UNIT 3: 7TH GRADE COMMON CORE MATH COMPREHENSIVE UNIT
Unit Description/ Topic Length: In this 3-week unit, students will engage in rigorous instructional
and assessment tasks that provide them with ample opportunities to connect the mathematical
practices to the mathematical content. The content will focus on ratios, proportional relationships,
multistep ratio and percent problems, operations with rational numbers, equivalent expressions,
linear equations and inequalities, scale drawings, and making inferences based on samples. The
variety of tasks is designed to help students engage with the content by making sense of the
problems, reasoning abstractly and quantitatively, constructing viable arguments and critiquing the
reasoning of others, modeling with mathematics, using appropriate tools strategically, attending to
precision and looking for and making use of structure.
Essential Question:
How can mathematical practices build up students’ understanding of mathematical content?
Big Ideas/Enduring Understandings
 Mathematical understanding is the
ability to justify why a particular
mathematical statement is true or
where a mathematical rule comes
from.
 Students will be able to explain the
meaning of a problem and look for
entry points to its solutions.
 They plan a solution pathway rather
than simply jumping into a solution
attempt.
 Students make sense of the quantities
and their relationships in problem
situations.
 Students will demonstrate quantitative
reasoning by creating a coherent
representation of the problem at hand.
 Students will use stated assumptions,
definitions, and previously established
results in constructing arguments.
 Students can apply the mathematics
they know to solve problems arising in
everyday life, society, and the
workplace.
 Students can identify the appropriate
tools to use for a particular situation
and use them efficiently.
 Students use appropriate vocabulary in
their discussions with others and in
expressing their own reasoning and
Guiding Questions:
RATIOS AND PROPORTIONAL
RELATIONSHIPS
1. What is unit rate?
2. How do you compute unit rates
associated with ratios of fractions?
3. How do you recognize and represent
proportional relationships between
quantities?
4. How do you use proportional
relationships to solve multistep ratio and
percent problems?
THE NUMBER SYSTEM
5. How do you add, subtract, multiply, and
divide rational numbers?
6. How do you solve real-world and
mathematical problems involving the
four operations with rational numbers?
EXPRESSIONS AND EQUATIONS
7. What are the properties of operations?
8. How can the properties of operations be
used to generate equivalent expressions?
9. How do you solve multi-step real-life
and mathematical problems posed with
positive and negative rational numbers
in any form (whole numbers, fractions,
and decimals), using tools strategically?
10. How do you use variables to represent
quantities in a real-world or
mathematical problem?
11. How do you construct simple equations
calculate accurately and efficiently.
 Students will discern a pattern or
structure.
 Students will make generalizations
and develop shortcuts from a
discerned pattern.
and inequalities to solve problems?
GEOMETRY
12. How do you solve problems involving
scale drawings of geometric figures?
13. What are the formulas for the area and
circumference of a circle and how do
you use them to solve problems?
14. How are the circumference and area of a
circle related?
STATISTICS AND PROBABILITY
15. How do you use random sampling to
draw inferences about a population?
16. How can chance processes be
investigated?
17. How do you develop, use, and evaluate
probability models?
18. How can you find probabilities of
compound events?
NYS Common Core Standards for Mathematics Assessed:
Mathematical Content
7.RP
Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.NS
Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
7.EE
Use properties of operations to generate equivalent expressions.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.SP
Use random sampling to draw inferences about a population.
Investigate chance processes and develop, use, and evaluate probability models.
7.G
Draw construct, and describe geometrical figures and describe the relationships between them.
 Solve problems involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale drawing at a
different scale.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
4. Know the formulas for the area and circumference of a circle and use them to solve
problems; give an informal derivation of the relationship between the circumference and
area of a circle.
Mathematical Practices
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.
Content

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ratios
proportional relationships
multistep ratio and percent problems
operations with rational numbers
equivalent expressions
linear equations and inequalities
scale drawings
making inferences based on samples
Skills
RATIOS AND PROPORTIONAL
RELATIONSHIPS
 Compute unit rates associated with
ratios of fractions
 Recognize and represent proportional
relationships between quantities
 Use proportional relationships to solve
multistep ratio and percent problems
THE NUMBER SYSTEM
 Add, subtract, multiply, and divide
rational numbers
 Solve real-world and mathematical
problems involving the four operations
with rational numbers
EXPRESSIONS AND EQUATIONS
 Identify the properties of operations
 Use the properties of operations to
generate equivalent expressions
 Use tools strategically to solve multistep real-life and mathematical problems
posed with positive and negative
rational numbers in any form
 Represent quantities in a real-world or
mathematical problem using variables
 Construct simple equations and
inequalities to solve problems
GEOMETRY
 Solve problems involving scale
drawings of geometric figures
 Use the formulas for the area and
circumference of a circle to solve
problems
 Determine the relationship between the
circumference and area of a circle
STATISTICS AND PROBABILITY
 Use random sampling to draw
inferences about a population
 Investigate chance processes
 Develop, use, and evaluate probability
models
 Find probabilities of compound events
Vocabulary/ Key Terms
RATIOS AND PROPORTIONAL RELATIONSHIPS
 complex fraction, constant of proportionality, coordinate, direct proportional relationship,
percent, proportion, proportional relationship, quantities, rate, rate of change, rate of
proportionality, ratio, slope, unit rate, x-coordinate, y-coordinate
THE NUMBER SYSTEM
 absolute value, additive inverse, associative property, commutative property, fractions,
integers, inverse operations, number line, order of operations, rational numbers, signed
numbers
EXPRESSIONS AND EQUATIONS
 algebraic solution, arithmetic solution, at least, at most, coefficients, constant, distributive
property, equation, equivalent, expressions, factor, GCF, inequalities, like terms, linear
equations, monomial, property of equality, solution set, two-step linear equations, two-step
linear inequalities, variable
GEOMETRY
 area, circle, circumference, lengths, radius, scale drawing
STATISTICS AND PROBABILITY
 biased sample, compound events, data, equally likely, event, experimental probability,
favorable outcomes, Fundamental Counting Principle, inference, outcomes, population,
possible outcomes, probability, probability model, random sampling, representative sample,
sample, sample space, simple events, simple probability, simulation, theoretical probability,
unlikely event
ASSESSMENT EVIDENCE
Diagnostic and Pre/Post Assessments:
 Results from the Math Grade 7 Spring Benchmark Assessment will be analyzed to gauge
students’ current levels of understanding and difficulties. The information gleaned from
the data will help teachers decide which standards need greater emphases in the unit.
 Teachers will administer the NYS Grade 7 Mathematics Common Core Sample
Questions on Friday, April 19, 2013. (Multiple-Choice Questions)
Formative Assessment Tasks:
Date
TASK
SPICY VEGGIES
March 18
March 20
This task challenges a student to use
knowledge of proportional reasoning and
to use equivalent ratios. It involves
conversion between representations of
rational numbers to compare and order
ratios.
25% SALE
In a sale, the store reduces all prices by
25% each week.
Does this mean that, after 4 weeks,
everything in the store will cost $0? If
not, why not?
TOY TRAINS
March 21-22
7.RP.1, 7.EE.3
This two-part task presents a recipe
MP2, MP4, MP6,
context in an atypical way. The recipe
MP7
describes how the ingredients are related
to the whole. Students must reason
proportionally with fractions to solve each
part of the task.
CEREAL
March 19
CCLS
This task challenges a student to use
Algebra to represent, analyze, and
generalize a variety of functions including
linear relationships. A student relates and
compares different forms of
representation for a relationship including
words, tables, graphs, and writing an
equation to describe a functional pattern.
7.RP.1, 7.RP.2, 7.RP.3
7.NS.2, 7.NS.3
MP2, MP4
7.RP.3
MP2, MP3, MP6,
MP7
7.EE.3, 7.EE.4a
MP4, MP8
PHOTOGRAPHS
April 8-9
In this task, you need to figure out how
to fit three different-sized photographs
on a single sheet.
HISTORIC BICYCLE
April 10
In this task, you will figure out some
problems about a strange old bicycle.
CARD GAME
April 11-12
In this task, you will use probability to
make predictions about a card game.
7.G.1
MP2, MP3, MP6,
MP7
7.G.4
MP2, MP3, MP6,
MP7
7.SP.5, 7.SP.6, 7.SP.7
MP2, MP3, MP6,
MP7
Summative Assessments:
 Please refer to the Spring Break Packet.
TEACHING PLAN
Teaching and Learning Activities:
Access the results of the Math Grade 7 Spring Benchmark Assessment on ACUITY. Analyze the
data to gauge students’ current levels of understanding and difficulties and determine which
standards need greater emphases in the unit.
March 18-22 (Monday – Friday)
2. Before each lesson, students work individually on a formative assessment task.
3. During the lesson, students work in pairs to analyze each other’s work.
o
In a whole-class discussion, students compare and evaluate the methods they have seen and
used.
o
Review the solutions and ask questions to help them improve their work. The Mathematical
practices embodied in each task will be evident in students’ work and class interactions.
o
Students use the task rubric to score their work.
o
Students review their initial, individual solutions and use their learning to complete a new
task. Additional tasks are incorporated in the Spring Break packet.
4. Hand out the Spring Break Packet on Wednesday, March 20, 2013.
1.
April 3-5 (Wednesday – Friday)
5. Go over the Spring Break Packet with the class. Give students plenty of opportunities to engage
in peer review/peer score.
April 8 – 12 (Monday – Friday)
6. Before each lesson, students work individually on a formative assessment task.
7. During the lesson, students work in pairs to analyze each other’s work.
o
In a whole-class discussion, students compare and evaluate the methods they have seen and
used.
o
Review the solutions and ask questions to help them improve their work. The Mathematical
practices embodied in each task will be evident in students’ work and interactions.
o
Students use the task rubric to score their work.
o
Students review their initial, individual solutions and use their learning to complete a new
task. Additional tasks are incorporated in the Post Assessment.
8. Administer the NYS Grade 7 Mathematics Common Core Sample Questions on Friday, April
19, 2013. (Multiple Choice)
Materials Needed:
 Calculators
 Graph papers
 Rulers
 Protractors
 Task packet
Web Resources:
Mathematics Assessments Resource Service (MARS)
BOCES Deep Curriculum Alignment Project for Mathematics
PARCC Item and Task Prototypes
Inside Mathematics
Illustrative Mathematics
CALENDAR
(13 Instructional Days)
Time Spent
on Standard
CCLS
Week 1
March 1822
(Mon. – Fri.)
7.RP
Analyze proportional
relationships and use them to
solve real-world and
mathematical problems.
7.NS
Apply and extend previous
understandings of operations
with fractions to add, subtract,
multiply, and divide rational
numbers.
7.EE
 Use properties of operations
to generate equivalent
expressions.
 Solve real-life and
mathematical problems
using numerical and
algebraic expressions and
equations.


7.EE
Solve real-life and
mathematical problems using
numerical and algebraic
expressions and equations.

Week 2
April 3-5
(Weds. –
Fri.)
Go over the
Spring Break
Packet
*If feasible,
emphasize
linear
equations
and
inequalities.
Topics To Assess



Materials
ratios
proportional
relationships
multistep ratio
and percent
problems
operations with
rational numbers
equivalent
expressions

rulers, graph papers,
calculators
linear equations
and inequalities

calculators

Week 3
7.G
April 8-12  Solve problems involving
(Mon. – Fri.)
scale drawings of geometric
figures, including
Geometry
computing actual lengths
and Statistics
and areas from a scale
(Instructional
drawing and reproducing a
Tasks and
scale drawing at a different
Assessment
scale.
Tasks)
 Know the formulas for the
area and circumference of a
circle and use them to solve
problems; give an informal
derivation of the
relationship between the
circumference and area of a
circle.
7.SP
Use random sampling to draw
inferences about a population.
Investigate chance processes
and develop, use, and evaluate
probability models.


scale drawings

making inferences
based on samples
rulers, graph papers