Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 8: Reasoning about Solving Equations (Part 2)

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Clip Art--The Language of Math--Numbers and Equations 46	Math Clip Art--The Language of Math--Numbers and Equations 46 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "1/1=1" in both numerical and word form. It introduces the concept of division, starting with the simplest case of dividing a number by itself. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand the basic concept of division and introduces the idea that any number divided by itself equals 1.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 47	Math Clip Art--The Language of Math--Numbers and Equations 47 Topic The Language of Math Description This image presents the equation "2/2=1" in both numerical and word form. It continues the progression of division concepts, now working with a fraction where the numerator and denominator are equal. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing a number by itself always results in 1.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 48	Math Clip Art--The Language of Math--Numbers and Equations 48 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "3/3=1" in both numerical and word form. It continues the series of division concepts, focusing on fractions where the numerator and denominator are equal. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand how division works and reinforces the concept that any number divided by itself equals 1.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 49	Math Clip Art--The Language of Math--Numbers and Equations 49 Topic The Language of Math Description This image presents the equation "4/2=2" in both numerical and word form. It advances the complexity of division concepts by introducing a fraction where the numerator is greater than the denominator. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by a smaller number results in a larger quotient.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 50	Math Clip Art--The Language of Math--Numbers and Equations 50 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "5/1=5" in both numerical and word form. It introduces the concept of dividing by 1, which is a fundamental principle in mathematics. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand that dividing a number by 1 results in the same number, reinforcing the identity property of division.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 51	Math Clip Art--The Language of Math--Numbers and Equations 51 Topic The Language of Math Description This image presents the equation "6/2=3" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and introducing the concept of halving. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 2 relates to finding half of a number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 52	Math Clip Art--The Language of Math--Numbers and Equations 52 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "7/7=1" in both numerical and word form. It reinforces the concept that any number divided by itself equals 1. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand a fundamental principle of division and introduces the concept of equivalent fractions.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 53	Math Clip Art--The Language of Math--Numbers and Equations 53 Topic The Language of Math Description This image presents the equation "8/4=2" in both numerical and word form. It advances the complexity of division concepts by introducing division with larger numbers and the concept of quartering. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 4 relates to finding a quarter of a number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 54	Math Clip Art--The Language of Math--Numbers and Equations 54 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "9/3=3" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and introducing the concept of thirds. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand how division works with larger numbers and reinforces the concept of equal sharing.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 55	Math Clip Art--The Language of Math--Numbers and Equations 55 Topic The Language of Math Description This image presents the equation "10/2=5" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and reinforcing the concept of halving. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 2 relates to finding half of a number, even with larger values.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 56	Math Clip Art--The Language of Math--Numbers and Equations 56 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "11/1=11" in both numerical and word form. It introduces the concept of dividing by 1, which is a fundamental principle in mathematics. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand that dividing a number by 1 results in the same number, reinforcing the identity property of division.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 57	Math Clip Art--The Language of Math--Numbers and Equations 57 Topic The Language of Math Description This image presents the equation "12/3=4" in both numerical and word form. It advances the complexity of division concepts by working with larger numbers and introducing the concept of dividing by 3. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 3 relates to grouping numbers into thirds.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 58	Math Clip Art--The Language of Math--Numbers and Equations 58 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "13/13=1" in both numerical and word form. It reinforces the concept that any number divided by itself equals 1, now using a larger number. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand a fundamental principle of division and introduces the concept of equivalent fractions with larger numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 59	Math Clip Art--The Language of Math--Numbers and Equations 59 Topic The Language of Math Description This image presents the equation "14/7=2" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and introducing the concept of halving with two-digit numbers. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by half of a number results in 2.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 60	Math Clip Art--The Language of Math--Numbers and Equations 60 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "15/3=5" in both numerical and word form. It advances the complexity of division concepts by working with larger numbers and introducing the concept of dividing by 3. The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand how division works with larger numbers and reinforces the concept of grouping into thirds.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 61	Math Clip Art--The Language of Math--Numbers and Equations 61 Topic The Language of Math Description This image presents a blank card, serving as the final piece in the series of 61 clip art images focused on the Language of Math: Numbers and Equations. While it doesn't contain a specific equation, its presence is significant in the collection.	Numerical Expressions
Math Clip Art: Equations vs. Inequalities	Math Clip Art: Equations vs. Inequalities This collection of clip art images show the contrast between graphs of equations and inequalities for one- and two-variable graphs.	Inequalities
Math Clip Art: Solving Equations and Inequalities	Math Clip Art: Solving Equations and Inequalities Use these clip art images to show how to solve linear equations and inequalities. Examples include situations where the inequality symbol changes.	Inequalities
Math Example--Function Concepts--Function Rules and Equations--Example 1	Math Example--Function Concepts--Function Rules and Equations--Example 1 Topic Arithmetic Description Example 1: Write a function equation of the form f(x) based on the Function Machine that takes an input and doubles its value. The input shown is 5, and the output is 10. To find the solution, replace the numerical input with the variable x. Since the machine doubles the input, the function equation is f(x) = 2x.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 10	Math Example--Function Concepts--Function Rules and Equations--Example 10 Topic Arithmetic Description Example 10: Write a function equation of the form f(x) based on the Function Machine that subtracts -1 (or adds 1) from the input and squares the sum. The input is 8, and the output is 81. Substitute x for the input. The machine subtracts -1 from x (equivalent to adding 1) and squares the result, so the function equation is f(x) = (x + 1)2.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 2	Math Example--Function Concepts--Function Rules and Equations--Example 2 Topic Arithmetic Description Example 2: Write a function equation of the form f(x) based on the Function Machine that takes an input and triples its value. The input shown is 4, and the output is 12. By replacing the numerical input with the variable x and applying the machine's rule to triple the input, the function equation is f(x) = 3x.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 3	Math Example--Function Concepts--Function Rules and Equations--Example 3 Topic Arithmetic Description Example 3: Write a function equation of the form f(x) based on the Function Machine that doubles the value of the input and then adds 3. The input is 5, and the output is 13. To determine the function, replace the input with x. The machine doubles the input and then adds 3, so the function equation is f(x) = 2x + 3.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 4	Math Example--Function Concepts--Function Rules and Equations--Example 4 Topic Arithmetic Description EΘample 4: Write a function equation of the form f(Θ) based on the Function Machine that multiplies the input by -3 and then adds 2. The input is 4, and the output is -10. Substitute the numerical input with x. Since the machine multiplies the input by -3 and adds 2, the function equation is f(x) = -3x + 2.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 5	Math Example--Function Concepts--Function Rules and Equations--Example 5 Topic Arithmetic Description Example 5: Write a function equation of the form f(x) based on the Function Machine that divides the input by 4 and then subtracts 1. The input shown is 16, and the output is 3. Replace the input with x. Applying the function machine's rule to divide by 4 and subtract 1, the function equation is f(x) = x / 4 - 1.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 6	Math Example--Function Concepts--Function Rules and Equations--Example 6 Topic Arithmetic Description Example 6: Write a function equation of the form f(x) based on the Function Machine that multiplies the input by itself (squares it). The input is 5, and the output is 25. Substitute the input with x. Since the machine squares the input, the function equation is f(x) = x2.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 7	Math Example--Function Concepts--Function Rules and Equations--Example 7 Topic Arithmetic Description Example 7: Write a function equation of the form f(x) based on the Function Machine that multiplies the input by itself and then multiplies the result by 2. The input is 6, and the output is 72. Replace the input with x. The machine squares the input and then multiplies it by 2, so the function equation is f(x) = 2x2.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 8	Math Example--Function Concepts--Function Rules and Equations--Example 8 Topic Arithmetic Description Example 8: Write a function equation of the form f(x) based on the Function Machine that adds 4 to the input and then squares the sum. The input is 3, and the output is 49. Substitute x for the input. The machine adds 4 to x and then squares the result, giving the function equation f(x) = (x + 4)2.	Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 9	Math Example--Function Concepts--Function Rules and Equations--Example 9 Topic Arithmetic Description Example 9: Write a function equation of the form f(x) based on the Function Machine that subtracts 5 from the input and then squares the sum. The input is 10, and the output is 25. Replace the input with x. Since the machine subtracts 5 from x and squares the result, the function equation is f(x) = (x - 5)2.	Relations and Functions
Math Example--Graphical Solutions to Rational Equations--Example 1	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 10	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 2	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 3	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 4	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 5	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 6	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 7	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 8	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 9	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1	Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Topic Linear Functions Description This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.	Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10	Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10 Topic Linear Functions Description This example illustrates the conversion of the linear equation x + y = 1 from standard form to slope-intercept form. The process involves isolating y, resulting in y = -x + 1. This simple transformation clearly reveals the slope and y-intercept of the line.	Standard Form

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 8: Reasoning about Solving Equations (Part 2)

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