Illustrative Math Alignment: Grade 8 Unit 3

Topic

Numerical Expressions

Description

This example illustrates the conversion of the verbal expression "Four over six" into a numerical expression. The solution demonstrates that this can be written as 4 / 6 or 4 ÷ 6, showcasing two common ways to represent division in mathematics.

Topic

Numerical Expressions

Description

This image describes how to convert "Negative four goes into four" into a numerical expression, resulting in 4 ÷ (-4). It clarifies that "goes 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.

Topic

Numerical Expressions

Description

This example shows the conversion of "Negative ten divided by eighteen" into a numerical expression, resulting in -10 ÷ 18.

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.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative fourteen over eight" into a numerical expression, resulting in -14 ÷ 8.

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.

Multiple worked-out examples are important for deep understanding. They offer diverse perspectives on solving problems, helping students build a robust understanding that can be applied across various contexts.

Topic

Numerical Expressions

Description

This example shows the conversion of "Negative fourteen to nine" into a numerical expression, resulting in -14 : 9.

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.

Topic

Numerical Expressions

Description

This example shows the conversion of "Eight into negative twelve" into a numerical expression, resulting in -12 ÷ 8. It explains 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.

Topic

Numerical Expressions

Description

This example shows how to convert "Nineteen goes into negative thirteen" into a division expression, resulting in -13 ÷ 19. The term "goes 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.

Topic

Numerical Expressions

Description

This example demonstrates converting "Negative seventeen divided by thirteen" into a numerical expression, resulting in -17 ÷ 13. Statements with "divided by" are straightforward to convert.

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.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative one over six" into a division expression, resulting in -1 ÷ 6. The word "over" is used for 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.

Multiple worked-out examples are important for deep understanding. They offer diverse perspectives on solving problems, helping students build a robust understanding that can be applied across various contexts.

Topic

Numerical Expressions

Description

This example explains converting "Negative seventeen to twenty" into a ratio expression, resulting in -17 : 20. The word "to" indicates a ratio, which is a form of 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.

Topic

Numerical Expressions

Description

This image explains converting a verbal statement into a division expression, resulting in -14 ÷ 14. The phrase "Fourteen into negative fourteen" is expressed as -14 ÷ 14.

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.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the verbal expression "Fifteen to three" into a numerical expression. The solution shows that this can be written as 15 / 3 or 15 ÷ 3, illustrating two common notations for division in mathematics.

Topic

Numerical Expressions

Description

This image describes converting a statement using "goes into" to a division expression, resulting in -9 ÷ 11. The phrase "Eleven goes into negative nine" is expressed as -9 ÷ 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.

Topic

Numerical Expressions

Description

This image shows converting a statement with "divided by" into a numerical expression, resulting in -20 ÷ (-12). The phrase "Negative twenty divided by negative twelve" is expressed as -20 ÷ (-12).

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

Topic

Description

This example demonstrates how to convert the verbal expression "negative thirteen over negative seventeen" into a mathematical expression. The correct numerical representation is -13 / (-17), which can also be written as -13 ÷ (-17). This conversion helps students understand how to translate verbal descriptions of division operations involving negative numbers into proper mathematical notation.

Numerical Expressions

Topic

Description

This example illustrates the conversion of the verbal expression "negative seventeen to negative one" into a mathematical expression. The correct numerical representation is -17 / (-1) or -17 ÷ (-1). This example helps students understand how to interpret the word "to" as an indicator of division when working with negative numbers.

Numerical Expressions

Topic

Description

This example demonstrates how to convert the verbal expression "negative five goes into negative sixteen" into a mathematical expression. The correct numerical representation is -16 / (-5) or -16 ÷ (-5). This example helps students understand how to interpret the phrase "goes into" as an indicator of division when working with negative numbers.

Numerical Expressions

Topic

Description

This example illustrates the conversion of the verbal expression "negative twenty goes into negative seven" into a mathematical expression. The correct numerical representation is -7 / (-20) or -7 ÷ (-20). This example helps students understand how to interpret the phrase "goes into" as an indicator of division when working with negative numbers, and how the order of the numbers affects the expression.

Numerical Expressions

Topic

Description

This example demonstrates how to convert the verbal expression "negative twenty divided by negative twelve" into a mathematical expression. The correct numerical representation is -20 / (-12) or -20 ÷ (-12). This example helps students understand how to interpret the phrase "divided by" when working with negative numbers.

Numerical Expressions

Topic

Description

This example illustrates the conversion of the verbal expression "negative ten over negative thirteen" into a mathematical expression. The correct numerical representation is -10 / (-13) or -10 ÷ (-13). This example helps students understand how to interpret the word "over" as an indicator of division when working with negative numbers.

Numerical Expressions

Topic

Description

This example demonstrates how to convert the verbal expression "negative eleven to negative three" into a mathematical expression. The correct numerical representation is -11 / (-3) or -11 ÷ (-3). This example helps students understand how to interpret the word "to" as an indicator of division when working with negative numbers.

Topic

Numerical Expressions

Description

This math example demonstrates how to convert the phrase "Negative fifteen into negative seventeen" into a numerical expression. The problem involves dividing negative numbers, specifically -15 ÷ -17. This example helps students understand how to interpret verbal descriptions of mathematical operations and translate them into proper numerical expressions.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the verbal expression "Thirteen into nineteen" into a numerical expression. The solution demonstrates that this can be written as 19 / 13 or 19 ÷ 13, showcasing two common ways to represent division in mathematics.

Topic

Numerical Expressions

Description

This math example illustrates the process of converting the phrase "Negative seven goes into negative ten" into a numerical expression. The problem involves dividing negative numbers, specifically -10 ÷ -7. This example helps students understand how to interpret verbal descriptions of mathematical operations and translate them into proper numerical expressions, particularly when dealing with negative numbers and division.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the verbal expression "Fourteen goes into seven" into a numerical expression. The solution shows that this can be written as 7 / 14 or 7 ÷ 14, illustrating the two common notations for division in mathematics.

Topic

Numerical Expressions

Description

This example demonstrates converting the phrase "Eighteen divided by four" into a numerical expression, resulting in 18 ÷ 4. It illustrates how verbal statements can be directly translated into mathematical expressions using division.

Topic

Numerical Expressions

Description

This example illustrates converting "Eleven over thirteen" into a numerical expression using division, resulting in 11 ÷ 13. It shows how phrases involving fractions can be interpreted as division expressions.

The topic of numerical expressions is foundational in mathematics, and these examples provide clarity on how language translates into math. By exploring various examples, students gain insight into different ways mathematical concepts are expressed verbally, enhancing their comprehension and skills.

Topic

Numerical Expressions

Description

This example explains how to interpret ratios as division expressions using the phrase "Three to sixteen," which converts to the numerical form 3 : 16.

The topic of numerical expressions is vital in understanding mathematical relationships. These examples help students connect verbal descriptions with mathematical operations, reinforcing their ability to translate language into math accurately.

Topic

Numerical Expressions

Description

This example shows how to convert "Three into eighteen" into a numerical expression using division, represented as 18 ÷ 3. It clarifies how specific language cues indicate mathematical operations.

The study of numerical expressions is fundamental in mathematics education. Through these examples, students learn how language can be systematically translated into mathematical expressions, aiding their problem-solving skills.

Topic

Numerical Expressions

Description

This math example demonstrates how to convert the verbal statement "Twenty times the quantity six plus three" into a numerical expression. The solution shows that this statement can be expressed as 20 * ( 6 + 3 ). This example illustrates the use of grouping symbols (parentheses) to clarify the order of operations in a numerical expression.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the verbal statement "Negative sixteen multiplied by the quantity fourteen plus five" into the numerical expression -16 * (14 + 5). The process involves replacing "multiplied by" with the multiplication symbol and using parentheses to group the terms following "the quantity."

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the verbal statement "Negative nineteen divided by the quantity sixteen plus seven" into the numerical expression -19 / (16 + 7). The process involves replacing "divided by" with the division symbol and using parentheses to group the terms following "the quantity."

Topic

Numerical Expressions

Description

This example illustrates the conversion of the verbal statement "Negative four over the quantity eleven plus nine" into the numerical expression -4 / (11 + 9). The process involves replacing "over" with the division symbol and using parentheses to group the terms following "the quantity."

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the verbal statement "Negative sixteen times the quantity three minus nineteen" into the numerical expression -16 * (3 - 19). The process involves replacing "times" with the multiplication symbol and using parentheses to group the terms following "the quantity."

Topic

Numerical Expressions

Description

This example illustrates the conversion of the verbal statement "Negative sixteen multiplied by the quantity fourteen minus five" into the numerical expression -16 * (14 - 5). The process involves replacing "multiplied by" with the multiplication symbol and using parentheses to group the terms following "the quantity."

Topic

Numerical Expressions

Description

This example illustrates converting the verbal statement "Negative nineteen divided by the quantity sixteen minus seven" into a numerical expression. The expression is written as -19 / (16 - 7), using division and grouping symbols to clearly indicate the order of operations.

Topic

Numerical Expressions

Description

This example shows how to convert "Negative four over the quantity eleven minus nine" into a numerical expression. The expression is written as -4 / (11 - 9), using division and grouping symbols to clarify the order of operations.

Topic

Numerical Expressions

Description

This example demonstrates converting "Negative six times the quantity negative one plus eight" into a numerical expression. The expression is written as -6 * (-1 + 8), using multiplication and grouping symbols to clearly show the order of operations.

Topic

Numerical Expressions

Description

This example illustrates how to convert "Negative eleven multiplied by the quantity negative sixteen plus nine" into a numerical expression. The expression is written as -11 * (-16 + 9), using multiplication and grouping symbols to indicate the order of operations.

Topic

Numerical Expressions

Description

This example presents converting "Negative sixteen divided by the quantity negative seven plus thirteen" into a numerical expression. The expression is written as -16 / (-7 + 13), utilizing division and grouping symbols for clarity.

Topic

Numerical Expressions

Description

This example focuses on converting the statement "Eleven multiplied by the quantity sixteen plus four" into a numerical expression. The solution demonstrates that this can be written as 11 * ( 16 + 4 ). This example reinforces the use of grouping symbols to represent the phrase "the quantity" in mathematical notation.

Topic

Numerical Expressions

Description

This example features converting "Negative six over the quantity negative ten plus eleven" into a numerical expression. The expression is written as -6 / (-10 + 11), using division and grouping symbols to clearly show the order of operations.

Topic

Numerical Expressions

Description

This example shows how to convert "Negative six times the quantity negative one minus eight" into a numerical expression. The expression is written as -6 * (-1 - 8), using multiplication and grouping symbols.

Topic

Numerical Expressions

Description

This example demonstrates converting "Negative eleven multiplied by the quantity negative sixteen minus nine" into a numerical expression. The expression is written as -11 * (-16 - 9), using multiplication and grouping symbols.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative sixteen divided by the quantity negative seven minus thirteen" into a numerical expression. The expression is written as -16 / (-7 - 13), using division and grouping symbols.

Topic

Numerical Expressions

Description

This example presents converting "Negative six over the quantity negative ten minus eleven" into a numerical expression. The expression is written as -6 / (-10 - 11), using division and grouping symbols.

Topic

Numerical Expressions

Description

This example shows how to convert "Negative fifteen times the quantity fifteen plus negative seven" into a numerical expression. The expression is written as -15 * (15 + (-7)), using multiplication and grouping symbols.

Topic

Numerical Expressions

Description

This example shows how to convert "Negative seventeen multiplied by the quantity eighteen plus negative eleven" into a numerical expression. The expression is written as -17 * (18 + (-11)), using multiplication and grouping symbols.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative ten divided by the quantity fifteen plus negative eighteen" into a numerical expression. The expression is written as -10 / (15 + (-18)), using division and grouping symbols.

Topic

Numerical Expressions

Description

This example shows how to convert "Negative sixteen over the quantity ten plus negative six" into a numerical expression. The expression is written as -16 / (10 + (-6)), using division and grouping symbols.