Content Standard(s):
Mathematics MA2019 (2019) Grade: 7 6. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Unpacked Content
Evidence Of Student Attainment:
Students:
Use properties of operations to produce combined and re-written forms of the expressions that are useful in resolving mathematical and contextual problems. Teacher Vocabulary:
Term like terms Constant Factor Expression Rational coefficient Knowledge:
Students know:
how to add, subtract, multiply, and divide rational numbers.
A(b + c) = ab + ac.
how to find the greatest common factor of two or more terms. Skills:
Students are able to:
apply properties of operations as strategies to add and subtract linear expressions with rational coefficients.
Apply properties of operations as strategies to factor linear expressions with rational coefficients.
Apply properties of operations as strategies to expand linear expressions with rational coefficients. Understanding:
Students understand that:
only like terms can be combined, e.g., x + y = x + y but x + x = 2x.
To factor an expression, one must factor out the greatest common factor.
There are many different ways to write the same expression. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.7.6.1: Define linear expression, rational, coefficient, and rational coefficient.
M.7.6.2: Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
M.7.6.3: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
M.7.6.4: Recognize the property demonstrated in a given expression.
M.7.6.5: Combine like terms of a given expression.
M.7.6.6: Recall how to find the greatest common factor.
M.7.6.7: Give examples of the properties of operations including distributive, commutative, and associative.
Prior Knowledge Skills:
Apply properties of operations for addition and subtraction.
Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
Combine terms that are alike of a given expression.
Recognize the property demonstrated in a given expression.
Simplify an expression by dividing by the greatest common factor. Example: 18x + 6y = 6(3x + y).
Determine the greatest common factor.
Alabama Alternate Achievement Standards
AAS Standard: M.AAS.7.5 Solve multiplication problems up to fifteen with whole number factors.
Mathematics MA2019 (2019) Grade: 7 Accelerated 12. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [Grade 7, 6]
Unpacked Content
Evidence Of Student Attainment:
Students:
Factor a linear expression with an integer as the greatest common factor.
Interpret the parts of an expression, such as the coefficient, constant, term, and variable, based on the context of problem. Teacher Vocabulary:
Term like terms Constant Factor Expression Rational coefficient Knowledge:
Students know:
How to add, subtract, multiply, and divide rational numbers.
A(b + c) = ab + ac.
how to find the greatest common factor of two or more terms. Skills:
Students are able to:
Apply properties of operations as strategies to add and subtract linear expressions with rational coefficients.
Apply properties of operations as strategies to factor linear expressions with rational coefficients.
Apply properties of operations as strategies to expand linear expressions with rational coefficients. Understanding:
Students understand that:
Only like terms can be combined, e.g., x + y = x + y but x + x = 2x.
To factor an expression, one must factor out the greatest common factor. Diverse Learning Needs:
Mathematics MA2019 (2019) Grade: 7 Accelerated 16. Express and compare very large or very small numbers in scientific notation. [Grade 8, 5]
a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used, expressing answers in scientific notation. [Grade 8, 6]
b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. [Grade 8, 6a]
c. Interpret scientific notation that has been generated by technology. [Grade 8, 6b]
Unpacked Content
Evidence Of Student Attainment:
Students:
Rewrite numbers using scientific notation.
Use use numbers in scientific notation to estimate measurements and values.
Use the laws of exponents to multiply
and divide expressions containing numbers
written in scientific and decimal notation to solve real-world problems.
Compare numbers written in scientific
notation and express the multiplicative
relationship between the numbers. Teacher Vocabulary:
Multiplicative relationship
Scientific Notation Knowledge:
Students know:
That scientific notation is formed using base ten system and is the reason a 10 is used as the base number.
Raising or lowering an exponent is has an effect on the place value of the decimal expansion.
That scientific notation is formed using a base ten system.
how to apply laws for multiplying and dividing exponents Skills:
Students are able to:
Write numbers in standard notation in scientific notation.
Convert numbers from scientific notation back to standard form.
Use information given in scientific notation to estimate very large or small quantities given in real-world contexts.
Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both scientific and decimal notation are used.
Choose between appropriate units of measure when determining solutions or estimating Understanding:
Students understand that:
The movement of decimals
in converting between scientific
and standard notation is a function
of an exponent.
Every decimal place represents
a power of ten (this is a connection
many students have not made yet
when thinking about place value).
Scientific notation has real-world
applications for very large and very
small quantities found in many
disciplines.
performing scientific notation
operations are another application
of integer exponent operations. Diverse Learning Needs: