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--Quadratics Concepts--Equations of Parabolas 07	Math Clip Art--Quadratics Concepts--Equations of Parabolas 07 Topic Quadratics Description This math clip art image advances the concept of deriving a parabola's equation. It shows a parabola with its focus at (0, f) and directrix, and introduces calculations for distances D1 and D2. These distances represent the key relationship that defines a parabola: the equidistance of any point on the parabola from the focus and the directrix.	Graphs of Quadratic Functions
Math Clip Art--Quadratics Concepts--Equations of Parabolas 08	Math Clip Art--Quadratics Concepts--Equations of Parabolas 08 Topic Quadratics Description This math clip art image presents the culmination of the parabola equation derivation process. It shows a parabola with its focus at (0, f) and directrix, along with distances D1 and D2 illustrated from a point (x, y) on the parabola to the focus and directrix, respectively. The image also includes the equation derivation, demonstrating how to equate the two distance formulas.	Graphs of Quadratic Functions
Math Clip Art--Quadratics Concepts--Equations of Parabolas 09	Math Clip Art--Quadratics Concepts--Equations of Parabolas 09 Topic Quadratics Description The ninth image in this collection visually reinforces the concepts previously introduced. It illustrates a graph of a parabola with a focus point (a, b), directrix y = c, and marking the distances D1 and D2. This composition emphasizes the link between the geometric definition of a parabola and its mathematical function.	Graphs of Quadratic Functions
Math Clip Art--Quadratics Concepts--Equations of Parabolas 10	Math Clip Art--Quadratics Concepts--Equations of Parabolas 10 Topic Quadratics Description This image continues the trend of analysis by showing the process of deriving the equation for a parabola. The focus at point (a, b), the directrix at y = c, and the marked distances D1 and D2 is crucial for visual learning and conceptual understanding. With these elements illustrated, the image reinforces the message of equidistance between a point on the parabola and its defining attributes, the focus and directrix. It serves as a key teaching tool to show how algebraic formulae arise from geometrical properties.	Graphs of Quadratic Functions
Math Clip Art--Quadratics Concepts--Equations of Parabolas 11	Math Clip Art--Quadratics Concepts--Equations of Parabolas 11 Topic Quadratics Description The final image in this set encapsulates the concepts presented throughout the earlier illustrations. It closely resembles the previous image while maintaining a focus on calculating the equation of a parabola. Here, the focus is again at (a, b) while the directrix follows the line y = c; D1 and D2 are marked, reiterating the need for distance calculations.	Graphs of Quadratic Functions
Math Clip Art--The Language of Math--Numbers and Equations 01	Math Clip Art--The Language of Math--Numbers and Equations 01 Topic The Language of Math Description This image from the Language of Math collection illustrates the equation "1+1=2" using both numerical symbols and words. It serves as a fundamental building block in teaching basic addition and the concept of equality in mathematics. By presenting the equation in both numerical and verbal forms, this clip art reinforces the connection between mathematical symbols and their linguistic representations. This dual presentation is crucial for developing students' ability to translate between mathematical language and everyday language.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 02	Math Clip Art--The Language of Math--Numbers and Equations 02 Topic The Language of Math Description This clip art image from the Language of Math series depicts the equation "1+2=3" in both numerical and word form. It builds upon the previous image, introducing the concept of adding a two-digit number to a one-digit number. The visual representation of this equation helps students understand how numbers combine to form larger values. By presenting the equation in both formats, it reinforces the connection between mathematical symbols and their verbal expressions, a crucial skill in mathematical literacy.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 03	Math Clip Art--The Language of Math--Numbers and Equations 03 Topic The Language of Math Description This clip art from the Language of Math collection presents the equation "1+3=4" in both numerical and word formats. It continues the progression of addition concepts, now introducing the sum of four. The dual representation of the equation reinforces the connection between mathematical symbols and their verbal counterparts. This visual aid helps students understand how numbers combine to create larger values and introduces the concept of "one more than" the previous equation.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 04	Math Clip Art--The Language of Math--Numbers and Equations 04 Topic The Language of Math Description This clip art image from the Language of Math series illustrates the equation "1+4=5" in both numerical and word form. It continues the pattern of increasing sums, now reaching five. The dual representation of the equation helps students connect the abstract mathematical symbols with their concrete verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of addition, particularly how combining smaller numbers results in larger ones.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 05	Math Clip Art--The Language of Math--Numbers and Equations 05 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "1+5=6" in both numerical and word formats. It continues the series of addition equations, now introducing the sum of six. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how numbers combine to form larger values and introduces the concept of "five more than" the initial number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 06	Math Clip Art--The Language of Math--Numbers and Equations 06 Topic The Language of Math Description This image illustrates the equation "6+2=8" in both numerical and word form, continuing the progression of addition concepts with larger numbers. The dual representation reinforces the connection between mathematical symbols and their verbal expressions, a crucial skill in developing mathematical literacy. This visual aid helps students understand how numbers combine to create larger values and introduces the concept of adding to a number greater than 5.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 07	Math Clip Art--The Language of Math--Numbers and Equations 07 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "7+1=8" in both numerical and word formats. It continues the series of addition equations, now introducing the concept of adding 1 to a larger number. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how numbers combine and introduces the concept of "one more than" a given number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 08	Math Clip Art--The Language of Math--Numbers and Equations 08 Topic The Language of Math Description This image presents the equation "8+3=11" in both numerical and word form, advancing the complexity of addition concepts by introducing a sum greater than 10. 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 addition, particularly how combining single-digit numbers can result in double-digit sums.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 09	Math Clip Art--The Language of Math--Numbers and Equations 09 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "9+5=14" in both numerical and word form. It continues the progression of addition concepts, now introducing a larger sum and the concept of adding a single-digit number to 9. The dual representation of the equation helps students connect the abstract mathematical symbols with their concrete verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of addition, particularly how combining numbers can result in sums greater than 10.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 10	Math Clip Art--The Language of Math--Numbers and Equations 10 Topic The Language of Math Description This image from the Language of Math collection presents the equation "10+1=11" in both numerical and word form. It marks a significant transition in the addition sequence, introducing the concept of adding to a double-digit number. 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 addition, particularly how adding to 10 results in the next consecutive number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 11	Math Clip Art--The Language of Math--Numbers and Equations 11 Topic The Language of Math Description This image from the Language of Math collection illustrates the equation "11+2=13" in both numerical and word form. It advances the complexity of addition concepts by introducing larger numbers and sums exceeding 10. 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 addition, particularly how combining numbers results in sums greater than 10.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 12	Math Clip Art--The Language of Math--Numbers and Equations 12 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "12+3=15" in both numerical and word formats. It continues the progression of addition concepts with larger numbers and sums. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how numbers combine and introduces the concept of adding to a number greater than 10.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 13	Math Clip Art--The Language of Math--Numbers and Equations 13 Topic The Language of Math Description This image from the Language of Math series presents the equation "13+4=17" in both numerical and word form. It continues the progression of addition concepts with increasingly larger numbers and sums. The dual representation of the equation helps students connect the abstract mathematical symbols with their concrete verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of addition, particularly how combining teen numbers with single-digit numbers results in larger sums.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 14	Math Clip Art--The Language of Math--Numbers and Equations 14 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "14+5=19" in both numerical and word form. It advances the complexity of addition concepts by working with larger teen numbers and approaching sums close to 20. 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 numbers combine and introduces the concept of adding to a number in the teens.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 15	Math Clip Art--The Language of Math--Numbers and Equations 15 Topic The Language of Math Description This image from the Language of Math series depicts the equation "15+6=21" in both numerical and word form. It continues the progression of addition concepts, now introducing sums that exceed 20. 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 addition, particularly how combining teen numbers with single-digit numbers can result in sums greater than 20.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 16	Math Clip Art--The Language of Math--Numbers and Equations 16 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "1-1=0" in both numerical and word form. It introduces the concept of subtraction and the idea of a difference of zero. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand the basic concept of subtraction and introduces the idea that subtracting a number from itself results in zero.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 17	Math Clip Art--The Language of Math--Numbers and Equations 17 Topic The Language of Math Description This image from the Language of Math series presents the equation "2-1=1" in both numerical and word form. It continues the introduction of subtraction concepts, now showing a non-zero difference. 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 subtraction, particularly how removing one from a quantity results in a smaller number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 18	Math Clip Art--The Language of Math--Numbers and Equations 18 Topic The Language of Math Description This image presents the equation "3-1=2" in both numerical and word form. It continues the progression of subtraction concepts, now working with a larger minuend. 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 subtraction works and introduces the concept of "one less than" a given number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 19	Math Clip Art--The Language of Math--Numbers and Equations 19 Topic The Language of Math Description This image illustrates the equation "4-1=3" in both numerical and word form. It continues the progression of subtraction concepts, now working with a larger minuend. 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 subtraction, particularly how removing one from a quantity results in a smaller number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 20	Math Clip Art--The Language of Math--Numbers and Equations 20 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "5-1=4" in both numerical and word formats. It continues the series of subtraction equations, now introducing a larger minuend. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how subtraction works and introduces the concept of "one less than" a given number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 21	Math Clip Art--The Language of Math--Numbers and Equations 21 Topic The Language of Math Description This image presents the equation "6-2=4" in both numerical and word form. It advances the complexity of subtraction concepts by introducing a subtrahend greater than 1. 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 subtraction, particularly how removing multiple units from a quantity affects the result.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 22	Math Clip Art--The Language of Math--Numbers and Equations 22 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "7-1=6" in both numerical and word form. It continues the progression of subtraction concepts, now working with a larger minuend. 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 subtraction works and reinforces the concept of "one less than" a given number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 23	Math Clip Art--The Language of Math--Numbers and Equations 23 Topic The Language of Math Description This image presents the equation "8-3=5" in both numerical and word form. It advances the complexity of subtraction concepts by introducing a larger subtrahend and working with single-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 subtraction, particularly how removing multiple units from a quantity affects the result.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 24	Math Clip Art--The Language of Math--Numbers and Equations 24 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "9-5=4" in both numerical and word formats. It continues the progression of subtraction concepts, now introducing a larger subtrahend and working with single-digit numbers. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how subtraction works with larger numbers and introduces the concept of "finding the difference" between two numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 25	Math Clip Art--The Language of Math--Numbers and Equations 25 Topic The Language of Math Description This image illustrates the equation "10-1=9" in both numerical and word form. It introduces subtraction with a two-digit number, marking a significant step in mathematical understanding. 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 subtraction, particularly how removing one from a round number results in a single-digit answer.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 26	Math Clip Art--The Language of Math--Numbers and Equations 26 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "11-2=9" in both numerical and word formats. It continues the progression of subtraction concepts, now working with larger two-digit numbers. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how subtraction works with larger numbers and introduces the concept of "finding the difference" between two numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 27	Math Clip Art--The Language of Math--Numbers and Equations 27 Topic The Language of Math Description This image presents the equation "12-3=9" in both numerical and word form. It advances the complexity of subtraction concepts by introducing larger two-digit numbers and a subtrahend greater than 1. 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 subtraction, particularly how removing multiple units from a quantity affects the result.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 28	Math Clip Art--The Language of Math--Numbers and Equations 28 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "13-4=9" in both numerical and word form. It continues the progression of subtraction concepts, now working with larger two-digit numbers and a subtrahend greater than 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 subtraction works with larger numbers and reinforces the concept of "finding the difference" between two numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 29	Math Clip Art--The Language of Math--Numbers and Equations 29 Topic The Language of Math Description This image presents the equation "14-5=9" in both numerical and word form. It advances the complexity of subtraction concepts by introducing larger two-digit numbers and a subtrahend of 5. 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 subtraction, particularly how removing half of 10 from a teen number results in a single-digit answer.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 30	Math Clip Art--The Language of Math--Numbers and Equations 30 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "15-6=9" in both numerical and word formats. It continues the progression of subtraction concepts, now working with larger two-digit numbers and a subtrahend greater than 5.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 31	Math Clip Art--The Language of Math--Numbers and Equations 31 Topic The Language of Math Description This image illustrates the equation "1*1=1" in both numerical and word form. It introduces the concept of multiplication, starting with the simplest case of multiplying 1 by itself. 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 multiplication as repeated addition.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 32	Math Clip Art--The Language of Math--Numbers and Equations 32 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "2*1=2" in both numerical and word formats. It continues the introduction of multiplication concepts, now showing multiplication by 1. The simultaneous presentation of the equation in symbols and words reinforces the connection between mathematical language and everyday language. This visual representation helps students understand how multiplication works and introduces the concept of the identity property of multiplication.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 33	Math Clip Art--The Language of Math--Numbers and Equations 33 Topic The Language of Math Description This image presents the equation "3*1=3" in both numerical and word form. It continues the progression of multiplication concepts, focusing on the multiplication of a single-digit number by 1. 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 multiplication, particularly how multiplying by 1 results in the same number.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 34	Math Clip Art--The Language of Math--Numbers and Equations 34 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "4*1=4" in both numerical and word form. It continues the progression of multiplication concepts, focusing on the multiplication of a single-digit number by 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 how multiplication works and reinforces the concept of the identity property of multiplication.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 35	Math Clip Art--The Language of Math--Numbers and Equations 35 Topic The Language of Math Description This image presents the equation "5*1=5" in both numerical and word form. It continues the progression of multiplication concepts, focusing on the multiplication of a single-digit number by 1. 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 multiplication, particularly how multiplying by 1 results in the same number.	Numerical Expressions

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 8: Reasoning about Solving Equations (Part 2)

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