Illustrative Math Alignment: Grade 7 Unit 9

Putting it All Together

Lesson 10: Measuring Long Distances Over Uneven Terrain

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Clip Art--Ratios, Proportions, Percents--Proportions 04	Math Clip Art--Ratios, Proportions, Percents--Proportions 04 Topic Ratios, Proportions, and Percents Description This image demonstrates proportions through a scale model example, comparing the height and width ratios of the Eiffel Tower in two scales. It highlights the application of proportions in scaling and models, bridging abstract and practical understanding. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 05	Math Clip Art--Ratios, Proportions, Percents--Proportions 05 Topic Ratios, Proportions, and Percents Description This image shows proportionality between dimes and pennies using equivalent ratios (1:4 and 3:12). Mathematical steps verify proportionality. It introduces proportional reasoning and calculation steps to ensure clarity in identifying proportional relationships. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 06	Math Clip Art--Ratios, Proportions, Percents--Proportions 06 Topic Ratios, Proportions, and Percents Description This image presents proportional triangles, with side lengths maintaining equivalent ratios (2:3:4 and 6:9:12). It demonstrates geometric applications of proportions, extending the concept to shapes and measurements. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 07	Math Clip Art--Ratios, Proportions, Percents--Proportions 07 Topic Ratios, Proportions, and Percents Description This image contrasts proportionality with non-proportional groups of coins (dimes and nickels). Ratios differ, clarifying when proportions do not exist. It explains non-proportionality to deepen understanding of proportional relationships. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 08	Math Clip Art--Ratios, Proportions, Percents--Proportions 08 Topic Ratios, Proportions, and Percents Description This image poses a question about proportional triangles, asking for the missing value (x) to maintain proportionality. It introduces problem-solving involving proportions, encouraging engagement and application. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 09	Math Clip Art--Ratios, Proportions, Percents--Proportions 09 Topic Ratios, Proportions, and Percents Description This image solves the posed proportion problem by finding the value of x using equivalent ratios (x/6 = 7/3). It breaks down the process of solving proportions, reinforcing mathematical reasoning. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 10	Math Clip Art--Ratios, Proportions, Percents--Proportions 10 Topic Ratios, Proportions, and Percents Description This image demonstrates proportionality in coins by calculating the number of nickels required for proportional groups (2/5 = 6/x). It closes the sequence with a real-world problem, consolidating the topic and providing a practical application. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Example--Math of Money--Calculating Tax--Example 1	Math Example--Math of Money--Calculating Tax--Example 1 Topic The Math of Money Description What is the tax due on a $1000 purchase when the sales tax rate is 5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 10	Math Example--Math of Money--Calculating Tax--Example 10 Topic The Math of Money Description What is the tax due on a $9999.99 purchase when the sales tax rate is 9.9%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 2	Math Example--Math of Money--Calculating Tax--Example 2 Topic The Math of Money Description What is the tax due on a $1500 purchase when the sales tax rate is 6%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 3	Math Example--Math of Money--Calculating Tax--Example 3 Topic The Math of Money Description What is the tax due on a $2550 purchase when the sales tax rate is 7%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 4	Math Example--Math of Money--Calculating Tax--Example 4 Topic The Math of Money Description What is the tax due on a $999 purchase when the sales tax rate is 8%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 5	Math Example--Math of Money--Calculating Tax--Example 5 Topic The Math of Money Description What is the tax due on a $999.99 purchase when the sales tax rate is 9%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 6	Math Example--Math of Money--Calculating Tax--Example 6 Topic The Math of Money Description What is the tax due on a $1250 purchase when the sales tax rate is 6.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 7	Math Example--Math of Money--Calculating Tax--Example 7 Topic The Math of Money Description What is the tax due on a $1399 purchase when the sales tax rate is 7.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 8	Math Example--Math of Money--Calculating Tax--Example 8 Topic The Math of Money Description What is the tax due on a $1575.50 purchase when the sales tax rate is 8.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 9	Math Example--Math of Money--Calculating Tax--Example 9 Topic The Math of Money Description What is the tax due on a $1999.99 purchase when the sales tax rate is 9.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 1	Math Example--Math of Money--Calculating Tips and Commissions--Example 1 Topic The Math of Money Description Calculate a 15% tip on a $50 restaurant bill. The problem requires finding 15% of 50. To calculate the tip, multiply the cost (50) by the tip rate (0.15). Tip = 50 * 0.15 = 7.50. The answer is $7.50. In general, the topic 'The Math of Money' covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 10	Math Example--Math of Money--Calculating Tips and Commissions--Example 10 Topic The Math of Money Description Calculate a 9.5% sales commission on a $350,999 sale. The problem requires finding 9.5% of 350,999. To calculate the commission, multiply the sale amount (350,999) by the commission rate (0.095). Commission = 350,999 * 0.095 ≈ 33,344.91. The answer is approximately $33,344.91.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 2	Math Example--Math of Money--Calculating Tips and Commissions--Example 2 Topic The Math of Money Description Calculate a 16% tip on a $55 restaurant bill. The problem requires finding 16% of 55. To calculate the tip, multiply the cost (55) by the tip rate (0.16). Tip = 55 * 0.16 = 8.8. The answer is $8.80. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 3	Math Example--Math of Money--Calculating Tips and Commissions--Example 3 Topic The Math of Money Description Calculate an 18% tip on a $75.50 restaurant bill. The problem requires finding 18% of 75.50. To calculate the tip, multiply the cost (75.50) by the tip rate (0.18). Tip = 75.50 * 0.18 = 13.59. The answer is $13.59. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 4	Math Example--Math of Money--Calculating Tips and Commissions--Example 4 Topic The Math of Money Description Calculate a 19.5% tip on a $49.99 restaurant bill. The problem requires finding 19.5% of 49.99. To calculate the tip, multiply the cost (49.99) by the tip rate (0.195). Tip = 49.99 * 0.195 Å 9.75. The answer is approximately $9.75. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 5	Math Example--Math of Money--Calculating Tips and Commissions--Example 5 Topic The Math of Money Description Calculate a 22.5% tip on a $159.99 restaurant bill. The problem requires finding 22.5% of 159.99. To calculate the tip, multiply the cost (159.99) by the tip rate (0.225). Tip = 159.99 * 0.225 ≈ 35.99. The answer is approximately $35.99. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 6	Math Example--Math of Money--Calculating Tips and Commissions--Example 6 Topic The Math of Money Description Calculate a 5% sales commission on a $1000 sale. The problem requires finding 5% of 1000. To calculate the commission, multiply the sale amount (1000) by the commission rate (0.05). Commission = 1000 * 0.05 = 50. The answer is $50. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 7	Math Example--Math of Money--Calculating Tips and Commissions--Example 7 Topic The Math of Money Description Calculate a 6% sales commission on a $1200 sale. The problem requires finding 6% of 1200. To calculate the commission, multiply the sale amount (1200) by the commission rate (0.06). Commission = 1200 * 0.06 = 72. The answer is $72. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 8	Math Example--Math of Money--Calculating Tips and Commissions--Example 8 Topic The Math of Money Description Calculate a 7.5% sales commission on a $25,500 sale. The problem requires finding 7.5% of 25,500. To calculate the commission, multiply the sale amount (25,500) by the commission rate (0.075). Commission = 25,500 * 0.075 = 1912.50. The answer is $1,912.50. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 9	Math Example--Math of Money--Calculating Tips and Commissions--Example 9 Topic The Math of Money Description Calculate an 8.5% sales commission on a $125,500 sale. The problem requires finding 8.5% of 125,500. To calculate the commission, multiply the sale amount (125,500) by the commission rate (0.085). Commission = 125,500 * 0.085 = 10,667.50. The answer is $10,667.50.	Percents
Math Example--Math of Money--Compound Interest: Example 1	Math Example--Math of Money--Compound Interest: Example 1 Topic Math of Money Description This example demonstrates compound interest calculation for a $1000 investment at a 2.5% interest rate over 5 years, compounded annually. Using the formula A = P(1 + r/n)nt, where P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years, the final amount is calculated to be $1131.41.	Compound Interest
Math Example--Math of Money--Compound Interest: Example 10	Math Example--Math of Money--Compound Interest: Example 10 Topic Math of Money Description This example calculates compound interest for a $1000 investment at a 5% interest rate over 5 years, compounded monthly. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.05, n = 12, and t = 5, the final amount is $1283.61. Compound interest is a key concept in financial mathematics that shows how investments grow over time. This example highlights monthly compounding, demonstrating the impact of more frequent compounding on returns. Understanding these differences helps students apply compound interest in real-world financial scenarios.	Compound Interest
Math Example--Math of Money--Compound Interest: Example 11	Math Example--Math of Money--Compound Interest: Example 11 Topic Math of Money Description This example calculates compound interest for a $1000 investment at a 5% interest rate over 5 years, compounded daily. The formula $$A = P(1 + r/n)nt is used with P = 1000, r = 0.05, n = 365, and t = 5, resulting in an amount of $1284.00. Understanding compound interest is crucial for financial literacy. This example demonstrates daily compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.	Compound Interest
Math Example--Math of Money--Compound Interest: Example 12	Math Example--Math of Money--Compound Interest: Example 12 Topic Math of Money Description This example calculates compound interest for a $1000 investment at a 5% interest rate over 5 years, compounded continuously. Using the formula A = Pert, where P = 1000, r = 0.05, and t = 5, the final amount is $1284.03. Compound interest is a fundamental concept in finance, illustrating how investments grow exponentially over time. This example highlights continuous compounding, which shows the impact of applying interest at every possible moment. Understanding these differences helps students apply compound interest in real-world financial scenarios.	Compound Interest
Math Example--Math of Money--Compound Interest: Example 13	Math Example--Math of Money--Compound Interest: Example 13 Topic Math of Money Description This example calculates compound interest for a $1000 investment with an interest rate of 2.5% over 10 years, compounded annually. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 1, and $$t = 10, the final amount is $1280.08. Understanding compound interest is crucial for financial literacy. This example demonstrates annual compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.	Compound Interest
Math Example--Math of Money--Compound Interest: Example 14	Math Example--Math of Money--Compound Interest: Example 14 Topic Math of Money Description This example calculates compound interest for a $1000 investment with a 2.5% interest rate, compounded semi-annually over 10 years. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 2, and t = 10, the final amount is $1282.04. Understanding compound interest is essential for financial literacy. This example demonstrates semi-annual compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.	Compound Interest
Math Example--Math of Money--Compound Interest: Example 15	Math Example--Math of Money--Compound Interest: Example 15 Topic Math of Money Description This example calculates compound interest for a $1000 investment with a 2.5% interest rate, compounded quarterly over 10 years. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 4, and t = 10, the final amount is $1283.03. Understanding compound interest is crucial for financial literacy. This example demonstrates quarterly compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.	Compound Interest

Illustrative Math Alignment: Grade 7 Unit 9

Putting it All Together

Lesson 10: Measuring Long Distances Over Uneven Terrain

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