th
6
Grade
MSP November 2015
• Keep your table groups to 3 or 4 participants
• Collaborate/sit with those whom you do not
normally work
Introductions and Training Purpose
• Grant Purpose and Background
• Partnerships
• Purpose of this Training
Target: Increase content knowledge of identified
Tennessee Education Standards for Math as
measured through a STEM challenge or a Math &
Science integrated activity.
Training Teams and Logistics
Mrs. Evelyn Bishop and Dr. Jamie James
Bathrooms/Breaks/Cell Phones
Materials
Emergency Exit
Agenda
Today’s Activities
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•
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Vertical Alignment
Deconstruction of Content Standards
White Board Exchange Sprints
MICA and MIST
Rigorous Classroom Assessments
Hands-On Manipulatives
Integrated Lesson or Challenges
Norms
Be an active participant
Be mindful of air time
Be mindful of sidebar conversations
Use technology at
appropriate times
Our Challenge
Should Pluto be reclassified as a planet or
an astronomical oddball? Make a
decision, explain your reasoning and
provide at least 2 supporting
mathematical and/or scientific evidences.
The best explanation will be submitted to
the International Astronomical Union for
consideration.
Standards
6.RP.A.3 Use ratio and rate reasoning to
solve real-world and mathematical
problems, e.g., by reasoning about tables
of equivalent ratios, tape diagrams,
double number line diagrams, or
equations.
6.RP.A.3a Make tables of equivalent ratios
relating quantities with whole-number
measurements, find missing values in the
tables, and plot the pairs of values on the
coordinate plane. Use tables to compare
ratios.
6.NS.B.3 Fluently add, subtract, multiply,
and divide multi-digit decimals using the
standard algorithm for each operation.
• SPI 0607.6.1 Use data to
draw conclusions about the
major components of the
universe.
• SPI 0607.6.2 Explain how the
relative distance of objects
from the earth affects how
they appear.
Vertical Alignment
• Using the Completed Vertical Progression
Guide– identify the vertical alignment of the
targeted standards.
• Identify the implications across the grade
levels.
• Discuss with your table group– modify if
needed.
• Choose one implication to share with the
whole group and write on chart paper.
• Identify common student misconceptions.
Deconstruction of Standards
• 6.RP.A.3 Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning
about tables of equivalent ratios, tape diagrams,
double number line diagrams, or equations.
• 6.RP.A.3a Make tables of equivalent ratios relating
quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of
values on the coordinate plane. Use tables to
compare ratios.
What does this standard mean?
What will the students need to be able to do?
Deconstruction of Standards
6.NS.B.3 Fluently add, subtract, multiply, and divide
multi-digit decimals using the standard algorithm for
each operation.
What does this standard mean?
What will the students need to be able to
do?
Think Time
• Why is it important to deconstruct
standards?
White Board Exchange
MICA
•
•
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•
MICA Fake Student Log-in
Username: first initial last name (lowercase)
jjames Example (some of you may have a number after the name)
Password: cmcss15
https://micatime.com
We will see you at 12:15
Four Corners
After Experiencing MICA
I feel
good
about…
I am
concerned
about…
In my
classroom, I
will be
strategic
about…
I need help
with …
Assessment Questions
It is important to know how these
standards will be assessed.
MICA
MIST
Grade Level Common
Assessments



TNReady Breakdown
What does it look like in the classroom?
Researched based strategies
(Concrete-pictorial-abstract – Jerome Bruner)
 tape diagrams
 number lines
 various other strategies rooted in
conceptual understanding
DOUBLE LINE GRAPHS and a variation of
TAPE DIAGRAMS
to solve problems.
7th Grade
6th Grade
6.RP.1 - Definition of ratio
7.RP.1 – Unit Rates associated with
ratios (with fractions and decimals)
6.RP.2 - Unit rate(s) associated to
ratio
Whole numbers
(6.RP.3) Given a proportional relationship represent it a variety of
ways:
. A table
. Plotting points on a coordinate graph.
. Tape diagrams
. Double number line diagrams.
6.RP.3 –Use ratios and rate reasoning to solve (single
step)real world mathematical problems using the
representations above and:
. Using the unit rate
. Seeing % as a rate
. Using ratio reasoning and manipulating units by
multiplying and dividing
The Standards requires that the strategies listed here
are not replaced by solving equations.
Anaya and Şahin IM&E CCSSM National
PD
7.RP.2.
Using the representations from 6th grade
a. Decide whether two quantities are in
a proportional relationship.
b. Identify the constant of
proportionality
7.RP.3 Use proportional
relationships to solve (multi-step)
ratios and percent problems.
7.RP.2
c. Represent proportional relationships
by equations.
d. Understanding the proportional
relationship on a graph most importantly
(0,0) and (1.r)
Tape Diagrams
Grade 1
Emi made a train with 6 yellow snap cubes and some green snap
cubes. The train was made of 9 snap cubes. How many green
cubes did she use?
6
3
9 snap cubes
Tape Diagrams
The baker packs 36 bran muffins in boxes of 4. Draw and
label a tape diagram to find the number of boxes he packs.
4 4 4 4 4 4 4 4 4
36 muffins
Grade 3
Tape Diagrams
Jerome, Kevin, and Seth shared a submarine
sandwich. Jerome ate ½ of the sandwich, Kevin
1
ate of the sandwich, and Seth ate the rest. What
3
is the ratio of Jerome’s share to Kevin’s share to
Seth’s share?
Jerome
3
Kevin
2
Seth
1
Practice ACT
Question
Tape Diagrams
Jaden is 5 years older than Harold and Sammy is twice as old as
Jaden. If Harold is 12, what is the sum of their ages?
Let’s consider double line graphs:
According to the double line graph below, we know that
1400 would represent 100%
0%
700
1400
50%
100%
So to find 50% of that, I would think of dividing the line
in ½ between zero and 1400 : 50% = 50 = 1
100 2
Since 100% ÷ 2 = 50% I would also do 1400 ÷ 2
to get 700
So what if we wanted to find 25%....ideas?
We could take 100% divided by 4 to get 25% which
means we would also divide 1400 by 4.
1400 ÷ 4 = 350
0%
350
700
1400
25%
50%
100%
Or we could take 50% divided by 2 to get 25% which
means we would also divide 700 by 2.
700 ÷ 2 = 350
Either way we get 25% will be 350 so now let’s
plug it in on the number line.
Now take a few minutes to discuss with
your shoulder partner
how you would find 75%.
0
350
700
1400
0%
25%
50%
100%
During private think time, consider how we would
divide this number line up for 20% then share with
the person sitting next to you.
Have table talk to share those thoughts as a whole group now.
0%
100%
Now draw this double number line on your paper and use it to find 20% of
400
and 80% of 400.
80
0%
20%
320
40%
60%
80%
400
100%
Sammie has spent $1,320 this month which is
75% of his monthly paycheck. Use a double
number line graph to determine the amount
of his monthly check.
Solution shown on next slide
X4
÷3
$440
0%
25%
50%
÷3
X4
$1,320
$1,760
75%
100%
The Ratio and Proportion strand starts
in 6th and ends in 7th. It leads directly
into:
•Understand the connections between proportional
relationships, lines, and linear equations.
•8.EE.5. Graph proportional relationships, interpreting the unit rate
as the slope of the graph. Compare two different proportional
relationships represented in different ways. For example, compare a
distance-time graph to a distance-time equation to determine which
of two moving objects has greater speed.
•8.EE.6. Use similar triangles to explain why the slope m is the same
between any two distinct points on a non-vertical line in the
coordinate plane; derive the equation y = mx for a line through the
origin and the equation y = mx + b for a line intercepting the
vertical axis at b.
What happens in 8th grade?
Anaya and Şahin IM&E CCSSM National
PD
Close Reading for Challenge “In 2003, U.S. astronomer Mike Brown discovered
a new object beyond Pluto. Brown thought he had discovered a new planet
because the object, which he named Eris (EER-is), is larger than Pluto. The
discovery of Eris caused other astronomers to talk about what makes a planet
a "planet." The International Astronomical Union is the group of astronomers
responsible for naming objects in space. The IAU decided that Pluto and
objects like it were not really planets at all because of their size and location in
the solar system. The IAU decided that Pluto and objects like it should now be
called dwarf planets.
Astronomers continue to study the solar system. They use high-power, groundbased telescopes to discover new objects in space. Ideas about the universe
and Earth's place in it keep changing as scientists get new information. This can
cause scientists to rethink what they know and how they classify objects.
Scientists are still considering what makes an object a planet as they learn
more about the most distant objects in the solar system.”
Our Challenge
Should Pluto be reclassified as a planet or
an astronomical oddball? Make a
decision, explain your reasoning and
provide at least 2 supporting
mathematical and/or scientific evidences.
The best explanation will be submitted to
the International Astronomical Union for
consideration.
Standards
6.RP.A.3 Use ratio and rate reasoning to
solve real-world and mathematical
problems, e.g., by reasoning about tables
of equivalent ratios, tape diagrams,
double number line diagrams, or
equations.
6.RP.A.3a Make tables of equivalent ratios
relating quantities with whole-number
measurements, find missing values in the
tables, and plot the pairs of values on the
coordinate plane. Use tables to compare
ratios.
6.NS.B.3 Fluently add, subtract, multiply,
and divide multi-digit decimals using the
standard algorithm for each operation.
• SPI 0607.6.1 Use data to
draw conclusions about the
major components of the
universe.
• SPI 0607.6.2 Explain how the
relative distance of objects
from the earth affects how
they appear.
In Science Class
• Infer: How are planets classified?
• What are the characteristics of each planet?
–
–
–
–
–
–
–
Distance from sun
Period Rotation
Period of Revolution
Diameter
Temperature
Gravity
Composition
Analyzing Data and Planet Classification
• Group planets by their characteristics.
• Determine which planets share similar
characteristics.
• Create a classification system for the planets and
justify your grouping system.
• How could you extend your classification system to
other members of our solar system such as moons,
comets, asteroids, and meteoroids?
• Set: How far away are the planets from the
sun? What is the size of planets in our solar
system?
Sun vs. Earth Size
Comparing the Sizes of
the Sun, Earth, Moon and Jupiter
The sun’s diameter is 1,392,000 km. If the sun’s
diameter of 1,392,000 km is represented by a 55 cm
or 22 inches poster board, determine the diameter of
the following bodies by finding the equivalent ratio:
• Moon is 3,475 km= _______________
• Earth is 12,756 km= ______________
• Jupiter is 142,984 km= ________________
Create a Model of the Sun, Earth,
Moon and Jupiter
• Use one full poster board as your sun’s diameter.
• Draw a line and label inside of this poster board each of the
diameters calculated for the Earth, Moon and Jupiter.
• Explain:
– How many times bigger is the sun in comparison to:
Earth?
Moon?
Jupiter?
Comparing Earth size to other
Universe Components
Earth as a
Frame of Reference
Earth Size as a Frame of Reference
Complete the following table by finding the missing data:
Name
Earth
Charon
Mercury
Venus
Mars
Ceres
Jupiter
Saturn
Uranus
Neptune
Pluto
Diameter (km)
12,756
1,184
4,879
12,104
142,984
49,528
2,390
Equivalent Ratio to
Earth
(12,756/12,756)= 1
(1,184/12,756)= 0.09
0.53
0.07
9.45
4.01
Rank the universal components from
smallest to largest using their
equivalent ratio to Earth.
-Which components are smaller than
Earth?
-Which components are larger than Earth?
Meter Stick Distance Scale
Inches vs. Centimeters Review
1 meter = ?
Calculate the Distance from the Sun in
Astronomical Units
Steps for Meter Stick Scale:
1. Use the meter stick scale from 0 to 100 centimeters
to place the 8 planets and Pluto.
2. Place the sun at the 0 centimeters or beginning
mark of the meter stick.
3. Pluto is 39.75 AU from the sun. If we round this
distance to the nearest whole number, Pluto is 40
AU from the sun. Place Pluto at the 100 centimeters
mark or end of the meter stick.
4. Create a distance scale for the reminder planets and
place them on the appropriate place.
Place the 8 Solar Systems Planets using
their equivalent ratio to their distance from
the Sun in Astronomical Units (AU)
SUN
PLUTO
10
20
30
40
50
60
70
80
90
100
How do mathematical principles
and equivalent ratios help us
understand the size of the planets,
their location in the Solar System
and their distance from the sun?
Explain using 1-2 examples.
MSP Wikispace
– Your Source for All Resources
• http://msptennessee.wikispaces.com
• Please take the time to visit the site
after today’s session
• Contact us if you have any questions or
need help.
Reflection
• How do I plan to share with others
my learning of today?
• What support do I need to use the
instructional resources shared today?