ALEX Lesson Plan

     

Tangram Fractions

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  This lesson provided by:  
Author:Jessica Jeffers
System: Enterprise City
School: Hillcrest Elementary School
The event this resource created for:GEMS
  General Lesson Information  
Lesson Plan ID: 24062

Title:

Tangram Fractions

Overview/Annotation:

The teacher will engage the class by reading Grandfather Tang. Students will solve a tangram puzzle. Students will find the fractional value for each piece of the tangram. Students will create a picture using the pieces of the tangram. Students will find the fractional value of their partner's tangram picture.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 3
13. Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

Unpacked Content
Evidence Of Student Attainment:
Students:
When given any fraction in form a/b,
  • Create an area model to represent the fraction.
  • Use a number line to represent the fraction.
  • Explain the relationship between the fraction and the model including the corresponding number of unit fractions. Example: 3/4 is composed of 3 units of 1/4 or 3/4 is the same as 1/4 + 1/4 + 1/4.
  • Identify a point to represent the fraction when given on a number line labeled with multiple points.
Note: Set models (parts of a group) are not models used in grade 3.
Teacher Vocabulary:
  • Unit fraction
  • Area model
  • Interval
  • Length (Linear) model
  • Partition
  • Numerator
  • Denominator
  • Part
  • Point
  • Whole
Knowledge:
Students know:
  • Fractional parts of a whole must be of equal size but not necessarily equal shape.
  • Denominators represent the number of equal size parts that make a whole.
  • The more equal pieces in the whole, the smaller the size of the pieces.
  • The numerator represents the number of equal pieces in the whole that are being counted or considered.
Skills:
Students are able to:
  • Use an area model and length model to show a unit fraction as one part of an equally partitioned whole.
  • Explain that given a fraction with a numerator greater than one, the numerator indicates the number of unit fraction pieces represented by the fraction. Example: 3/4 is the same as 3 units of 1/4 size, or three 1/4 pieces, 3 copies of 1/4, or 3 iterations of 1/4.
  • Identify and describe the fractional name given a visual fraction model.
  • Identify and demonstrate fractional parts of a whole that are the same size but not the same shape using concrete materials.
Understanding:
Students understand that:
  • Given the same size whole, the larger the denominator, indicating the number of equal parts in the whole, the smaller the size of the pieces because there are more pieces in the whole.
  • Fractions are numbers that represent a quantity less than, equal to, or greater than 1.
  • Fractions represent equal partitions of a whole.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.3.15 Compare fractions.
M.AAS.3.15a Use models to identify two equivalent fractions (limit to fourths and halves).
M.AAS.3.15b Recognize two equivalent fractions (limit to fourths and halves).
M.AAS.3.15c Use models of fourths and halves to make a whole.


Mathematics
MA2019 (2019)
Grade: 3
15. Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

a. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

b. Compare two fractions with the same numerator or with the same denominator by reasoning about their size (recognizing that fractions must refer to the same whole for the comparison to be valid). Record comparisons using < , >, or = and justify conclusions.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use a variety of area models and length models to identify equivalent fractions.
  • Use a variety of area models and length models to illustrate equivalent fractions.
  • Use visual representations to find fractions equal to 1.
  • Illustrate and explain fractions equivalent to whole numbers (limited to 0 through 5).
  • Compare two fractions by reasoning about their size and use <, >, or = to record the comparison.
  • Compare two fractions using visual fraction models.
  • Use symbols <, >, or = to record the comparison between two fractions.
Note: Tasks in grade 3 are limited to fractions with denominators 2, 3, 4, 6, or 8.
Teacher Vocabulary:
  • Equivalence
  • Visual fraction model
  • Number line
  • Numerator
  • Denominator
  • Reasoning
  • Conclusions
  • Comparison
  • Point
Knowledge:
Students know:
  • Fractions with different names can be equal.
  • Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
  • Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
  • Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
  • Comparing two fractions is only reasonable if they refer to the same whole.
  • The meaning of comparison symbols <, >, = .
  • Reason about the size of a fraction to help compare fractions.
  • Use a variety of area and length models to represent two fractions that are the same size but have different names.
  • Use a fraction model to explain how equivalent fractions can be found.
  • Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
  • Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
  • Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts. -Determine when two fractions can not be compared because they do not refer to the same size whole.
Skills:
Students are able to:
  • Explain equivalence of two fractions using visual models and reasoning about their size.
  • Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
  • Express whole numbers as fractions.
  • Identify fractions equivalent to whole numbers.
  • Record comparisons of two fractions using <, >, or = and justify conclusion.
  • Explain that the whole must be the same for the comparing of fractions to be valid.
Understanding:
Students understand that:
  • A fraction is a quantity which can be illustrated with a length model or an area model.
  • Two fractions can be the same size but have different fraction names.
  • A fraction can be equivalent to a whole number.
  • Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
  • The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
  • The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in a whole.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.3.15 Compare fractions.
M.AAS.3.15a Use models to identify two equivalent fractions (limit to fourths and halves).
M.AAS.3.15b Recognize two equivalent fractions (limit to fourths and halves).
M.AAS.3.15c Use models of fourths and halves to make a whole.


Mathematics
MA2019 (2019)
Grade: 4
13. Using area and length fraction models, explain why one fraction is equivalent to another, taking into account that the number and size of the parts differ even though the two fractions themselves are the same size.

a. Apply principles of fraction equivalence to recognize and generate equivalent fractions.

Example: a/b is equivalent to (n x a)/(nĂ— b).
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use visual models to create equivalent fractions.
  • Explain the generalized pattern, a/b = (n x a) / (n x b).
  • Use the generalized pattern to create equivalent fractions.

Set models (parts of a group) are not models used in grade 4.
Teacher Vocabulary:
  • Fraction
  • Numerator
  • Denominator
  • Equivalent
  • Fraction model
  • Area model -Length model
Knowledge:
Students know:
  • Fractions can be equivalent even though the number of parts and size of the parts differ.
  • Two fractions are equivalent if they are at the same point on a number line or if they have the same area.
Skills:
Students are able to:
  • Use area and length fraction models to explain why fractions are equivalent.
  • Recognize and generate equivalent fractions.
Understanding:
Students understand that:
  • equivalent fractions are fractions that represent equal value.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.13 Identify and compare models of a whole (1), one-half (1/2), one-third (1/3), and one fourth (1/4) using models, manipulatives, numbers lines, and a clock.


Mathematics
MA2019 (2019)
Grade: 4
15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • When given any fraction or mixed number, apply unit fraction understanding to decompose the given fraction or mixed number into the sum of smaller fractions, including unit fractions.
  • When given a problem solving situation involving addition and subtraction of fractions or mixed numbers with like denominators, explain and justify solutions using unit fractions, visual models, and equations involving a single unknown.
Teacher Vocabulary:
  • Decomposition
  • Unit fraction
  • Area model
  • Length model
  • Equation
  • Mixed number
  • Visual fraction model
  • Whole
  • Sum
  • Difference
  • Recomposition
Knowledge:
Students know:
  • Situation contexts for addition and subtraction problems.
  • A variety of strategies and models to represent addition and subtraction situations.
  • The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
  • A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction. Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.
Skills:
Students are able to:
  • Decompose fractions as a sum of unit fractions.
  • Model decomposition of fractions as a sum of unit fractions.
  • Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
  • Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.
Understanding:
Students understand that:
  • A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
  • A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
  • The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.15 Model decomposing fractions having like denominators, using visual fraction models (limit to half and fourths).


Mathematics
MA2019 (2019)
Grade: 5
10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use a variety of strategies and fraction equivalence to find sums and differences of fractions and mixed numbers with unlike denominators.
Teacher Vocabulary:
  • Fraction
  • Denominator
  • Numerator
  • Visual Model
  • Sum
  • Difference
  • Equivalence
  • Unlike denominators
  • Unlike units
Knowledge:
Students know:
  • Strategies to determine if two given fractions are equivalent.
  • How to use a visual model to illustrate fraction equivalency.
  • Contextual situations for addition and subtraction.
Skills:
Students are able to:
  • Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.
Understanding:
Students understand that:
Addition and subtraction of fractions and mixed numbers with unlike units,
  • Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit.
  • Can be assessed for reasonableness of answers using estimation strategies.

Local/National Standards:

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers (NCTM National Standard 3rd - 5th grade).

Primary Learning Objective(s):

Students will be able to label fractional parts of the tangram.

Additional Learning Objective(s):

Students will be able to create a picture using tangram pieces. Students will be able to solve a tangram puzzle.

 Preparation Information 

Total Duration:

91 to 120 Minutes

Materials and Resources:

Tangram pieces, square puzzle, the book Grandfather Tang, paper, crayons

Technology Resources Needed:

LCD or Interactive WhiteBoard (optional)

Background/Preparation:

Students need to have a basic understanding of fractions.

  Procedures/Activities: 
1.)Read the book Grandfather Tang (this can be skipped if the book is unavaliable).

2.)Pass out the puzzle square and pieces of the tangram (see puzzle square document).
(Grandfather Tang's Animal Puzzle)
This site offers the tangram puzzle as a printable and also offers patterns of the animals built in the book.

3.)Place students randomly into pairs or groups and ask them to try and fit the pieces of the tangram into the square.

4.)Walk the room offering hints to groups that need help.

5.)Students can share with the class how they went about solving the problem using online manipulative tangram pieces.
(Tangrams NLVM)
This site allows students to manipulate pieces of the tangram.

6.)Display the completed tangram and ask students if this tangram represents the whole, what fractional value would each piece represent (see tangram solved document).

7.)Allow students time to work with their group to determine the value of each piece.

8.)Have groups share with the class the various approaches they used in order to determine the value of each piece.

9.)Allow students to use the pieces of the tangram to create their own picture by tracing the different pieces.

10.)Be sure to encourage students to use pieces more than once or even omit some of the pieces.

11.)Once students have completed their pictures, they should swap papers with a partner and figure out the fractional value of their partners picture.

12.)Remind students that the whole was the completed tangram square.

13.)Have students share with the group how they determined the value of their partners picture.


Attachments:
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  Assessment  

Assessment Strategies

Have students write and explain the strategy they used to determine the fractional value of their partner's picture.

Acceleration:

Students that have already aquired this skill can be challenged to create a picture that has a fractional value of exactly 2 1/16.

Intervention:

Students that need additional practice on this topic can be allowed the use of fraction strips.


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.