Essential Questions:
Lesson Plan A.1: Factor, Distribute, and Combine
Lesson Seed A.1: Mystery Polygons
Lesson Seed A.1: Tricky Triangles
Lesson Seed A.2: Flooring Confusion
Unit Overview
Content Emphasis By Clusters in Grade 7
Progressions from Common Core State Standards in Mathematics
Send Feedback to MSDE’s Mathematics Team
Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.
This unit builds on prior understandings of addition, subtraction, multiplication and division and applies them as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. The unit also focuses on ways in which rewriting an expression for a specific problem can clarify how the values and quantities in the problem are interconnected.
At the completion of this unit on the use of properties of operations to generate equivalent expressions, the student will understand that:
Students will be able to:
The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.
Students may
Interdisciplinary Connections:
Interdisciplinary connections fall into a number of related categories:
Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:
Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
Part I – Focus Cluster Use Properties of Operations to Generate Equivalent Expressions
factor: A factor is a term that divides a given quantity evenly (with a remainder of 0). As a verb, factor means to divide a given quantity in the form of its factors. For example, 6 is factored in the form of 2 x 3. The terms 2 and 3 are factors of the given quantity 6. 4x_{3} – 5x_{2} is factored in the form of x_{2} (4x – 5). The terms x_{2} and (4x – 5) are the factors of 4x_{3} – 5x_{2}.
expand linear expressions: The form a quantity takes when written as a continued product, using the distributive property of multiplication over addition. For example, the quantity 6(4x – 5) in expanded form is 24x – 30.
properties of operations: The properties of operations apply to the rational number system, the real number system, and the complex number system, when a, b and c stand for arbitrary numbers in a given number system. The properties include:
Part II – Instructional Connections outside the Focus Cluster
rational numbers: Numbers that can be expressed as an integer, as a quotient of integers (such as ^{1}/_{2} , ^{4}/_{3} , 7), or as a decimal where the decimal part is either finite or repeats infinitely (such as 2.75 and 33.3333…) are considered rational numbers.
algebraic solution: An algebraic solution is a proof or an answer that uses letters (algebraic symbols) to represent numbers, and uses operations symbols to indicate algebraic operations of addition, subtraction, multiplication division, extracting roots, and raising to powers.
arithmetic solution: An arithmetic solution is a proof or an answer that uses rational numbers under the operations of addition, subtraction, multiplication and division
rational numbers: Numbers that can be expressed as an integer, as a quotient of integers (e.g., ^{1}/_{2} , ^{4}/_{3} , 7, - ^{1}/_{2} , - ^{4}/_{3} , ‾ 7 ), or as a decimal where the decimal part is either finite or repeats infinitely (e.g., 2.75, ‾2.75, 3.3333… and ‾3.3333…) are considered rational numbers.
additive inverse: The additive inverse of a number a is the number ‾a for which a + (‾a) = 0.
absolute value: The absolute value of a number a, written |a|, is the non-negative number which is equal to a if a is non-negative, and equal to ‾a if a is negative. For example: |3| = 3; |0| = 0; and = |‾3| = 3.
complex fraction: A complex fraction has a fraction for the numerator or denominator or both.
order of operations: The steps for simplifying expressions are:
vertical number line:
Additional Resources: