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# Fractions In Action

Fractions In Action is an interactive activity that consists of direct instruction, cooperative
learning and is inquire based. As the students explore and manipulate pattern blocks they will
develop an understanding of fractions as parts of a unit whole. The students will have the
experience to generate equivalent forms of fractions with the use of pattern blocks as they model
and judge the size of fractions.

Subject: Mathematics

Lesson: Fractions

NYS Mathematics Science, and Technology Standard: Standard 3
4.N.8
Students will recognize and generate equivalent fractions (halve, fourths, thirds, fifths,
sixths, and tenths) using manipulatives, visuals, models, and illustrations.

4.N.9
Students will use concrete materials and visual models to compare and order unit fractions
or fractions with the same denominator.

4.PS.13 Students will work in collaboration with others to solve problems.

Content Strands:
Number Sense and Operations Strand
• The students will understand numbers, multiple ways of representing numbers, relationships
of numbers, and number systems;
• The students will understand meanings of operations and procedures, and how they relate to
one another;

Geometry Strand
• The students will identify and justify geometric relationships, formally and informally.

Objective: The students will develop an understanding of fractions as parts of a unit whole.

Purpose:
• The students will understand the concepts of and become proficient with the skills of
mathematics;
• The students will communicate and reason mathematically;
• The students will become problem solvers by using appropriate tools and strategies.

Materials:
• Pattern Blocks
• Activity Sheet # 1 Fractions In Action!
• Activity Sheet # 2 Challenge Question

• Students will cooperatively work together to determine how to divide the class into 1/2,
1/3, and. 1/6.
• Students will use pattern blocks to show the relationships between a whole, 1/2, 1/3,
1/4, and 1/6.
• Students will become familiar and use the geometric shapes hexagon, trapezoid,
rhombus, and triangle to develop an understanding of fractions as part of a whole unit.
• Students will problem solvers using pattern blocks as they explore fractions.

Procedure:
• A class discussion will begin with the representation of the yellow hexagon representing the
whole class.
• The students will be asked to divide into half of the students on one side of the classroom
and the other half on the other side of the room.
• The students will explain how they divided into two equal halves.
• One half will be represented with a red trapezoid.
• The students will be asked which is greater, one half or the whole?
• The students will then be asked to divide into thirds.
• The students will share how they determined what they need to do to divide into thirds.
• One thirds will be represented by the blue rhombus.
• The students will be asked how many thirds are needed to make a whole.
• The students will then be asked to into fourths.
• One fourth will be represented with a green triangle.
• The students will be asked how they determined how many students were needed to divide
the class into fourths.
• The students will return to their groups and use their pattern blocks to complete activity
sheets # 1 & # 2.
• The students will discuss the relationship between the pattern blocks and use the overhead

Extension
• The students will be given a sheet that has a challenge question. See Activity Sheet # 3.
• The students will use their pattern blocks to determine their answers.
• A class discussion with follow with the students sharing their answers and the relationship
of fractions.

Teacher Interaction:
• The teacher guide students with directions and questions.
• The teacher will encourage students to discuss the relationship between the pattern blocks.
• The teacher will model the pattern blocks and their relationship.
• The teacher will challenge students to explore different ways to make a whole.
• The teacher will encourage students to participate in discussion with questions that will
challenge students. Example: Is there any other combinations fractions that you could use
to make a whole unit?
• The teacher will answer any questions that the students may have.

What Will Be Accomplished?
• The students will build new mathematical knowledge through problem solving as they
understand the relationship between a whole and fractions.
• The students will apply and adapt a variety of appropriate strategies to show the relation
between fractions.
• The students will become familiar with the functions and representation of a hexagon,
trapezoid, rhombus, and triangle.
• The students will apply a variety of different strategies to solve problems using fractions.
• The students will expand their mathematical knowledge as the understand fractions and
their functions.

Evaluation:
1. The students will complete activity sheets #1 to show that they understand the
concept and relationships of fractions.
2. The students will complete activity sheet #2 to show that they have a deep
understanding of fractions through problem solving.
3. The student’s explanations to their answers will demonstrate the depth of their
understanding of fractions.
4. The students will be evaluated for contributing through oral responses and
participation.

Activity Sheet #1 This is the triangle and it is the smallest of all the shapes. This is the rhombus or parallelogram. Its size or area is exactly twice that of the triangle. I.e. you can fit two triangles inside of it. This is the trapezoid. Its size or area is exactly three times that of the triangle. That means that you can fit three triangles inside of a trapezoid or one blue rhombus and one triangle. This is the hexagon and it is the largest of all the shapes. Its size or area is exactly six times that of the triangle. You can fit six triangles or three blue rhombus or two trapezoids inside of it.

How many green triangles are in one blue rhombus ? __________
How many green triangles are in one red trapezoid ? __________
How many green triangles are in one yellow hexagon ? __________
How many blue rhombuses are in one yellow hexagon ? __________
How many red trapezoids are in one yellow hexagon ? __________

Activity Sheet # 2

1. Is there a way to represent the red trapezoid using blue and green pattern blocks?

2. Can you cover the red trapezoid using only one color?

3. What does this tell us about the relationship between the blue rhombus and the green triangle?

4. Are there other ways to represent various pattern blocks (for example, the yellow hexagon)
using more than one color pattern block?

Activity Sheet # 3 Challenge Question !

Queen Paula has three children, two boys and one girl that she would like to give her kingdom to.
She would like to give 1/3 of the kingdom to each of her sons and 2/3 to her daughter. Using your
pattern blocks decide if Queen Paula can do this. Explain your answer.

If Queen Paula cannot do this what would be a solution?