Open Wide, Look Inside

This post will focus on resources to help teach 1st grade money. More specifically the skills of identifying denomination of coins and how groupings of different coins can have the same value. Also using addition to determine the value of a collection of coins and subtraction to determine the correct change.

I have selected several books that I think cover a wide range of money themes while providing entertainment, instruction, multi-cultural experiences and cross curricular opportunities.

•  My Rows and Piles of Coins by Tololwa M. Mollel, illustrated by E.B. Lewis – This book centers around a young boy who helps his mother work the market in Tanzania. She rewards him for his hard work but his only desire is to use his money to make her job easier. This book offers a glimpse into another culture and is embedded with lessons about generosity, determination and the rewards of saving money.

• Money Madness by David A Adler, illustrated by Edward Miller –  Ever tried to use dried fish to by milk at the grocery? Money Madness tells us how we use money today and gives a history of how we used to buy our good before we had real money. You also get an idea of how money changes value from day to day and in different countries. This book has cross-curricular opportunities for economics and early-American culture.
• The Coin Counting Book written and illustrated by Rozanne Lanczak Williams – This is the perfect book to introduce coin values, identification, grouping and counting.The coins are represented in both words and numbers with a large photograph of the coin for visual comparison. The book also shows coins arranged in sets with equations and their equivalents as well as showing how one coins can be exchanged still represent the same amount. The rhyming helps draw students in and encourages them to use actual coins while they read.
• A Dollar for Penny by Julie Glass, illustrated by Joy Allen – Penny needs money to buy her mother a birthday card so she sets up a lemonade stand to earn money. Her prices increase through out the day as she sells and she finally makes one dollar. This books teaches addition and shows coin denominations and their value. At the back of the book is a chart showing coins and their equivalence to other coins. It is a wonderful rhyming book and is part of the “Step into Reading + Math” series, level 2.
• Pigs Will Be Pigs: Fun with Money and Math by Amy Axelrod, illustrated by Sharon McGinley-Nally –   This book is as fun to look at as it is to read because of the wacky pigs and answers to math problems hidden in the illustrations. Students are encouraged to count along while the pigs destroy the house collecting spare change for dinner at the Enchanted Enchilada. Once at the restaurant the readers get to add along with the pigs to see what they can afford to eat. The addition and multiplication needed for the calculations are shown at the end of the book.

The following websites are for students to explore, practice and expand their knowledge and skills in reference to 1st grade math. Some sites offer basic knowledge and practice while others are more challenging.  Hopefully there is a good mix to meet all student levels and needs.

• BrainPOP Jr–   This educational site is very entertaining and kids can navigate through it easily themselves. The site is suitable for grades K-3 and contains videos, audio prompts and great graphics. This link leads to the money activities that are separated into two categories, counting coins and dollars and cents. Each set of activities contains games, jokes, writing and drawing that kids can print, word walls and online quizzes, all centered around money.  There is also a cartoon movie to watch staring their favorite BrainPOP characters. Portions of this site do require a membership, check with your school to see if they have already subscribed. Also they do offer a trial visit to check out the site.
• The Federal Reserve Bank of San Francisco, Welcome to FedVille – This is a fun interactive site that allows kids to earn and use money in their community of FedVille. Starting at home, they get money in the mail for their birthday, kids can then go to the bank and open a savings account, get a job to earn more money, go shopping, see a movie (about money of course), and play games. They get to see their money increase and decrease as they move about town. Kids can also tour the Federal Reserve or grab a bite at the deli, all while earning trivia cards (about money) for their collection. This site has great cross-curricular possibilities when focusing on community helpers and civics.
• Toon University –  Toon University is a huge website containing activities for all core subjects, teacher resources and links to other educational  websites, but what caught my eye was a simple math game called Discovering Coin Values.The student try to match the amount of money shown by dragging the coins up to the slide or onto the thumb to be flipped into the cup. The object is to use a variety of combinations of coins to come up with the correct match. As the student adds coins the amount is shown on the cup, if the student adds too much money, they are prompted to try a coin of lesser value. Because there is no score kept, trial and error is allowed as the students begin to learn the value of a group of coins. This game is simple yet very effective.
• H.I.P. Pocket Change – For Kids – The United States Mint – This is a really fun website for kids to learn just about everything there is to know about US coin currency. When teaching kids how to count money it’s also a great time to teach them how we make money, the history of coin currency, what did coins used to look like, coin collecting and how to save money. This is a great site full of games, cartoons, news, collectors tips and some very funny characters kids can get to know. The site is sponsored by the United States Mint so you can feel comfortable letting the kids navigate on their own. There are great cross-curricular opportunities here as well.
• Mathematics Lessons, All About Money – Elementary students can use this web based learning site to learn all about the basics of money. The four coins, penny, nickel, dime and quarter,are photographed and appear realistic with both front and back showing.When a student clicks on a coin, basic information is given. For a penny, student’s are told it is worth .01 cent, who is on the front, what is on the back, and a picture of both. The student can then count pennies or chose a new coin to investigate. By going to the tutorial page students can practice counting groups of each coin or combination of coins. The site offers congratulations or try again as the students progress. It is very realistic in appearance and basic in nature. However, that is what makes this website so appealing.

My next websites are for teachers. They provide lesson plans, activities, coin templates, and cross curricular ideas to help teach students money skills and about our US currency.

• H.I.P. Pocket Change  – For Teachers – The United States Mint – This website is packed with lesson plans for all four core subjects. Math alone has 40 lessons plans ranging from grades K-8. There are so many cross-curricular opportunities available here. The teacher feature page has tons of activities with templates for all the manipulative’s and worksheets you will need. All are approved by the US Mint to be reproduced. In the coin curricula center there is a representation of each coin with a printable template and a page of information, games, cartoons and activities associated with that coin. The reference page has access to a library of coins dating back to the 1600’s, book resources, websites and a glossary. This website also has a kids site with games, arts and crafts, cartoons and so much more.
• Money Instructor: Counting Money – Money Instructor covers many levels of teaching money, however this link is specifically for teaching coin counting and identification. You will find lesson plans, exercises, worksheets and manipulatives all to help you teach counting coins. The worksheets and interactive exercises can be adapted to suit the needs of your students depending on their level and ability. There are activities such as How Much?, and Matching Values. As your students advance in their skills you can look to Money Math for more lessons and activities. This website does require free registration for access to worksheets and some lessons require a membership, however there is still an abundance of materials available at no cost.
•  Math Fact Cafe – Fact Sheet Factory – Build your own money worksheets here. This site allows you to make your own worksheets based on four different skill levels and four different types of money math problems. You can show heads and/or tails or hide the value labels all together. There is also a jumbo size available for special needs students and the choice of natural looking coins or black and white outlines. You also have the option of being able to focus on one particular coin if students need more practice in one area or mix it up using penny up to quarter.

Introduction:

Addition and Subtraction are necessary skills for children to practice and develop so that they may continue to be successful throughout their journey in understanding and using mathematical concepts.  As they grow and develop, students will use addition, subtraction, and fact families in their daily lives and will be well serviced to have the ability to recall these facts quickly, efficiently, and accurately.

The resources found here can be used with first graders to help develop understanding, or with second graders as opportunities for more practice.  The associated Virginia Standards of Learning for this topic is: 1.5: The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.

Recommended books for assisting in teaching this topic:

1) One More Bunny, By Rick Walton, Illustrated by Paige Miglio

In this book, animals are joined together to make sums up to 10.  The animals are depicted with single numerals and the equations are also included.  Another great aspect to this book is that partitions of integers are shown such as: 4+2=6, 3+3=6 and 1+5=6, which is a great way to get kids thinking about the patterns of addition and the different numbers that can be used to find equal sums.

2) Domino Addtion, By Lynette Long

Long combines dominoes, counting, and addition in this straight-forward book.  Educators could easily make this an interactive activity, with the use of personal dominoes and addition mats while the book is read aloud.  Domino Addition, like One More Bunny, also includes basic examples of partitions of integers, so that 8 can be found by: 0+8, 1+7, 2+6, 3+5, and 4+4.

3)  Twenty is Too Many, By Kate Duke

This fun book incorporates a problem (too many guinea pigs will make their boat capsize), mathematical language and symbols (minus, -, =), and vivid pictures to engage students and get them having fun while practicing subtraction.  The book also serves to get imaginations guessing about what might happen next; on one page an observant reader might notice that the rope one guinea pig is holding has a fraying end, the next page shows that little guy floating in the water, resulting in one less guinea pig.  Fun for all while getting in some subtraction practice!

4)  Elevator Magic, By Stuart J. Murphy, Illustrated by Frank Remkiewicz and G. Brian Karas

In this book, Ben joins his mother on the 10th floor of her office building.  They begin to ride the elevator, but there are some errands that must be completed along the way.  Ben’s job is to subtract the number of floors from the number 10 to know what button to press on the elevator.  A simple, yet real-world problem that many kids can relate to; what kid doesn’t love pressing buttons?

5)   Hershey Kisses Addition Book, By Jerry Pallotta, Illustrated by Rob Bolster

This book includes math symbols (+, -, =), addition of single digits and addition of single digits to the number 10, and addition depicted both vertically and horizontally.   The author also includes addition of greater numbers and briefly introduces taking away, but educators can easily focus on what is applicable to their class.   This book could easily be used with manipulative (Hershey kisses, anyone?) to help kids have something tangible (and tasty) to add or subtract, making it another way to get kids practicing the process of addition while having fun, too.

Recommended Web Sites:

1) Max’s Math Adventures – Available on this great site provided by Scholastic, kids can play games, do interactive worksheets, and practice concepts learned in the classroom all on their own!  They could visit this site at home or during computer time in the classroom with a partner.  They can do it on their own, even in these early elementary grades, because audio directions are provided for each game or activity!  There are some excellent activities, but for specific practice of addition and subtraction activities, I might direct my students to: Farmer Fred’s Counting fun,  Card Castle Addition, or Subtraction Square Dance Sing-Along.

2) Ten Frame Addition Practice– This game is provided by Illuminations found at the website for the National Council of Teachers of Mathematics.  The game is fantastic, particularly when played on the “Play All” function.  Students can practice using a ten frame in which they physically move red and/or blue markers to the 10 frame to determine how many chips are displayed, “build” a provided number, add the correct number of chips to fill the frame (some blue chips are already included), or add red and blue chips to sums of 20 or less.  There are many math concepts being practiced, not to mention that students will gain facility with using the mouse, AND they are having fun, too!

3)  Math Games at A Plus Math – I would direct my students to games like Hidden Picture Subtraction (also has addition and Mult. version) or MATHO.  The Hidden Picture game provide cross-curricular elements.  Students uncover a real photograph by finishing addition or subtraction equations.  The picture is generally of something from nature (coral, sea turtle, etc.) and, upon uncovering all of the squares, the student is provided with a  brief description of where the picture was taken and something about the object’s significance.  MATHO is an addition version of BINGO.

4) Harcourt School has mutliple resources for elementary students to practice Operations – Student would have fun playing games like A Day at the Beach, where an equation using subtraction is displayed, and the program models what the answer would be by crossing off the correct number of fish.  The player supplies the correct difference in the equation and, when a group of problems have been solved, the player can paint the beach scene.  Students would also enjoy playing Busy Bees.  For these subtraction problems, a sentence is displayed such as: “There were 9 bees.  Some flew in the hive, 5 are left.  How many flew in the hive?”  The player supplies the correct answer and then the hive becomes transparent so that he can see the 4 buzzing bees inside.  A fun game to practice addition is Adding Bricks.  Here, the player watches as two construction workers walk across the screen, each pushing a wheelbarrow of bricks in two different colors.  They dump their bricks, one pile on one side of the screen and one pile on the other.  Then the equation is shown: 4+2=, and the player must supply the answer.  There are many other games and models for students to practice a variety of math concepts, all which are presented in sections titled “Addition,” “Subtraction,” etc., so that even younger students could be directed to games that are age and developmentally-appropriate.

5) Math is Fun – This site has many resources involving mathematical concepts from measurement, algebra, money, and addition/subtraction.  However, this does not make the site too difficult to navigate, and students would benefit from checking it out on their own.  For specific investigation and practice of addition and subtraction, I would direct my students to an addition page, where they can see models of addition and Math trainer, where they can fill in answers to supplied addition equations.  The Subtraction page  and the Subtraction Trainer would also be  great places for them to check out on the site.  The subtraction page gives a subtraction table and give visual models for subtraction.  The subtraction trainer responds to the supplied answers, so there are opportunities for practicing equations that are troubling students.

Additional resources

1) This is a link to an addition/subtraction card game found at public education site for New South Wales.  It would be an easy game to have at a math center, as a “Math-Tub” activity, or whenever there is some ‘down’ time (yeah, right!).  It is a cheap and easy game that will get students practicing math facts and really thinking about strategy for making the largest single-digit number they can with adding and subtracting 4 playing cards.  You could assign all the face cards as being 1, or simply remove them.

2) Kathy Gursky is a first grade teacher and workshop presenter.  She has created a wonderful website where she shares a wealth of information to help with instructing lower elementary grades.  She has an entire section dedicated to instructing students on fact families.  I particularly like this card game for practicing addition fact families.  She uses a gameboard for the number 9, but includes links to gameboards for numbers 5 through 18.  For the example of 9, she explains that students place a marker on the start.  They draw a card (Aces are 0, kings/queens/jacks are 1), and the card drawn tells them what number they place their marker on.  So, if a child draws a 4, he would move to the next available 5, because 4+5=9.  In this example, there is a ‘winner’s circle,’ where the winner must draw a 4, 3, or 6 to make 9.  This game can be played with 2 to 4 players, and would also be a great game to use as a center or Math Tub idea.

3) This site is a good refresher on addition and subtraction math facts for teachers.  It also goes through how you can introduce the topic to your students, complete with examples to use (call 3 students to the front, class counts, adds one more student, etc.)  The class sees their classmates being added/subtracted, but they also use snap blocks (or manipulatives of your choice) to work through the suggestions as well.  Check out the Introducing and Developing the Concept, as well.

Students need opportunities to identify, describe, and trace the 4 basic shapes in kindergarten.  They should also explore and manipulate the shapes.

Some Cute Books to Read to Students:

Brown Rabbit’s Shape Book, written and illustrated by Alan Baker – Brown Rabbit receives a colorfully-wrapped surprise package. As he unwraps each layer, various shapes such as circle and squares are highlighted.  Some of the shapes are unusual, like the sausage shape or the curly-wurly shape.

So Many Circles, So Many Squares, written and illustrated by Tana Hoban – This book introduces squares and circles through appealing photographs. The photographs are a variety of circle and square shapes. Circles and squares can be seen in many diverse objects, from dishwashers to colorful teapots, to brightly patterned fabrics.

Secret Birthday Message,  written and illustrated by Eric Carle – In this book the reader is lead through this suspenseful story using shape matching and recognition. A young boy has to carefully follow instructions to find his birthday surprise.

The Shapes We Eat, written and illustrated by Simone T. Ribke – This book explores shapes by describing various edibles such as a rectangular cereal bar, a hexagon shaped cracker and an oval egg. The foods are real photographs.

The Greedy Triangle, written by Marilyn Burns and illustrated by Gordon Silveria – This book is about a triangle with gleaming black eyes and a perky grin that leads a full life.  The triangle  can take the shape of a slice of pie or rest in an elbow's angle when people put their hands on their hips. The triangle is greedy so it asks a shape-shifter to turn it into various other shapes only to change back into a triangle in the end.

Web Sites for Kids:

These are great web sites for young children to explore shapes.  It also gives the child a chance to practice beginning computer skills such as clicking, dragging, and opening and closing a window.  All games are interactive sites and allows the child to be involved.

1. Toy Shapes– In this game students will drag the toys to the matching picture shape on the shelf.
2. Let’s Play with Shapes –  students will play a variety of games with circles, rectangles, triangles.
3. I Spy Shapes– students will click on all the triangles in the picture.
4. Story of Shapes-the students will listen to poems about the 4 shapes and watch the shape as it is drawn.
5. Marigold’s Mathematics Shapeville– students will click on a specified shape they chose in the real-life pictures.

Teachers- Look Here for Additional Resources:

1. Lesson plans for shape activities, printables, templates, and related themes involving shapes.
   http://www.first-school.ws/theme/shapes.htm
2. Links to various early childhood resources. There is a math connection link that has shape songs, lessons, and activities.  At the end, it lists other sites to visit for shapes.
   http://www.thevirtualvine.com/math.html
3. There are 8 shape games linked to the website for students to play such as Shape Story (audio and video descriptions of shapes), Paint the Shapes ( listening and following directions game), Oochy Goes to the Fair (matching shapes), Matching Shape with Krog (matching shapes), Astronomy Shape Match (matching shapes to outlines), Put it on the Shelf (matching shapes with outline), Rat’s Catch the Shape (rat catches shapes), Shapeville (find shapes in the picture).
   http://www.lc-ps.org/Schools/Carkenord/mediaCenter/sitesByGrade/

The resources described here are designed to help 5th grade students and their teachers explore some topics related to measurement and geometry, namely: finding and differentiating among perimeter, area, and volume, and measurement of right, acute, obtuse, and straight angles. There’s lots of great stuff out there, and I hope these resources will be helpful!

Fantastic Books:

Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander, illustrated by Wane Geehan.This charming book follows the adventures of Radius, son of Sir Cumference and Lady Di of Ameter on his first quest to rescue the King of Lell. In order to rescue the King, Radius must use his trust family medallion – which looks suspiciously like a protractor – to solve a maze of many angles. A wonderful introduction to angles and how to measure them. There’s even a replica of Radius’ medallion in the back of the book. 

What’s Your Angle, Pythagoras? by Julie Ellis, illustrated by Phyllis Hornung. This fictionalized history follows the famous mathematician as a young boy as he discovers his famous theorum on a trip to Alexandria with his merchant father. It’s a fun introduction to the unique features of the right triangle, with rich, whimsical illustrations that really enhance the journey. A great way to begin exploring angles and triangles.

Spaghetti and Meatballs for All! by Marilyn Burns, illustrated by Gordon Silveria. Mr. and Mrs. Comfort are planning a big family dinner. The food is ready and the tables are set – 8 tables, to be precise, with 32 chairs. But as the guests arrive, they begin to change the seating plan and chaos ensues! This book is a fun way to get kids thinking about perimeter and area.

Racing Around by Stuart J. Murphy, illustrated by Mike Reed. This book may be a little juvenile for many fifth graders, but it remains an excellent introduction to the concept and measurement of perimeter, while making a strong real-world case for why this math matters.

Millions to Measure by David M. Schwarz, illustrated by Steven Kellogg. Kids often understand a topic better if they know its history. This book traces the development of standard units of measure for distance, weight, volume, and more, going on to detail the development of the metric system. A fun and brightly illustrated melding of history and math.

Web Sites for Kids:

Here are some sites that are great for encouraging kids to explore measurement of angles and perimeter, area, and volume on their own. These are all interactive and engaging, and provide some wonderful opportunities for kids to lead their own learning.

"Measuring Angles"  – Interactive practice for kids learning about how to measure angles. Kids drag a protractor over a specified angle in a random polygon and select the correct measurement.

"Everything About Area and Perimeter" – Interactive game in which children find the perimeter or area of a shape. There are three levels, and at the most complex, kids are asked to find the perimeter or area of a compound shape. Step-by-step instructions break the process into easily manageable steps.

 "Shape Explorer"  – Students explore the relationship between area and perimeter, and are able to keep a running record of their findings. This site allows for varying levels of expertise. Beginners can restrict the shapes to rectangular arrays, while more experienced students can expand the size of more unusual shapes.

"Finding Volume"  – Kids watch as rectangular prisms are constructed by the computer, then calculate the volume of the resulting figure. Comes with a printable recording sheet to expand student learning.

"Angle Invasion!"  – Alien spaceships are invading, and you have to save the world! Kids estimate angles between 0 and 180 degrees in 10-degree increments to shoot a laser and blow up the invader – 3 strikes and game over. A fun way to hone kids' sense of angles and their ability to estimate outside the "easy" angles.

Additional Resources:

These resources are some good, general supports for instruction in measuring angles and perimeter, area, and volume.

 "What's My Angle?" – A set of 10 online activities that support the teaching and investigation of angles, as well as an introduction to relevant vocabulary. Includes activities ranging from estimating to specific measurement, and is kid friendly enough to make an independent activity.

"Electronic Geoboard" – This site can be used in conjunction with the "Building a Clubhouse" lesson provided in the print component. Alternately, this is a great way to demonstrate how to use a geoboard to find perimeter and area. Kids can explore further electronically to reinforce their hands-on classroom discoveries.

 “Geometry Festival” – This is a link to a week’s worth of activities about area and perimeter, based on Marilyn Burns’ “Spaghetti and Meatballs for All” and Cynthia Rylant’s “The Relatives Came.” The layout is a bit dense, but the activities are nice and detailed, and there are ideas included for extensions and for assessments.

“Geometry Bingo” –  Help students review geometry terms with this fun bingo game! This is a printable PDF that includes game boards and calling cards.

“Rules and Practice with Angles” –  Practice with measuring angles and types of angles (acute, obtuse, right, and straight). This is a free printable PDF. It includes all the relevant answer keys.

Introduction – SOL 4.2 a. & b. focuses on the comparing, ordering, and representation of equivalent fractions and mixed numbers.  For the student to be successful with these concepts, a clear understanding of SOL 2.3 (identifying parts of a whole to the tenths and the writing of fractions) is essential.  The online resources below are aimed at addressing this topic from the perspective of both the educator and the student.  Aside from online resources, the educator will want to include fraction strips and circles, along with class manipulatives to foster fraction concepts with his or her students.  Fractions can be fun after all!

5 Best Books

1. Working with Fractions by D. Adler and illustrated by E. Miller is aimed for ages 9 -12 years and offers graphic explanations of fraction problems.  Definitions are given for numerator and denominator along with the function of comparison of fractions.
2. Holiday Fractions by J. Roy and G. Roy are for readers 8 -12 years of age, grades 3 -7.  Holiday fractions combine the holidays with fractions to bolster the student’s understanding of fractions.
3. The Hershey’s Milk Chocolate Bar Fraction Book by Jerry Pallotta and illustrated by R. Bolster offer a “yummy” set of visuals to show how a chocolate bar can be divided into to rectangular blocks to represent fractional equivalents.
4. Polar Bear Math by A. Nagda and C. Bickel is for students who already have a working knowledge of basic fractions (ages 7-12).   Fractions and  delightful polar bears are combined to broaden the student understanding of fractions.  There are pictographs along with problems that compares and ask students to calculate fractions.
5. Eating Fractions by B. McMillan is a book designed for students who may need a little more of a refresher on fraction basic (grades 2-3).  The book shows children eating their way through various foods displayed in fraction form.

5 Best Web Sites for Kids

1. Game – Fresh Baked Fractions.  Site offers an interactive game where the student must choose the fraction that does not belong in the equivalent set.  It is then displayed if the fraction chosen is correct and resets to a new problem.
2. Math League will give definitions for fractions, equivalents, and comparisons of fractions.  Be sure to click on each new page.  Mixed fractions are also covered.  Site offer good background information but requires reading and is technical.
3. Fraction Fun is an interactive site where students can see visual representations of divided fraction squares, circles, triangles, and rectangles.  Equivalent fractions uses a “put cursor over” the correct answer and if you see the smiling face, your choice is correct.  Just use the pencil for “next” or “back”.  Audio sounds included.
4. Ordering Fractions Game is an game where the student will order a fraction by hanging it as a picture on the wall from smallest to largest.  The student can rearrange the fractions and once all 5 fractions are displayed to the student’s liking, the student will click done and the game will display if the set was ordered correctly.
5. Play a game of Equivalent Fractions or Comparing Unlike Fractions.  First read though the background information on equivalent or comparing fractions.  Then scroll down to practice.  The website will give a problem where you choose the equivalent fraction from the list.  If your answer is right, then you are given a new question.  Scroll on down to the PLAY section to test your knowledge.

Additional Resources

• Cross Curricular Book, Music Math, by K. Collins explores how fractions are used in other content area of music.  A lot can be said on 1/4, 1/8, and 1/2 (fraction) notes on a sheet of music.
• Fraction Jugglers, by R. Alexander, is a book of 19 fraction games along with 86 cards.  The games build on the student’s understanding and application on how to manipulate fractions.
• Fraction posters, worksheets, and activities can be found all under one site.  Enjoy.
• Funny and Fabulous Fraction Stories by D. Greenberg and J. Lee is a book of reproducible stories that end with a corresponding fraction problem for the student to solve.  Intended for grades 3-6.

Conclusion

Though fractions can be confusing for many,  learning the basic principles of fractions is a must as we use fractions many times throughout each day.  How could we cook or even decide who got the biggest piece of the pie without them?  I hope from the resources above you will find that teaching and learning about fractions can be exciting and manageable.