Fun Differentiated Tasks and New Standards

NJEA 2011 Convention, 1-4 p.m. room 411FOCUS - MIDDLE SCHOOL

*CHANGE PROCESS Not Content

Presented by Judith T. BrendelSupervisor of Mathematics and ArtPascack Valley Regional HS District

jbrendel@pascack.k12.nj.us

*Things we shouldn’t forget

*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

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

*ABCD monitor each

Which one Doesn’t Belong and Why?

A B

DC

Grade-5: Classify 2-D figures in a hierarchy based on properties. (Not new, but a focus.)

*ABCD monitor each

Which one Doesn’t Belong and Why ?

B 11

D √4C. 50

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)

*ABCD monitor and challenge ALL

Which one Doesn’t Belong and Why ? B.

4272.1

2714.2 D.

5246 6275

C. 1234 2143

A. 3562 2653

*ABCD monitor each

Which one Doesn’t Belong and Why ? B.

427.21

271.42 698.68

D. 5246

6275 1,1521

C. 1234 2143 3377

A. 3562 2653 6215

GR.3: Fluently add and subtract within 1000 using strategies …. 3NBT.2GR.4: Fluently add and subtract multidigit whole numbers. 4.NBT.4GR.5: Add, subtract, multiply, and divide decimals to hundredths … 5.NBT.7

*ABCD monitor each

Which one Doesn’t Belong and Why? B.

1 2/5 + 2 1/5 =

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.

*ABCD monitor each

Which one Doesn’t Belong and Why?

B. 6 > 2+1

D. √4 > 12 + √9

C. 2+4 < 1+ 5

A. 5 < 6

See ‘A’ above: Compare 2 two-digit numbers … record results of comparisons with symbols > < = (New.Gr.1)

*http://www.corestandards.

org/

Let’s take a quick look at the CCSSCommon 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)

*ENGAGEMENT

*I HAVE WHO HAS?

*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

I Have 0.125Who 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: A Creative Piece

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 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.

*Math+Fun=more learning

*4-Mat-4 Learning

*Portfolio: Choices

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 ….

AlgebraCONCEPTUAL 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.

*SEE EACH ONE THINKING

DISTRIBUTE SmartPAL sleeves and markers

Donated byEAI education

*Meaningful Math

*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?

*Meaningful Math

*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.

*Portfolio: Error Analysis

Unit 1 – Error Analysis (handout page-8)Basic Algebra (collab)

Problem 1: Simplifying radicalsProblem 2: Comparing fractions

*Portfolio: Error Analysis

Unit 1 – Error Analysis (handout p.9) Basic Algebra (collab)

Problem 4: Graph the fraction on a number lineProblem 5: Add Fractions; combine integers

*Math+Fun=more learning

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

1 2 369

547 8

Use your SMART PALS

*Math+Fun=more learning

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

-3/2 7 1/4 0=01/4

2 3/11

-1 7/110=-2831/7 10

Use your SMART PALS

*Change the Question not

Textbook

ORIGINAL NEW QUESTION same example1 Add 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.

2 4 x 2/3 = Estimate your answer. The product is(a) >4 b) <4 (c) <1 (d) < 2

3 Find the sum5/126/127/12

REWRITE this example using only two fractions so you will get the same answer when they are added.

4 What 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

*Change the Question not the

Textbook

ORIGINAL NEW QUESTION same example5 2/3 + ¾ = ?

A. 5/7B. 17/24C. 5/12

Choices ‘A’ and ‘B’ are incorrect. What do you think someone might have thought if they selected one of these choices?

6 0.25, 50% and 2/3

Create two different examples using these numbers. Solve them.

7 5/12 + 6/12 + 7/12

What could you add to these three fractions so the sum would beA) 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 = ____

8 1/20 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 13-14

Use your SMART PALS

*Change the Homework

Question

WHICH 2 are the easiest and which 2 are the most difficult to solvet? Why?

1 Solve for n: 2n – 4 = 12

6 Solve for x: 3x = 22 + 2

2 Solve for x: 10 = 3 x + 4

7 Solve for w: √25 = w

3 Solve for a: 1/3 a = 10 8 Solve for a: 2900 = 100a

4 Solve for x: 2 (x +1) = 12

9 Evaluate if x = 4: x2 + x – 16

5 Solve for w: 3 (2 - w) = 12

10 Evaluate if y = 3: 9 – y + y3

*Change the Homework

Question

WHICH 2 are the easiest and which 2 are the most difficult to solve? Why?

1 Solve for n: 2n – 4 = 12n=8

6 Solve for x: 3x = 22 + 2 x = 2

2 Solve for x: 10 = 3 x + 4 2=x

7 Solve for w: √25 = w5 = w

3 Solve for a: 1/3 a = 10a = 30

8 Solve for a: 2900 = 100 xx=29

4 Solve for x: 2 (x +1) = 12x = 5

9 Evaluate if x = 4: x2 + x – 164

5 Solve for w: 3 (2 - w) = 12w = 6

10 Evaluate if y = 3: 9 – y + y3

33Use your SMART PALS

*Change the Homework

Question

Separate these 10 examples into 2 groups and explain why you separated them that way.

1 Solve for n: 2n – 4 = -12

6 Solve for x: 3x = 22 + 2

2 Solve for x: 10 = 3 x + 7 Solve for w: √25 = w

3 Solve for a: 1/3 a = 10 8 Solve for a: 2900 = 100 x4 Solve for x: 2 (x +1) =

-179 Evaluate if x = 4: x2 + x –

16

5 Solve for w: 3 (2 - w) = 12

10 Evaluate if y = 3: 9 – y + y3

*Change the Homework

Question

Separate these 10 examples into 2 groups and explain why you separated them that way.

1 Solve for n: 2n – 4 = -12n = -8

6 Solve for x: 3x = 22 + 2 x = 2

2 Solve for x: 10 = 3 x + 4 2= x

7 Solve for w: √25 = w + 32

-4 = w

3 Solve for a: 1/3 a = 10a = 30

8 Solve for a: 2900 = 100 xx =29

4 Solve for x: 2 (x +1) = -17x = -19/2 = -9.5

9 Evaluate if x = 4: x2 + x – 164

5 Solve for w: 3 (2 - w) = 12w = 6

10 Evaluate if y = 3: 9 – y + y3

33

*CHALLENGE all at the same time

*RANGE PROBLEMS (calculators helpful)(handout pages 15-16)

What are the rules?

4 2 83 5 7

*MATCH-the-GRAPH

*Play the game: Graphing Linear Equations*Play the game: Graph Systems of Equations

(handouts pages 17-18)

*MATCH-the-GRAPH

*Play the game: Geometric Shapes on a Grid

*21st Century Assembly Line

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.

*BROKEN KEYS

*MY CALCULATOR is BROKEN

(handout p.24)

*Pretend the [2] key is broken … Find*Pretend the [4] key is broken … Find

*CUT THE CAKE

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

*MATHEMATICAL PRACTICES p.26

* 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.

*UNDERSTAND PERIMETER

*FIND THE PERIMETER (handout p.26a) individual or pair activity

Algebra Tiles Black = “x” yellow = “1”)

*AREA with PERIMETER

*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

*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)

*IDE portal sample

*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)

*RUN FOREST RUN

*A WEBQUEST for ALGEBRA students*Introduction*The Task*The Process*Evaluation*Conclusion

(handout pgs.33-37)

*NCTM free Illuminations

*How Do We Get to School? (handout p.38)

Organize Data-Graph Comprehension in grades ?-8

*NCTM free Illuminations

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

*NCTM free Illuminations

*Sports Numbers * (handout page-

40)

*NCTM free Illuminations

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

*NCTM free Illuminations

*Rolling Dice: from Mathematics Teaching in the Middle School handout p.42

EAIeducation.comDonated the dice

CCSS Moved from grade-8 to grade-7: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

*NCTM free Illuminations

*Cranberry Punch: (handout p.43-44)

*from Focus in Grades 6-8 (April 2010 Focus issue)

*NCTM free Illuminations

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

(handout pages 45-46)

*KEEP IN TOUCH

*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]