I began this website in 1997, but just now completed it as part of my course work with Connected University.
©Copyright October 28, 2001. All rights reserved. This lesson is intended to be used by classroom teachers not for publication. If you have any suggestions for improvement or changes to the lesson, please share them with me. I appreciate any constructive criticism you may want to give. I will also be happy to share your ideas with others by making changes to this lesson plan or adding an addendum to share these experiences, so please email me. 

Note: Some of the problems here are not typical "easy number" results. My students struggle with them, even with a calculator. It is my intention to give such problems to make them think "outside the box". 

Overview:

This lesson will cover the topic of solving mixture problems in Algebra and Chemistry. It is intended for Algebra and Chemistry classes at the high school level, but can be used as enrichment or remediation at other levels.

This lesson takes at least two 50-minute class periods. The goal is to teach students to solve verbal problems about mixing solutions. There will be two types of problems. In the first type the students will be given two solutions to combine and will be asked to find concentrations of the resulting mixture. The second type will ask the student how much of a given substance should be added to a starting solution to obtain a desired resulting solution. This lesson involves guided practice, cooperative learning, manipulatives, modeling and independent practice.

Objectives:

• use equations to solve mixture problems involving percents.
• write and evaluate of linear expressions from verbal descriptions.
• determine the solution to problem situations by writing and solving linear one-variable equations and inequalities.

Audience and Prerequisite skills:

The student should be able to
1) solve linear equations involving decimals.
2) solve linear equations with variables on both sides of the equal sign.
3) use a chart or picture to design the solution of a verbal problem.

Materials needed:

colored chips for the overhead
M&M's®
raisins
paper towels (and small paper cups, if you like)
student worksheets for cooperative activity
student worksheets for guided practice
student worksheets for independent practice

Procedures:

1. If you mix 50 apples and 25 peaches in a basket, what part of the basket mixture is apples? What percent of the basket mixture is peaches?
2. If a mixture of 10 items is 60% nails, how many nails are in the mixture?
3. If a mixture of 60 items is 40% pencils, how many pencils are in the mixture?

III. Get the students' focus back to the large group and briefly review the mathematics used to find the answers they have found. Be sure they have all completed Part 1 and then have them share their answers and discuss why they believe their answer is correct. Then have them begin Part 2 of the worksheet. This is where they may want to use the small cups to build each individual mixture and then combine the two. Encourage them to do this. Later, this process will help them visualize the problems they will not be able to actually build. Allow the students enough time to complete this activity. (Time required depends upon the group.) Again, while the students are completing this activity the teacher needs to walk among the groups and answer any questions and "evaluate" the discussions among the students. As the groups finish, have an answer key ready for them to check against their answers. If they get any wrong, have them go back and rebuild that mixture and check their calculations.

IV. Get back together as a large group and discuss the students' answers. You may want to draw pictures to show each individual mixture's amounts and percentages and the final mixture's amounts and percentages. Have the students look for relationships among these numbers. (If your class periods are only 45 or 50 minutes long, this may be a good homework assignment.)

V. Have the students complete Part 3 and Part 4 of the worksheet. Discuss their answers as a large group. The students should now see a relationship between tjhe amount of items in a mixture and the percentage of the item in the mixture.

VI. Hand out the Guided Practice Worksheet. Work the first problem together as a large group. Draw pictures (or have the students draw pictures) of what is happening in the problem, create a chart containing information that is know and that which is needed, and then create an algebraic sentence to answer the question. Some examples of this process can be found on the webpage Examples. Then have the students work in their pairs or teams to do the same for the remaining problems. Either have each team work on every question, or assign one or two problems to each team , then have the teams share with the large group. Different solving methods may appear during this sharing time and may require some discussion. When this is complete, answer any questions which have not yet been answered.

VII. Have the students return to working individually and hand out the Independent Practice Worksheet.
 
 

Evaluation:

Check the work completed on the Independent Practice Worksheet
Journal Writing: Create and solve 3 mixture problems.
Quiz

Websites that may help

Online Algebra Practice and Assistance

Algebra Modules

College Algebra Review