Students play an Expressions Game in which they describe expressions to their partners using the vocabulary of expressions: term, coefficient, exponent, constant, and variable. Their partners try to write the correct expressions based on the descriptions.Key ConceptsMathematical expressions have parts, and these parts have names. These names allow us to communicate with others in a precise way.A variable is a symbol (usually a letter) in an expression that can be replaced by a number.A term is a number, a variable, or a product of numbers and variables. Terms are separated by the operator symbols + (plus) and – (minus).A coefficient is a symbol (usually a number) that multiplies the variable in an algebraic expression.An exponent tells how many copies of a number or variable are multiplied together.A constant is a number. In an expression, it can be a constant term or a constant coefficient. In the expression 2x + 3, 2 is a constant coefficient and 3 is a constant term.Goals and Learning ObjectivesIdentify parts of an expression using appropriate mathematical vocabulary.Write expressions that fit specific descriptions (for example, the expression is the sum of two terms each with a different variable).

Students critique the work of other students and revise their own work based on feedback from the teacher and peers.Key ConceptsConcepts from previous lessons are integrated into this unit task: rewriting expressions, using parentheses, and using the distributive property. Students apply their knowledge, review their work, and make revisions based on feedback from you and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply knowledge of expressions to correct the work of other students.Track and review the choice of strategy when problem solving.

Students express the lengths of trains as algebraic expressions and then substitute numbers for letters to find the actual lengths of the trains.Key ConceptsAn algebraic expression can be written to represent a problem situation. More than one algebraic expression may represent the same problem situation. These algebraic expressions have the same value and are equivalent.To evaluate an algebraic expression, a specific value for each variable is substituted in the expression, and then all the calculations are completed using the order of operations to get a single value.Goals and Learning ObjectivesEvaluate expressions for the given values of the variables.

Students write an expression for the length of a train, using variables to represent the lengths of the different types of cars.Key ConceptsA numerical expression consists of a number or numbers connected by the arithmetic operations of addition, subtraction, multiplication, division, and exponentiation.An algebraic expression uses letters to represent numbers.An algebraic expression can be written to represent a problem situation. Sometimes more than one algebraic expression may represent the same problem situation. These algebraic expressions have the same value and are equivalent.The properties of operations can be used to make long algebraic expressions shorter:The commutative property of addition states that changing the order of the addends does not change the end result:a + b = b + a.The associative property of addition states that changing the grouping of the addends does not change the end result:(a + b) + c = a + (b + c).The distributive property of multiplication over addition states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together:a(b + c) = ab + ac.Goals and Learning ObjectivesWrite algebraic expressions that describe lengths of freight trains.Use properties of operations to shorten those expressions.

Students represent problem situations using expressions and then evaluate the expressions for the given values of the variables.Key ConceptsAn algebraic expression can be written to represent a problem situation.To evaluate an algebraic expression, a specific value for each variable is substituted in the expression, and then all the calculations are completed using the order of operations to get a single value.Goals and Learning ObjectivesDevelop fluency in writing expressions to represent situations and in evaluating the expressions for given values.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Students are introduced to classroom routines and expectations, and complete a full mathematics lesson. The class discusses how to clearly present work to classmates. Partner work is modeled, and partners then work to match numerical expressions to corresponding word descriptions. Students read and discuss a summary of the math in the lesson, and then write a reflection about their thoughts.Key ConceptsStudents match a numerical expression to its corresponding description in words. Students interpret parentheses and brackets in numerical expressions and they construct viable arguments and critique the reasoning of others. Students learn to use the exponent 2 to represent squaring.Goals and Learning ObjectivesDescribe the classroom routines and expectations.Consider how to present work clearly to classmates.Collaborate with a partner.Critique a partner’s reasoning.Connect a numerical expression to its corresponding word description.Learn to use an exponent of 2 to represent squaring.

Students are introduced to classroom routines and expectations, and complete a full mathematics lesson. The class discusses how to clearly present work to classmates. Partner work is modeled, and partners then work to match numerical expressions to corresponding word descriptions. Students read and discuss a summary of the math in the lesson, and then write a reflection about their thoughts.Key ConceptsStudents match a numerical expression to its corresponding description in words. Students interpret parentheses and brackets in numerical expressions and they construct viable arguments and critique the reasoning of others. Students learn to use the exponent 2 to represent squaring.Goals and Learning ObjectivesDescribe the classroom routines and expectations.Consider how to present work clearly to classmates.Collaborate with a partner.Critique a partner’s reasoning.Connect a numerical expression to its corresponding word description.Learn to use an exponent of 2 to represent squaring.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

Students explore the outermost planets of our solar system: Saturn, Uranus and Neptune. They also learn about characteristics of Pluto and its interactions with Neptune. Students learn a little about the history of space travel as well as the different technologies that engineers develop to make space travel and scientific discovery possible.

This supplemental resource provides problems and activities related to Patterns, Relationships and Functions in Middle School Mathematics.

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. Students then have to use the expression to evaluate the perimeter for specific values of the two variables.

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Tune in to STEM in 30 to learn all about real world applications of Math, and learn a little magic along the way.

Students investigate the critical nature of foundations as they learn differences between shallow and deep foundations, including the concepts of bearing pressure and settlement. Using models representing a shallow foundation and a deep pile foundation, they test, see and feel the effects in a cardboard box test bed composed of layers of pebbles, soil and sand. They also make bearing pressure calculations and recommendations for which type of foundations to use in various engineering scenarios.

Khan Academy Video Tutorial. Introduction to basic algebraic equations of the form Ax=B

Students learn about the variety of materials used by engineers in the design and construction of modern bridges. They also find out about the material properties important to bridge construction and consider the advantages and disadvantages of steel and concrete as common bridge-building materials to handle compressive and tensile forces.