Essential Questions:
Lesson Plan B.3: Multi-Step Problems
Lesson Seed B.3: Multi-Steps Situation Cards
Lesson Seed B.4a: Equations Mobile
Lesson Seed B.4a: Two Step Equations
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 using the four operations with rational numbers (integers, fractions, and decimals) and applies the operations as multi-step strategies to construct and solve problems based on expressions, equations, and inequalities. The unit focuses on using variables to present quantities in algebraic expressions, equations, and inequalities; and it relies on properties of operations to calculate and estimate with rational numbers in any form. Teacher Notes:
At the completion of this unit on the use of properties of operations to generate equivalent expressions, the student will understand that:
Evidence of Student Learning
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.
Fluency Expectations and Examples of Culminating Standards:
Common Misconceptions:
Students May:
Interdisciplinary connections fall into a number of related categories:
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
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.
Part II – Instructional Connections outside the Focus Cluster
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 , is the non-negative number which is equal to |3| = 3; |0| = 0; and |-3| = 3.
Order of 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:
complex fraction: A complex fraction has a fraction for the numerator or denominator or both.
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:
Additional Resources: