Abstract
Through the combination of imagination, block manipulation, and computer applets, students learn about fractions. Using this variety of tools will help grab the interest of all students, while teaching them about fractions.
Objectives
Upon completion of this lesson, students will:
- understand naming fractions
- work with finding a fraction of a whole number
- be able to compare fractions with different denominators using concrete representations such as manipulatives and pictures
Standards Addressed
Grade 3
-
Numeration
- The student demonstrates conceptual understanding of simple fractions with denominators 2, 3, 4, or 10.
Grade 4
-
Numeration
- The student demonstrates conceptual understanding of fractions with denominators 2 through 12.
Grade 5
-
Numeration
- The student demonstrates conceptual understanding of positive fractions with denominators 1 through 12 and 100 with proper and mixed numbers and benchmark percents (10%, 25%, 50%, 75%, 100%).
Grade 6
-
Numeration
- The student demonstrates conceptual understanding of fractions (proper or mixed numbers), decimals, percents (whole number), or integers.
- The student demonstrates conceptual understanding of fractions, mixed numbers, or percents.
Grade 7
-
Numeration
- The student demonstrates conceptual understanding of rational numbers (fractions, decimals, percents, or integers).
- The student demonstrates conceptual understanding of positive fractions, decimals, or percents.
Grade 8
-
Numeration
- The student demonstrates conceptual understanding of real numbers.
- The student demonstrates conceptual understanding of rational numbers (fractions, decimals, or percents including integers).
Grade 9
-
Estimation and Computation
- The student accurately solves problems (including real-world situations).
-
Numeration
- The student demonstrates conceptual understanding of real numbers.
Grade 10
-
Estimation and Computation
- The student accurately solves problems (including real-world situations).
-
Numeration
- The student demonstrates conceptual understanding of real numbers.
Third Grade
-
Number and Operations-Fractions
- Develop understanding of fractions as numbers.
Fourth Grade
-
Number and Operations-Fractions
- Extend understanding of fraction equivalence and ordering.
- Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Fifth Grade
-
Number and Operations-Fractions
- Use equivalent fractions as a strategy to add and subtract fractions.
- Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Grades 3-5
-
Numbers and Operations
- Compute fluently and make reasonable estimates
3rd Grade
-
Number and Operations
- The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.
3rd Grade
-
Numbers and Operations
- The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.
4th Grade
-
Number and Operation
- The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.
Grade 3
-
Number, Operation, and Quantitative Reasoning
- 2. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects.
Grade 4
-
Number, Operation, and Quantitative Reasoning
- 2. The student describes and compares fractional parts of whole objects or sets of objects.
3rd Grade
-
Number and Number Sense
- 3.05a The student will divide regions and sets to represent a fraction;
- 3.05b The student will name and write the fractions represented by a given model (area/region, length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths.
Student Prerequisites
-
Technological:
Students must be able to:
- perform basic mouse manipulations such as point, click and drag
- use a browser for experimenting with the activities
Teacher Preparation
- a browser
- pencil and paper
- 50 blocks, 50 chips, or 50 pieces of similarly sized pieces of paper
Key Terms
denominator
In a rational number, the number below the fraction bar that indicates how many parts the whole is divided into.
fraction
A rational number of the form a/b where a is called the numerator and b is called the denominator
numerator
The number above the fraction bar that indicates the number of parts of the whole there are in a rational number
Lesson Outline
-
Focus and Review
- Review vocabulary
- Tell the students that today they will be learning about fractions
-
Objectives
Students will be able to demonstrate their knowledge of fractions through the use of manipulatives and computer applets.
-
Teacher Input
- Have the students participate in the King Fraction scenario.
- Pass 50 blocks or small square similarly sized pieces of paper to each student.
- Students should work in pairs.
-
Guided Practice
- Instruct partner A to place 30 of his/her blocks in 5 equal piles and to ignore the rest of his/her blocks. Instruct partner B to place 30 of his/her blocks into 3 equal piles and to ignore the rest.
- Once all the students have their blocks grouped properly ask them the total number of blocks each person placed in groups.
- Begin asking the students questions like:
- What number of blocks is equal to 3/5 of 30?
- What number of blocks is equal to 1/5 of 30?
- What number of blocks is equal to 4/5 of 30?
- Once the students no longer have difficulty with this activity begin asking them questions like:
- What is 3/4 of 24?
- What is 1/6 of 24?
- What is 2/8 of 48?
- Have the students arrange their blocks to calculate the answer to each of the above questions.
- Walk around the class spot checking the students blocks.
- Once the students no longer have difficulty with this activity begin asking them questions like:
- Which fraction is larger 3/5 or 8/10?
Be sure to mention when the students answer these questions they need to be using the same number of blocks to calculate the fractions from each question. You may also want to work through the first question as a class.
For example: Have the students arrange 2 sets of 10 blocks. Have them arrange the first set into 10 equal groups and the other set into 5 equal groups. Finally have them compare 3/5 of 10 to 8/10 of 10 and tell you which one is larger.
- Which fraction is larger 2/3 or 3/9?
- Which fraction is larger 1/2 or 1/5?
- Which fraction is larger 3/5 or 8/10?
- Have the students open the Fraction Finder applet.
- Walk the students through 1 or 2 of the computer generated problems.
-
Independent Practice
- Have the students work in pairs taking turns with the Fraction Finder applet.
- You may or may not want to have the students draw and label each of their computer generated problems so that you can have something written to check.
-
Closure
- Review pertinent vocabulary such as: fraction, denominator, and numerator
- Review what each of the different parts of a fraction represent.
- Review that fractions can be part of 1 whole object or part of a number of objects.
Alternate Outline
- For the more advanced students you may want to have the students challenge each other by setting the boundary fractions using the Bounded Fraction Finder applet.
- For the students who may not be able to answer the questions provided by the Fraction Finder applet you may want to have them use the Bounded Fraction Finder applet, so that the lower end students can set their own bounding fractions. For example: 1/4 and 3/4.
- You may want to extend this lesson over several days in order to slow its pace.