Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
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
Math Clip Art--The Language of Math--Numbers and Equations 36	Math Clip Art--The Language of Math--Numbers and Equations 36 Topic The Language of Math Description This clip art from the Language of Math collection showcases the equation "6*2=12" in both numerical and word formats. It advances the complexity of multiplication concepts by introducing multiplication by a number other than 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 with larger numbers and introduces the concept of repeated addition.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 37	Math Clip Art--The Language of Math--Numbers and Equations 37 Topic The Language of Math Description This image presents the equation "7*3=21" in both numerical and word form. It continues the progression of multiplication concepts, now introducing multiplication with larger 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 multiplication, particularly how it relates to repeated addition and grouping.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 38	Math Clip Art--The Language of Math--Numbers and Equations 38 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "8*3=24" in both numerical and word form. It continues the progression of multiplication concepts, focusing on multiplication with larger single-digit numbers. 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 with larger numbers and reinforces the concept of repeated addition and grouping.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 39	Math Clip Art--The Language of Math--Numbers and Equations 39 Topic The Language of Math Description This image presents the equation "9*5=45" in both numerical and word form. It advances the complexity of multiplication concepts by introducing larger single-digit numbers and a product greater than 40. 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 it relates to repeated addition and grouping with larger numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 40	Math Clip Art--The Language of Math--Numbers and Equations 40 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "10*2=20" in both numerical and word form. It introduces multiplication with a two-digit number, marking a significant step in mathematical understanding. 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 with larger numbers and reinforces the concept of repeated addition and grouping.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 41	Math Clip Art--The Language of Math--Numbers and Equations 41 Topic The Language of Math Description This image presents the equation "11*2=22" in both numerical and word form. It continues the progression of multiplication concepts, now working 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 multiplication, particularly how it relates to repeated addition and grouping with larger numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 42	Math Clip Art--The Language of Math--Numbers and Equations 42 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "12*3=36" in both numerical and word form. It advances the complexity of multiplication concepts by introducing larger two-digit numbers and a product greater than 30. 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 with larger numbers and reinforces the concept of repeated addition and grouping.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 43	Math Clip Art--The Language of Math--Numbers and Equations 43 Topic The Language of Math Description This image presents the equation "13*4=52" in both numerical and word form. It continues the progression of multiplication concepts, now working with larger two-digit numbers and a product greater than 50. 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 it relates to repeated addition and grouping with larger numbers.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 44	Math Clip Art--The Language of Math--Numbers and Equations 44 Topic The Language of Math Description This clip art from the Language of Math collection illustrates the equation "14*5=70" in both numerical and word form. It advances the complexity of multiplication concepts by introducing larger two-digit numbers and a product reaching 70. 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 with larger numbers and reinforces the concept of repeated addition and grouping.	Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations 45	Math Clip Art--The Language of Math--Numbers and Equations 45 Topic The Language of Math Description This image presents the equation "15*6=90" in both numerical and word form. It continues the progression of multiplication concepts, now working with larger two-digit numbers and a product reaching 90. 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 it relates to repeated addition and grouping with larger numbers.	Numerical Expressions
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

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

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