapes have the largest & smallest area? • Which has the largest & smallest perimeter? (handout page-28) AREA with PERIMETER

  39. Ski Indoors(handout page-30) • Notes to the teacher: (2-3 week project) • Benchmark lessons (whole-class, concept-based skills, such as: • 1. concept of slope • 2. concept of relationship among numbers (rise/run; 3 sides of a right triangle). • Assignments – individual for content mastery • Mini-Lessons – small group, short lessons on a specific skills such as: • How-To-Sheets – step-by-step directions for skill development • Web Resources (handout page-32) • Teacher Notes (handout page-32a) IDE portal sample

  40. A WEBQUEST for ALGEBRA students • Introduction • The Task • The Process • Evaluation • Conclusion (handout pgs.33-37) RUN FOREST RUN

  41. How Do We Get to School? (handout p.38) Organize Data-Graph Comprehension in grades ?-8 NCTM free Illuminations

  42. How Do You Spend Saturday? from Developing Data-Graph comprehension in Grades K-8(handout page-39) NCTM free Illuminations

  43. Sports Numbers • (handout page-40) NCTM free Illuminations

  44. Squares and Parallelograms: handout p.41 • The Peak in the Middle NCTM free Illuminations

  45. Rolling Dice: from Mathematics Teaching in the Middle Schoolhandout p.42 EAIeducation.com Donated the dice NCTM free Illuminations CCSS Moved from grade-8 to grade-7: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

  46. Cranberry Punch: (handout p.43-44) • from Focus in Grades 6-8 (April 2010 Focus issue) NCTM free Illuminations

  47. Hay Bale Farmer: from Free Online at: illuminations.nctm.org (This activity targets grades 6-8) (handout pages 45-46) NCTM free Illuminations

  48. JUDITH T. BRENDEL • jbrendel@pascack.k12.nj.us Supervisor of Mathematics and Art • http://www.pascack.k12.nj.us [Curriculum] [Departments] [Math] [CCSS NJEA convention 2011] KEEP IN TOUCH

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