**Title:** A Slice of the Pie

**Description:**
Students will gain knowledge on how to recognize and generate simple equivalent fractions. They will learn the criss cross method of checking to see if their process of elimination is accurate in naming an equivalent fraction. Students will then model equivalent fractions.
**Standard(s): **

[MA2015] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3-NF3]

**Subject:**Mathematics (3)

**Title:**A Slice of the Pie

**Description:**Students will gain knowledge on how to recognize and generate simple equivalent fractions. They will learn the criss cross method of checking to see if their process of elimination is accurate in naming an equivalent fraction. Students will then model equivalent fractions.

**Title:** Fraction Find!

**Description:**
Students will explore fractions through an interactive website. They will apply this knowledge while finding shapes with equivalent fractions.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3-NF3]

**Subject:**Mathematics (1 - 3), or Technology Education (K - 2)

**Title:**Fraction Find!

**Description:**Students will explore fractions through an interactive website. They will apply this knowledge while finding shapes with equivalent fractions. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Fractions on a Number Line

**Description:**
As students master the concept of the number line, they may be curious about where fractions would fit on a standard number line. Students will work cooperatively to explore the possibilities where fractions lie on number lines. Students will also work independently to extend and enrich their new knowledge of fractions on number lines.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4-NF1]

**Subject:**Mathematics (3 - 4)

**Title:**Fractions on a Number Line

**Description:**As students master the concept of the number line, they may be curious about where fractions would fit on a standard number line. Students will work cooperatively to explore the possibilities where fractions lie on number lines. Students will also work independently to extend and enrich their new knowledge of fractions on number lines. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Numerator/Denominator Introduction

**Description:**
This is an introductory lesson on numerators and denominators. Students will have the opportunity to practice dividing using hands-on activities.
**Standard(s): **

[MA2015] (4) 14: Understand a fraction ^{a}/_{b} with *a* > 1 as a sum of fractions ^{1}/_{b}. [4-NF3]

**Subject:**Mathematics (3 - 4), or Technology Education (3 - 5)

**Title:**Numerator/Denominator Introduction

**Description:**This is an introductory lesson on numerators and denominators. Students will have the opportunity to practice dividing using hands-on activities.

**Title:** Equivalent Fractions

**Description:**
This lesson helps students discover how to obtain equal fractions by using both fraction strips and playing a fraction matching game. Students will learn that to obtain equal fractions they will need to multiply the numerator and denominator by the same number.
**Standard(s): **

[MA2015] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4-NF4]

**Subject:**Mathematics (3 - 4), or Technology Education (3 - 5)

**Title:**Equivalent Fractions

**Description:**This lesson helps students discover how to obtain equal fractions by using both fraction strips and playing a fraction matching game. Students will learn that to obtain equal fractions they will need to multiply the numerator and denominator by the same number.

**Title:** Exploring the Value of the Whole

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students consider the size or value of the same fraction when different wholes are compared. This lesson promotes problem-solving and reasoning as the students compare similar fractions with different wholes. Students develop communication skills as they work in pairs and share their understanding about the relationship between the value of a fraction and the whole.
**Standard(s): **

[MA2015] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3-NF3]

**Subject:**Mathematics

**Title:**Exploring the Value of the Whole

**Description:**In this lesson, one of a multi-part unit from Illuminations, students consider the size or value of the same fraction when different wholes are compared. This lesson promotes problem-solving and reasoning as the students compare similar fractions with different wholes. Students develop communication skills as they work in pairs and share their understanding about the relationship between the value of a fraction and the whole.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Eggsactly Equivalent

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use twelve eggs to identify equivalent fractions. Construction paper cutouts are used as a physical model to represent various fractions of the set of eggs. Students investigate relationships among fractions that are equivalent.
**Standard(s): **

[MA2015] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4-NF1]

**Subject:**Mathematics

**Title:**Eggsactly Equivalent

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use twelve eggs to identify equivalent fractions. Construction paper cutouts are used as a physical model to represent various fractions of the set of eggs. Students investigate relationships among fractions that are equivalent.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Fun with Fractions

**Description:**
In this seven-lesson unit from Illuminations, students explore relationships among fractions through work with the set model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency.
**Standard(s): **

[MA2015] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5-NF1]

**Subject:**Mathematics

**Title:**Fun with Fractions

**Description:**In this seven-lesson unit from Illuminations, students explore relationships among fractions through work with the set model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Expanding Our Pattern Block Fraction Repertoire

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students expand the number of fractions they can represent with pattern blocks by increasing the whole. Instead of representing the whole with one yellow hexagon, the students explore fractional relationships when two, three, and four yellow hexagons constitute the whole.
**Standard(s): **

[MA2015] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4-NF2]

**Subject:**Mathematics

**Title:**Expanding Our Pattern Block Fraction Repertoire

**Description:**In this lesson, one of a multi-part unit from Illuminations, students expand the number of fractions they can represent with pattern blocks by increasing the whole. Instead of representing the whole with one yellow hexagon, the students explore fractional relationships when two, three, and four yellow hexagons constitute the whole.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Investigating Equivalent Fractions with Relationship Rods

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students investigate the length model by working with relationship rods to find equivalent fractions. Students develop skills in reasoning and problem solving as they explain how two fractions are equivalent (the same length). Relationship rods are wooden or plastic rods in ten different colors, ranging in length from one to ten centimeters.
**Standard(s): **

[MA2015] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5-NF2]

**Subject:**Mathematics

**Title:**Investigating Equivalent Fractions with Relationship Rods

**Description:**In this lesson, one of a multi-part unit from Illuminations, students investigate the length model by working with relationship rods to find equivalent fractions. Students develop skills in reasoning and problem solving as they explain how two fractions are equivalent (the same length). Relationship rods are wooden or plastic rods in ten different colors, ranging in length from one to ten centimeters.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** More Fun with Fraction Strips

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students work with fraction strips to compare and order fractions. Building on work done with fraction relationships in a previous lesson, students develop skills in problem solving and reasoning as they make connections between various fractions.
**Standard(s): **

[MA2015] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4-NF2]

**Subject:**Mathematics

**Title:**More Fun with Fraction Strips

**Description:**In this lesson, one of a multi-part unit from Illuminations, students work with fraction strips to compare and order fractions. Building on work done with fraction relationships in a previous lesson, students develop skills in problem solving and reasoning as they make connections between various fractions.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Making and Investigating Fraction Strips

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students make and use a set of fraction strips to represent the length model, discover fraction relationships, and work with equivalent fractions. They then create a virtual set of fraction strips using an online interactive activity.
**Standard(s): **

[MA2015] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3-NF3]

**Subject:**Mathematics

**Title:**Making and Investigating Fraction Strips

**Description:**In this lesson, one of a multi-part unit from Illuminations, students make and use a set of fraction strips to represent the length model, discover fraction relationships, and work with equivalent fractions. They then create a virtual set of fraction strips using an online interactive activity.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Inch by Inch

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use an actual ruler to represent various fractions as lengths. This lesson builds on work done in a previous lesson with nonstandard measurement as students use a standard instrument to measure a variety of items. Several pieces of literature appropriate for use with this lesson are suggested.
**Standard(s): **

[MA2015] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5-MD2]

**Subject:**Mathematics

**Title:**Inch by Inch

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use an actual ruler to represent various fractions as lengths. This lesson builds on work done in a previous lesson with nonstandard measurement as students use a standard instrument to measure a variety of items. Several pieces of literature appropriate for use with this lesson are suggested.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** The Variable Machine

**Description:**
This Illuminations lesson provides an introduction to the use of variables. Students explore the idea of variable as a symbol that can stand for any member of a set of numbers, and they substitute numbers for variables (letters) to discover unknown values.
**Standard(s): **

[MA2015] (5) 6: Read, write, and compare decimals to thousandths. [5-NBT3]

**Subject:**Mathematics

**Title:**The Variable Machine

**Description:**This Illuminations lesson provides an introduction to the use of variables. Students explore the idea of variable as a symbol that can stand for any member of a set of numbers, and they substitute numbers for variables (letters) to discover unknown values.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Fraction That!

**Digital Tool:**
ABCya.com **Web Address URL:**
http://www.abcya.com/equivalent_fractions_bingo.htm **Standard(s): **

[MA2015] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3-NF3]**Digital Tool Description:** ABCya.com is a free educational site equipped with computer games and activities for elementary students to learn on the web. All computer activities were created or approved by certified school teachers. All educational games are free and are modeled from primary grade lessons and enhanced to provide an interactive way for children to learn.

**Title:**Fraction That!

**Digital Tool:**ABCya.com

**Digital Tool Description:**ABCya.com is a free educational site equipped with computer games and activities for elementary students to learn on the web. All computer activities were created or approved by certified school teachers. All educational games are free and are modeled from primary grade lessons and enhanced to provide an interactive way for children to learn.

**Title:** Interactive Fraction Comparisons

**Digital Tool:**
Illuminations:Fraction Game **Web Address URL:**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=18 **Standard(s): **

[MA2015] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5-NF1]**Digital Tool Description:** This interactive game allows students to practice finding equivalent fractions, and adding fractions

**Title:**Interactive Fraction Comparisons

**Digital Tool:**Illuminations:Fraction Game

**Digital Tool Description:**This interactive game allows students to practice finding equivalent fractions, and adding fractions

**Title:** Number and Operations Web Links

**Description:**
This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.
**Standard(s): **

[MA2015] (5) 26: Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

**Subject:**Mathematics

**Title:**Number and Operations Web Links

**Description:**This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,1,2,3,4,5,6,7,8,9,10,11,12

**Title:** Communicating about Mathematics Using Games: Playing Fraction Tracks

**Description:**
Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This e-example from Illuminations contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
**Standard(s): **

[MA2015] (5) 26: Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

**Subject:**Mathematics

**Title:**Communicating about Mathematics Using Games: Playing Fraction Tracks

**Description:**Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This e-example from Illuminations contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Concentration

**Description:**
This student interactive from Illuminations allows students to play the classic game of Concentration by themselves or against a friend. The interactive can be used to review numbers, shapes, multiplication facts, fractions, decimals, and percents.
**Standard(s): **

[MA2015] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4-MD5]

**Subject:**Mathematics

**Title:**Concentration

**Description:**This student interactive from Illuminations allows students to play the classic game of Concentration by themselves or against a friend. The interactive can be used to review numbers, shapes, multiplication facts, fractions, decimals, and percents.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2,3,4,5

**Title:** Calculation Nation

**Description:**
Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.
**Standard(s): **

[MA2015] DM1 (9-12) 1: Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. (Alabama)

**Subject:**Mathematics

**Title:**Calculation Nation

**Description:**Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8,9

**Title:** Fraction Models

**Description:**
This student interactive, from Illuminations, explores several representations for fractions using adjustable numerators and denominators. Students can see decimal and percent equivalents, as well as a model that represents each fraction.
**Standard(s): **

[MA2015] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7-NS2]

**Subject:**Mathematics

**Title:**Fraction Models

**Description:**This student interactive, from Illuminations, explores several representations for fractions using adjustable numerators and denominators. Students can see decimal and percent equivalents, as well as a model that represents each fraction.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Fraction Game

**Description:**
This student interactive, from Illuminations, simulates a flash card fraction game. Students flip cards one at a time and try to match the values to the given number lines.
**Standard(s): **

[MA2015] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5-MD2]

**Subject:**Mathematics

**Title:**Fraction Game

**Description:**This student interactive, from Illuminations, simulates a flash card fraction game. Students flip cards one at a time and try to match the values to the given number lines.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Equivalent Fractions

**Description:**
This student interactive, from Illuminations, allows students to create equivalent fractions by dividing and shading squares or circles. The fractions are simultaneously displayed on a number line so students can see the relationship between the fractions.
**Standard(s): **

[MA2015] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4-NF1]

**Subject:**Mathematics

**Title:**Equivalent Fractions

**Description:**This student interactive, from Illuminations, allows students to create equivalent fractions by dividing and shading squares or circles. The fractions are simultaneously displayed on a number line so students can see the relationship between the fractions.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5