Grade 7
Math Unit 6
Title
Suggested Time Frame
Data/ Graphs
Time Frame 5th 6 Weeks
Suggested Duration : 15 Days
Guiding Questions
Big Ideas/Enduring Understandings
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Using proportional relationships, make inferences and
predictions from data of random samples of populations
Using statistical representations, make inferences and
predictions from data of random samples of populations
Read, interpret, and solve real world problems using data from
various kinds of graphs
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How do you know which type of graph to use when displaying
data?
• How can I organize ideas to analyze multiple samples of data by
making predictions?
• How can I select tools and techniques to use the measure of
center and the range to compare 2 populations?
• How can I analyze the relationships between 2 dot plots and 2 box
plots?
• How can I use a circle graph to create and compare percentages
and my personal budget?
• What information can the shape, center, and spread on a dot plot
or box plot give us?
Vertical Alignment Expectations
*TEKS one level below*
*TEKS one level above*
TEA Vertical Alignment 5th Grade – Algebra I
Sample Assessment Question
Coming Soon……….
7th Math Unit 6
Updated November 19, 2015
Page 1 of 10
Grade 7
Math Unit 6
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. A portion of the District Specificity and
Examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents available on the Region XI Math website.
Ongoing TEKS
Math Processing Skills
7.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
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Focus is on application
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Students should assess which tool to apply rather than trying only one
or all
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Students should evaluate the effectiveness of representations to ensure
they are communicating mathematical ideas clearly
Students are expected to use appropriate mathematical vocabulary and
phrasing when communicating ideas
Students are expected to form conjectures based on patterns or sets of
examples and non-examples
(B) use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
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(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical
language in written or oral communication
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7th Math Unit 6
Updated November 19, 2015
Precise mathematical language is expected.
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Grade 7
Math Unit 6
Knowledge and Skills
with Student
Expectations
District Specificity/ Examples
Supplemental Vocabulary: Line plot, Shapes, Venn diagram, Quartile
(upper, lower, 1,2,3,4), Justify, Biased Sample, Statistics, Measure of
Center, Survey, Systematic Random Sample, Unbiased sample,
Voluntary Response, Sample, Convenience Sample, Equivalents,
Part-to-part, Experimental probability, Theoretical probability,
Comparative
• Determine an appropriate graphical representation: bar graph,
circle graph, line plots (dot plot), and box plot.
• Select and construct bar graphs to compare sets of data.
• Select and sketch circle graphs to show parts of a whole and
part-to-part comparison.
• Justify the selection of a graphical representation.
• Draw conclusions or make inferences based on an analysis of
the given or collected data or sampling.
• Support conclusions based on an analysis of data with
convincing arguments.
• Use vocabulary appropriate to communicate the conclusion
drawn.
• Calculate or identify the median to describe the middle
number. (for box and whisker plots)
• Identify and use the mode to describe the value(s) occurring
most frequently. (line plots)
• Determine the range to describe the spread of the data.
7th Math Unit 6
Updated November 19, 2015
Vocabulary
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Bar graph
circle graph
Data
dot plot
part-to-part,
part-to-whole
box plot (boxand-whisker)
center
distribution
interquartile
range (IQR)
mean
median
mode
numeric data
range
shape
spread
data
inference
population
rand om
sample
Suggested Resources
Resources listed and categorized
to indicate suggested uses. Any
additional resources must be
aligned with the TEKS.
Textbook Resources:
McGraw Hill Ch 9
Web Resources:
Mean, Median, & Mode
IQR- Inter Quartile Range
Measures of Central
Tendency
Possibly Biased Data
Reasonable Samples
Shapes of Distribution
Measures of Dispersion
Reading Bar Graphs
Reading Line Graphs
Reading Circle Graphs
Box Plots
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Grade 7
Math Unit 6
7.06 Proportionality –
The student applies
mathematical process
standards to use
probability and
statistics to descrivbe or
solve problems
involving proportional
relationships. The
student is expected to:
•7.06G solve problems
using data represented
in bar graphs, dot plots,
and circle graphs,
including part-to-whole
and part-to-part
comparisons and
equivalents Readiness
Standard
7th Math Unit 6
Updated November 19, 2015
• Use the mean to describe the equal distribution of number
values, be able to solve for variable when given the mean. Ex:
85+82+97+X/4=91, solve for x.
• Use the median to describe the middle number.
• Compare shapes, centers, and spreads using 2 dot plots or box
plots.
• Compare shapes, centers, and spreads using 2 dot plots or box
plots with 2 populations
7.06G
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Grade 7
Math Unit 6
7.12 Measurement and
Data – The student
applies mathematical
process standards to
use statistical
representations to
analyze data. The
student is expected to:
•7.12A compare two
groups of numeric data
using comparative dot
plots or box plots by
comparing their shapes,
centers, and spreads
Readiness Standard
7.12A
Students will interpret box plots and dot plots individually. Students
understand what components of box plots mean (median, extremes,
outliers, quartiles) in relation to the situation. Students understand what
the shape of a box or dot plot implies about a situation (likewise with
center and spread).
Misconceptions:
• Students think that a larger quartile box means there is more data
in it.
• Students assume that a “x” or “dot” on a dot plot always
represents
Examples:
Describe the least and greatest amounts of tickets purchased. The
smallest quantity of tickets purchased is 225. The greatest number of
tickets purchased is 425.
7th Math Unit 6
Updated November 19, 2015
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Grade 7
Math Unit 6
Describe the range in attendance for the p lays. The range between
the greatest and least number of attendees is 205. The least number of
attendees is 200. The greatest number of attendees is 405.
Compare the data for the number of tickets purchased with the data
for actual attendance. It is evident that not all tickets purchased were
used to attend the shows. The median number of tickets purchased is
350. The median number of attendance is 325. The majority of the
data values fall in the lower quartile for both sets of data, purchases,
and attendance.
Compare the median number of CDs owned by boys and girls. The
median number of CDs owned by boys is four more than the girls. The
median number of CDs owned by boys is 18. The median number of
CDs owned by girls is 14.
What is the least number of CDs owned by boys and girls? The
smallest amount of Cs owned by both boys and girls is 3.
7th Math Unit 6
Updated November 19, 2015
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Grade 7
Math Unit 6
Identify the greatest number of CDs owned by both girls and boys.
The greatest amount of Cs owned by girls is 37. The greatest amount
of Cs owned by boys is 31.
What conclusions can be drawn about the number of CDs owned by
girls? You can see that more than half of the data falls in the upper
quartile. Therefore, more than half of the girls own more than the
median number of CDs.
What conclusions can be drawn about the number of CDs owned by
boys? More than half of the data falls in the lower quartile. Therefore,
more than half of the boys own less than the median number of CDs.
Showing the two graphs vertically rather than side by side helps students
make comparisons. For example, students would be able to see from the
display of the two graphs that the ideas scores are generally higher than
7th Math Unit 6
Updated November 19, 2015
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Grade 7
Math Unit 6
the organization scores. One observation students might make is that the
scores for organization are clustered around a score of 3 whereas the
scores for ideas are clustered around a score of 5.
7.12BC
•7.12B use data from
a random sample to
make inferences about
a population
Supporting Standard
•7.12C compare two
populations based on
data in random samples
from these populations,
including informal
comparative inferences
about differences
between the two
populations
Supporting Standard
7th Math Unit 6
Updated November 19, 2015
Students need to apply proportional reasoning to make predictions about a
population. Students extend information from samples of populations to
make generalizations about the whole populations. Students compare
data from samples and interpret their implications about the differences
of the whole populations. Students need to be able to identify whether a
sample is random or not.
Misconceptions:
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Students oversimplify how to randomly sample. (They
assume that sampling every 5th person, makes it random.)
Students believe that the characteristics of the sample match
exactly the characteristics of the population.
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Grade 7
Math Unit 6
For example, estimate the mean word length in a book by
randomly sampling words from the book; predict the winner of a
school election based on randomly sampled survey data. Gauge
how far off the estimate or prediction might be.
Decide whether the words in a chapter of a seventh-grade science
book are generally longer than the words in a chapter of a fourthgrade science book.
7.13 Personal Financial
Literacy – The student
applies mathematical
process standards to
develop an economic
way of thinking and
problem solving useful
in one’s life as a
knowledgeable
consumer and investor.
7th Math Unit 6
Updated November 19, 2015
7.13B
Students need to be able to calculate the percent of a number (for each
category of a budget) or find the percent from the part and whole.
Understand parts of a budget (ie. income vs expenses). Understand
vocabulary related to budgets: income, expenses, assets, liabilities, net
worth, wages, taxes, savings).Question stems for the teacher.
Misconceptions:
• Students may think that everyone needs to budget their
money in the same way.
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Grade 7
Math Unit 6
The student is expected
to:
•7.13B identify the
components of a
personal budget,
including income;
planned savings for
college, retirement, and
emergencies; taxes;
and fixed and variable
expenses, and calculate
what percentage each
category comprises of
the total budget
Supporting Standard
7th Math Unit 6
Updated November 19, 2015
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Students may think that people’s expenses are the same,
regardless of their career.
3. Students may think that a budget is a fixed set of values
that does not vary. They may not understand that it may
vary from month to month.
Examples:
See clarifying tasks from TCEE/SmarterTexas
Sample family budget estimator:
http://www.finaid.org/calculators/budget.phtml
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