Illustrative Math Alignment: Grade 7 Unit 7

Description

Video Tutorial: Algebra Tiles: Modeling Variable Expressions Using Algebra Tiles. In this tutorial, students review the basic definition of what algebra tiles are and how they are used. Then the video focuses on how to model variable expressions using algebra tiles.

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

Description

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

The following section reviews the basics of algebra tiles. Use this material as background material, and also as a supplement to the video series.

Video Tutorial: Integers: Numerical Expressions with Integers. In this video, students simplify various numerical expressions that use integers.

This is part of a series of videos on the topic of Integers. This includes defining integers, modeling integers, integer operations, and integer expressions.

The following section includes background information on integers (and also rational numbers). Refer to this section as you view the videos, or as review material afterward.

Video Tutorial: Integers: Variable Expressions with Integers. In this video, students simplify various variable expressions that use integers. A

This is part of a series of videos on the topic of Integers. This includes defining integers, modeling integers, integer operations, and integer expressions.

The following section includes background information on integers (and also rational numbers). Refer to this section as you view the videos, or as review material afterward.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to multiply rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Topic

Equations

Definition

An algebraic expression is a combination of variables, constants, and arithmetic operations, without an equality sign.

Description

Algebraic expressions are fundamental components of algebra. They represent quantities and relationships without asserting equality. Examples include 3x + 4 and 5y − 2. Unlike equations, expressions cannot be solved but can be simplified or evaluated for given variable values.

Topic

Equations

Definition

A numerical expression is a mathematical phrase involving numbers and operation symbols, but no variables.

Description

Numerical expressions consist of numbers and operations such as addition, subtraction, multiplication, and division. For example, 

3 + 4 × 2

is a numerical expression. These expressions are evaluated to find their value.

In real-world applications, numerical expressions are used in everyday calculations such as budgeting, measuring, and data analysis. Understanding numerical expressions helps students perform arithmetic operations and develop computational skills.

Topic

Equations

Definition

A variable expression is a mathematical phrase involving variables, numbers, and operation symbols.

Description

Variable expressions consist of variables, numbers, and operations such as addition, subtraction, multiplication, and division. For example, 

3x + 4

is a variable expression. These expressions are used to represent quantities and relationships in algebra.

Topic

Factors and Multiples

Definition

Factoring algebraic expressions involves breaking down a polynomial into simpler components called factors that, when multiplied together, give the original polynomial.

Description

Factoring algebraic expressions is a fundamental concept in algebra that plays a crucial role in simplifying expressions, solving equations, and understanding polynomial functions. This process involves expressing a polynomial as a product of its factors, which are simpler polynomials or numbers. For instance, the polynomial x^2 - 5x + 6 can be factored into (x - 2)(x - 3).

Topic

Rationals and Radicals

Definition

Partial fraction decomposition is a method used to express a rational expression as a sum of simpler fractions.

Description

Partial Fraction Decomposition is a powerful tool in the study of Rational Numbers, Expressions, Equations, and Functions. It involves breaking down a complex rational expression into a sum of simpler fractions, which are easier to integrate or differentiate. For example, the rational function 

$$\frac{2x+3}{(x+1)(x-2)}$$

can be decomposed into 

Topic

Rationals and Radicals

Definition

A radical expression is an expression that contains a radical symbol, which indicates the root of a number.

Description

Radical Expressions are a core component of Radical Numbers, Expressions, Equations, and Functions. These expressions involve roots, such as square roots, cube roots, or higher-order roots, and are denoted by the radical symbol (√). For example, the expression 

$$\sqrt{16}$$ 

Topic

Rationals and Radicals

Definition

Rational expressions are fractions in which the numerator and/or the denominator are polynomials.

Description

Rational Expressions are a fundamental aspect of Rational Numbers, Expressions, Equations, and Functions. These expressions are fractions where the numerator and/or the denominator are polynomials. Simplifying rational expressions often involves factoring the polynomials and canceling common factors. For example, the rational expression 

$$\frac{x^2 - 1}{x - 1}$$

can be simplified to x + 1, provided that 

$$x \neq 1$$

Topic

Rationals and Radicals

Definition

Simplifying a radical expression involves reducing the expression to its simplest form by factoring the radicand and removing any perfect square factors (for square roots) or perfect cube factors (for cube roots).

Description

Simplifying a Radical Expression is a fundamental skill in the study of Radical Numbers, Expressions, Equations, and Functions. This process involves reducing a radical expression to its simplest form, which often makes it easier to work with and understand. For example, simplifying 

$$\sqrt{18}$$

results in 

Topic

Rationals and Radicals

Definition

Simplifying a rational expression involves reducing the fraction to its lowest terms by factoring both the numerator and denominator and canceling common factors.

Description

Simplifying a Rational Expression is a crucial skill in the study of Rational Numbers, Expressions, Equations, and Functions. This process involves reducing a rational expression to its simplest form by factoring both the numerator and denominator and canceling common factors. For example, simplifying 

$$\frac{x^2 - 1}{x - 1}$$

results in x + 1 for 

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

Topic

Multiplication and Division

Definition

A division expression is a mathematical phrase that involves division, such as 12 ÷ 3.

Topic

Multiplication and Division

Definition

A multiplication expression is a mathematical phrase that involves multiplication, such as 5 × 7.

Description

Multiplication expressions are used to represent the multiplication of numbers in a concise form. For example, the expression 

6 × 8 

Topic

Addition and Subtraction

Definition

An addition expression is a mathematical phrase that shows the sum of two or more numbers without an equals sign.

Description

An addition expression is a mathematical phrase that involves adding two or more numbers but does not include an equals sign. For example, 

3 + 4

is an addition expression. These expressions are used to represent sums in a concise manner and are fundamental in understanding arithmetic operations.

Topic

Addition and Subtraction

Definition

A subtraction expression is a mathematical phrase that shows the difference between two numbers without an equals sign.

Description

A subtraction expression is a mathematical phrase that involves subtracting one number from another but does not include an equals sign. For example, 

7 − 4

is a subtraction expression. These expressions are used to represent differences in a concise manner and are fundamental in understanding arithmetic operations.

This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve addition. Note: The download is a PPT file. NOTE: The download is a PPT file.

This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve division. Note: The download is a PPT file. NOTE: The download is a PPT file.

This set of tutorials provides 32 examples of converting verbal expressions into numerical expressions that involve grouping symbols. Note: The download is a PPT file. NOTE: The download is a PPT file.

This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve multiplication. Note: The download is a PPT file. NOTE: The download is a PPT file.

This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve subtraction. Note: The download is a PPT file. NOTE: The download is a PPT file.

This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and addition. Note: The download is a PPT file. NOTE: The download is a PPT file.

This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and subtraction. Note: The download is a PPT file. NOTE: The download is a PPT file.

This tutorial provides an overview of numerical expressions in the context of multiplication and division expressions.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

In this tutorial students learn about rational expressions and use the properties of fractions to combine them.

—Press PREVIEW to see the tutorial—

In this Slide Show, learn about variables and variable expressions.

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Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

In this drag-and-drop game, a verbal expression to a numerical expression with addition. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

Related Resources

In this drag-and-drop game, match a verbal description of an addition expression with its numerical counterpart.

Related Resources

In this drag-and-drop game, a verbal expression to a numerical expression with grouping symbols. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

Related Resources

In this drag-and-drop game, match a verbal expression to a numerical expression with multiplication. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

Related Resources

In this drag-and-drop game, match a verbal description of a subtraction expression with its numerical counterpart.

Related Resources

In this drag-and-drop game, a verbal expression to a variable expression with multiplication and addition. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

Related Resources

In this drag-and-drop game, a verbal expression to a variable expression with multiplication and subtraction. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

Related Resources

In this Math Riddles Game, have your students review vocabulary around the topic of expressions and equations. The Math Riddles games are useful for practicing: Math Vocabulary, Key Concepts, Critical Thinking.

Related Resources

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

This is part of a collection of math examples that focus on combinatorics and factorial expressions.