Fun Differentiated Tasks and New Standards NJEA 2011 Convention, 1-4 p.m. room 411 FOCUS - MIDDLE SCHOOL Presented by Judith T. Brendel Supervisor of Mathematics and Art Pascack Valley Regional HS District

* 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?

* HANDS ON PRACTICE ! * CONCRETE EXPERIENCES K-12 ! * SELECT THE BEST TOOL

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

Which one Doesn’t Belong and Why ? B 11 D √4 C. 5 0 A. 49 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)

Which one Doesn’t Belong and Why ? B D C A

Which one Doesn’t Belong and Why ? B D ,1521 C A 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

Which one Doesn’t Belong and Why? B. 1 2/ /5 = 3 3/5 D. 8 2/3 – 3 1/3 = 5 1/3 C. 6 x 1/3= 6/3 A. 5/4 = 5 x 1/4 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.

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

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)

* OPERATIONS: MIXED OPERATIONS PROBLEMS (grades 5-6) * FRACTIONS, DECIMALS and PERCENTS (grades 5-6) * EQUIVALENCY, RATIOS, and PROPORTIONS (grades 7+) EAI – I Have Who has 1/3 as a % ? 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.

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 7 th 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 Dev i. 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.

* 4-Mat-4 Learning

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.

DISTRIBUTE SmartPAL sleeves and markers Donated by EAI education

* 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) WHAT GRADE LEVELS? WHAT STANDARDS?

* 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.

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

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

* Equation Tic Tac Toe (handout p.11) * What standards are met here? Use your SMART PALS

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

ORIGINALNEW QUESTION same example 1Add 3/8 and 4/8Is the sum of these two fractions closer to ½ or closer to 1 whole? Explain or show how you know. 24 x 2/3 =Estimate your answer. The product is (a) >4 b) <4 (c) <1 (d) < 2 3Find the sum 5/12 6/12 7/12 REWRITE this example using only two fractions so you will get the same answer when they are added. 4What is the total? 5 and 5/7, and 4 and 6/7 How can you tell by just looking at this example that your answer will be greater than 10? EXPLAIN in WORDS. Handout page-13 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) 2. 4 x 2/3 = Use your SMART PALS

ORIGINALNEW QUESTION same example 52/3 + ¾ = ? A.5/7 B.17/24 C. 5/12 Choices ‘A’ and ‘B’ are incorrect. What do you think someone might have thought if they selected one of these choices? 60.25, 50% and 2/3 Create two different examples using these numbers. Solve them. 75/12 + 6/12 + 7/12 What could you add to these three fractions so the sum would be A)A mixed number? Add ___ new sum = _____ B)A whole number? Add ___ new sum = _____ C)A negative integer? Add ___ new sum = ____ D)Zero? Add ____ new sum = ____ 81/20 1/10 1/5 and 1/8 Mark says there is a very easy way to put these fractions in order without making common denominators. Explain. Handout pages Use your SMART PALS

WHICH 2 are the easiest and which 2 are the most difficult to solvet? Why? 1Solve for n: 2n – 4 = 126Solve for x: 3x = Solve for x: 10 = 3 x + 47Solve for w: √25 = w 3Solve for a: 1/3 a = 108Solve for a: 2900 = 100a 4Solve for x: 2 (x +1) = 129Evaluate if x = 4: x 2 + x – 16 5Solve for w: 3 (2 - w) = 1210Evaluate if y = 3: 9 – y + y 3

WHICH 2 are the easiest and which 2 are the most difficult to solve? Why? 1Solve for n: 2n – 4 = 12 n=8 6Solve for x: 3x = x = 2 2Solve for x: 10 = 3 x + 4 2=x 7Solve for w: √25 = w 5 = w 3Solve for a: 1/3 a = 10 a = 30 8Solve for a: 2900 = 100 x x=29 4Solve for x: 2 (x +1) = 12 x = 5 9Evaluate if x = 4: x 2 + x – Solve for w: 3 (2 - w) = 12 w = 6 10Evaluate if y = 3: 9 – y + y 3 33 Use your SMART PALS

Separate these 10 examples into 2 groups and explain why you separated them that way. 1Solve for n: 2n – 4 = -126Solve for x: 3x = Solve for x: 10 = 3 x +7Solve for w: √25 = w 3Solve for a: 1/3 a = 108Solve for a: 2900 = 100 x 4Solve for x: 2 (x +1) = -179Evaluate if x = 4: x 2 + x – 16 5Solve for w: 3 (2 - w) = 1210Evaluate if y = 3: 9 – y + y 3

Separate these 10 examples into 2 groups and explain why you separated them that way. 1Solve for n: 2n – 4 = -12 n = -8 6Solve for x: 3x = x = 2 2Solve for x: 10 = 3 x + 4 2= x 7Solve for w: √25 = w = w 3Solve for a: 1/3 a = 10 a = 30 8Solve for a: 2900 = 100 x x =29 4Solve for x: 2 (x +1) = -17 x = -19/2 = Evaluate if x = 4: x 2 + x – Solve for w: 3 (2 - w) = 12 w = 6 10Evaluate if y = 3: 9 – y + y 3 33

* RANGE PROBLEMS (calculators helpful) (handout pages 15-16) What are the rules?

* Play the game: Graphing Linear Equations * Play the game: Graph Systems of Equations (handouts pages 17-18)

* Play the game: Geometric Shapes on a Grid

21 ST 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) * [ ÷ 2 – 10 + (2 x 5 2 )] ÷ 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.

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

* Individual, Pair, Group Activity (handout page-25)

* 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.

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

* 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)

* 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)

* 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)

* A WEBQUEST for ALGEBRA students * Introduction * The Task * The Process * Evaluation * Conclusion (handout pgs.33-37)

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

* How Do You Spend Saturday? from Developing Data-Graph comprehension in Grades K-8 (handout page-39)

* Sports Numbers * (handout page-40)

* Squares and Parallelograms: handout p.41 * The Peak in the Middle

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

* Cranberry Punch: (handout p.43-44) * from Focus in Grades 6-8 (April 2010 Focus issue)

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

* JUDITH T. BRENDEL * Supervisor of Mathematics and Art * [Curriculum] [Departments] [Math] [CCSS NJEA convention 2011]