Beacon Lesson Plan Library
Mixed Expressions and Complex Fractions
Johnny Wolfe
Santa Rosa District Schools
Description
Algebraic expressions such as (a + b/c), and (5 + (x-y)/(x+3)) are called mixed expressions. Changing mixed expressions to rational expressions is similar to changing mixed numbers to improper fractions.
Standards
Florida Sunshine State Standards
MA.A.1.4.4
Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.
MA.A.3.4.1
Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.
MA.A.3.4.3
Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).
Florida Process Standards
Numeric Problem Solvers
03 Florida students use numeric operations and concepts to describe, analyze, communicate, synthesize numeric data, and to identify and solve problems.
Materials
-Overhead transparencies (if examples are to be worked on overhead) for Mixed Expressions and Complex Fractions (see Attached Files).
-Marking pens (for overhead).
-Mixed Expressions and Complex Fractions Examples (See Attached Files.)
-Mixed Expressions and Complex Fractions Worksheet (See Attached Files.)
-Mixed Expressions and Complex Fractions Checklist (See Attached Files.)
Preparations
1. Prepare transparencies (if teacher uses overhead for examples) for Mixed Expressions and Complex Fractions Examples (See Attached Files.)
2. Have marking pens (for overhead).
3. Have Mixed Expressions and Complex Fractions Examples (see Attached Files) prepared and ready to demonstrate to students.
4. Have enough copies of Mixed Expressions and Complex Fractions Worksheet (see Attached Files) for each student.
5. Have enough copies of Mixed Expressions and Complex Fractions Checklist (see Attached Files) for each student.
Procedures
Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving quadratic equations, and factoring. NOTE: This lesson does not address percents, scientific notation, radicals, absolute value or logarithms in SSS MA.A.1.4.4. This lesson does not address square roots in SSS MA.A.3.4.1 or SSS MA.A.3.4.3. Also this lesson does not address inverse relationships in SSS MA.A.3.4.1
1. Give students an example of a mixed expression. Review with students how to change a mixed number to an improper fraction and then show the resemblance for changing a mixed expression to a rational expression (see # 1 on attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
2. Work Example # 2 (see attached file Mixed Expressions and Complex Fractions Examples). Work with students on recognizing this type of problem as a mixed expression. Answer student questions and comments.
3. Work Example # 3 (see attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
4. Go over definition of a complex fraction then give some examples (see # 4 on attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
5. Work Example # 5 (see attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
6. Do Example # 6 (see attached file Mixed Expressions and Complex Fractions Examples). Go over shortcut. Answer student questions and comments.
7. Help students develop the Simplifying Complex Fraction Rule (see # 7 on attached file Mixed Expressions and Complex Fractions Examples).
8. Work Example # 8 (see attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
9. Work example # 9 (see attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
10. Ease student apprehension and nervousness. Discuss how to separate the expressions and then put them back together (see # 10 on attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
11. Work example # 11 (see attached file Mixed Expressions and Complex Fractions Examples). Answer student questions and comments.
12. Distribute the Mixed Expressions and Complex Fractions Worksheet (see Attached Files).
13. Distribute the Mixed Expressions and Complex Fractions Checklist (see Attached Files). Describe what is required from the students based on the checklist.
14. The student will write their response on the worksheet.
15. The teacher will move from student to student observing the students work and lending assistance.
Assessments
The student worksheet will be collected and scored according to the Mixed Expressions and Complex Fractions Checklist (see Attached Files).
Extensions
Give students the solution to a complex fraction and have them develop as many expressions as they can that equal the given complex fraction.
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