Grade 7 – Pre-AP Math
2016-17 Unit 1
Title
Suggested Time Frame
1st
Numbers and Operations
*CISD Safety Net Standards: 7.3B
Six Weeks
15 Days
Big Ideas/Enduring Understandings
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Guiding Questions
Problems can be solved easier when using variety of
equivalent forms.
All numbers fall within the real number system.
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How do I add and subtract with rational numbers?
How do I multiply and divide with rational numbers?
To what extent can rational numbers represent real world
concepts?
Where do numbers fit in the real number system?
Vertical Alignment Expectations
*TEKS one level below*
*TEKS one level above*
TEA Vertical Alignment 5th Grade – Algebra I
Sample Assessment Question
7.3B
2016 STAAR #8
2016 STAAR #37
2016 STAAR #21
Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
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Grade 7 – Pre-AP Math
2016-17 Unit 1
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. Some district Specificity and examples
are a product of the Austin Area Math Supervisors TEKS Clarifying documents accessible on the Region XI website.
Ongoing TEKS
Math Processing Skills
7.1 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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Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
Precise mathematical language is expected.
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Grade 7 – Pre-AP Math
2016-17 Unit 1
Knowledge and Skills with
Student Expectations
District Specificity/ Examples
Supplemental Vocabulary: Rational Number, Bar Notation, Common
Denominator, Least Common Multiple, Least Common Denominator,
Repeating Decimal, Nonrepeating Decimal, Unlike Fraction, Dividend,
Divisor, Terminating Decimal, Reciprocal, Multiplicative Inverse,
Reasonableness, Justify, Absolute Value, Zero Pair, Evaluate, Simplify,
Irrational Numbers, Real Numbers
Expected Learner Outcomes
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Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
Describe integers as quantities.
Define sets and subsets of real numbers counting numbers, whole
numbers, integers, rational numbers and irrational numbers using
a graphical representation such as a Venn Diagram.
Select an appropriate form of rational number to solve real-life
problems.
Based on the problem situation (context clues), select and use an
appropriate operation to solve problems.
Explain and justify the selection of operations and the problemsolving process used to solve problems.
Apply a problem-solving method to solve multi-step problems.
Use vocabulary such as integers, place value, greater than, less
than, equal or equivalent and absolute value.
Describe the order of operation in a given numerical expression
including integers.
Vocabulary
• Integers
• Negative
• Nonnegative
• Nonpositive
• Positive
• Rational numbers
• Sets
• Subsets
• Venn Diagram
• Whole Numbers
Suggested Resources
Resources listed and categorized to
indicate suggested uses. Any
additional resources must be
aligned with the TEKS.
McGraw Hill
Chapter 1
Mathematical
Processes Handbook
McGraw Hill
Web Resources:
Region XI: Livebinder
NCTM: Illuminations
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Grade 7 – Pre-AP Math
2016-17 Unit 1
•
7.2 Number and
operations. The student
applies mathematical
process standards to
represent and use rational
numbers in a variety of
forms. The student is
expected to
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7.2A - extend previous
knowledge of sets and
subsets using a visual
representation to
describe relationships
between sets of rational
numbers.
Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
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Simplify numerical expressions using order operations
(parentheses, exponents, multiply, divide, add, and subtract)
including integers.
Based on the problem situation (context clues), select an
appropriate operation to solve the problem.
Explain and justify the selection of operation, problem-solving
process, and reasonableness of answer, especially in terms of the
estimate.
Use a variety of techniques to evaluate the reasonableness of a
solution.
TEKS Clarifications:
7.2A
In 6th grade, students “classify” sets of numbers (whole, integers, and
rational numbers). In 7th grade, the verb changes to “describe
relationships” between sets of rational numbers. Students need to
have experiences using visual representations (such as a Venn
diagrams) to classify number systems
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Common Misconceptions:
1. Knowing only a limited number of models for interpreting fractions;
for example, not recognizing fractions as locations on a number line or
as division calculations.
2. Understanding the symbol “-“ Used to signify subtraction and a
negative.
Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
Grade 7 – Pre-AP Math
2016-17 Unit 1
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Grade 7 – Pre-AP Math
2016-17 Unit 1
7.3 Number and
operations. The student
applies mathematical
process standards to add,
subtract, multiply, and
divide while solving
problems and justifying
solutions.
• 7.3A - add, subtract,
multiply, and divide
rational numbers fluently
7.3AB
Extend the fluent computation with positive rational numbers from
6th grade to 7th grade by now including all rational numbers (includes
negative). Apply rational number operations in problem situations.
Students will need to have a solid understanding of integer rules to be
able to apply to rational numbers. While students need to be fluent in
operations with both positive and negative rational numbers, the
application problems will may tend to focus on positive numbers for
meaningful examples, such as change in temperature, stock market
loss and gains
Example 1:
A recipe that makes 1.5 dozen cookies requires 0.75 cups of sugar.
Shanika wants to make 6 dozen cookies. How many cups of sugar will
she need?
McGraw Hill
Chapter 1
Mathematical
Processes Handbook
McGraw Hill
Web Resources:
Region XI: Livebinder
NCTM: Illuminations
Example 2:
Ocean water freezes at about −2 1⁄2 degrees C. Fresh water freezes at
0 degrees C. Antifreeze, a liquid used to cool most car engines, freezes
at −64 degrees C.
Imagine that the temperature is exactly at the freezing point for ocean
water. How many degrees must the temperature drop for the
antifreeze to turn to ice?
Common Misconceptions:
1. Students may believe that all rational numbers are positive.
2. Students have trouble using models to illustrate operations or to
connect operations on objects to algorithms.
Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
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Grade 7 – Pre-AP Math
2016-17 Unit 1
*CISD Safety Net*
• 7.3B - apply and extend
previous understandings
of operations to solve
problems using addition,
subtraction,
multiplication, and
division of rational
numbers
Grade 7 Pre-AP Math- Unit 1
Updated May 19, 2016
7.3B
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