Illustrative Math Alignment: Grade 8 Unit 3
Linear Equations and Linear Systems
Lesson 1: Number Puzzles
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example: Language of Math--Numerical Expressions--Addition--Example 10 | Math Example: Language of Math--Numerical Expressions--Addition--Example 10TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Seven more than eighteen" into a numerical expression. The image shows how this verbal statement translates to the expression 18 + 7, emphasizing that "more than" indicates addition with a specific order of numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 11 | Math Example: Language of Math--Numerical Expressions--Addition--Example 11TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Eleven plus negative twenty" into a numerical expression. The image demonstrates how this verbal statement translates directly to the expression 11 + (-20), introducing the concept of adding negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 12 | Math Example: Language of Math--Numerical Expressions--Addition--Example 12TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Nineteen increased by negative four" into a numerical expression. The image shows how this verbal statement translates to the expression 19 + (-4), further exploring the concept of adding negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 13 | Math Example: Language of Math--Numerical Expressions--Addition--Example 13TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Negative five added to thirteen" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 13 + (-5), emphasizing the order of numbers when using the phrase "added to." |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 14 | Math Example: Language of Math--Numerical Expressions--Addition--Example 14TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Negative three in addition to four" into a numerical expression. The image shows how this verbal statement translates to the expression 4 + (-3), highlighting the importance of word order in determining the structure of the expression. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 15 | Math Example: Language of Math--Numerical Expressions--Addition--Example 15TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Negative twenty more than nine" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 9 + (-20), emphasizing the interpretation of "more than" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 16 | Math Example: Language of Math--Numerical Expressions--Addition--Example 16TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Twenty plus negative four" into a numerical expression. The image shows how this verbal statement translates directly to the expression 20 + (-4), illustrating a straightforward use of the word "plus" with a negative number. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 17 | Math Example: Language of Math--Numerical Expressions--Addition--Example 17TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Fifteen increased by negative four" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 15 + (-4), emphasizing the interpretation of "increased by" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 18 | Math Example: Language of Math--Numerical Expressions--Addition--Example 18TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Negative sixteen in addition to fifteen" into a numerical expression. The image shows how this verbal statement translates to the expression 15 + (-16), highlighting the importance of word order in determining the structure of the expression. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 19 | Math Example: Language of Math--Numerical Expressions--Addition--Example 19TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Negative six added to nine" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 9 + (-6), emphasizing the interpretation of "added to" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 2 | Math Example: Language of Math--Numerical Expressions--Addition--Example 2TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Six increased by eight" into a numerical expression. The image highlights how this verbal statement translates to the expression 6 + 8, demonstrating another way to express addition in mathematical language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 20 | Math Example: Language of Math--Numerical Expressions--Addition--Example 20TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Negative five more than nineteen" into a numerical expression. The image shows how this verbal statement translates to the expression 19 + (-5), highlighting the interpretation of "more than" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 21 | Math Example: Language of Math--Numerical Expressions--Addition--Example 21TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Negative fourteen plus two" into a numerical expression. The image demonstrates how this straightforward verbal statement translates directly to the expression -14 + 2, emphasizing the simplicity of using "plus" in numerical expressions. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 22 | Math Example: Language of Math--Numerical Expressions--Addition--Example 22TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Negative fifteen increased by ten" into a numerical expression. The image shows how this verbal statement translates to the expression -15 + 10, emphasizing that "increased by" is equivalent to "plus" in mathematical language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 23 | Math Example: Language of Math--Numerical Expressions--Addition--Example 23TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Eight in addition to negative eight" into a numerical expression. The image demonstrates how this verbal statement translates to the expression -8 + 8, highlighting that "in addition to" is equivalent to "plus" in mathematical language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 24 | Math Example: Language of Math--Numerical Expressions--Addition--Example 24TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Eight added to negative fourteen" into a numerical expression. The image shows how this verbal statement translates to the expression -14 + 8, emphasizing that "added to" is equivalent to "plus" in mathematical language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 25 | Math Example: Language of Math--Numerical Expressions--Addition--Example 25TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Eight more than negative two" into a numerical expression. The image demonstrates how this verbal statement translates to the expression -2 + 8, highlighting the interpretation of "more than" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 26 | Math Example: Language of Math--Numerical Expressions--Addition--Example 26TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Negative seventeen plus seven" into a numerical expression. The image shows how this straightforward verbal statement translates directly to the expression -17 + 7, emphasizing the simplicity of using "plus" in numerical expressions, even with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 27 | Math Example: Language of Math--Numerical Expressions--Addition--Example 27TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Ten increased by negative one" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 10 + (-1), emphasizing the interpretation of "increased by" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 28 | Math Example: Language of Math--Numerical Expressions--Addition--Example 28TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Four in addition to negative four" into a numerical expression. The image shows how this verbal statement translates to the expression -4 + 4, highlighting that "in addition to" is equivalent to "plus" in mathematical language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 29 | Math Example: Language of Math--Numerical Expressions--Addition--Example 29TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Eleven added to negative ten" into a numerical expression. The image demonstrates how this verbal statement translates to the expression -10 + 11, emphasizing that "added to" is equivalent to "plus" in mathematical language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 3 | Math Example: Language of Math--Numerical Expressions--Addition--Example 3TopicNumerical Expressions DescriptionThis example showcases the conversion of the phrase "Ten added to twelve" into a numerical expression. The image highlights how this verbal statement translates to the expression 12 + 10, emphasizing the importance of order in addition expressions. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 30 | Math Example: Language of Math--Numerical Expressions--Addition--Example 30TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Seven more than negative four" into a numerical expression. The image shows how this verbal statement translates to the expression -4 + 7, highlighting the interpretation of "more than" when dealing with negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 31 | Math Example: Language of Math--Numerical Expressions--Addition--Example 31TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Negative twelve plus negative four" into a numerical expression. The image demonstrates how this straightforward verbal statement translates directly to the expression -12 + (-4), emphasizing the simplicity of using "plus" in numerical expressions, even with multiple negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 32 | Math Example: Language of Math--Numerical Expressions--Addition--Example 32TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Negative thirteen increased by negative eight" into a numerical expression. The image shows how this verbal statement translates to the expression -13 + (-8), emphasizing the interpretation of "increased by" when dealing with two negative numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 33 | Math Example: Language of Math--Numerical Expressions--Addition--Example 33TopicNumerical Expressions DescriptionThis example illustrates converting the phrase "Negative sixteen in addition to negative three" into a numerical expression. The image emphasizes key terms with color coding, showing how this verbal statement translates to the expression -3 + (-16). The phrase "in addition to" signifies addition. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 34 | Math Example: Language of Math--Numerical Expressions--Addition--Example 34TopicNumerical Expressions DescriptionThis example explains converting "Negative twenty added to negative eleven" into a numerical expression. The image uses color coding for emphasis, demonstrating how this statement is expressed as -11 + (-20). The term "added to" indicates addition. Understanding how to interpret phrases like "added to" in the context of negative numbers is crucial for students' mathematical development. It helps them grasp that the order of numbers in an expression can differ from their order in a verbal statement. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 35 | Math Example: Language of Math--Numerical Expressions--Addition--Example 35TopicNumerical Expressions DescriptionThis example shows how to convert "Negative eight more than negative one" into a numerical expression. The image uses color coding to highlight different parts, translating this phrase into -1 + (-8). The term "more than" indicates addition. Understanding how to interpret phrases like "more than" when dealing with negative numbers is crucial for students' mathematical development. It helps them grasp that adding a negative number results in moving further from zero on the number line. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 36 | Math Example: Language of Math--Numerical Expressions--Addition--Example 36TopicNumerical Expressions DescriptionThis example presents converting "Negative three plus negative nineteen" into a numerical expression. Key terms are color-coded for clarity, showing how this statement is written as -3 + (-19). The term "plus" indicates straightforward addition. The use of "plus" when dealing with negative numbers is straightforward but essential for understanding more complex operations involving negatives. This concept reinforces that addition can involve multiple negatives, preparing students for advanced algebraic concepts. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 37 | Math Example: Language of Math--Numerical Expressions--Addition--Example 37TopicNumerical Expressions DescriptionThis example involves converting "Negative two increased by negative nine" into an addition expression. Key terms are highlighted in different colors, resulting in the expression -2 + (-9). The phrase "increased by" when used with negatives highlights that increasing by a negative results in further decrease, an important concept for understanding operations involving negatives. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 38 | Math Example: Language of Math--Numerical Expressions--Addition--Example 38TopicNumerical Expressions DescriptionThis example shows converting "Negative six in addition to negative eight" into a numerical expression. It uses bold and colored text to highlight key parts, resulting in the expression -8 + (-6). The phrase "in addition to" signifies addition and helps students understand how to handle multiple negative numbers in expressions. This example reinforces students' understanding of numerical expressions involving negatives, preparing them for more complex mathematical concepts. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 39 | Math Example: Language of Math--Numerical Expressions--Addition--Example 39TopicNumerical Expressions DescriptionThis example illustrates transforming "Negative twelve added to negative two" into a numerical expression. Using color to emphasize important words, it becomes -2 + (-12). The term "added to" indicates addition and demonstrates how order can change when converting verbal statements into expressions. This example helps students understand how to interpret and translate verbal statements involving negatives into mathematical expressions. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 4 | Math Example: Language of Math--Numerical Expressions--Addition--Example 4TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Thirteen in addition to fourteen" into a numerical expression. The image shows how this verbal statement is translated into the expression 14 + 13, highlighting another variation of addition language. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 40 | Math Example: Language of Math--Numerical Expressions--Addition--Example 40TopicNumerical Expressions DescriptionThis example features converting "Negative thirteen more than negative six" into an addition expression, with colored text for emphasis. It becomes -6 + (-13). The term "more than" signifies addition and helps students understand how order affects expressions involving multiple negatives. This example reinforces students' ability to translate complex verbal statements into numerical expressions accurately. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 5 | Math Example: Language of Math--Numerical Expressions--Addition--Example 5TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Eight more than two" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 2 + 8, emphasizing that "more than" indicates addition with a specific order of numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 6 | Math Example: Language of Math--Numerical Expressions--Addition--Example 6TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Sixteen plus fifteen" into a numerical expression. The image shows how this straightforward verbal statement translates directly to the expression 16 + 15, illustrating a clear one-to-one correspondence between words and mathematical symbols. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 7 | Math Example: Language of Math--Numerical Expressions--Addition--Example 7TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Seventeen increased by fifteen" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 17 + 15, highlighting that "increased by" indicates addition. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 8 | Math Example: Language of Math--Numerical Expressions--Addition--Example 8TopicNumerical Expressions DescriptionThis example demonstrates the conversion of the phrase "Four added to fifteen" into a numerical expression. The image shows how this verbal statement translates to the expression 15 + 4, emphasizing that "added to" indicates addition with a specific order of numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Addition--Example 9 | Math Example: Language of Math--Numerical Expressions--Addition--Example 9TopicNumerical Expressions DescriptionThis example illustrates the conversion of the phrase "Seven in addition to four" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 4 + 7, highlighting that "in addition to" indicates addition with a specific order of numbers. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 1 | Math Example: Language of Math--Numerical Expressions--Division--Example 1TopicNumerical Expressions DescriptionThis example demonstrates how to convert the verbal expression "Fourteen divided by five" into a numerical expression. The solution shows that this can be written as 14 / 5 or 14 ÷ 5, illustrating the two common notations for division in mathematics. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 10 | Math Example: Language of Math--Numerical Expressions--Division--Example 10TopicNumerical Expressions DescriptionThis example explains converting "Seventeen goes into two" into a numerical expression as 2 ÷ 17, demonstrating how verbal cues translate into mathematical operations. The topic of numerical expressions is crucial for understanding math language and operations. These examples guide students through the process of interpreting language mathematically, enhancing their analytical skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 11 | Math Example: Language of Math--Numerical Expressions--Division--Example 11TopicNumerical Expressions DescriptionThis example demonstrates converting "Five divided by negative two" into a numerical expression, resulting in 5 ÷ (-2). It shows how to handle division with negative numbers. The topic of numerical expressions is essential for understanding mathematical operations and their representations. These examples help students navigate the complexities of translating verbal statements into mathematical expressions, enhancing their problem-solving skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 12 | Math Example: Language of Math--Numerical Expressions--Division--Example 12TopicNumerical Expressions DescriptionThis example illustrates converting "Eight over negative two" into a numerical expression, resulting in 8 ÷ (-2). It highlights how "over" signifies division. The study of numerical expressions is vital for interpreting mathematical language. These examples provide clarity on how verbal cues translate into math, aiding students in developing analytical skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 13 | Math Example: Language of Math--Numerical Expressions--Division--Example 13TopicNumerical Expressions DescriptionThis example shows how to convert "One to negative eighteen" into a numerical expression, resulting in the ratio 1 : (-18). It explains how "to" can express division as a ratio. The topic of numerical expressions is fundamental in understanding mathematical relationships. These examples guide students through interpreting language mathematically, enhancing their analytical skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 14 | Math Example: Language of Math--Numerical Expressions--Division--Example 14TopicNumerical Expressions DescriptionThis example demonstrates converting "Negative three into seventeen" into a numerical expression, resulting in 17 ÷ (-3). It clarifies how "into" indicates division. The study of numerical expressions is crucial for understanding math language and operations. Through these examples, students learn how language can be systematically translated into mathematical expressions, aiding their problem-solving skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 15 | Math Example: Language of Math--Numerical Expressions--Division--Example 15TopicNumerical Expressions DescriptionThis example shows an example converting "Negative nineteen goes into eleven" into a numerical expression, resulting in 11 ÷ (-19). It explains that "goes into" signifies division. The topic of numerical expressions is essential for understanding mathematical operations and their representations. These examples help students navigate the complexities of translating verbal statements into mathematical expressions, enhancing their problem-solving skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 16 | Math Example: Language of Math--Numerical Expressions--Division--Example 16TopicNumerical Expressions DescriptionThis example provides an example of converting "Thirteen divided by negative nine" into a numerical expression, resulting in 13 ÷ (-9). It notes that "divided by" is straightforward to convert. The study of numerical expressions is vital for interpreting mathematical language. These examples provide clarity on how verbal cues translate into math, aiding students in developing analytical skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 17 | Math Example: Language of Math--Numerical Expressions--Division--Example 17TopicNumerical Expressions DescriptionThis example explains how to convert "Twenty over negative one" into a numerical expression, resulting in 20 ÷ (-1). The topic of numerical expressions is essential for understanding mathematical operations and their representations. These examples help students navigate the complexities of translating verbal statements into mathematical expressions, enhancing their problem-solving skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 18 | Math Example: Language of Math--Numerical Expressions--Division--Example 18TopicNumerical Expressions DescriptionThis example shows the conversion of "Twelve to negative eleven" into a numerical expression, resulting in the ratio 12 : (-11). The study of numerical expressions is crucial for understanding math language and operations. Through these examples, students learn how language can be systematically translated into mathematical expressions, aiding their problem-solving skills. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Division--Example 19 | Math Example: Language of Math--Numerical Expressions--Division--Example 19TopicNumerical Expressions DescriptionThis image demonstrates converting "Negative five into eight" into a numerical expression, resulting in 8 ÷ (-5). The topic of numerical expressions is essential for understanding mathematical operations and their representations. These examples help students navigate the complexities of translating verbal statements into mathematical expressions, enhancing their problem-solving skills. |
Numerical Expressions |
