1st
7th grade Math
Six Weeks Unit 1 -- Number and Operations
9 Days
Readiness TEKS in bold
7.2A
7.3A
7.3B
7.13A
7.13C
extend previous knowledge of sets and subsets using a visual representation to describe relationships
between sets of rational numbers.
add, subtract, multiply, and divide rational numbers fluently.
apply and extend previous understandings of operations to solve problems using addition,
subtraction, multiplication, and division of rational numbers.
calculate the sales tax for a given purchase and calculate income tax for earned wages.
create and organize a financial assets and liabilities record and construct a net worth statement.
Students are expected to use these sets of numbers in this unit:
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments
of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Integers – the set of counting (natural numbers), their opposites, and zero
{–n, …, –3, –2, –1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol Z.
a
 Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers
b
and b ≠ 0, which includes the subsets of integers, whole numbers, and counting (natural) numbers
1 11
3
(e.g., –3, 0, 2, - ,
, 1 , -5.36, 0. 233 ) . The set of rational numbers is denoted by the symbol Q.
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2 7
Supporting TEKS 7.2A
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 extend previous
knowledge of sets and subsets using a visual
representation to describe relationships between
sets of rational numbers.
Subsets of rational numbers include natural numbers,
whole numbers, and integers.
A Venn diagram is an applicable visual representation.
As there is not a unified definition for these terms, the
natural numbers will be taken to mean {1, 2, 3 . . .},
and the whole numbers will be taken to mean {0, 1, 2,
3 . . .}.
Examples of visual representations of the relationships between sets and subsets of rational numbers:
 All counting (natural) numbers are a subset of whole numbers, integers, and rational numbers.
o Ex: Two is a counting (natural) number, whole number, integer, and rational number.
 All whole numbers are a subset of integers and rational numbers.
o Ex: Zero is a whole number, integer, and rational number, but not a counting (natural) number.
 All integers are a subset of rational numbers.
o Ex: Negative two is an integer and rational number, but neither a whole number nor a counting
(natural) number.
 All counting (natural) numbers, whole numbers, and integers are a subset of rational numbers.
o Ex: Four is a counting (natural) number, whole number, integer, and rational number.
 Not all rational numbers are an integer, whole number, or counting (natural) number.
o Ex: One-half is a rational number, but not an integer, whole number, or counting (natural) number.
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 Terminating and repeating decimals are rational numbers but not integers, whole numbers, or counting
(natural) numbers.
o Ex: is a repeating decimal; therefore, it is a rational number.
 Number line relationship
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Supporting TEKS 7.3A
7(3)(A) Number and
operations. The student
applies mathematical process
standards to add, subtract,
multiply, and divide while
solving problems and
justifying solutions.
The student is expected to
add, subtract, multiply, and
divide rational numbers
fluently.
The addition, subtraction, multiplication, and division of rational numbers include
positive and negative fractions and decimals. In the TEKS, students are expected
to be fluent with multiplying and dividing positive rational numbers and integers
in grade 6 with 6(3)(E) and 6(3)(D).
When paired with 7(1)(A) and 7(3)(B), the expectation is that students solve
problems. This SE includes the addition, subtraction, multiplication, and division
of both positive and negative rational numbers including percents and integers.
“Procedural fluency refers to knowledge of procedures, knowledge of when and
how to use them appropriately, and skill in performing them flexibly, accurately,
and efficiently” (National Research Council, 2001, p. 121). In an effort to
determine fluency with each operation, these may be one step and one operation.
a
, where a and b are integers and b
b
≠ 0, which includes the subsets of integers, whole numbers, and counting (natural) numbers
1 11
3
(e.g., –3, 0, 2, - ,
, 1 , -5.36, 0. 233 ) . The set of rational numbers is denoted by the symbol Q.
8
2 7
Fluency – efficient application of procedures with accuracy. NOTE: 7th grade is the first time students have
done operations with negative rational numbers. In 6th grade, students modeled integer operations. Grade 5
added and subtracted positive rational numbers fluently. Grade 6 multiplied and divided positive rational
numbers fluently.
One-step, one operation problems and/or situations can be used to determine fluency with each operation
Addition, subtraction, multiplication, and division involving various forms of positive and negative rational
numbers
o Whole numbers
o Integers
o Decimals (less than or greater than one)
o Fractions (proper, improper, and mixed numbers)
o Percents converted to equivalent decimals or fractions for multiplying or dividing fluently
Mathematical and real-world problem situations
Multi-step problems
Multiple operations
 Rational numbers – the set of numbers that can be expressed as a fraction






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Readiness TEKS 7.3B
7(3)(B) Number and operations. The student
applies mathematical process standards to add,
subtract, multiply, and divide while solving problems
and justifying solutions.
The student is expected to apply and extend
previous understandings of operations to solve
problems using addition, subtraction,
multiplication, and division of rational
numbers.
The phrase “apply and extend previous understandings of
operations” refers to applying the algorithms for operations
with integers and operations with fractions and decimals to
perform operations with rational numbers. This SE
includes the addition, subtraction, multiplication, and
division of both positive and negative rational numbers
including percents and integers. Students may be
expected to perform multiple steps and multiple operations
for this SE.
a
 Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b
b
≠ 0, which includes the subsets of integers, whole numbers, and counting (natural) numbers
1 11
3
(e.g., –3, 0, 2, - ,
, 1 , -5.36, 0. 233 ) . The set of rational numbers is denoted by the symbol Q.
8
2 7
 Various forms of positive and negative rational numbers
o Whole numbers
o Integers
o Decimals (less than or greater than one)
o Fractions (proper, improper, and mixed numbers)
o Percents converted to equivalent decimals or fractions for multiplying or dividing
 Equivalent representations of a negative number
o Ex:
 Generalizations for operations
o Addition and subtraction
 If a pair of addends has the same sign, then the sum will have the sign of both addends.
 If a pair of addends has opposite signs, then the sum will have the sign of the addend with the
greatest absolute value.
 A subtraction problem may be rewritten as an addition problem by adding the opposite of the integer
following the subtraction symbol, and then applying the rules for addition.
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o
Multiplication and division
 If two rational numbers have the same sign, then the product or quotient is positive.
 If two rational numbers have opposite signs, then the product or quotient is negative.
 When multiplying or dividing two or more rational numbers, the product or quotient is positive if
there are no negative signs or an even number of negative signs.
 When multiplying or dividing two or more rational numbers, the product or quotient is negative if
there is one negative sign or an odd number of negative signs.
 Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent
values. (from gr 6)
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 Mathematical and real-world problem situations
o Multi-step problems
o Multiple operations
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Supporting TEKS 7.13A
7(13)(A) 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.
The student is expected to calculate the sales tax for a given
purchase and calculate income tax for earned wages.
This SE builds upon 5(10)(A).
Students are expected to calculate
these forms of taxes.
This SE connects to 7(4)(D) with
problems involving rates and percents.
a
, where a and b are
b
integers and b ≠ 0, which includes the subsets of integers, whole numbers, and counting (natural) numbers
1 11
3
(e.g., –3, 0, 2, - ,
, 1 , -5.36, 0. 233 ) . The set of rational numbers is denoted by the symbol Q.
8
2 7
 Various forms of positive rational numbers
o Counting (natural) numbers
o Decimals (greater than zero)
o Percents converted to equivalent decimals or fractions for multiplying or dividing
 Sales tax – a percentage of money collected by a store (retailer), in addition to a good or service that was
purchased, for the local government as required by law
o Sales tax is set by the local government (city, county, and state) and the money stays within those local
systems
 Positive rational numbers –the set of numbers that can be expressed as a fraction
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 Earned wages – the amount an individual earns over a given period of time
 Income tax – a percentage of money paid on the earned wages of an individual or business for the federal
and/or state governments as required by law
o Determined by a fixed rate on different brackets (levels) of taxable income and an individual’s income
tax filing status of single, married joint, or head of household
 Income tax filing status
o Single can be claimed by any individual filing an income tax return.
o Married-joint can be claimed by married couples or individuals who have been widowed
within the last two years.
o Head of household can be claimed individuals who pay for more than half of the household
expenses and have at least one dependent (usually a child) that lives with them.
o Income tax brackets and rates are published by the state and/or federal government annually
 Income tax goes directly to federal government; the state of Texas does not collect income tax.
 Income tax rates fluctuate from year to year due to inflation and other federal and/or state
government budgets.
 Earned income is rounded to the nearest whole dollar for purposes of tax brackets.
 Income tax is rounded to the nearest whole dollar.
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Note:
Grade 5 defined income tax, payroll tax, sales tax, and property tax.
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Supporting TEKS 7.13C
7(13)(C) 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.
The student is expected to create and organize a financial assets and
liabilities record and construct a net worth statement.
This SE builds upon the
knowledge from (14)(C).
Negative net worth is a
possibility.
 Financial asset – an object or item of value that one owns
o Assets represent a positive value in relation to net worth.
 Financial liability – an unpaid or outstanding debt
o Liabilities represent a negative value in relation to net worth; values may or may not be indicated by a
negative sign.
 Financial assets and liabilities records may fluctuate each month depending on payments made towards
liabilities, whether additional liabilities are taken on, or if the value of an asset changes due to appreciation or
depreciation.
o
Ex:
 Net worth – the total assets of an individual after their liabilities have been settled
 An individual’s net worth may be positive or negative depending on the amount of their assets and liabilities.
 Process of constructing a net worth statement
o Calculate the value of an individual’s assets.
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

Ex:
o
Calculate the value on an individual’s liabilities.
 Ex:
o
Calculate the net worth, the difference between an individual’s assets and liabilities.
 Ex:
Determine the missing value of an asset or liability when given net worth and remaining values.
o Ex:
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