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
Page 1 of 27
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)
Algebra (an equation)
3
3
3. 21st Century Assembly Line “Do One and Pass Right”
Geometry
4
4. Match Your Partner’s Answer
Expressions (set A and B)
Equations (set A ad B)
Inequalities (set C and D)
Blank form (template)
5-6
7-8
9-10
11
5. Carousel
PARCC-type items
Plan Q & A Teacher form (create levels)
Algebra (levels 1, 2, and 3)
Student Answer blank form
12-16
17
18-23
24
6. Battleship
Not included in this workbook
7. Vocabulary Ladder
25-6
8. Exit Card
27
Page 2 of 27
Your
initials
Given
Do ONE STEP only, then move right or pass right
(Do not skip steps; be neat and copy the remainder of the
expression.)
2(8 – 3)2 + 23
1
- 15 ÷ 3 + 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) = 10x - 2(x - 10)
2
Page 3 of 27
21ST CENTURY ASSEMBLY LINE Do ONE step, then MOVE/PASS to the right
GEOMETRY (area and perimeter)
Your name
or initials
STEP 1:
________
STEP 2:
________
STEP 3:
________
STEP 4:
________
STEP 5:
________
TASK
YOUR WORK SPACE
Draw and Label a diagram of a
rectangle that is 4-inches wide
and 6-inches long.
Write a formula (or explain)
how you would find the
perimeter of this rectangle.
Find the perimeter of this
rectangle using the information
in Step 2 above. Show all work.
Label your answer.
Write a formula (or explain)
how you would find the area of
the rectangle in Step 1 above.
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:
________
STEP 7:
________
STEP 8:
________
Page 4 of 27
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.)
What is the area of this new
rectangle (in Step 6)? Show
your work.
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.
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:
2)
Evaluate this expression if w = 3.
3a + 14 +5a - 12 – a
3w + 15 + w2
Answer: w = _____
Answer: ________________
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)
5)
4)
Simplify this expression.
16
a + 5b - 2 2 +3(9 - 7)2 -2a
2
Answer: ___________________
6)
For 5) and 6) above, create two different expression examples with the same answer.
Page 5 of 27
Name: ____________________________Partner: ________________________________________
MATCH YOUR PARTNER’S ANSWER (set B: 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)
2)
Combine like terms:
Evaluate this expression if w = -3.
8(2a) + 12 -2(5) – 9a
2w + 42 +2(w+6) + 17
Answer: ________________
3)
Answer: w = _____
4)
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)
5)
Simplify this expression.
a(32 ) + 2b +12 - 22 - 3a + 3b
Answer: ___________________
6)
For 5) and 6) above, create two different expression examples with the same answer.
Page 6 of 27
Name: ____________________________Partner: ________________________________________
MATCH YOUR PARTNER’S ANSWER (set A: Equations)
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)
2)
Solve for “a”
24 = -3x - 6
-3(2a) + 19 = a - 30
Answer: x = _____
3)
Answer: a = _____
4)
When you solve this equation which
step should you do first?
Solve for b.
-3b - 25 = -5b –(32)
w(6)2 + 3(9-5) = 20 + 3 – w
___ A. (6)2
___ B. 20 + 3
___ C. +w to both sides
___ D. (9-5)
5)
Answer: b = ____
6)
For 5) and 6) above, create two different equation examples with the same answer.
Page 7 of 27
Name: ____________________________Partner: ________________________________________
MATCH YOUR PARTNER’S ANSWER (set B: Equations)
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)
2)
Solve for a
Solve for w
-16 = 2 a + 4
8w + 22 = 12(5)
Answer: w = _____
Answer: a = ___________
3)
4)
___ A)
___ B)
___ C)
___ D)
5)
Solve for z
Solve for x.
2z – 8 = 10z + 4
3(x – 2) + 2x = 34
-1
1
1½
-1½
Answer: x = _______
6)
For 5) and 6) above, create two different equation examples with the same answer.
Page 8 of 27
Name: ____________________________Partner: ________________________________________
MATCH YOUR PARTNER’S ANSWER (set C: INEQUALITIES)
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)
2)
Solve for a
Solve for z
5z – (32) < 13(2)
3a + 6 > -24
Answer: a = _____
3) Select all that are true. The
black lines (rays) represent “x”
-3
Answer: z = _____
4) x represents the amount of money I
can spend at the store.
2x + 3(x – 2) < 19
3
___ A. x could = -6
___ B. x could = 9½
___ C. x could = 0
___ D. x could = 3
___ E. x could = -8.2
___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)
Check all that are true:
For 5) and 6) above. create two different inequality examples with the same answer.
Page 9 of 27
Name: ____________________________Partner: ________________________________________
MATCH YOUR PARTNER’S ANSWER (set D: INEQUALITIES )
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)
2)
Solve for a
Solve for w
8w + 22 < 12(5)
2 a + 4 > -24
Answer: a ____
3)
Check all that are true.
-4
4
Answer: w _____
4)
x represents the price of a movie ticket.
x + 2(x – 4) > 19
x
___ A)
___ B)
___ C)
___ D)
___ E)
5)
x could be 2
x could = -3
x could = -5
x could be 4
x could = 2.5
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
6)
For 5) and 6) above. create two different inequality examples with the same answer.
Page 10 of 27
Name: ____________________________Partner: ________________________________________
MATCH YOUR PARTNER’S ANSWER (set :)
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)
2)
Answer: _____
3)
Answer: _____
4)
Select all that apply.
___ A)
___ B)
___ C)
___ D)
___ E)
___A)
___B)
___C)
___D)
5)
6)
Check all that are true:
For 5) and 6) above. create two different examples with the same answer.
Page 11 of 27
(1) Solve for
x
Copy this equation onto your sheet.
Show all work (all steps).
Circle your final answer.
1
(x + 5) = 16
2
(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?
2
y = x -16
a)
3
c)
Page 12 of 27
x + 20 = y
b) y = -3
x +12
2
1
d) y = x - 4
3
(4) Which lines are perpendicular to the line described by the
equation shown below? Select ALL that are correct.
4x + y = 16
a)
1
y = x + 2
4
b)
4 - 2y = x
c)
3x - 4 = y
d)
4y = x + 20
e)
1
2y = x + 6
2
f)
1
-y = - x + 15
4
Page 13 of 27
(5) What is the relationship between the x and y in the graph below?
y
x
3
a) y = x + 1
4
b) y =
4
x + 1
3
c) y =
-4
x + 1
3
-4
x -1
d) y =
3
Page 14 of 27
(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
= 16 + a
d
(a)
6
d = 8+ a
(c)
2b
d = 16
2ab
= d
(b)
16 + a
(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.
Page 15 of 27
(7) Solve for w.
aw = 2(a - 4)
-3
2
(8) If the slope of line “m” = , and the slope of line “w” =
2 then
3
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.
Page 16 of 27
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?
Page 17 of 27
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.
Page 18 of 27
** 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?
Page 19 of 27
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
Page 20 of 27
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.
Page 21 of 27
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.
Page 22 of 27
*** 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
Page 23 of 27
Name _________________________________________________________________ Date: _________________________
ALGEBRA LEVEL *1 _________
1.
2.
3.
4.
5.
Page 24 of 27
** 2___________
***3 ____________
CAROUSEL
LADDER MATH GAME: for 2 studen
(fold on the dotted line)
VOCABULARY WORDS and TERMS for GRADE-5 (focus: fractions)
WORD(S)
10 Decimal Divisor
DEFINITIONS
What do we call the number that divides the whole and
that has units of tenths, hundredths, thousandths, etc.
Using the largest fractional unit possible to express an
equivalent fraction is called __________ the fraction.
3 1
3 1
Ex. =
or
=
6 2
9 3
9
Simplifying
8
Denominator
This number denotes the fractional unit, such as the 5
3
2
in or the 7 in .
5
7
7
Distributive Property
Which property is shown here? 4(x + 2) = 4x +8
Commutative Property
Which property is shown here?
2+6 = 6+2 or
3+1+4 = 1+3+4
6
5
Equivalent fractions
4
Equation
3
Expression
2
Factors
1
Area
or
4´2 = 2´ 4
What do we call fractions that represent the same value
but have different denominators, such as
5
1
6
3
1
and
or
and and
10
2
18
9
3
A statement that two expressions are equal is called an
______. Example: 3 x 4 = 24 ÷ 2 or 12 - 2 = 5 x 2
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
Numbers that are multiplied to obtain (to get) a product.
(For the number 12: 2 and 6, or 3 and 4 are examples.)
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
1
3
inches ´ inches = sq. inch
4
2
8
Note #1 should be known from earlier grade.
J. Brendel 3/23/15
Page 25 of 27
LADDER MATH GAME: for 2 students
(fold on the dotted line)
VOCABULARY WORDS and TERMS for GRADE-6 (focus: expressions)
Word(s)
10
EQUATION
9
EQUIVALENT
Expressions
8
7
6
LINEAR Expression
EXPONENT
LIKE Terms
Definition
An _____________ is a statement of equality between two
expressions (such as y = 3x + 2 or 2x + 2 = 8x -10 )
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)
An expression that has no exponent greater than “1” is
called a __________ expression.
1
(such as 2ab + 5 or
x - 3wy or - 6(2 + a) + a
2
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.
4
3
For example x = x · x · x · x or y = y· y· y
Terms that have the same variable and their corresponding
variables have the same exponent are called _____ terms.
2
2
2
(Such as: The x in x + 2x 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.)
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.
4
9
(such as
)
or
3
4
1
A MIXED number
3
The sum of a whole number and a fraction.
1
3
(such as 2
or 5 )
3
4
Note: #1 and 2 should be known from earlier grades. J. Brendel 3/23/15
Page 26 of 27
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 ____
E
Students work in pairs: students teach each Ladder “game”
other; students create examples
6____
F
Students practice effective problem-solving Which one doesn’t belong? Why?
strategies; they must show all steps
7 ____
A quick warm-up; everyone engaged,
watching, listening, thinking, participating
… many right answers
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.
Page 27 of 27
G
Match Your Partner’s Answer