creatively engage all students -...

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CREATIVELY

ENGAGE ALL STUDENTS (differentiate instruction)

while teaching

grades 6-12 math classes

presented by Judith T. Brendel

Educational Consultant: njFEA, AMTNJ, TMI

[email protected]

FEA fall conference October 20, 2016

mailto:[email protected]

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RESOURCES Page

1. Which One Doesn’t Belong? Why? (a Paul Lawrence favorite) Not included in this workbook

2. 21st Century Assembly Line “Do One and Move Right” Arithmetic (an expression with positive integers) 3 Algebra (an equation) 3

3. 21st Century Assembly Line “Do One and Pass Right” Geometry 4

4. Match Your Partner’s Answer

Expressions (set A and B) 5-6 Equations (set A ad B) 7-8 Inequalities (set C and D) 9-10 Blank form (template) 11

5. Carousel PARCC-type items 12-16 Plan Q & A Teacher form (create levels) 17

Algebra (levels 1, 2, and 3) 18-23 Student Answer blank form 24

6. Battleship Not included in this workbook 7. Vocabulary Ladder 25-6

8. Exit Card 27

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Your initials

Do ONE STEP only, then move right or pass right (Do not skip steps; be neat and copy the remainder of the

expression.) Given

2(8 – 3)2 + 23 - 15 ÷ 3 + 1

2[ 3 (6 - 8)2 ]

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

Step 10 Step 11 Step 12 Step 13

Do ONE step, then move to the right and continue.

3x - 14 + (3)2 = 10x - 2(x - 10)

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21ST CENTURY ASSEMBLY LINE Do ONE step, then MOVE/PASS to the right GEOMETRY (area and perimeter)

Your name or initials

TASK

YOUR WORK SPACE

STEP 1: ________

Draw and Label a diagram of a rectangle that is 4-inches wide and 6-inches long.

STEP 2: ________

Write a formula (or explain) how you would find the perimeter of this rectangle.

STEP 3: ________

Find the perimeter of this rectangle using the information in Step 2 above. Show all work. Label your answer.

STEP 4: ________

Write a formula (or explain) how you would find the area of the rectangle in Step 1 above.

STEP 5: ________

Find the area of this rectangle using the information in Step 4 above. Show all work.

If we doubled the perimeter of the rectangle drawn in Step 1, how would this change the area?

STEP 6: ________

Draw a new rectangle with double the perimeter of the “rectangle described in Step 1 and label all. (Yes, this can be done different ways.)

STEP 7: ________

What is the area of this new rectangle (in Step 6)? Show your work.

STEP 8: ________

In Step 6, could a different triangle have been drawn with different measurements that would still have a perimeter double the rectangle in Step 1? If so, describe one.

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PName: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set A: Expressions)

Do the examples, show all work, select or write in your answers.

Check your work. You and your partner’s answers should match. Have fun! :-)

1) Combine like terms:

3a + 14 +5a - 12 – a

Answer: ________________

2)

Evaluate this expression if w = 3.

3w + 15 + w2

Answer: w = _____

3)

When you simplify this expression

what step should you do first?

12 – 6 ÷ 3 x 2 + 2(9-2)

___ A. 12-6

___ B. 6 ÷ 3

___ C. 2 + 2

___ D. (9-2)

4)

Simplify this expression.

16

2a + 5b - 22 +3(9 - 7)2 -2a

Answer: ___________________

5)

6)

For 5) and 6) above, create two different expression examples with the same answer.

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Name: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set B: Expressions )



1) Combine like terms:

8(2a) + 12 -2(5) – 9a

Answer: ________________

2)

Evaluate this expression if w = -3.

2w + 42 +2(w+6) + 17

Answer: w = _____

3)

When you simplify this expression

what step should you do first?

18 – 9 ÷ 3 + 2(5-2) x 42

___ A. 18-9

___ B. 9 ÷ 3

___ C. 3 + 2

___ D. (5-2)

4)

Simplify this expression.

a(32 ) + 2b +12 - 22 -3a + 3b

Answer: ___________________

5)

6)

For 5) and 6) above, create two different expression examples with the same answer.

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Name: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set A: Equations)


Check your work; you and your partner’s answers should match. Have fun! :-)

1)

24 = -3x - 6

Answer: x = _____

2)

Solve for “a”

-3(2a) + 19 = a - 30

Answer: a = _____

3)

When you solve this equation which

step should you do first?

w(6)2 + 3(9-5) = 20 + 3 – w

___ A. (6)2

___ B. 20 + 3

___ C. +w to both sides

___ D. (9-5)

4)

Solve for b.

-3b - 25 = -5b –(32)

Answer: b = ____

5)

6)

For 5) and 6) above, create two different equation examples with the same answer.

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Name: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set B: Equations)


Check your work; you and your partner’s answers should match. Have fun! :-)

1) Solve for a

-16 = 2 a + 4

Answer: a = ___________

2)

Solve for w

8w + 22 = 12(5)

Answer: w = _____

3)

Solve for z

2z – 8 = 10z + 4

___ A) -1

___ B) 1

___ C) 1 ½

___ D) - 1 ½

4)

Solve for x.

3(x – 2) + 2x = 34

Answer: x = _______

5)

6)

For 5) and 6) above, create two different equation examples with the same answer.

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Name: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set C: INEQUALITIES)



1)

Solve for a

3a + 6 > -24

Answer: a = _____

2)

Solve for z

5z – (32) < 13(2)

Answer: z = _____ 3) Select all that are true. The

black lines (rays) represent “x”

___ A. x could = -6

___ B. x could = 9½

___ C. x could = 0

___ D. x could = 3

___ E. x could = -8.2

4) x represents the amount of money I

can spend at the store.

2x + 3(x – 2) < 19

Check all that are true: ___A) I can spend $5

___B) I can buy something for $4.50

___C) I have enough money to spend $8

___D) I will get change if I spend $3

5)

6)

For 5) and 6) above. create two different inequality examples with the same answer.

-3 3

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Name: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set D: INEQUALITIES )

Do the examples, show all work; select or write in your answers.


1) Solve for a

2 a + 4 > -24

Answer: a ____

2)

Solve for w

8w + 22 < 12(5)

Answer: w _____

3)

Check all that are true.

-4 4

___ A) x could be 2

___ B) x could = -3

___ C) x could = -5

___ D) x could be 4

___ E) x could = 2.5

4)

x represents the price of a movie ticket.

x + 2(x – 4) > 19

Check all that are true: ___ A) The price of a ticket could be $7

___ B) The ticket price could be $12

___ C) The ticket price could be $6

___ D) The ticket price could be $10.50

5)

6)

For 5) and 6) above. create two different inequality examples with the same answer.

x

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Name: ____________________________Partner: ________________________________________

MATCH YOUR PARTNER’S ANSWER (set :)



1)

Answer: _____

2)

Answer: _____ 3)

Select all that apply.

___ A)

___ B)

___ C)

___ D)

___ E)

4)

Check all that are true:

___A)

___B)

___C)

___D)

5)

6)

For 5) and 6) above. create two different examples with the same answer.

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(1) Solve for x

1

2(x+ 5) = 16

Copy this equation onto your sheet. Show all work (all steps). Circle your final answer. (2) Look at the equations of the two lines below. They are on the same plane.

3y = 6x+21 y = 2x+7

Re-write them on your sheet. Write them both in slope-intercept form. Which statement below is true about these two lines?

a) They are parallel lines. b) They are perpendicular to each other. c) They coincide. d) They intersect at one point but are not perpendicular.

(3) Which equation shows the greatest rate-of-change?

a) y = 2

3x -16

b) y = -3

2x +12

c) x + 20 = y d) 1

3y = x - 4

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(4) Which lines are perpendicular to the line described by the equation shown below? Select ALL that are correct.

4x + y = 16

a) y =

1

4x + 2

b) 4 - 2y = x

c) 3x - 4 = y d) 4y = x + 20

e) 2y = 1

2x + 6 f)

-y = -1

4x + 15

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(5) What is the relationship between the x and y in the graph below?

a) y = 3

4x + 1

b) y = 4

3x + 1

c) y = -4

3x + 1

d) y = -4

3x -1

x

y

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(6) Solve for d. Copy this equation onto your sheet. Show all work (all steps). Then select your final answer: (a), (b), (c), or (d) ?

2ab

d = 16 + a

(a) d =

6

8+ a (b) 2ab

16 + a = d

(c) d =

2b

16 (d) 2ab -16 - a = d

Answers: (1) x = -37 (2) c (3) d (4) a, e and f are correct. (5) b Notice that the y-intercept is at (0,1) and the slope is 4/3

(6) b

(7) w = 2(a- 4)

a

(8) c, d, and f are correct.

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(7) Solve for w.

aw = 2(a- 4)

(8) If the slope of line “m” =2

3, and the slope of line “w” =

-3

2then

what is true about the two lines m and n? (There are three correct

choices.)

(a) When graphed they look like one line on top of the other.

(They coincide.)

(b) They are parallel to each other (they never meet or intersect).

(c) They intersect at one point.

(d) There is not enough information to tell.

(e) They are perpendicular to each other and meet at right angles.

(f) One line slants to the right; the other slants to the left.

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PLANNING with CAROUSEL EXAMPES 1-8 (Grade 8 and/or Algebra-I) Let’s assume you have a range of students in your class with different abilities on this topic. Still, they all need to demonstrate basic understanding of linear equations and to read directions carefully, especially where there is more than one correct answer. Note: The student’s worksheet should be graph paper; they also should use a straight edge, but no calculator.

(1) Which three examples might you assign to your more advanced students? Why?

(2) Which three examples might you assign to your struggling students? why?

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CAROUSEL CARDS for Algebra levels 1,2,3 This is for level-2

** ALGEBRA LEVEL-2

1. a, b, c and d each represent a different value. If a = 2, find b, c, and d. a + b = c a – c = d a + b = 5 ** ALGEBRA LEVEL-2

2. EXPLAIN the mathematical reasoning involved in solving card 1. ** ALGEBRA LEVEL-2

3. EXPLAIN IN WORDS what the equation 2x + 4 = 10 means. Solve the problem.

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** ALGEBRA LEVEL-2

4.

CREATE an interesting word problem that is modeled by 8x – 2 = 7x. ** ALGEBRA LEVEL-2

5. DIAGRAM how to solve 2x = 8 ** ALGEBRA LEVEL-2

6. EXPLAIN what changing the “3” in 3x = 9 to a “2” does to the value of x. WHY is this true?

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ALGEBRA CAROUSEL LEVEL – 1

* ALGEBRA LEVEL-1

1. a, b, c and d each represent a different value. If a = -1, find b, c, and d.

a + b = c b + b + d c – a + -a

* ALGEBRA LEVEL-1

2. Explain the mathematical reasoning involved in solving Algebra Level-1, card-1. * ALGEBRA LEVEL-1

3. Explain how a variable is used to solve word problems. * ALGEBRA LEVEL-1

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4. Create an interesting word problem that is modeled by 2x + 4 = 4x – 10. Solve the problem. * ALGEBRA LEVEL-1

5. Diagram how to solve 3x + 1 = 10.

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ALGEBRA CAROUSEL LEVEL – 3 *** ALGEBRA LEVEL-3

1. a, b, c, and d each represent a different value. If a = 4, find b, c, and d.

a + c = b b – a = c d + d = a

*** ALGEBRA LEVEL-3

2. Explain the mathematical reasoning involved in solving Algebra Level-3 card 1. *** ALGEBRA LEVEL-3

3. Explain the role of a variable in mathematics. Give examples.

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*** ALGEBRA LEVEL-3

4. Create an interesting word problem that is modeled by 3x – 1 < 5x + 7. Solve the problem. *** ALGEBRA LEVEL-3

5. Diagram how to solve 3x + 4 = x + 12

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Name _________________________________________________________________ Date: _________________________ ALGEBRA LEVEL *1 _________ ** 2___________ ***3 ____________ CAROUSEL

1.

2.

3.

4.

5.

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LADDER MATH GAME: for 2 studen (fold on the dotted line)

VOCABULARY WORDS and TERMS for GRADE-5 (focus: fractions)

WORD(S) DEFINITIONS

10

Decimal Divisor

What do we call the number that divides the whole and that has units of tenths, hundredths, thousandths, etc.

9

Simplifying

Using the largest fractional unit possible to express an equivalent fraction is called __________ the fraction.

Ex. 3

6=

1

2or

3

9=

1

3

8 Denominator This number denotes the fractional unit, such as the 5

in 3

5or the 7 in

2

7.

7 Distributive Property Which property is shown here? 4(x+2) = 4x+8

6

Commutative Property

Which property is shown here? 2+6 = 6+2 or 3+1+4 = 1+3+4 or 4´2 = 2´4

5

Equivalent fractions

What do we call fractions that represent the same value but have different denominators, such as

5

10and

1

2or

6

18and

3

9and

1

3

4 Equation A statement that two expressions are equal is called an ______. Example: 3 x 4 = 24 ÷ 2 or 12 - 2 = 5 x 2

3

Expression

A combination of numbers or numbers and variables with at least one operation (+ - x and/or ÷ ) such as: 14 + 3 or 30 – 16 ÷ 4 or 3x – 2·4

2

Factors

Numbers that are multiplied to obtain (to get) a product. (For the number 12: 2 and 6, or 3 and 4 are examples.)

1

Area

When you multiply the length times the width of a rectangle you are finding its ______________. Examples: 5 yds x 2 yds = 10 sq.yds. or

3

4inches ´

1

2inches =

3

8sq. inch

Note #1 should be known from earlier grade. J. Brendel 3/23/15

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LADDER MATH GAME: for 2 students

(fold on the dotted line) VOCABULARY WORDS and TERMS for GRADE-6 (focus: expressions)

Word(s) Definition

10

EQUATION

An _____________ is a statement of equality between two

expressions (such as y = 3x+2 or 2x+2 =8x -10)

9

EQUIVALENT Expressions

What do we call two expressions that name the same number regardless of which value is substituted into them? (For example, the expressions 𝑦𝑦 + 𝑦𝑦 + 𝑦𝑦 and 3𝑦𝑦)

8

LINEAR Expression

An expression that has no exponent greater than “1” is called a __________ expression.

(such as 2ab+ 5 or1

2x-3wy or - 6(2+a)+a

7

EXPONENT

What do we call the “2” in the term x2? The “2” is the _______. It tells the number of times x is used as a factor (the number of times x is multiplied by itself.

For example x4 = x·x·x·x or y3 = y·y·y

6

LIKE Terms

Terms that have the same variable and their corresponding variables have the same exponent are called _____ terms.

(Such as: The x2 in x2 + 2x2 or the b in - 4b+2b)

5

COEFFICIENT

The numerical factor of a term that contains a variable is called the _____ (such as the 2 in 2z )

4

TERM

When addition or subtraction signs separate an algebraic expression into parts, each part is called a __________ (such as in 3x + 4ab; 3x is one and 4ab is another.)

3 ALGEBRIAC EXPRESSION

A combination of variables, numbers, and at least one operation is called an _______ (such as 2a+b or x-16 )

2 An IMPROPER fraction

A fraction that is greater than or equal to 1.

(such as 4

3or

9

4)

1

A MIXED number

The sum of a whole number and a fraction.

(such as 21

3or 5

3

4)

Note: #1 and 2 should be known from earlier grades. J. Brendel 3/23/15

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EXIT CARD

1. ____ Students work in pairs: students give and follow verbal directions (Shhh; no peaking.)

A Carousel cards posted about room

2. ____ Students work with different levels of the same standard

B 21st Century: Do one step, Move right

3 ____ Everyone see other students’ methods and strategies (Shhhh; no speaking.)

C 21st Century: Do one step, Pass right

4 ____ Student pairs practice with vocabulary words (many times over)

D Battle Ship

5 ____ Students work in pairs: students teach each other; students create examples

E Ladder “game”

6____ Students practice effective problem-solving strategies; they must show all steps

F Which one doesn’t belong? Why?

7 ____ A quick warm-up; everyone engaged, watching, listening, thinking, participating … many right answers

G Match Your Partner’s Answer

8 ____ Students model following the correct algebraic order-of-operations

9 ____ The whole class is moving around the room.

10 ___ Recognize mistakes; teach each other.

creatively engage all students -...

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