Friday, April 29, 2011

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.

Thursday, April 28, 2011

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.

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

Wednesday, April 27, 2011

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.

• 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.

Tuesday, April 26, 2011

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:

Monday, April 25, 2011

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.

Friday, April 22, 2011

Math-Literature Connection: A Quarter from the Tooth Fairy

In this book, Caren Holtzman [Hello Math Reader, Level 3] recounts in verse how a young boy spends the quarter he got from the Tooth Fairy for his tooth.   He first buys a monster for his quarter but then decides it wasn't quite right and returns it, getting 2 dimes and 1 nickel back.   Each time he buys and returns an item, he gets his 25 cents back in a different combination of coins, making this book an excellent introduction to the problem of how many different ways students can make 25 cents.

Challenge: What other ways could the character have gotten his 25 cents in change?
Writing Extension:  Each student writes additional pages for the story that describe what the character buys and what combination of coins he gets back when he ultimately returns the item.

Thursday, April 21, 2011

Math-Literature Connection: Pezzettino

Pezzettino by Leo Lionni is a great introduction to the concept of area as how many small squares cover a surface.  In this book, small squares are used to create the characters.
• After reading the book, have students use color tiles or paper squares to first estimate how many squares will cover an object then actually use the squares to measure the object.
• Students can also create their own Pezzettino characters using colored construction paper squares.   The class discussion should focus on comparing the "sizes" of these Pezzettino characters based on their area or the number of squares used to construct each character.
Download the Pezzettino Characters handout and squares template.   The squares template can be used to copy squares onto construction paper that has been trimmed to 8.5 x 11 inch size to use in a copier.   Ellison pattern block square cutouts will also produce small squares from construction paper.

Wednesday, April 20, 2011

Developing Number Sense

Students in Everyday Math classes play a game called Name That NumberMake It Count is a very similar online game.  Students are dealt number cards, given operations and a target number.  The students must use only those cards (all or some) and the given operations to produce the target number.  They click on Submit to check their solution and get immediate feedback.  If the student is stumped by a particular combination of cards, they may click on See Answer to view a possible solution

These games provide practice of basic factsThe real beauty is that students rehearse many different options in the search for one successful combination, developing number sense.  There are often several possible solutions, so students believe they will be successful, motivating them to search for a solution when one is not initially evident.

After a class presentation of the game, students often benefit from playing as pairs, generating mathematical discussion and debate in the search for a solution.  This online game might also be added to Parent Resources as students may play for free at home.

The Make the Number template may be downloaded and used in class as a warm-up or Do Now! activity.  For renewable use, students insert the template into a clear sheet protector and use dry erase markers to write in the target number and the number cards.  They use the white space to write down and check possible solutions.

NOTE:  Teachers may opt to make an overhead of this template so that students are able to record different solutions they find.  If the overhead is also inserted into a sheet protector, students may use dry erase markers to record their solutions.  The sheet protector is easy to clean and the overhead may be kept in a teacher binder for easy retrieval as needed.

Extension:  The Contig game is a natural extension of this activity and it develops number sense as students search for the best possible solution that will win them the most points.  Students should know multiplication and division facts, but older students are easily challenged by this game.  Try it!

In the Contig Game students toss three dice.   They use those three numbers and any operations to form a number on the game mat.   Players earn an extra point for each covered number the new number touches, so students quickly learn to search for the best move that will yield the maximum possible points.   The instructional benefit of the game is that students try many different combinations in search of that best move.

Contig Jr. is designed to provide that same format for younger students who need to develop mastery of addition and subtraction facts.

Suggestions:
• Introduce these games to students and provide students time for supervised play.
• Make the games available in the math center for use during center time or indoor recess or game day.
• Insert the game mats into clear sheet protectors and use dry erase markers for renewable play.
• Home Connection:  Send a copy of the game mat home for students to teach parents and play at home for additional practice.

Monday, April 18, 2011

Earth Day Math Activities

In a time when environmental activists are urging every American to make small changes, there are many online lesson plans and activities that help students think about the environment and how daily choices and practices impact our earth either positively or negatively.

Mathwire has assembled a collection of links to online activities.  Be sure to check out the Earth Day Math Activities when planning your classroom celebration.

Friday, April 15, 2011

by Eric Carle

by Richard Fowler

• See NCTM Illumination's Ladybug Lengths unit that helps students develop the concept of measurement through the use of nonstandard units including a ladybug tape that may be downloaded from the site.
• Let students play with the Hiding Ladybug applet to practice measurement skills.
• Ladybug Leaf is another online version of this applet game that requires students to estimate distances in a Logo-like environment.

by Michael Dahl

This book was designed to provide practice in counting by fives, offering yet another way to include math in a ladybug unit.  Each page adds five more spots to count until you reach 50.

NOTE:  The worksheet is designed as a companion to the Lots of Ladybugs book.
• Worksheet 1 has all numbers in a traceable font.
• Worksheet 2 has some missing numbers.  Printed numbers are in traceable font.

The ladybug cards are all scrambled and students must put them in the correct order.  This deck is designed to be printed on card stock, cut apart and stored in plastic bags for use in a math center.
Differentiation:  This activity is easily differentiated by varying the number of cards given to students to accommodate the varied learning levels in the class.  Consider creating A, B, C sets in baggies that contain different number of cards.  Students may move to the harder level once they have mastered the first set.

Thursday, April 14, 2011

For those who remember the Logo language, NCTM Illuminations offers a similar experience for students today.  The Ladybug Adventures unit requires students to use geometric and measurement skills to program a sequence to move the ladybug under a leaf or through a maze.

• Students use NCTM's Hiding Ladybug applet to design a path that will take the ladybug beneath the leaf for a great problem solving experience. This online applet encourages students to refine their paths until they are ultimately successful.
• Making Triangles and Making Rectangles require students to teach the ladybug to use specific angles to create shapes that will hide the ladybug under the leaf.
• Finally, Ladybug Mazes challenges students to develop a series of moves that will successfully navigate the ladybug through the given maze.
These online applets are exceptional tools to help students think about and experience geometric concepts.  Students are motivated by the challenge and get immediate feedback on their success.  The applets allow students to refine their initial attempts, another plus in motivating students to successfully master the skills to meet a challenge.

Wednesday, April 13, 2011

The Ladybug, Fly Away Home! game uses a one-die toss to move that numbered ladybug one space closer to her home. Students add their results to the Class Recording sheet by adding a tally mark for the winning ladybug. Class discussion focuses on the fairness of the game by asking if each ladybug has an equal chance to win? PDF file includes directions, game mat, recording sheet and math center icons

Tuesday, April 12, 2011

Ladybug Patterns introduces students to the algebraic concept of growing patterns or functions. In this case, the dots on the ladybug change with age. Students may use the picture and a function table to analyze the pattern's growth and write a rule in words and/or variables/numbers.

• Download a blank Ladybug Patterns handout so that students can create their own original patterns to challenge their classmates.
• NOTE:  teachers may use an overhead of the blank pattern handout to create additional patterns for students to analyze (e.g. double the age, 2 more than age, etc. )

Monday, April 11, 2011

Students use counters and their ladybug mats. Count out the correct number of counters for the given number. Place counters, alternating sides, onto the ladybug mat until all counters are placed. If there are the same number of counters on each side of the ladybug, then the number is an even number. If one side has an extra counter (spot), then the number is an odd number.

• Download for directions for Odd and Even Ladybugs, recording sheet, number cards and Odd/Even Recording Sheet.
• B/W Ladybug Mat includes mat, recording sheet and number sentence template.
• Color Ladybug Mat may be used with round counters or black foam circles.

Suggestion for Morning Math Routines: Place a ladybug template in a sheet protector or laminate the ladybug. Use a dry-erase marker to add a new spot each day. Discuss whether the ladybug has an odd or even number of spots, based on whether there are the same number of spots on each side of the ladybug. Incorporate this practice into morning routines to reinforce odd and even numbers.

Tuesday, April 5, 2011

Question of the Day

Collecting, organizing and analyzing data are essential skills in today's world.  Some teachers incorporate daily practice by including a question of the day in the morning routines.  Students have markers with their names, and they are accustomed to completing this task when they arrive in the classroom, placing their marker in the correct spot.  If students are non-readers, assign one student to be the interviewer, repeating the question to classmates as they arrive in the classroom.

Suggestions:
• Vary the format of the data organization, providing practice by using bar graphs, clothespin graph, Venn diagram, tally chart, line plot, glyph, etc.
• Use seasonal, weather, holiday prompts to collect data.
• Coordinate math question of the day to current literature, science or social studies units.
• Extend assembly and field trip experiences by graphing data about the particular theme.
• Check out this list of data questions for young learners.

Monday, April 4, 2011

Free the Animals Game

Who will free their animals first?   Students toss two dice, calculate the difference and free an animal from that number cage.   Younger students will enjoy this animal version of the Release the Prisoners game and learn subtraction facts as well.   Both the 6-sided dice game mat and the 12-sided dice game mat are included with directions.

• Download the Free the Animals game directions and game mats for 6-sided dice to practice easier subtraction facts or 12-sided dice to practice harder subtraction facts.
• Download the Free the Animals game recording sheet designed so that students can track how many animals each player places in his/her cages and who wins.   Hopefully, students will learn something about probability while mastering subtraction facts.

Friday, April 1, 2011

Money: Coin Values

Coin Race
Mrs. Higgins and Ms. Gillespie's first graders at Port Monmouth Road School in Keansburg, NJ, use large magnetized coin cutouts to make the correct money amount.   This activity provides a platform for discussing different ways to make the same amount as student pairs often choose different coin combinations.   Students at their seats use coins to create combinations as well and record them on whiteboards, if desired.

Many Coins, Many Ways
Challenge students to find all of the different ways to use coins to express the day's date.   Students may start this challenge haphazardly, but this activity presents older students the opportunity to learn the value of using an organized approach to solving these types of problems so that they will be confident that they have found all of the possibilities.   Teachers might model the use of a chart, for instance, to record combinations.   Students should be prompted to talk about the orderly approaches they used.