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--Multiplication--Example 9 | Math Example: Language of Math--Numerical Expressions--Multiplication--Example 9TopicNumerical Expressions DescriptionThis example illustrates how to convert the phrase "Twelve groups of seven" into a numerical expression. The term "groups of" refers to multiples of a number, indicating multiplication. In this case, it translates to the expression 7 * 12. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 1 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 1TopicNumerical Expressions DescriptionThis math example demonstrates how to convert the verbal statement "Seven take away fourteen" into a numerical expression. The phrase "take away" is translated into the subtraction operation, resulting in the expression 7 - 14. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 10 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 10TopicNumerical Expressions DescriptionThis example shows how to convert the verbal statement "Four from one" into a numerical expression. The word "from" indicates subtraction, leading to the expression 1 - 4. Numerical expressions are vital for translating everyday language into mathematical notation. This collection of examples helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations and number order. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 11 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 11TopicNumerical Expressions DescriptionThis example involves converting the phrase "One take away negative ten" into a numerical expression. The phrase "take away" indicates subtraction, resulting in the expression 1 - (-10). Understanding numerical expressions is essential as they connect everyday language with mathematical notation. This collection aids students in interpreting various verbal phrases and converting them into precise mathematical expressions. By exploring expressions involving negative numbers, students gain insight into how language influences mathematical operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 12 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 12TopicNumerical Expressions DescriptionThis example demonstrates converting the phrase "Three minus negative eight" into a numerical expression. The word "minus" indicates subtraction, resulting in the expression 3 - (-8). Numerical expressions are crucial for translating everyday language into mathematical notation. This collection helps students learn to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring expressions involving negatives, students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 13 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 13TopicNumerical Expressions DescriptionThis example shows how to convert the phrase "Twenty less negative four" into a numerical expression. The word "less" indicates subtraction, resulting in the expression 20 - (-4). Numerical expressions are crucial for translating everyday language into mathematical notation. This collection helps students learn to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, including handling negatives, students understand how language influences operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 14 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 14TopicNumerical Expressions DescriptionThis example illustrates converting "Negative eighteen subtracted from five" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression 5 - (-18). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 15 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 15TopicNumerical Expressions DescriptionThis example shows how to convert "Negative fourteen from fourteen" into a numerical expression. The word "from" indicates subtraction, leading to the expression 14 - (-14). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 16 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 16TopicNumerical Expressions DescriptionThis example demonstrates converting the phrase "Ten take away negative ten" into a numerical expression. The phrase "take away" indicates subtraction, resulting in the expression 10 - (-10). Numerical expressions are crucial for translating everyday language into mathematical notation. This collection helps students learn to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, including handling negatives, students understand how language influences operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 17 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 17TopicNumerical Expressions DescriptionThis example illustrates converting "Eighteen minus negative fifteen" into a numerical expression. The word "minus" indicates subtraction, resulting in the expression 18 - (-15). Understanding numerical expressions is essential as they connect everyday language with mathematical notation. This collection aids students in interpreting various verbal phrases and converting them into precise mathematical expressions. By exploring expressions involving negative numbers, students gain insight into how language influences mathematical operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 18 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 18TopicNumerical Expressions DescriptionThis example presents converting "Nineteen less negative seventeen" into a numerical expression. The word "less" indicates subtraction, resulting in the expression 19 - (-17). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "less," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 19 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 19TopicNumerical Expressions DescriptionThis example demonstrates converting "Negative twelve subtracted from twenty" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression 20 - (-12). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 2 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 2TopicNumerical Expressions DescriptionThis example illustrates the conversion of the verbal statement "Nineteen minus four" into a numerical expression. The word "minus" directly translates to the subtraction operation, resulting in the expression 19 - 4. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 20 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 20TopicNumerical Expressions DescriptionThis example explains converting "Negative seven from fourteen" into a numerical expression. The word "from" indicates subtraction, leading to the expression 14 - (-7). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 21 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 21TopicNumerical Expressions DescriptionThis example demonstrates converting the phrase "Negative two take away seventeen" into a numerical expression. The phrase "take away" indicates subtraction, resulting in the expression -2 - 17. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 22 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 22TopicNumerical Expressions DescriptionThis example illustrates converting "Negative sixteen minus ten" into a numerical expression. The word "minus" indicates subtraction, resulting in the expression -16 - 10. Understanding numerical expressions is essential as they connect everyday language with mathematical notation. This collection aids students in interpreting various verbal phrases and converting them into precise mathematical expressions. By exploring expressions involving negative numbers, students gain insight into how language influences mathematical operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 23 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 23TopicNumerical Expressions DescriptionThis example shows how to convert "Negative six less nine" into a numerical expression. The word "less" indicates subtraction, leading to the expression -6 - 9. Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "less," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 24 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 24TopicNumerical Expressions DescriptionThis example illustrates converting "Sixteen subtracted from negative three" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression -3 - 16. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 25 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 25TopicNumerical Expressions DescriptionThis example shows how to convert "Ten from negative eighteen" into a numerical expression. The word "from" indicates subtraction, leading to the expression -18 - 10. Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 26 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 26TopicNumerical Expressions DescriptionThis example illustrates converting the phrase "Negative ten take away sixteen" into a numerical expression. The phrase "take away" indicates subtraction, resulting in the expression -10 - 16. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 27 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 27TopicNumerical Expressions DescriptionThis example provides an illustration of converting "Negative one minus thirteen" into a numerical expression. The word "minus" indicates subtraction, resulting in the expression -1 - 13. Understanding numerical expressions is essential as they connect everyday language with mathematical notation. This collection aids students in interpreting various verbal phrases and converting them into precise mathematical expressions. By exploring expressions involving negative numbers, students gain insight into how language influences mathematical operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 28 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 28TopicNumerical Expressions DescriptionThis example shows how to convert "Negative eight less thirteen" into a numerical expression. The word "less" indicates subtraction, leading to the expression -8 - 13. Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "less," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 29 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 29TopicNumerical Expressions DescriptionThis example illustrates converting "Six subtracted from negative five" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression -5 - 6. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 3 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 3TopicNumerical Expressions DescriptionThis example demonstrates how to convert the verbal statement "Five less two" into a numerical expression. The word "less" is interpreted as subtraction, resulting in the expression 5 - 2. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 30 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 30TopicNumerical Expressions DescriptionThis example shows how to convert "Thirteen from negative sixteen" into a numerical expression. The word "from" indicates subtraction, leading to the expression -16 - 13. Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 31 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 31TopicNumerical Expressions DescriptionThis example demonstrates converting the phrase "Negative sixteen take away negative twenty" into a numerical expression. The phrase "take away" indicates subtraction, resulting in the expression -16 - (-20). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 32 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 32TopicNumerical Expressions DescriptionThis example illustrates converting "Negative fifteen minus negative nine" into a numerical expression. The word "minus" indicates subtraction, resulting in the expression -15 - (-9). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 33 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 33TopicNumerical Expressions DescriptionThis example shows how to convert "Negative sixteen less negative nineteen" into a numerical expression. The word "less" indicates subtraction, leading to the expression -16 - (-19). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "less," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 34 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 34TopicNumerical Expressions DescriptionThis example illustrates converting "Negative fourteen subtracted from negative four" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression -4 - (-14). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 35 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 35TopicNumerical Expressions DescriptionThis example explains converting "Negative five from negative eleven" into a numerical expression. The word "from" indicates subtraction, leading to the expression -11 - (-5). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 36 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 36TopicNumerical Expressions DescriptionThis example illustrates converting "Negative six take away negative fifteen" into a numerical expression. The phrase "take away" indicates subtraction, resulting in the expression -6 - (-15). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 37 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 37TopicNumerical Expressions DescriptionThis example shows how to convert "Negative four minus negative six" into a numerical expression. The word "minus" indicates subtraction, resulting in the expression -4 - (-6). Understanding numerical expressions is essential as they connect everyday language with mathematical notation. This collection aids students in interpreting various verbal phrases and converting them into precise mathematical expressions. By exploring expressions involving negative numbers, students gain insight into how language influences mathematical operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 38 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 38TopicNumerical Expressions DescriptionThis example presents converting "Negative sixteen less negative nineteen" into a numerical expression. The word "less" indicates subtraction, resulting in the expression -16 - (-19). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "less," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 39 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 39TopicNumerical Expressions DescriptionThis example illustrates converting "Negative ten subtracted from negative thirteen" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression -13 - (-10). |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 4 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 4TopicNumerical Expressions DescriptionThis example illustrates how to convert the verbal statement "Two subtracted from seventeen" into a numerical expression. The phrase "subtracted from" indicates subtraction, but it's important to note the order of the numbers. The result is the expression 17 - 2. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 40 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 40TopicNumerical Expressions DescriptionThis example shows how to convert "Negative fifteen from negative nineteen" into a numerical expression. The word "from" indicates subtraction, leading to the expression -19 - (-15). Numerical expressions are vital for translating everyday language into mathematical notation. This collection helps students learn how to interpret various verbal phrases and convert them into accurate mathematical expressions. By exploring different ways to express subtraction, such as using "from," students understand how language affects operations. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 5 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 5TopicNumerical Expressions DescriptionThis example demonstrates how to convert the verbal statement "Ten from twenty" into a numerical expression. The word "from" indicates subtraction, and the order of the numbers is important. The resulting expression is 20 - 10. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 6 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 6TopicNumerical Expressions DescriptionThis example illustrates how to convert the verbal statement "Nineteen take away one" into a numerical expression. The phrase "take away" clearly indicates subtraction, resulting in the expression 19 - 1. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 7 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 7TopicNumerical Expressions DescriptionThis example demonstrates how to convert the verbal statement "Eighteen minus five" into a numerical expression. The word "minus" directly translates to the subtraction operation, resulting in the expression 18 - 5. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 8 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 8TopicNumerical Expressions DescriptionThis example demonstrates how to convert the verbal statement "Four less seven" into a numerical expression. The word "less" indicates subtraction, resulting in the expression 4 - 7. |
Numerical Expressions |
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Math Example: Language of Math--Numerical Expressions--Subtraction--Example 9 | Math Example: Language of Math--Numerical Expressions--Subtraction--Example 9TopicNumerical Expressions DescriptionThis example illustrates how to convert the verbal statement "Nine subtracted from eighteen" into a numerical expression. The phrase "subtracted from" indicates subtraction, resulting in the expression 18 - 9. |
Numerical Expressions |
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Math in the News: Issue 63--Columbus's Voyages | Math in the News: Issue 63--Columbus's Voyages
October 2012. In this issue of Math in the News we look at Columbus' voyages. We make some calculations based on map data. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Multiples Table, 1-10 | A table that lists all the multiples for the numbers 1-10. Note: The download is a PDF file. Related ResourcesTo see the complete collection of Worksheets on this topic, click on this link: https://bit.ly/3gxcawE |
Numerical and Algebraic Expressions |
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Multiples Table, 1-20 | A table that lists all the multiples for the numbers 1-20. Note: The download is a PDF file. Related ResourcesTo see the complete collection of Worksheets on this topic, click on this link: https://bit.ly/3gxcawE |
Numerical and Algebraic Expressions |
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Multiples Table, 1-5 | A table that lists all the multiples for the numbers 1-5. Note: The download is a PDF file. Related ResourcesTo see the complete collection of Worksheets on this topic, click on this link: https://bit.ly/3gxcawE |
Numerical and Algebraic Expressions |
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Paper-and-Pencil Quiz: Equations with Fractions (Easy) | Paper-and-Pencil Quiz: Equations with Fractions (Easy)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Fractions (Hard) | Paper-and-Pencil Quiz: Equations with Fractions (Hard)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Fractions (Medium) | Paper-and-Pencil Quiz: Equations with Fractions (Medium)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Easy) | Paper-and-Pencil Quiz: Equations with Percents (Easy)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Hard) | Paper-and-Pencil Quiz: Equations with Percents (Hard)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
