Download 7th-Grade-Math

7th Grade Mathematics Quarter 3 Curriculum Map
2013-2014
Unit 4: Geometry
3rd 9 Weeks
Suggested Instructional Days: 20
Unit Summary (Learning Target/Goal):
Draw, construct, and describe geometrical figures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
CCSS for Mathematical Practice:
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
Unit
Timeline
1 day
Geometry
Draw, construct,
and describe
geometrical
figures and
describe the
relationships
between them.
Solve real-life
and
mathematical
problems
involving angle
measure, area,
surface area, and
volume.
2 days
Standards
7.G.2: Draw (freehand, with ruler
and protractor, and with technology)
geometric shapes with given
conditions. Focus on constructing
triangles rom three measure of angles
or sides, noticing when the condition
determines unique triangle, more than
one triangle, or no triangle.
7.G.5: Supplementary,
complementary, adjacent, and vertical
angles
Learning Expectation & Example
Activity Lab: Drawing geometric figures
Vocabulary
line segment;
triangles;
rhombus
Resources
Prentice Hall Mathematics
6-1a
Use understandings of angles and
deductive reasoning to write and solve
equations
Angles
acute;
right;
obtuse;
straight;
complimentary;
supplementary;
adjacent
vertical;
congruent
Prentice Hall Mathematics
6-1
trapezoid;
area
Prentice Hall Mathematics
6-2a
Example
If angle G and angle H are supplementary
and the measure of angle G is 4 times the
measure of angle H, what are the measures of
angle G and angle H?
.5 day
7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Activity Lab: Generating formulas for
area
7th Grade Math Quarter 3
1 7th Grade Mathematics Quarter 3 Curriculum Map
2013-2014
1 day
1 day
2.5 days
3 days
1 day
Prentice Hall Mathematics
6-2
triangle
base; height
Prentice Hall Mathematics
6-3
Area of a parallelogram, relating
perimeter and area
7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Area of triangle, relating side lengths and
area
Example
A carpenter has blueprints for a wooden,
triangular patio. The base is 5 m and the
height is 7 m. What is the area of the patio?
tri = 𝐴 = 𝑏ℎ 7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Area of other figures (trapezoids,
irregular figures)
trapezoid
base; height
Example
trap = 𝐴 =
Example
A playground has the shape of a
parallelogram. If the base is 30 ft., and the
corresponding height is 25 ft., what is its
area?
The top of a trapezoid is 17 in long, and the
bottom edge is 39 in long. The distance from
the top edge to the bottom edge is 16 in.
What is the area of the trapezoid?
7.G.4: Know the formulas for the area
and circumference o a circle and use
them to solve problems; give an
informal derivation of the relationship
between the circumference and area of
a circle.
Circumference and are of a circle
7.G.3: Describe 2-d figures that result
from slicing 3-d figures, as in plane
sections of right rectangular prisms
and right rectangular pyramids.
Drawing and naming three dimensional
figures
Example
Example
Find the circumference and area of a circle
with a given diameter or radius.
Identify the number of faces, edges, and
vertices a hexagonal pyramid has.
parallelogram
base; height
rect A = lw
parr A = bh
7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
!
!
!
!
Prentice Hall Mathematics
6-4
ℎ(𝑏1 + 𝑏2)
circumference;
diameter;
radius;
pi;
circle;
C=πd
C=2 πr
A= πr2
3-D figure; face;
edge; prism; base;
height; cube;
cylinder; pyramid;
vertex; cone; sphere;
center; 3-D
Prentice Hall Mathematics
6-5
Prentice Hall Mathematics
7-1
7th Grade Math Quarter 3
2 7th Grade Mathematics Quarter 3 Curriculum Map
2013-2014
2.5 days
.5 day
3 days
7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
7.G.6: Solve real world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes, and right prisms.
1 day
1 day
7.G.3: Describe 2-d figures that result
from slicing 3-d figures, as in plane
sections of right rectangular prisms
and right rectangular pyramids.
Determine the dimensions of the figures
given the area or volume, surface area of
prisms and cylinders, drawing nets
surface area net
Prentice Hall Mathematics
7-2
Example
The diameter of the base of a cylindrical can
is 4 in. The height of the can is 6.5 in. Find
the can's surface area to the nearest tenth.
Activity Lab: Patterns in 3-d Figures
Students determine the dimensions of the
figures given the area or volume.
Prentice Hall Mathematics
7-2b
volume;
cubic unit
Prentice Hall Mathematics
7-3
Example
Mrs. Sanchez has a can of concentrated
orange juice, 8 cm tall and with a diameter of
7 cm. What is the volume of the can in cubic
centimeters?
Word problem practice
Describe the resulting face shape from cuts
made parallel and perpendicular to the bases
of right rectangular prisms and pyramids.
Prentice Hall Mathematics
Pp. 269-270
cross-section plane
Prentice Hall Mathematics
7-4
Example
Jorge and Patti are eating sushi rolls shaped
like cylinders. Jorge cut his sushi roll
vertically. Patti cut her sushi roll
horizontally. What is the shape of each cross
section?
1 day
All standards taught
Review
Formative Assessment Lesson: Using Dimensions- Designing a Sports Bag
http://map.mathshell.org/materials/lessons.php
Formative Assessment Lesson: Estimations and Approximations
http://map.mathshell.org/materials/lessons.php?taskid=220&subpage=problem
7th Grade Math Quarter 3
3 7th Grade Mathematics Quarter 3 Curriculum Map
2013-2014
Formative Assessment Lesson: Maximizing Area- Gold Rush
http://map.mathshell.org/materials/lessons.php?taskid=415&subpage=problem
INTERIM ASSESSMENT 3: JANUARY 21-FEBRUARY 6
Suggested Instructional Days: 10 Unit 5: Statistics and Probability
3rd 9 Weeks
Unit Summary (Learning Target/Goal):
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models
bar graph
Prentice Hall Mathematics
Central tendency measures, plots,
pie chart
Supplemental Materials
and various graphs and charts
histogram
Example
scatter plots
Assessment Task:
Jason wanted to compare the mean
line
plots
Temperatures
height of the players on his favorite
line
graph
http://map.mathshell.org/m
Statistics and
basketball and soccer teams. He thinks
mean
aterials/tasks.php?taskid=3
Probability
the mean height of the players on the
median
84#task384
basketball team will be greater but
mode
Use random
doesn’t know how much greater. He
range
sampling to
also wonders if the variability of
draw inferences
heights of the athletes is related to the
about a
sport they play. He thinks that there
population.
will be a greater variability in the
7.SP.3: Informally assess the degree of visual
heights of soccer players as compared
overlap of two numerical data distributions with
Draw informal
to basketball players. He used the
5
similar variability’s, measuring the difference
comparative
rosters and player statistics from the
between
the
centers
by
expressing
it
as
a
multiple
inferences about days
of a measure of variability.
team websites to generate the
two populations.
following lists.
Investigate
chance
processes and
develop, use,
and evaluate
probability
models.
Basketball Team – Height of Players
in inches for 2010 Season
75, 73, 76, 78, 79, 78, 79, 81, 80, 82,
81, 84, 82, 84, 80, 84
Soccer Team – Height of Players in
inches for 2010
73, 73, 73, 72, 69, 76, 72, 73, 74, 70,
65, 71, 74, 76, 70, 72, 71, 74, 71, 74,
73, 67, 70, 72, 69, 78, 73, 76, 69
To compare the data sets, Jason
7th Grade Math Quarter 3
4 7th Grade Mathematics Quarter 3 Curriculum Map
2013-2014
creates a two dot plots on the same
scale. The shortest player is 65 inches
and the tallest players are 84 inches.
2 days
7.SP.3: Informally assess the degree of visual
overlap of two numerical data distributions with
similar variabilities, measuring the difference
between the centers by expressing it as a multiple
of a measure of variability.
7.SP.4: Use measures of center and measures of
variability for numerical data from random
samples to draw informal comparative inferences
about two populations.
1.5
days
7.SP.5: Understand that the probability of a
chance event is a number between 0and 1 that
expresses the likelihood of the event occurring.
Larger numbers indicate greater likelihood. A
probability near 0 indicates an unlikely event, a
probability around ½ indicates an event that is
neither unlikely nor likely, and a probability near 1
indicates a likely event.
7.SP.7: Develop a probability model and use it to
find probabilities of events. Compare probabilities
from a model to observed frequencies; if the
agreement is not good, explain possible sources of
the discrepancy.
Data variability (comparing
populations and interpreting data.
Example:
The two data sets below depict
random samples of the management
salaries in two companies. Based on
the salaries below which measure of
center will provide the most accurate
estimation of the salaries for each
company?
• Company A: 1.2 million, 242,000,
265,500, 140,000, 281,000, 265,000,
211,000
• Company B: 5 million, 154,000,
250,000, 250,000, 200,000, 160,000,
190,000
Solution:
The median would be the most
accurate measure since both
companies have one value in the
million that is far rom the other values
and would affect the mean.
Recognize that the probability of any
single event can be can be expressed
in terms such as impossible, unlikely,
likely, or certain or as a number
between 0 and 1.
Example
There are three choices of jellybeans –
grape, cherry and orange. If the
probability of getting a grape is and
the probability of getting cherry is ,
what is the probability of getting
box-plot
lower quartile
upper quartile
interquartile range
variability
mean absolute value
Prentice Hall Mathematics
8-4
outcome
event
Prentice Hall Mathematics
9-1
theoretical probability
complement
favorable outcomes
possible outcomes
unlikely
likely
7th Grade Math Quarter 3
5 7th Grade Mathematics Quarter 3 Curriculum Map
2013-2014
orange?
1.5
days
7.SP .8: Find probabilities of compound events
using organized lists, tables, tree diagrams, and
simulation.
7.SP.8b. Represent sample spaces for compound
events using methods such as organized lists,
tables and tree diagrams. For an event described in
everyday language (e.g., “rolling double sixes”),
identify the outcomes in the sample space which
compose the event.
Solution
The combined probabilities must
equal 1. The combined probability of
grape and cherry is . The probability
of orange must equal to get a total of
1.
Use tree diagrams, frequency tables,
and organized lists, and simulations to
determine the probability of
compound events.
Example
How many ways could the 3 students,
Amy, Brenda, and Carla, come in 1st,
2nd and 3rd place?
Solution:
Making an organized list will identify
that there are 6 ways for the students
to win a race
A, B, C
Sample space
counting principle
Prentice Hall Mathematics
9-3
A, C, B
B, C, A
B, A, C
C, A, B
C, B, A
Formative Assessment Lesson: Estimating- Counting Trees
http://map.mathshell.org/materials/lessons.php?taskid=422&subpage=problem
10
REVIEW for state assessments
All standards taught
days
NOTES/REFLECTIONS:
7th Grade Math Quarter 3
6