Wentzville School District
Curriculum Development Template
Stage 1 – Desired Results
Unit Three – Operations with Rational Numbers
Unit Title: Operations with Rational Numbers
Course: Pre-Algebra
Brief Summary of Unit: Students will learn how to perform operations with rational numbers. In addition, students will
compare and contrast various forms of rational numbers - fractions, decimals, and mixed numbers. Finally, students will
solve real world problems involving rational numbers using multiple strategies.
Textbook Correlation: Glencoe Math Accelerated Chapter 3
Time Frame: 3 weeks
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
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How accurate do I need to be?
When is estimating the best solution to a
problem?
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strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
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Use rational numbers to model and interpret real-world situations such as cooking, time, money, scores,
temperature, and elevation, among others.
Meaning
Essential Questions
Understandings
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What happens when you add, subtract, multiply,
and divide rational numbers?
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When is it appropriate to convert between
different forms of rational numbers?
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When is estimation or mental math useful in real
world situations?
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Converting between different forms of rational
numbers can assist in solving real-world
problems.
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There are many tools and strategies we can use
in solving real-world problems, including
estimation and mental math.
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The number line can be used as a tool to
understand addition and subtraction of rational
numbers.
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How do mathematical properties of addition,
subtraction, multiplication, and division make
calculations easier?
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What are efficient methods for finding sums and
differences? (number line, integer properties,
concrete models, etc.)
Properties of operations on whole numbers apply
to all rational numbers.
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Rational numbers expressed as a decimal will
either terminate in 0s or repeat.
How can rational numbers be represented as
decimals?
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Rational numbers are used to compare, compute,
and analyze real world situations.
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What real-world situations could be represented
by multiplying or dividing rational numbers?
Acquisition
Key Knowledge
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Key Skills
Properties of operations on rational numbers
Terminating decimal
Repeating decimal
Bar Notation
Rational numbers
Like Fractions
Unlike Fractions
Multiplicative Inverse
Reciprocal
Complex fractions
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Solve multi-step real life problems with positive
and negative rational numbers in any form.
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Use estimation and mental math to justify the
reasonableness of answers.
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Convert between fractions and decimals as
needed to solve a problem.
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Recognize fractions and some decimals as types of
rational number.
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Apply properties of addition or subtraction to find
sums or differences of rational numbers.
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Apply properties of multiplication or division to
find the product or quotient of rational numbers.
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Convert rational numbers from fractions to
decimals using long division.
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Give contextual examples of rational number
operations.
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Explain how the properties of operations apply to
rational numbers, including complex fractions.
Standards Alignment
MISSOURI LEARNING STANDARDS
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
(7.EE.3) 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. Apply properties of
operations to calculate with numbers in any form; convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and estimation strategies. For example: If a woman
making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new
salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches
wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the
exact computation.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
(7.NS.1) Apply and extend previous understandings of addition and subtraction to add and subtract rational
numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom
has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction
depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0
(are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse,
p – q = p + (–q). Show that the distance between two rational numbers on the number line is the
absolute value of their difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
(7.NS.2) Apply and extend previous understandings of multiplication and division and of fractions to multiply
and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that
operations continue to satisfy the properties of operations, particularly the distributive property,
leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products
of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of
integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–
q). Interpret quotients of rational numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
(7.NS.3) Solve real-world and mathematical problems involving the four operations with rational numbers.
(Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 5