Illustrative Math Alignment: Grade 8 Unit 3

Topic

Numerical Expressions

Description

This example illustrates converting "Negative fifteen times the quantity fifteen minus 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 illustrates how to convert the statement "Twenty divided by the quantity nineteen plus seven" into a numerical expression. The solution shows that this can be expressed as 20 / ( 19 + 7 ). This example introduces division in combination with grouping symbols, expanding students' understanding of complex numerical expressions.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative seventeen multiplied by the quantity eighteen minus 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 demonstrates converting "Negative ten divided by the quantity fifteen minus 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 minus negative six" into a numerical expression. The expression is written as -16 / (10 - (-6)), using division and grouping symbols.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the statement "Seventeen over the quantity twenty plus two" into a numerical expression. The solution shows that this can be written as 17 / ( 20 + 2 ). This example reinforces the use of grouping symbols in division expressions and introduces the term "over" as an alternative way to express division.

Topic

Numerical Expressions

Description

This example illustrates how to convert the statement "Twenty times the quantity six minus three" into a numerical expression. The solution demonstrates that this can be expressed as 20 * ( 6 - 3 ). This example introduces subtraction within grouping symbols, further expanding students' understanding of complex numerical expressions.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the statement "Eleven multiplied by the quantity sixteen minus four" into a numerical expression. The solution shows that this can be written as 11 * ( 16 - 4 ). This example reinforces the use of grouping symbols in multiplication expressions involving subtraction.

Topic

Numerical Expressions

Description

This example illustrates how to convert the statement "Twenty divided by the quantity nineteen minus seven" into a numerical expression. The solution demonstrates that this can be expressed as 20 / ( 19 - 7 ). This example combines division with subtraction within grouping symbols, further expanding students' understanding of complex numerical expressions.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the verbal statement "Seventeen over the quantity twenty plus two" into a numerical expression. The solution involves replacing "over" with the division symbol and using parentheses to represent "the quantity". The resulting expression is 17 / (20 + 2), which clearly shows the order of operations to be performed.

Topic

Numerical Expressions

Description

This example demonstrates how to convert a verbal statement into a numerical expression using multiplication and grouping symbols. The statement "Negative sixteen times the quantity three plus nineteen" is translated into the expression -16 * (3 + 19). This conversion involves replacing the word "times" with the multiplication symbol and using parentheses to represent "the quantity" which usually refers to two or more terms grouped together.

Topic

Numerical Expressions

Description

This example illustrates how to translate a verbal statement into a numerical expression. The phrase "Five times twenty" is converted to the mathematical expression 5 * 20. This straightforward conversion demonstrates how the word "times" directly translates to multiplication in mathematical notation.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the statement "Twelve multiples of ten" into a numerical expression. The phrase "multiples of" indicates multiplication, with the number on the right being multiplied by the number on the left. In this case, it translates to the expression 10 * 12.

Topic

Numerical Expressions

Description

This example illustrates how to convert the statement "Eight times negative eleven" into a numerical expression. The word "times" clearly indicates multiplication, and the presence of a negative number introduces the concept of multiplying positive and negative integers. The resulting expression is 8 * (-11).

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Thirteen multiplied by negative seven" into a numerical expression. The term "multiplied by" clearly indicates multiplication, and the presence of a negative number introduces the concept of multiplying a positive number by a negative one. The resulting expression is 13 * (-7).

Topic

Numerical Expressions

Description

This example illustrates how to convert the statement "Two by negative twenty" into a numerical expression. The word "by" is often used to express dimensions and can indicate multiplication, especially when calculating area. In this case, it translates to the expression 2 * (-20), introducing the concept of multiplying a positive number by a negative one.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Negative three groups of ten" into a numerical expression. The term "groups of" indicates multiplication, with the number on the right being multiplied by the number on the left. In this case, it translates to the expression 10 * (-3), introducing the concept of multiplying a positive number by a negative one.

Topic

Numerical Expressions

Description

This example demonstrates converting "Negative fifteen multiples of two" into a numerical expression. The phrase indicates multiplication, resulting in the expression 2 * (-15).

Numerical expressions are essential in mathematics, bridging verbal descriptions and mathematical operations. This collection helps students recognize and interpret language that signifies multiplication, including negative numbers.

Topic

Numerical Expressions

Description

This example shows how to convert "Nine times negative eleven" into a numerical expression. The word "times" indicates multiplication, resulting in the expression 9 * (-11).

Understanding numerical expressions is fundamental in mathematics as it allows students to translate verbal descriptions into mathematical language. This collection helps students recognize key phrases that represent multiplication, including negative numbers.

Topic

Numerical Expressions

Description

This example illustrates converting "Nine multiplied by negative nine" into a numerical expression. The term "multiplied by" indicates multiplication, resulting in the expression 9 * (-9).

Numerical expressions help bridge verbal descriptions and mathematical operations. This collection aids students in recognizing phrases that signify multiplication, including those with negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates converting "Three by negative two" into a numerical expression. The word "by" indicates multiplication, resulting in the expression 3 * (-2).

Understanding numerical expressions is crucial for translating verbal descriptions into mathematical operations. This collection helps students identify phrases that signify multiplication, including those involving negative numbers.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative eleven groups of sixteen" into a numerical expression. The phrase "groups of" indicates multiplication, resulting in the expression 16 * (-11).

The concept of numerical expressions bridges verbal descriptions and mathematical operations. This collection aids students in recognizing phrases that signify multiplication, including those with negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the phrase "Five multiplied by nine" into the numerical expression 5 * 9. It showcases how the term "multiplied by" is directly translated into the multiplication symbol in mathematical notation.

Topic

Numerical Expressions

Description

This example demonstrates converting "Negative twenty multiples of eleven" into a numerical expression. The phrase indicates multiplication, resulting in the expression 11 * (-20).

Understanding numerical expressions is fundamental for translating verbal descriptions into mathematical operations. This collection helps students recognize phrases that signify multiplication, including those involving negative numbers.

Topic

Numerical Expressions

Description

This example shows how to convert "Negative seven times two" into a numerical expression. The word "times" indicates multiplication, resulting in the expression -7 * 2.

Understanding numerical expressions is fundamental in mathematics as it allows students to translate verbal descriptions into mathematical language. This collection helps students recognize key phrases that represent multiplication, including negative numbers.

Topic

Numerical Expressions

Description

This example illustrates converting "Negative eight multiplied by eighteen" into a numerical expression. The term "multiplied by" indicates multiplication, resulting in the expression -8 * 18.

Numerical expressions help bridge verbal descriptions and mathematical operations. This collection aids students in recognizing phrases that signify multiplication, including those with negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates converting "Negative three by twelve" into a numerical expression. The word "by" indicates multiplication, resulting in the expression -3 * 12.

The concept of numerical expressions bridges verbal descriptions and mathematical operations. This collection aids students in recognizing phrases that signify multiplication, including those with negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Thirteen groups of negative eleven" into a numerical expression. The solution explains that "groups of" refers to multiples, resulting in the expression -11 * 13. This conversion illustrates how verbal descriptions of mathematical operations can be translated into concise symbolic notation.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Nine multiples of negative eighteen" into a numerical expression. The solution explains that "multiples of" indicates multiplication, with the number on the right being multiplied by the number on the left. The resulting expression is -18 * 9, demonstrating how verbal mathematical statements can be concisely represented symbolically.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the statement "Negative fifteen times nine" into a numerical expression. The solution explains that statements using "times" are straightforward to convert, resulting in the expression -15 * 9. This example highlights how negative numbers are handled in multiplication expressions.

Topic

Numerical Expressions

Description

This example illustrates how to convert the phrase "Negative nine multiplied by three" into a numerical expression. The solution demonstrates that "multiplied by" is directly translated to the multiplication symbol, resulting in the expression -9 * 3. This example emphasizes the importance of maintaining the order of terms when converting verbal statements to mathematical notation.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the phrase "Negative eleven by fifteen" into a numerical expression. The solution explains that the word "by" is often used to express dimensions and can indicate multiplication, especially when calculating area. The resulting expression is -11 * 15, showing how everyday language can be translated into precise mathematical notation.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Eight groups of negative nine" into a numerical expression. The solution demonstrates that "groups of" indicates multiplication, with the resulting expression being -9 * 8. This example emphasizes the importance of recognizing verbal cues that signify mathematical operations.

Topic

Numerical Expressions

Description

This example illustrates how the phrase "Three by ten" is converted into the numerical expression 3 * 10. It demonstrates that the word "by" is often used to express dimensions and can indicate multiplication, especially when calculating area.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the phrase "Six multiples of negative sixteen" into a numerical expression. The solution explains that "multiples of" indicates multiplication, with the resulting expression being -16 * 6. This example highlights how verbal mathematical statements can be concisely represented symbolically.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the verbal statement "Negative fourteen times negative three" into a numerical expression. The solution shows that this statement translates to -14 * (-3). This example highlights the importance of understanding how to interpret negative numbers in multiplication.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Negative sixteen multiplied by negative three" into a numerical expression. The solution demonstrates that this verbal statement translates to -16 * (-3). This example emphasizes the importance of correctly interpreting the phrase "multiplied by" in the context of negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the statement "Negative nineteen by negative eleven" into a numerical expression. The solution explains that the word "by" is often used to express dimensions and can be used to calculate area. In this case, it translates to multiplication, resulting in the expression -19 * (-11).

Topic

Numerical Expressions

Description

This example illustrates how to convert the statement "Negative thirteen groups of negative nineteen" into a numerical expression. The solution explains that the term "groups of" refers to multiples of a number, with the number on the right being the multiplier of the number on the left. This results in the expression -19 * (-13).

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Negative eleven multiples of negative nineteen" into a numerical expression. The solution explains that the term "multiples of" refers to multiples of a number, with the number on the right being the multiplier of the number on the left. This results in the expression -19 * (-11).

Topic

Numerical Expressions

Description

This example illustrates how to convert the statement "Negative ten times negative sixteen" into a numerical expression. The solution explains that statements using "times" are straightforward to convert, resulting in the expression -10 * (-16). This example emphasizes the importance of recognizing common multiplication terminology.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Negative five multiplied by negative six" into a numerical expression. The solution shows that this statement translates to -5 * (-6). This example highlights the importance of understanding how to interpret the phrase "multiplied by" when dealing with negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Negative three by negative fourteen" into a numerical expression. The image uses color coding to break down the verbal statement, helping students understand how to translate words into mathematical symbols. This conversion illustrates the process of transforming "by" into multiplication, resulting in the expression -3 * (-14).

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Negative eleven groups of negative twelve" into a numerical expression. The image uses visual cues to show how the verbal statement translates into mathematical symbols, resulting in the expression -12 * (-11). This example highlights the importance of understanding the order of multiplication when dealing with negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates how the phrase "Nine groups of ten" is converted into the numerical expression 10 * 9. It illustrates that the term "groups of" refers to multiples of a number and is another way to express multiplication.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Negative nine multiples of negative fifteen" into a numerical expression. The image uses color-coded text and arrows to guide students through the process of translating this verbal statement into mathematical symbols, resulting in the expression -15 * (-9). This example emphasizes the importance of understanding the order of factors in multiplication, especially when dealing with negative numbers.

Topic

Numerical Expressions

Description

This example illustrates how the phrase "Ten multiples of nineteen" is converted into the numerical expression 19 * 10. It demonstrates that the term "multiples of" indicates multiplication, with the number on the right being multiplied by the number on the left.

Topic

Numerical Expressions

Description

This example demonstrates how the phrase "Fifteen times sixteen" is converted into the numerical expression 15 * 16. It illustrates that the word "times" is a straightforward indicator of multiplication in mathematical language.

Topic

Numerical Expressions

Description

This example illustrates how the phrase "Fourteen multiplied by eighteen" is converted into the numerical expression 14 * 18. It demonstrates that the term "multiplied by" is directly translated to the multiplication symbol in mathematical notation.

Topic

Numerical Expressions

Description

This example demonstrates how to convert the phrase "Six by seventeen" into a numerical expression. The word "by" is often used to express dimensions and can be used to calculate area. In this case, it indicates multiplication, resulting in the expression 6 * 17.