First
Introduced
(grade)
What Are the Changes 6-8?
New TEKS
Statement
Should be
Mastered
(grade)
(New concept, deleted concept,
clarify language, etc.)
Nature of Change
Tarleton State University
Handout 1
1-7
Implications for the Classroom
TEKS Refinement and Implications for the Classroom
Mathematics TEKS Refinement 2006 – 6-8
What’s the Difference?
0
1
Mathematics TEKS Refinement 2006 – 6-8
2
3
Remove One
4
Transparency 5/Handout 1
3-14
5
Tarleton State University
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
What’s the Difference?
Sample Space
(1,1)
(1,2)
(1,3)
(1,4)
(1,5)
(1,6)
(2,1)
(2,2)
(2,3)
(2,4)
(2,5)
(2,6)
(3,1)
(3,2)
(3,3)
(3,4)
(3,5)
(3,6)
(4,1)
(4,2)
(4,3)
(4,4)
(4,5)
(4,6)
(5,1)
(5,2)
(5,3)
(5,4)
(5,5)
(5,6)
(6,1)
(6,2)
(6,3)
(6,4)
(6,5)
(6,6)
What’s the Difference?
Transparency 6/Handout 2
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Three-Minute Pause
adapted from Ralph Tyler and further developed by Grant Wiggins, Jay McTighe
What Is a Three-Minute Pause?
The Three-Minute Pause provides a chance to stop, reflect on the concepts and ideas
that have just been introduced, make connections to prior knowledge or experience,
and seek clarification.
How Does It Work?
1) Summarize Key Ideas Thus Far. Instruct participants to get into groups. Give them
a total of three minutes for the ENTIRE process. First, they should focus in on the key
points of the presentation up to this point. It's a way for them to stop to see if they are
getting the main ideas.
2) Add Your Own Thoughts. Next, the participants should consider prior knowledge
connections they can make to the new information. Suggested questions: What
connections can be made? What does this remind you of? What would round out your
understanding of this? What can you add?
3) Pose Clarifying Questions. Are there things that are still not clear? Are there
confusing parts? Are you having trouble making connections? Can you anticipate
where we're headed? Can you probe for deeper insights?
Why Should I Take the Time for a 3-Minute Pause?
It depends on how much "stuff" you want participants to be thinking about before they
get a chance to process the new information. If you don't want to have to keep
reteaching information, then you should give participants time to think about, make
sense of, organize, and reflect on their learning.
The Three-Minute Pause is a perfect bridge, a chance for participants to consolidate
and clarify their emerging understanding, before you move on to teach more new ideas
or concepts. It's simple, straightforward, productive, efficient, and instantly useful.
Where is the Math?
Handout 1
3-18
Check It Out
Tarleton State University
Let’s Talk Probability
Roll a number cube/die
Event A = roll is a 5
Roll a number cube/die
Event B = roll is a prime number
Roll a red and a green number cube/dice
Event C = sum is 12
Roll a red and a green number cube/dice
Event D = Sum is a prime number
Event E = Sum is even
Flip a coin and spin an equally divided 4
part spinner
Event F = flip a head and spin a 3
Flip a coin and spin an equally divided 4
part spinner
Event G = flip a tail and spin an even
number
Pull one card from a deck of cards
Event H = draw a 10
Event J = draw a heart
Pull two cards from a deck of cards
Event K = 1st draw an 8
Event L = 2nd draw an 8
Experiment
N/A
Transparency 4/Handout 1
3-32
Type of experiment
Type of events
Type of events
Simple Composite Simple Compound Independent Dependent
For each of the following experiments, determine the type of experiment (simple or composite); the type
of event (simple or compound); and if there are two events, whether the events are independent or
dependent.
Mathematics TEKS Refinement 2006 – 6-8
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Graphic Organizer
Simple experiment:
Simple experiment:
Simple event:
Compound event:
Composite experiment:
Composite experiment:
Simple event:
Compound event:
Let’s Talk Probability
Transparency 8/Handout 2
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
What’s the Probability?
For each of the following, draw a model (if appropriate) that will help you solve the
problem. Identify each experiment as simple or composite, and each event as simple or
compound. Does your model help you determine when to add probabilities and when to
multiple probabilities? Explain.
1.
A large basket of fruit contains 7 apples, 8 oranges, and 10 pears. If a piece of
fruit is chosen at random, what is the probability of getting:
an orange?
an orange or a pear?
2.
A pair of dice is rolled. What is the probability of getting a sum of 2? a sum of 7?
3.
In a class of 30 students, there are 17 girls and 13 boys. Five are “A” students,
and three of these students are girls. If a student is chosen at random, what is the
probability of choosing a girl or an “A” student?
4.
In the United States, 43% of people wear a seat belt while driving. If two people
are chosen at random, what is the probability that both of them wear a seat belt?
What is the probability of only one wearing a seat belt?
What is the probability of at least one wearing a seat belt?
5.
Three cards are chosen at random from a deck without replacement. What is the
probability of getting a jack, a ten, and a nine in order?
6.
A city survey found that 47% of teenagers have a part time job. The same survey
found that 78% plan to attend college. If a teenager is chosen at random, what is
the probability that the teenager has a part time job and plans to attend college?
What is the probability that the teenager does not have a part time job and plans to
attend college?
7.
In a shipment of 100 televisions, 6 are defective. If a person buys two televisions
from that shipment, what is the probability that both are defective?
What’s the Probability?
Handout 1
3-43
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Sample Assessment Items – What’s the Difference?
Yesterday we rolled a pair of dice, found differences, and represented the data.
1. Bonnie correctly removed the counter above the 3. What might have been rolled?
0
1
2
3
4
5
2. PB & J played the Remove One game and they got the following line plot.
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0
1
2
3
4
5
? Why or why not?
Based on their plot, did they roll
3. Could Group 8 have gotten the following line plot? Explain why or why not?
X
X
X
X
X
1
X
X
X
X
2
X
X
X
3
X
X
4
X
X
5
X
6
4. Design a line plot so that the following experimental probabilities are represented for
the differences of rolling 2 dice.
p(0) =
1
2
2
3
1
, p(1) = , p(2) = , p(3) = , p(4) = , p (5 ) = ___
10
10
10
10
10
What’s Your Problem?
Handout 1-1
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
5. Create two different line plots that represent that the experimental probability of rolling
a difference of 2 was 1/12.
6. Which graph below would best represent the data on the line plot?
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0
1
2
3
4
5
a.
b.
c.
d.
What’s Your Problem?
Handout 1-2
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What’s Your Problem?
Mathematics TEKS Refinement 2006 – 6-8
Handout 2-1
4-27
Tarleton State University
What’s Your Problem?
Mathematics TEKS Refinement 2006 – 6-8
Handout 2-2
4-28
Tarleton State University
What’s Your Problem?
Mathematics TEKS Refinement 2006 – 6-8
Handout 2-3
4-29
Tarleton State University
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Create a six-value data set that would produce
the following graph:
What’s Your Problem?
Handout 3-1
4-30
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Find a pair of numbers, if possible, whose lcm is
a.
b.
c.
d.
the larger of the pair of numbers
the smaller of the pair of numbers
the product of the pair of numbers
a number between the larger of the pair and
the product of the pair.
What’s Your Problem?
Handout 3-2
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Generate two 5-value data
sets that have a mean of 12.
What’s Your Problem?
Handout 3-3
4-32
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
The mean number of children in 6 families
is 5 children.
a. What is the total number of children in
the six families?
b. Other than the six families of 5 children,
create a set of families that fits this
information.
c. Would another classmate’s set of
families for question b have to be the
same as yours?
Connected Mathematics Project
What’s Your Problem?
Handout 3-4
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
a. Give three pairs of
numbers, each consisting
of a positive and a
negative number, with a
difference of 100.
b. Give three pairs of negative
numbers with a difference
of 50.
Mathematics in Context
What’s Your Problem?
Handout 3-5
4-34
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Make up a context problem that
1 3
fits with 10 ÷
2 4
Mathematics in Context
What’s Your Problem?
Handout 3-6
4-35
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Find a six-value data set that would produce
the following graph:
What’s Your Problem?
Handout 3-7
4-36
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Create a context and a 6-value
data set where the mean is a
better average of the data than
the median or the mode.
Discuss why.
What’s Your Problem?
Handout 3-8
4-37
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Jana wants to be able to have 30
completely different outfits consisting
of pants, a shirt, and shoes. Create 2
different possible wardrobes for her.
What’s Your Problem?
Handout 3-9
4-38
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Create 3 different spinners so that the
probability of landing on blue is 1/2.
What’s Your Problem?
Handout 3-10
4-39
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Create a context and a 6-value data set
where the mode is a better average of
the data than the median or the mean.
Discuss why.
What’s Your Problem?
Handout 3-11
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Write three new “frog
problems” – one that you
think is easy, one that is more
difficult, and one that is very
difficult. Describe how to
solve each problem
.
Mathematics in Context
What’s Your Problem?
Handout 3-12
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
If the probability of Abby winning the
drawing at the school carnival is 1/30,
name 3 possible combinations of
tickets she bought and total tickets
sold.
What’s Your Problem?
Handout 3-13
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Create a spinner so that the chance for
getting hot dogs is 12.5%, the chance
for pizza is 37.5%, the chance for
hamburgers is 25%. The last choice is
ham sandwiches. What is the chance
of ham sandwiches?
Adapted from Connected Mathematics Project
What’s Your Problem?
Handout 3-14
4-43
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
toppings
Ice cream
flavors
x
Cones
x
x
x
x
x
x
x
Tom
Tom is choosing an ice-cream cone.
1. How many kinds of cones does he have to
choose from?
2. How many ice-cream flavors does he have
to choose from?
3. How many toppings does he have to
choose from?
What’s Your Problem?
Handout 3-15
4-44
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Design a line plot so that the
following probabilities are
represented for the differences
of rolling 2 dice.
p(0) =
1
2
2
3
1
, p(1) = , p(2) = , p(3) = , p(4) = , p (5 ) = ___
10
10
10
10
10
What’s Your Problem?
Handout 3-16
4-45
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
A bag contains several marbles. Some are
red, some are white, and some are blue. You
count the marbles and find the theoretical
probability of choosing a red marble is 1/5.
You also find the theoretical probability of
choosing a white marble is 3/10.
a. What is the least number of marbles that
can be in the bag?
b. Can the bag contain 60 marbles? If so
how many of each color does it contain?
c. If the bag contains 4 red marbles and 6
white marbles, how many blue marbles
does it contain?
d. How can you find the probability of
choosing a blue marble?
Connected Mathematics Project
What’s Your Problem?
Handout 3-17
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
About how many feet of fencing are
needed to enclose a rectangular garden
with a 6 ft long side and a 10 ft long
diagonal?
Abby wrote:
2
2
6 + 10 = 136
136 = 100 + 36 = 16
2(16) + 2(6) = 32 + 12 = 44
44 ft. of fencing
What’s Your Problem?
Handout 3-18
4-47
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
If you have a rectangle that is 2 cm by
3 cm and you dilate it by a scale factor
of 4, what is the area of the new figure?
Joanne showed the following work:
2×3= 6
6(4) = 24
24 cm2
What do you say to Joanne?
What’s Your Problem?
Handout 3-19
4-48
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
A hat had two blue cubes, four yellow
cubes, and six red cubes. Ralph says
that the probability the cube is blue is
12/4. Eleanor says that 12/4 is
impossible. Who is correct? Explain.
What’s Your Problem?
Handout 3-20
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
The rectangle DAWN was enlarged by a scale
factor of 2:3 to form a new similar rectangle
COLD. What is the perimeter of COLD?
D
20
A
10
N
W
Justin’s work is below. What do you say to
Justin?
10 to 15, 20 to 30
so (15) (30) = 450
450 cm
What’s Your Problem?
Handout 3-21
4-50
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Aran knows that if you roll a number
cube once, there is a 50% chance of
getting an even number. He says that
if you roll a number cube twice, the
chance of getting at least one even
number is doubled. Is he correct?
Explain.
Connected Mathematics Project
What’s Your Problem?
Handout 3-22
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Carrie wonders what would happen to the
figure she made if she multiplied the
coordinates by –3. This is what some of her
classmates think.
John says, “It would be upside down and
three times as big.”
Mauri says, “I guess it would be nine times
as big.”
Emily says, “The coordinates of the top point
which were (2,3) would be (9,8).”
Reflect: Comment on the thinking of each of
Carrie’s three classmates.
Adapted from Mathematics in Context
What’s Your Problem?
Handout 3-23
4-52
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Connected Mathematics Project
What’s Your Problem?
Handout 3-24
4-53
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Michael said that the mean, median,
and the mode of the following data is
7. What do you think?
3, 5, 6, 8, 9, 11
What’s Your Problem?
Handout 3-25
4-54
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
How many different ice-cream cones
are possible?
toppings
Ice cream
flavors
x
Cones
x
x
x
x
x
x
x
Tom
Tom wrote:
2 + 3+ 4 = 7
What do you tell him?
What’s Your Problem?
Handout 3-26
4-55
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Gil, Lashonda, and Greg are discussing
how they might shrink a triangle.
Gil says, “You could multiply the
coordinates by – 2,”
Lashonda says, “That is not right. You
would have to multiply the coordinates
by ½.”
Greg says, “Why not multiply by
– ½?”
Which of these statements do you
think is/are correct?
Adapted from Mathematics in Context
What’s Your Problem?
Handout 3-27
4-56
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Robin found the probability of hitting
section A in the dart game below. Is
she correct?
3
A
B
3
2
C
9π
9
32 π
=
= , so the probability of
2
4 π 16π 16
hitting the A section is 9/16.
What’s Your Problem?
Handout 3-28
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
In the ClueR board game, players try to
solve a murder mystery. To win, a player
must identify the murderer, the murder
weapon, and the room in which the
murder was committed. Amadi claims
that there are 118 possible solutions to the
game. His sister Ayana, who has never
played the game, says she can’t believe
this is true. Why does she say this?
Connected Mathematics Project
What’s Your Problem?
Handout 3-29
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Grades
4
3
2
1
0
0
37
50
55
56
65
71
73
74
75
76
78
80
81
85
86
88
89
90
92
95
98
Percentage
Which of the graphs is more helpful to
the teacher to see the grade layout
quickly?
What’s Your Problem?
Handout 3-30
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Molly designs a game for a class project. She
makes the three spinners shown. She tests to
see which one she likes best for her game. She
spins each pointer 20 times and writes down
her results, but she forgets to record which
spinner gives which set of data. Match each
spinner with one of the data sets. Explain your
answer.
Connected Mathematics Project
What’s Your Problem?
Handout 3-31
4-60
Mathematics TEKS Refinement 2006 – 6-8
.....
7
Tarleton State University
50
.....
1500
60
.....
14
a. Copy and complete the area model in
your notebook and fill in the missing
numbers.
b. What multiplication problem fits
problem a? Use the area model to find
the answer.
Mathematics in Context
What’s Your Problem?
Handout 3-32
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Yesterday we walked around in front of
the motion detector. Which person
below was walking faster? Why?
Amanda
What’s Your Problem?
Jessica
Handout 3-33
4-62
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
A math teacher at Springfield Middle
School would like to have calculators for
her class. The school store offers
calculators for $7 each. She asked her
sixth-grade students to calculate the total
price for 32 calculators. Here is the
strategy of one of her students. Describe
the steps Sondra used for her ratio table.
Sondra:
Number of
Calculators
Price (in dollars)
1
7
10
70
20
30
2
32
140 210 14
224
Adapted from Mathematics in Context
What’s Your Problem?
Handout 3-34
4-63
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Yesterday we walked around in front of
the motion detector. What direction was
the person walking below? Why?
What’s Your Problem?
Handout 3-35
4-64
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
In the What’s the Difference game,
Bonnie removed the counter above the
3. What might have been rolled?
0
What’s Your Problem?
1
2
3
4
5
Handout 3-36
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Three Problem Types – How to Write
Snap Shot Problems:
What are two ideas, processes, or representations that students mix up?
Juxtapose them and ask which is which.
What part of a large activity can you grab to assess if students got the
gist of the large activity?
Un-Doing Problems:
Can you start with the answer?
Can you start in the middle?
Can you change one constraint?
Can you start with a different representation?
Ask students to create or invent the beginning of a problem.
Error Analysis
What are the typical errors that students make?
Pose an incorrect solution.
Ask students to explain what went wrong.
Sometimes show the incorrect process, sometimes just show the
incorrect answer.
What’s Your Problem?
Handout 4
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