Cracking the Cookie Code: Solving Proportion Problems

Algebra 1 Grades High School 5:48 Video
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Lesson Description

Learn how to solve real-world proportion problems using ratios and cross-multiplication, illustrated with a delicious cookie recipe example!

Video Resource

Proportion word problem (example 1) | 7th grade | Khan Academy

Khan Academy

Duration: 5:48
Watch on YouTube

Key Concepts

  • Ratio
  • Proportion
  • Cross-multiplication
  • Algebraic manipulation

Learning Objectives

  • Students will be able to set up proportions to represent real-world problems.
  • Students will be able to solve proportions using cross-multiplication and algebraic methods.
  • Students will be able to interpret the solution of a proportion problem in the original context.

Educator Instructions

  • Introduction (5 mins)
    Begin by discussing the concept of ratios and proportions. Ask students to provide real-life examples where proportions are used (e.g., scaling recipes, map reading). Briefly introduce the idea that proportions represent equivalent ratios.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Proportion word problem (example 1)'. Instruct students to take notes on the two methods presented: scaling and cross-multiplication.
  • Guided Practice (10 mins)
    Work through the cookie recipe problem from the video as a class, reinforcing both the scaling method and the cross-multiplication method. Emphasize the algebraic reasoning behind cross-multiplication.
  • Independent Practice (10 mins)
    Provide students with similar proportion word problems to solve independently. Encourage them to use either the scaling or cross-multiplication method, and to check their answers. Example problems: 1. If 3 apples cost $2.25, how much would 7 apples cost? 2. A map has a scale of 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between them?
  • Wrap-up & Discussion (3 mins)
    Summarize the key concepts and address any remaining questions. Preview the next steps, such as solving more complex proportion problems or applying proportions to other areas of mathematics.

Interactive Exercises

  • Proportion Match
    Create cards with ratio statements (e.g., 2:5) and corresponding word problems that can be solved using that ratio (e.g., 'If 2 notebooks cost $5, how much will 10 notebooks cost?'). Have students match the ratios to the correct word problems.
  • Error Analysis
    Provide students with worked-out proportion problems that contain common errors. Ask students to identify the error and correct the solution.

Discussion Questions

  • In what real-world situations might you use proportions?
  • Which method (scaling or cross-multiplication) do you find easier to use, and why?
  • Can you explain why cross-multiplication works from an algebraic perspective?

Skills Developed

  • Problem-solving
  • Algebraic reasoning
  • Critical thinking
  • Ratio and proportional reasoning

Multiple Choice Questions

Question 1:

A recipe calls for 1 cup of sugar for every 2 cups of flour. If you want to use 6 cups of flour, how much sugar do you need?

Correct Answer: 3 cups

Question 2:

What is the main principle behind solving proportions?

Correct Answer: Maintaining equivalent ratios

Question 3:

In the proportion a/b = c/d, what is the result of cross-multiplication?

Correct Answer: a * d = b * c

Question 4:

If a map uses a scale of 1 inch = 25 miles, and two cities are 4 inches apart on the map, what is the actual distance between the cities?

Correct Answer: 100 miles

Question 5:

Which method involves finding a scaling factor to solve the proportion?

Correct Answer: Scaling

Question 6:

If 5 notebooks cost $10, how much will 2 notebooks cost, assuming the price per notebook is the same?

Correct Answer: $4

Question 7:

A proportion is a statement that two _______ are equal.

Correct Answer: Ratios

Question 8:

When using cross-multiplication to solve a proportion, you multiply the _______ across the equals sign.

Correct Answer: Diagonals

Question 9:

If 2 pizzas can feed 8 people, how many pizzas are needed to feed 20 people?

Correct Answer: 5

Question 10:

What is the first step in solving a word problem involving proportions?

Correct Answer: Set up the proportion

Fill in the Blank Questions

Question 1:

A _______ is a comparison of two quantities by division.

Correct Answer: ratio

Question 2:

A _______ states that two ratios are equal.

Correct Answer: proportion

Question 3:

The method of multiplying diagonally across a proportion is called _______.

Correct Answer: cross-multiplication

Question 4:

If 4 gallons of gas cost $12, then 1 gallon of gas costs $_______.

Correct Answer: 3

Question 5:

Scaling a recipe up or down is an example of using _______.

Correct Answer: proportions

Question 6:

In a proportion, the top number is the _______ and the bottom number is the _______.

Correct Answer: numerator

Question 7:

If 3 oranges cost $1, then 9 oranges will cost $_______.

Correct Answer: 3

Question 8:

When solving proportions, you're trying to find an _______ value.

Correct Answer: unknown

Question 9:

Setting up the _______ correctly is key to solving proportion problems.

Correct Answer: proportion

Question 10:

Proportions relate two _______ to each other.

Correct Answer: ratios

Educational Standards

A1.A.1.1:Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context. A1.A.3.1:Solve equations involving several variables for one variable in terms of the others.

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