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 10

Estimation and Computation

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of real numbers.

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.

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.

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.

Third Grade

Number and Operations-Fractions

Develop understanding of fractions as numbers.

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.

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.