Pattern Block Fraction Design

These open-ended assessments require students to use pattern blocks to fill the shape so that it has a line of symmetry.  Students must draw a dotted line to show the line of symmetry and they must write a fraction to represent the part of the whole for each color pattern block used in the design.

• Download the Pattern Block Fraction Design handouts.

Who Has? Fraction Deck

This deck was designed to provide practice in using the area model of fractions.  The teacher distributes the cards and picks any student to begin the round.  In the case above, the sequence would go:

• [red shading] I have 1/12.  Who has 3/8?
• [green shading] I have 3/8.  Who has 4/5?
• [yellow shading]  I have 4/5.  Who has 5/12?

The beauty of all of the Who Has? games are that students remain active participants throughout the game.  Even after they have read their card aloud, they continue to attend to the card at hand, so students get lots of practice.

Differentiation:   Teachers may differentiate the game to accommodate learners with special needs by:

• specially selecting cards when distributing them so that each learner may be successful in naming his/her fraction
• allowing partners to work together to participate, thus providing the opportunity for gentle prompting for students who need this help to successfully participate in this activity.

Materials:  Download the Who Has? Fraction deck which is designed to be printed on 2x4 inch labels which may then be affixed to index cards to easily create a classroom deck of cards.

Variation:  Students may play this game in groups of 2-4.  They simply deal out all of the cards and place them face up on their desks.  One player begins, reading a card, then turning it over.  Whoever has the answer to that card, reads it and then turns it over.  Play continues in this way until one player has turned over all of his/her cards.  He/she is the winner.  

Of course, this is totally random, based on the distribution of the cards and the selection of the starting card, but students are fascinated with this version and willingly play and practice fractions in this game format.  Make the game available in the math center and schedule time for students to play.

Learn More:  Read more about using Who Has? decks to practice basic facts, scan some classroom management strategies for maximizing the potential benefits of these simple activities or download additional Who Has? decks in Mathwire's Who Has? collection.

Spin to Win Game

Landmarks are an important concept in the study of fractions.  Students need to have a conceptual understanding of whether a fraction is close to 0, close to 1/2, close to 1, larger than 1, etc. in order to correctly evaluate fractions and check the reasonableness of their answers.  The Spin to Win Game was designed to practice these skills in a fun game.

Students should be encouraged to use various methods of comparing the fractions (e.g. drawing pictures, folding paper, fraction strips, etc.)   It's not uncommon for students to use a more sophisticated approach.  Your fraction is larger than 1/2.  My fraction is less than 1/2, so  my fraction is closer to 0.

Directions for Spin to Win Game

• Students play in pairs. 
• Each student draws a card from the fraction deck.
• One student spins the spinner.

• In this case, the spinner landed on closer to 0.  Students decide whose fraction is closer to 0.  That player wins both cards.
• NOTE:  If the spinner lands on closer to 1/2 or closer to 1, then the player whose fraction is closest to these landmarks wins both cards.
• If the spinner lands on PLAY for 4!  Draw new cards, then both players pick another fraction card, place it on top of their original card, then spin the spinner.  The player whose new fraction card best matches the spinner wins all 4 cards.
• If the players turn over equivalent fractions, then they drawn new cards, spin the spinner and the player whose new fraction card best matches the spinner wins all 4 cards.
• Teachers may set the end of the game to be most points in 5 minutes, first player to get 10 points, etc. to fit available time and best meet student needs.

Download the Spin to Win Game directions and spinner.

Download Fraction Cards.


DIFFERENTIATION:  It may be helpful to provide this fraction strip handout for students still struggling with the size of fractions.  Slip the handout into a clear sheet protector and provide dry erase markers.  Students may then use the fraction strips to compare their fractions to see who is closer to the landmark.


Download Fraction Strip handout from the internet.

Fall Fraction Words

This activity requires students to put together fractional parts of words to create a new word.  It's a verbal take on the fractional set model.  If correctly solved, the fractional parts spell out a fall word.


Extension:  Students may enjoy creating their own fraction words, using local clues, seasonal prompts or even holidays. Use student-generated fraction word activities as an easy do-now exercise at the beginning of class.  It's a great way to develop understanding of the set model of fractions.


Download the Fall Fraction Words handout and answer key.

Problem Solving: Fractions 2

Students sometimes find the set model of fractions harder to understand and use.  These problems were designed to help students concretely work with the set model to solve problems.


Let's look at a sample problem:

Mrs. Puglisi’s third graders visited the park nature center to see the tadpoles and 

frogs.  They counted 20 animals in the tank. 

•  3/4 of the animals had already changed to frogs.  

•  The rest  were still tadpoles. 

•  How many frogs were in the tank? 

•  How many tadpoles were in the tank? 

•  Explain how you know your answers are correct.

Concretely Solving the Problem:  

• Students should begin by counting out 20 manipulative objects they will use to solve the problem.
• Next, students look at the fraction 3/4.  The denominator tells us that the animals were divided into 4 groups.   NOTE:  It is often helpful to use a piece of paper that is folded into quarters so that students may sort the manipulatives evenly into each of the 4 spaces. 
• Students deal out the manipulatives as if they were cards, placing one in each of the 4 spaces and repeating until all of the manipulatives have been distributed.  
• Students check to make sure that each quarter has the same number of animals.
• Now students look back at the fraction 3/4.  The denominator of 4 told students how many groups.  The numerator of 3 in this case tells students how many of the groups had already changed to frogs.  
• Students count the total number of frogs in 3 groups.
• The other group are still tadpoles.  Students count how many animals are still tadpoles.
• Finally, students may use words, pictures and numbers to record their thinking and explain how they knew their answer was correct.

Extension:  After students have mastered this concrete approach to solving fraction problems using the set model, they may move to a paper-and-pencil semi-concrete solution method.

• The student draws a square on his paper. 
• He checks the denominator of the fraction to see how many groups are needed.  The student divides the square into that many identical parts.
• The student then makes dots or tally marks in each section, as above, dividing the total number of objects evenly among the groups.
• The student checks the numerator of the fraction to see how many groups he must label for his answer.

• NOTE:  The beauty of this method is that students may easily use this approach in standardized testing situations.  It's completely portable!
• Students may also simply draw four circles to represent the 4 groups and proceed as above.

Practice Problems:

• Tadpoles and Frogs requires students to use fractions to figure out how many tadpoles and frogs there were in the tank.
• Animal Shelter requires students to use fractions to figure out how many cats and dogs were available for adoption at the animal shelter.
• Ask students to write original problems, peer solve and edit, then add to your classroom collection for future use.  

Problem Solving: Fractions

Problem solving activities help students develop conceptual understanding of fractions as they use appropriate fraction models to think about and solve the different tasks.  These Mathwire open-ended assessments were designed to measure students' conceptual understanding of fractions.


Pattern Block Fraction Design requires students to fill a shape with pattern blocks to create a design that meets certain requirements.   Students must also write a fraction that describes the part of the total design represented by each different color pattern block.


Fraction Game simulates a Fraction War game but students must draw a representation of each fraction and explain who won, based on the drawings.  This assessment was designed for students in an Everyday Math program.  Students may draw any representation that helps them decide which fraction is larger and explain their thinking.


Mrs. Meatball challenges students to solve pizza fraction problems pictorially.  The problems are listed on one page, but students should use lots of room to draw pictures, label and explain how they solved each problem pictorially.  NOTE:   This task was originally designed for a teacher in-service class where participants were not allowed to use any previous fraction knowledge to solve the problems.  They were instructed to use only words, pictures and numbers to solve the problems and explain their thinking.  They were not allowed to use any fraction algorithms, etc.

Thirteen Ways of Looking at a Half

This online Cyberchase activity challenges students to find the 13 different ways to shade in the figure to show one-half.

• Download a Thirteen Ways recording sheet so that students can shade in their solutions to find all 13 before entering them into the computer.
• Visit the Thirteen Ways of Looking at a Half website to enter all of the one-half shaded solutions you found.

Math-Literature Connection: Give Me Half!

Give Me Half by Stuart J. Murphy 

This book takes a humorous look at splitting things in half. Follow a reading and discussion with this worksheet where students practice splitting shapes (area fraction model) and groups of shapes (set fraction model) into half fairly.

• Download Give Me Half! worksheet.

Folded Fractions

Students need many concrete experiences with fractions to develop a deep understanding of the three models of fractions: area, linear and set models. Teachers need to address all three models in well-designed instructional activities so that students develop a rich concept of fractions that they can use to make sense of numbers, operations, measurement and probability. 

Folded Fractions:  For this area model, students use 4 pieces of construction paper to create this set of fraction manipulatives.  Students fold the paper following instructions, unfolding to easily see how many pieces are now in the whole.  After marking each piece with the correct fraction part, students cut apart the fractional pieces.

This model is easily created from classroom materials and students should keep their sets in their desks.  Students may use the fraction pieces during instruction, in problem solving or to play games.   By using the yellow "1" or "whole" mat, students may easily combine different fractional pieces to create a whole, etc., placing pieces on top of the yellow mat to see different ways of making a whole.

• Download directions for making Folded Fractions.

Other Area Models

Students divide shapes into the appropriate number of equal sections given by the denominator, then shade in the appropriate number of sections, given by the numerator to create a picture of the fraction. Equivalent fractions are also developed using this area model. Teachers may also use any of these manipulatives to develop the area model: 

• pattern blocks
• circular fraction regions
• pizzas
• geoboards
• spinners

Problem Solving: Fractions

Students are challenged to solve these problems by drawing pictures rather than using traditional fraction algorithms.  This is an extremely effective strategy to develop student conceptual understanding of fractions, fractional parts and fraction operations.

• Tadpoles and Frogs requires students to use fractions to figure out how many tadpoles and frogs there were in the tank.
• Animal Shelter requires students to use fractions to figure out how many cats and dogs were available for adoption at the animal shelter.
• Fraction Game simulates a Fraction War game but students must draw a representation of each fraction and explain who won, based on the drawings.
• High Number Game requires that students apply their knowledge of fractions, decimals and percents to decide whose number card is highest.
• Pattern Block Fraction Design requires students to use pattern blocks to fill the shape so that it has a line of symmetry. They must then write a fraction for each color pattern block used in the design.
• The Adventures of Mrs. Meatball problem set challenges students to draw pictures to solve each problem and prove their answers. 
• Monkey Business challenges students to work backwards to solve this fraction division problem. 
• Bake Sale challenges students to work backwards to solve another fraction division problem involving disappearing cookies.

Fractions: Spin to Win Game

It is important that students develop numerical sense in fractions.  One excellent activity is sorting fractions as close to 0, close to 1/2, close to 1.  This activity forces students to think about fractions in a whole different way and enriches student understanding.

The Spin to Win Game was developed to provide fun practice in this skill.  Students play in pairs. Each student draws a card from the fraction deck. One student spins the spinner. If the spinner lands on "closer to 0" then the student whose fraction is closer to 0 wins both cards. The same holds true for "closer to 1/2" or "closer to 0." If the students turn over equivalent fractions, they pick another card and spin to win all 4 cards. 

Materials:

• Download Spin to Win Game directions and spinner.
• Download Fraction Cards.  

Writing to Learn: Fractions

Headline:  3 out of 2 people don't understand fractions.

Journal entries, student-illustrated definitions and open-ended problems help students use writing to learn fractional concepts and terms. Students should be encouraged to draw pictures to illustrate fraction concepts or to solve problems.

 

These are some sample writing prompts to probe student understanding of fractions:

• Explain what the numerator and denominator of a fraction tell you. Give 2-3 different examples that include numbers, pictures and words.
• Is 1/4 or 1/8 larger? Use words, pictures and numbers to explain your thinking to someone who doesn't understand. Can you write a general rule that helps you decide quickly?
• John says that 1/100 is the smallest fraction. Do you agree or disagree? Use words, pictures and numbers to support your position.
• Is 7/8 or 9/10 closer to 1? Use words, pictures and numbers to explain your thinking to someone who doesn't understand. Can you write a general rule that helps you decide quickly?
• Sort the fraction cards into groups of close to 0, close to 1/2 or close to 1. What strategies did you use to quickly sort the cards into these groups? Which fractions were harder to place? Why?

 Teachers might elect to use the Think-Pair-Write-Share strategy with these prompts. 

• Think:  Ask students the question, then provide some quiet think time for students to grapple with the concept and organize their thinking, perhaps selecting an appropriate fraction model to explain their thinking. 
• Pair:  After a few minutes, student pairs discuss their thinking.  This is especially beneficial for the reluctant writer as they often find it easier to "talk" a solution.  Students also benefit from hearing different approaches to the problem, adding to their repertoire of strategies they have available for future tasks.
• Write:  Each student writes (words, pictures, numbers) to explain their thinking in response to the prompt.
• Share:  Teachers use a variety of strategies for this sharing session.  Sometimes teachers select students to represent the different ways of thinking about the prompt, asking those students to read their responses aloud.  Other times, teachers might circulate around the room as small groups discuss their responses.

Winter Fraction Words

This is a fun way to practice fractions with a little winter play on words.  Students read each clue and enter the letters in the appropriate boxes.  If they correctly calculate the fractional parts, the box should spell a wintry word.

Extension:  Challenge students to create their own fraction word collections.  After completing their collection, they should ask classmates to edit their creations and verify the correct clues.  Add these student-generated activities to the classroom math center or use them as a do-now for quick fraction review.

Download Winter Fraction Words.

Math App: Motion Math

This app targets students' understanding of fractions.  As students work their way back into space, they must sort fractions by tilting the iTouch (iPhone, iPad) so that the ball bounces in the proper spot.

The app provides practice in different representations of fractions.  Students must drop the ball at the correct location on a number line in one level.  Another level presents a visual representation of the fraction which students must also bounce at the correct location.

Still other levels ask students to sort fractions as less than, equal to, or more than the given fraction.  These sorts may contain fractions, visual representations, percents, and decimals so that students become accustomed to equivalent representations of fractions.

This is a great app for fraction practice.  Students are playing AND learning at the same time.  Students only need to move the iTouch to make the ball bounce in the correct location.  Correct responses generate a corresponding marking on the number line.  Incorrect responses prompt an arrow indicating which way the user should bounce the ball the next try.

The app is available through iTunes for 99 cents.  It's certainly worth the price to provide fraction practice in a game mode.  Be sure to check out more about the game and the research behind this app at Motion Math.