Grade 5 Fractions Unit Part 5-Improper Fractions And Mixed Numbers Lesson Plan

Aug 25, 2011 by

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Be sure to check out the other parts to this Grade 5 Fractions Unit:

- Grade 5 Fractions Unit Part 1-Significance Statement, General Objectives, Motivation, And Evaluation Pages

- Grade 5 Fractions Unit Part 2-Fraction Puzzles Lesson Plan

- Grade 5 Fractions Unit Part 3-Equivalent Fractions Lesson Plan

- Grade 5 Fractions Unit Part 4-Comparing Fractions Lesson Plan

In addition, feel free to download the text file of this entire Grade 5 Mathematics unit on Fractions or download the text file of improper fractions and mixed numbers lesson plan that you see on this page

I. Lesson Data:

Subject Area: Mathematics
Grade Level: 5
Unit Title: Fractions
Time: 45-60 minutes
Lesson Topic: Improper Fractions and Mixed Numbers

II. Instructional Data:

A. New York State Learning Standards:

Standard 3 – Mathematics: Number Sense and Operations Strand

5.N.20 Students will convert improper fractions to mixed numbers, and mixed numbers to improper fractions.


Ontario Curriculum Expectation(s):

Overall Expectations: Number Sense And Numeration

-read, represent, compare, and order whole numbers to 100 000, decimal numbers to hundredths, proper and improper fractions, and mixed numbers;


Specific Expectations: Quantity Relationships

- demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that ¾ is equal to 9/12);

- represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation;


Specific Expectations: Proportional Relationships

- describe multiplicative relationships between quantities by using simple fractions and decimals (e.g.,“If you have 4 plums and I have 6 plums, I can say that I have 1 ½ or 1.5 times as many plums as you have”);

- determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions (i.e.,with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent decimal forms (e.g., use a 10 x 10 grid to show that 2/5 = 40/100 which can also be represented as 0.4);


Overall Expectations: Data Management And Probability

- represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models.


Specific Expectations: Collection And Organization Of Data

- represent, using a common fraction, the probability that an event will occur in simple games and probability experiments (e.g.,“My spinner has four equal sections and one of those sections is coloured red. The probability that I will land on red is ¼);


B. Essential Question(s)/Overarching Objectives:
How can we represent and rename improper fractions as mixed numbers?
C. Lesson Behavourial Objective(s):

  • Students will compare and order whole numbers.
  • Students will identify improper fractions and mixed numbers using concrete material and drawings.
  • Students will represent improper fractions and mixed numbers using concrete material and drawings.


III. Materials:

-          Worksheet

-          Student Math Notebook

-          Math Textbook

-          Fraction circles

-          Grid paper

-          Chalk board

-          Chalk

-          Pattern Blocks


IV. Procedure / Presentation:

A. Anticipatory Set / Motivation:

Ask students to look around the classroom for things that come in pairs or sets.  For example, the desks are arranged in groups of 6.  Ask students how many groups of desks can we make with 15 desks?  To count you would say, 1/6 of a group, 2/6 of a group, 3/6 of a group, 4/6 of a group, 5/6 of a group, 1 group, 1 1/6 of a group, 1 2/6 of a group, 1 3/6 of a group, 1 4/6 of a group, 1 5/6 of a group, 2 groups, 2 1/6 of a group, 2 2/6 of a group, 2 3/6 of a group.


B. Procedure / Development:

1. Ask students to open their math textbooks to page 342.

2. Inform the students that today we will be discussing how to represent and rename improper fractions and mixed number.

3. Read “Teresa is helping her dad roast a small chicken.  It will take 1 ¼ hours to cook.  She must baste it every quarter hour.  She sets the timer to ring every 15 minutes.”

4. Read the central question with the students. “How many times will the timer ring until the chicken is cooked?

5. Read through Teresa’s explanation of how to find the number of times the clock will ring.

6.  Ask students why they think Teresa used fraction circles to calculate her answer.

7. Provide the students with the definition of mixed numbers and improper fractions.  A mixed number is a number made up of a whole number and a fraction.  An improper fraction is a fraction with a numerator that is greater than or equal to the denominator.

8. Discuss how Teresa came up with 5 rings.  Students could use fraction circles to represent the time.

9. Ask students why they think Teresa used a fraction circle with four parts to represent a clock?  Answer would be that since Teresa needed to baste the chicken every 15 minutes, which is ¼ of one hour.  She needed to count around the clock until 1 ¼ hours had passed.  So it was helpful to work with fourths.

10. Ask students if an improper fraction 8/3 says there are eight parts and each part is 1/3 of a whole.  What mixed number is equivalent to 8/3?  How do you know? Answer should be that 2 2/3 is equivalent to 8/3.  Students could explain this by stating that they used a fraction circle that is divided into three parts, and they counted thirds around the circle until they reached 8 thirds.

C. Summary / Closure:

Today we learned that a mixed number is a number made up of a whole number and a fraction.  For example, 1 ¼ is a mixed number.  We also learned that an improper fraction is a fraction with a numerator that is greater than or equal to the denominator.  For example, 5/4 is an improper fraction.  Mixed numbers can be renamed as improper fractions.  For example, 1 ¼ = 5/4.

Draw circle fractions on the board.


D. Application / Guided Practice:

With pairs students are to complete question 3.  Students could use fraction circles divided in half to represent each half hour on the clock face.


E. Closure

Ask students to summarize what an improper fraction is and have them display one on the board.  Ask students to summarize what a mixed number is and have them display one on the board.  Have students think of a definition for a mixed number and a improper fraction.  Record students definition on the board.


F. Reinforcement / Independent Work:

Students will be instructed to complete Question 6 – 8 on page 343 of their textbook. Also, an additional worksheet will also be given to each student.


G. Assessment:

Throughout the lesson I will asses the students through class discussions and observe them as they are working in pairs and independently.  Question 4 and 5 from their independent work will be used as a key assessment to determine the level of understandings.  Question 4 instructs students to draw a picture for each mixed number.  Question 5 asks students to rename each mixed number in question 4 as an improper fraction.  Students will be assessed on whether they are able to create drawing of mixed fractions and whether they understand how to change mixed numbers into improper fractions.


V. Other Considerations:

A. Diversity:

The lesson will accommodate the diversity of the class by encouraging everyone to voice their answers on mixed numbers and improper fractions. They are also given the opportunity to summarize what they have learned.  Students will be given the opportunity to work in pairs and to share their answers with the entire class.


B. Accommodations/Special Needs:

To accommodate for the student with little English speaking skills, I have located two easier worksheets and I will sit with her to work through the questions on each sheet until I know that she understands the concept of mixed numbers and improper fractions.


C. Remedial Activities:

For those students that may be having difficulty working with improper fractions and mixed numbers, have the students use concrete materials to help support their understandings.  I will provide them with fraction circles.  For those students that are having difficulty changing the mixed number to improper fractions, point out what changes from improper fractions to mixed numbers.  I will demonstrate to these students by using pattern blocks.  Demonstrate the fraction 1 1/6 of a hexagon.  Explain to the students that you have six triangles shaped into a hexagon, with one extra triangle.  To convert it to the improper fraction 7/6, all you have to do is break up the hexagon and count the parts.  You will determine that there are 7.  Therefore there are six parts in a whole hexagon, which is why the denominator is still 6.  By reversing it you can get from an improper fraction to a mixed number.  If I still feel that the student requires additional assistance, I will pair a stronger student with the weaker student to assist them with the completion of their work.


D. Enrichment Activities:

For those students that have completed their independent activity, I will hand out two additional worksheets.  One on changing improper fractions to mixed numbers and the other one on drawing lines form mixed numbers to improper fractions.


E. Technology:

F. Other:

At home students can use a chart to record the number of minutes they watch television for short periods of time after school.  They can then add up the total time and change the number into an improper fraction and a mixed number.  Students will then be asked to illustrate the total time on a fraction circle.


VI. Reflections:

1. What was the most effective part of the lesson?

2. In what ways could I have improved the lesson?

3. What additional considerations should I take into account for the next time that I conduct this lesson?

VII: Bibliography:

Nelson Mathematics 5, Teachers Resource, Chapter 12: Fractions.