Illustrative Math Alignment: Grade 7 Unit 7

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Equations

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Equations

Description

This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.

Topic

Equations

Description

This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.

Topic

Equations

Description

This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.

Topic

Equations

Description

This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.

Topic

Equations

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Equations

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Equations

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Equations

Description

This example likely demonstrates solving a more complex one-variable equation. It may involve multiple steps, such as combining like terms, using the distributive property, or dealing with fractions or decimals. The solving process typically includes isolating the variable on one side of the equation by performing inverse operations on both sides. This type of problem enhances students' algebraic manipulation skills and prepares them for more advanced equation solving. The specific solution would involve carefully following the order of operations and checking the final answer by substituting it back into the original equation.

Topic

Equations

Description

This example likely showcases a more challenging one-variable equation. It may involve variables on both sides of the equation, requiring students to consolidate like terms before solving. The problem might also include parentheses, necessitating the use of the distributive property. Solving this equation would involve carefully balancing operations on both sides, possibly dealing with negative numbers or fractions. This type of problem helps students develop their algebraic reasoning skills and reinforces the importance of maintaining equation balance throughout the solving process.

Topic

Equations

Topic

Equations

Description

This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.

Topic

Equations

Description

This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.

Topic

Equations

Description

This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.

Topic

Equations

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Equations

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Equations

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Equations

Description

This example demonstrates solving equations involving angle measures in a kite. A kite has two pairs of adjacent congruent angles. In this case, we have angles represented as (x+50)°, (x+50)°, (y+20)°, and y°. To solve this problem, we apply two key principles: the sum of angles in a quadrilateral is 360°, and the sum of the angles of a triangle is 180°. You can use the triangle equation to solve for y. Once you determine the value for y, you can use that to find x using either the triangle or the quadrilateral equation. In the solution shown, the triangle equation is used. 

Topic

Equations

Description

This example illustrates solving equations involving angle measures in a kite. The kite has two known angles of 70° and 40°, and two unknown angles represented as (x+y)°. To solve this problem, we look at the triangles formed by one of the diagonals of the kite and use the triangle equation. First solve for x with the top triangle. Once you find x, use that value to solve for y in the bottom triangle. You could also use the quadrilateral equation to solve for y.

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Ratios, Proportions, Percents

Description

This example demonstrates how to find 50% of 250 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 250. By aligning 50% on the percentage line with its corresponding value on the numerical line, we can see that 50% of 250 is 125. This method visually represents the concept that 50% is equivalent to one-half of a quantity.

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to determine an unknown value using a double number line when given a part and its corresponding percentage, involving a decimal percentage. The image shows two number lines: one ranging from 0 to 100% and another from 0 to an unknown number x. The position 70 is marked on the second line, visually illustrating the process of finding x when 70 is 12.5% of x.

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Ratios, Proportions, Percents

Description

This example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 75, with 25 marked as an intermediate point. This visual representation helps students understand the relationship between the part (25) and the whole (75) in percentage terms.

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Ratios, Proportions, Percents

Description

This example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 220, with 55 marked as an intermediate point. This visual representation helps students understand the relationship between the part (55) and the whole (220) in percentage terms.

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 495, with 99 marked as an intermediate point. This visual representation helps students understand the relationship between the part (99) and the whole (495) in percentage terms.

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 396, with 198 marked at the midpoint. This visual representation helps students understand the relationship between the part (198) and the whole (396) in percentage terms.

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Ratios, Proportions, Percents

Description

This example demonstrates how to determine what percent one number is of another using a double number line, particularly when dealing with more complex ratios. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 856, with 107 marked at an eighth of the way. This visual representation helps students understand the relationship between the part (107) and the whole (856) in percentage terms.

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to calculate 25% of 180 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 180. By aligning 25% on the percentage line with its corresponding value on the numerical line, we can determine that 25% of 180 is 45. This method visually demonstrates that 25% is equivalent to one-quarter of a quantity.

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Ratios, Proportions, Percents

Description

This example demonstrates how to find 33 1/3% of 240 using a double number line. The solution displays two parallel number lines: one ranging from 0 to 100% and the other from 0 to 240. By aligning 33 1/3% on the percentage line with its corresponding value on the numerical line, we can see that 33 1/3% of 240 is 80. This method visually represents the concept that 33 1/3% is equivalent to one-third of a quantity.

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Ratios, Proportions, Percents

Description

This example illustrates how to calculate 40% of 105 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 105. By aligning 40% on the percentage line with its corresponding value on the numerical line, we can determine that 40% of 105 is 42. This method visually demonstrates that 40% is equivalent to two-fifths of a quantity.

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to find 12.5% of 88 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 88. By aligning 12.5% on the percentage line with its corresponding value on the numerical line, we can see that 12.5% of 88 is 11. This method visually represents the concept that 12.5% is equivalent to one-eighth of a quantity.