This tutorial for students new to algebra provides explanations, definitions, examples, and …

This tutorial for students new to algebra provides explanations, definitions, examples, and practice problems. The practice tests cover topics such as real numbers, fractions, equations, graphing, and exponents.

This tutorial offers definitions, examples, and practice problems for looking at various …

This tutorial offers definitions, examples, and practice problems for looking at various components of terms and for simplifying algebraic expressions.

Walk through this tutorial to see exactly how rational expressions are simplified. …

Walk through this tutorial to see exactly how rational expressions are simplified. When you're finished, try the practice problems to see how much you've learned.

This Algebra lesson focuses on writing algebraic expressions to represent real-world problems, …

This Algebra lesson focuses on writing algebraic expressions to represent real-world problems, using the properties of numbers to simplify expressions, and evaluating equations by isolating the variable.

In this video segment from Cyberchase, Harry has a fixed budget for …

In this video segment from Cyberchase, Harry has a fixed budget for clothing, so he must figure out what combination of jackets and pants he can buy with $100.

The concept of equivalent fractions is applied to algebraic expressions. Examples of …

The concept of equivalent fractions is applied to algebraic expressions. Examples of how to simplify expressions are included, along with when to stop simplifying. Includes practice problems.

After their carts collide in a hardware store, two teachers discover that …

After their carts collide in a hardware store, two teachers discover that they both bought the same items in different quantities. With limited information, this segment demonstrates how to use an equation to determine the cost of each item.

Students practice using algebraic expressions by recording data from a video segment …

Students practice using algebraic expressions by recording data from a video segment in which two staircases ascend at different rates. They record the patterns in two-column tables, draw line graphs and write simple algebraic relations.

This QuickTime movie provides an opportunity to translate English words into an …

This QuickTime movie provides an opportunity to translate English words into an algebraic expression. As you watch and listen to the teacher and student interact it helps clarify the thinking behind applying this concept.

Expressions Type of Unit: Concept Prior Knowledge Students should be able to: …

Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers. Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols. Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Students analyze how two different calculators get different values for the same …

Students analyze how two different calculators get different values for the same numerical expression. In the process, students recognize the need for following the same conventions when evaluating expressions.Key ConceptsMathematical expressions express calculations with numbers (numerical expressions) or sometimes with letters representing numbers (algebraic expressions).When evaluating expressions that have more than one operation, there are conventions—called the order of operations—that must be followed:Complete all operations inside parentheses first.Evaluate exponents.Then complete all multiplication and division, working from left to right.Then complete all addition and subtraction, working from left to right.These conventions allow expressions with more than one operation to be evaluated in the same way by everyone. Because of these conventions, it is important to use parentheses when writing expressions to indicate which operation to do first. If there are nested parentheses, the operations in the innermost parentheses are evaluated first. Understanding the use of parentheses is especially important when interpreting the associative and the distributive properties.Goals and Learning ObjectivesEvaluate numerical expressions.Use parentheses when writing expressions.Use the order of operations conventions.

Students do a card sort in which they match expressions in words …

Students do a card sort in which they match expressions in words with their equivalent algebraic expressions.Key ConceptsA mathematical expression that uses letters to represent numbers is an algebraic expression.A letter used in place of a number in an expression is called a variable.An algebraic expression combines both numbers and letters using the arithmetic operations of addition (+), subtraction (–), multiplication (·), and division (÷) to express a quantity.Words can be used to describe algebraic expressions.There are conventions for writing algebraic expressions:The product of a number and a variable lists the number first with no multiplication sign. For example, the product of 5 and n is written as 5n, not n5.The product of a number and a factor in parentheses lists the number first with no multiplication sign. For example, write 5(x + 3), not (x + 3)5.For the product of 1 and a variable, either write the multiplication sign or do not write the "1." For example, the product of 1 and z is written either 1 ⋅ z or z, not 1z.Goals and Learning ObjectivesTranslate between expressions in words and expressions in symbols.

Students write an expression for the length of a train, using 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.

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