Hands-on Math Activities

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Mathematics: Active Hands-On Learning

Children learn and truly understand math and mathematical concepts when engaged in hands-on activities and games. By manipulating everyday objects, playing games and finding out ways to solve everyday problems, children gain a true understanding of math and mathematical concepts. Only with this understanding does the meaning of abstract numbers become apparent.

You will find dozens of games, ideas and activities for bringing mathematical concepts to life for children of all ages. Bring out the seashells, beans and rulers. Let's make math become a part of our children's lives...

Photo Credit: Cuisenaire Rods by ameliabedelia74
on Photobucket, Creative Commons

Hands-On Math is fun and encourages children to think about math

Hands-On Math leads to a deep understanding of Mathematical Concepts

Mrs. Thompson asked the first grade girls to go to the front of the room. Then she asked the boys to go to the front of the room. Then she told us that 3+2=5. You see, there were only 5 children in my first grade class.
learning mathfirst grade mathPlus SignFirst GraderLearning to AddGirl

Photo Credit: Boys and Girls
on WPClipart


This is the first math lesson that I can remember and the only one that I can remember for years. What was it about that lesson that made it so memorable? I believe that it was the concreteness of the activity.

For years I was always one of the best math students in the class. I was always able to get the right answers but I never enjoyed math. Math never made sense to me. It was just playing with numbers.

Algebra Tiles

Algebra Tiles
Available on Amazon


I disliked it so much that I vowed that my last day of high school would be the last day I took a class in math. When I went to get my teaching certificate, however, the state required that I take a class in teaching math.

That class was the most fun, exciting class I had ever taken. The professor brought out Cuisenaire Rods, pattern blocks and geoboards. He showed us how wooden Cuisenaire Rods could be dropped to play a musical scale.

The feel of the wooden blocks was smooth and the colors were exciting. Using these blocks brought math to life.

Cuisenaire Rods

Photo Credit: Cuisenaire Rods
on Photobucket


When I started student teaching I was introduced to Mary Barretta-Lorton's Mathematics Their Way, work jobs and the calendar. We used math to make art, to describe objects found in nature, and to understand history. Integrating math throughout the curriculum made the numbers have meaning.

Mathematics Their Way Calendar

Photo Credit: Frog and Log Math Patterns


When I started homeschooling my children I continued to use the games and activities that I had used when teaching. Together we discovered that often ordinary board games also teach or reinforce mathematical concepts. We played Snakes and Ladders or Go to the Head of the Class to learn the Hundred's Board. Playing Monopoly is a great way to practice adding and subtracting the number sentences in the 10's family. There are 10 spaces from corner to corner and the railroads are exactly halfway between the corners.

I believe that counting on fingers is a good thing and there are books that can teach you how if you didn't figure it out on your own.

Counting on Fingers
When we got to Algebra I had a problem. Algebra was abstract. It had no meaning for me. I had done very well in all my high school classes and even won the award for the top of the class but it never made any sense to me. How was I going to teach it to my children? I started researching for ways to make the subject come alive and discovered Mary Laycock's book Algebra in the Concrete. It was just what I was looking for. Mary Laycock, a teacher of High School math for over 60 years, developed a method of teaching Algebra using Cuisenaire Rods which makes algebra hands-on. My daughter and I worked through the book and looked for more.

Photo Credit: Finger Counting
From WPClipart



Hands-On Algebra

Photo Credit: 4 Pan Algebra Balance Scale
Available on Amazon


We discovered that Mary Laycock had founded a company, Activity Resources. We next tried What's my Rule? It is so much fun! We used it to find the functions of the algebra problems that go through the robot's heads. The answers are in the back for times when the solution is not self-evident.

fibonacci sequence

Photo Credit: Espiral de semillas de Girasol
on WikiCommons


From there we dabbled in the Pythagorean Theorem starting with the unlikely source, Donald in Mathmagic Land and then went on to fractals and then the Fibonacci sequence where we counted the swirls in sun flowers and predicted the number of rabbit descendants that could be born to one pair of rabbits.

Hands-on Learning with Ladybug Math Manipulatives

Ladybug Math Mats

Pass out a leaf to each child. Then distribute a ten ladybugs. Tell the children that ladybugs like to land on leaves. Ask the children how many ladybugs there are on the leaf? Zero. Write the numeral 0 on the board.

Pick up a ladybug and have her fly around looking for a leaf. When she lands on the leaf, ask the children how many ladybugs there are on the leaf now? One Write on the board 0+1=1.

Continue adding ladybugs until there are ten.

Leaf Math MatLadybug Math Manipulatives

Photo Credit: Ladybug Buttons Available on Amazon
Photo Credit: Leaf Math Mat Available on Amazon

Learn the addition facts to ten using a flannel board with leaves that ladybugs love to eat and flannel ladybugs for moving from leaf to leaf.Another day you might subtract ladybugs. Children can also use this as a game by using dice to add and subtract ladybugs.

You might keep sets of ladybugs in Altoids tins for easy distribution. Use a permanent marker to draw ten circles in the bottom of the Altoids box so that children can make sure that they have collected and saved all their ladybugs and not lost any on the floor.
Activities : Make a Ladybug Storyboard!
This flannel board will give your child hands-on practice with math, but in a fun format, full of ladybugs.

Children Learn Best Through Hands-On Learning

Melissa & Doug Classic Wooden Abacus



Children learn math best through hands-on learning. A hands-on approach requires students to become active participants in their own learning manipulating objects in order to understand concepts in a concrete way.

A hands-on approach encourages experimentation and a questioning mind. The hands-on approach is all about exploring ideas to discover meaning and understanding.

The hands-on approach may require that your students get wet, muddy, tired, excited, and thoughtful. WATCH OUT!!!! You may be learning too...

March 3, 2013 is World Maths Day!

Registration and practice is now open!
Unite with students and schools from around the world to set a new world record! The Challenge - to correctly answer more than 182,445,169 questions in 48 hours.

Official Site of World Maths Day

Countdown to World Maths Day!

World Maths Day!: March 3, 2013

Research on Math Manipulatives

Pie Fractions Math ManipulativesMath Tiles


Photo Credit: Rainbow Fraction Circles, Math Manipulatives Available on Amazon
Photo Credit: Square Color Math Tiles Available on Amazon


When I first started teaching math my grandmother gave me the book that she used to learn how to teach in a one room classroom. This book, written in about the 1920's suggested using acorns and stones for illustrating mathematical concepts. The idea of using concrete objects for teaching math is not a new one, it is just the best one and the one that works the best for most children.

Ask the children to make collections of small objects that are interesting to them. Place these collections in your math area and label them. Each day, show the children how to illustrate mathematical concepts with a new collection of objects.

Here are some links to research on using math manipulatives to teach math to young children.
Effects of Learning with Diverse Manipulatives
Using concrete materials to teach mathematics is a long-established pedagogical strategy based on theories claiming that children need concrete referents to develop abstract mathematical concepts.
Math Manipulatives by Louise Johnson
Top math authorities agree that young children learn to understand math concepts best with the use of manipulatives.
Multi-Sensory Manipulatives in Mathematics: Linking the Abstract to the Concrete
Experiential education is based on the idea that active involvement enhances students' learning. Applying this idea to mathematics is ...

Manipulative Mathematics

Math Manipulatives Ideas for Hands-On

These are some of the very best books I have run across for teaching math using math manipulatives for upper elementary aged children.
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Math Games

In order to truly understand mathematics children need many experiences with hands-on concrete objects. Mathematics Their Way by Mary Baretta-Lorton is one of the best resources I have yet found to create and understand the activities needed by young children in order to truly understand mathematics. She explains how to create materials and games that engage for them as well as how to use these in rotating centers.

Read the Mathematics Their Way Summary Newsletter for a sample of this method.

Mathematics Their Way, Spiral-bound Teacher guide plus Blackline Masters


One of our favorite activities is the Rote Counting Group Activity.

1. Choose a counting sequence such as counting by one's from 1 to 7, skip counting by two's from 2 to 12, counting backwards by 10's from 80 etc.
2. Pick a familiar object in the classroom such as the door, flag or calendar
3. Name the object in the room and then close your eyes and count the sequence together aloud.
4. On the final number, everyone jumps and turns with eyes closed toward the object named.
5. Everyone opens their eyes to check.
6. Name a second object and repeat the process. Repeat the sequence over and over without pausing. Keep the final number constant within any one day.
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Workjobs Math Activities

Fun, Hands-on Math Activities

Math Workjobs

Photo Credit: Frog Mathmats
on Flickr, Creative Commons


Mary Baretta-Lorton seems to have been the teacher who invented the idea of Workjobs for the classroom. Each box is labeled and has a math activity inside. There could be apple trees with apples to add or subtract. There could be ponds with tadpoles to hatch or frogs to jump off logs. Whatever theme you are studying can be made into a Workjob. Month by month and year by year it is easy to accumulate 100's of these handy activities which keep your children happily working on their math skills.
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Workjob Math

Hands-on Math Activities

Count to 10! Birthday Cakes

Lakeshore Counting Cakes at Lakeshore Learning
Learn number families to 10. Pick a cake and some candles. Try to find all the ways that you can add to make that number. With cake number 5 for example you can make 0+5, 1+4, 2+3 etc.

I like to give the children a worksheet with cakes on it and have them draw the candles that they find and write the number sentence below the cake.
Math Centers for Elementary school. Teaching ideas for mathematics.
Egg Carton Workjob

Photo Credit: Egg Carton Mathjobs
on Flickr, Creative Commons


Addition problems with regrouping Mathjob
1. Cut an egg carton in half:
2. Open it, on the side that is the top write a problem such as 38+64
3. On the side where the eggs would be, students use math manipulatives to represent each number...

Place 3 pieces in the left side and 8 in the egg section next to it
then underneath, 6 pieces, then 4 pieces.

4. Students can use math manipulatives to solve problem
Remember: if you have ten pieces in one section you need to trade...

Math Mats

Learning the number facts 1-10

Math Mats & More



Math mats are wonderful tools for developing mathematical concepts and reasoning. They are also effective assessment tools, enabling teachers to see how students work through a problem, and allowing teachers to work with individuals or small groups for remediation or enrichment, as needed. Finally, math mat work provides a format for mathematical discussion, encouraging students to use mathematical language as they describe their thinking to other students.
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Fall Theme Math Manipulatives

Unique Math Manipulatives for Fall, Halloween or Thanksgiving

Stringing Bead PatternsAABBB Patterns

Photo Credit: Threading Beads on Flickr, Creative Commons
Photo Credit: 10 is a triangular number on Flickr, Creative Commons


Pick two types of manipulatives and make a pattern. Write the pattern on a paper and see if your friend can replicate the pattern.

Patterns are the basis for all mathematics. These manipulatives can be used to make patterns.

AABBB Patterns

Photo Credit: Melissa & Doug Bead Sequencing Set
Available on Amazon



Patterns made using an ABAB pattern can be used to Skip Count by 2's.

Patterns made using an AABBB pattern can be used to learn 2+3=5 or to Skip Count by 5's.
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Natural Math Manipulatives

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Cookie Jar Math Workjob

Cookie Jar Math

Photo Credit: Smart Snacks Counting Cookies
Available on Amazon



Take 2 cookies from the cookie jar. Write the number sentence on a worksheet. Count the chips to make sure you are right.
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Pancake Math

Flip the Pancake Game

Pancake Math Game

Photo Credit: Pancake Math
on Flickr, Creative Commons


Students use the spatula to snag the flapjack with the correct number of dots as well as the corresponding numeral and put them on the plate with the correct numeral.

Counting: You can also program a plate with a number and let students add the correct number of pancakes.

More Counting: If you made big paper pancakes on plates and program the pancake with a number. Then the kids can add the correct number of pats of butter, strawberries, or blueberries etc. These could be felt, painted Lima beans or flat glass beads.

Monkey Math

Learning Mates Monkey Math



Just hang an equal number of colorful bananas from each of the monkey's hands. If you've done your addition correctly, the monkey will look straight ahead and his arms will be level. If the numbers are not equal, his eyes will be crossed and his arms will be up and down.
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Flash My Brain

Make Cards for Hands-On Math Games

Number Spinners 0-9 (set of 5)


Create your own flashcards for creating math games. Include math manipulatives to create fun, hands-on games to practice math skills. Allowing your children to make up their own games will help your children to understand the math concepts even better.
Flash My Brain
Create and print out your own flashcards.

Hungry Alligator Greater Than Less Than Game

Alligator Math Manipulative

Greater Than Less Than Alligator Math

1. Turn over two cards.
2. The alligator eats the higher number.
3. If the numbers are equal feed the alligator two more numbers.

Greater Than Less Than Math Card Game

Hands-On Learning Card Game

Play War adding a step of deciding which symbol should go between the two numbers greater than, less than, or equal to.
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Skip Counting with Money Math

Hands-on Money Math

Hands-on Money Math

Photo Credit: Counting Coins
on Flickr, Creative Commons.

Pumpkin Patch: Piggy Bank Math Game
I like just how quickly they saw the importance of skip counting, how they were able to count coins quickly, and how simplistic the game is...

Math Gnomes

Waldorf Math Gnomes

The four gnomes represent the four operations, addition, subtraction, multiplication, and division.

I have just started to discover Math Gnomes which are used in the Waldorf method of teaching math. They look intriguing and I will be updating about them soon.
Math Gnome Work
Children can learn all about Roman Numerals using Math Gnomes. The Waldorf method emphasizes the magic in learning. Notice the sticks that the gnomes have placed in front of them to make the roman numerals from 1-5.
Serendipity: Gnomes and Gnumbers: A Mathematical Tale
Once upon a time, in the deepest, darkest recesses of the earth, there lived a clan of four greedy gnomes. The first was as blue as a crisp, clear sky. The second was the shade of a red apple in...
Waldorf Without Walls
Includes movement games, manipulative activities, and beanbag games to teach and
reinforce basic math for Waldorf Homeschoolers, Grades 1-3

Waldorf Math

Waldorf Math Manipulatives

Teaching Mathematics in Rudolf Steiner Schools: For Classes I-VIII



Teaching mathematics for first and second grades in Waldorf Schools: Math curriculum, basic concepts, and their developmental foundation
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Montessori Math

Fish Bubbles

Photo Credit: Fish with Bubbles
on WPClipart


Take a look in the fish tank. Notice how the bubbles all go up. Flat sided glass marbles are used for the bubbles. First lay out fish in order from 1 to 10. The numbers tell the child how many bubbles are coming up from the fish's mouth.
Montessori--Math
A blog about Montessori education

The Eureka Moment!

Unique Ways to Catch Your Student's Attention

Smell the NumbersThe child was trying to do a page of math problems with her nose so close that it appeared that she was smelling the numbers. The teachers asked what the numbers smelled like and was very surprised at the answer. The little girl said that they smell horrible.

The teacher suggested that she simply change the smell.

Photo Credit: Studying Math
on WPClipart



Smell the Math

Finally returning to the child after attending to other students. The teacher asked again what the numbers smelled like? The little girl replied with a smile, "roses".
How could you turn a math lesson into one that explore numbers using all five senses?
The Smell of Numbers: A Real Story
In this blog Limeehai tells of discovering that virtually smelling numbers can lead to mathematical progress and focus. You can't help but be inspired by these blogs.

Photo Credit: Smell by Dennis Wong
on Flickr, Creative Commons

Smelling the Math

It makes me wonder how else we could use the sense of smell in math.

When I teach volume I often use rice or dried beans in a rice table. I might try coffee beans next time. Adding flavoring to water or spices to dried rice.

I wonder how Scratch and Sniff numbers would work? Maybe I will add flavoring to glue when attaching objects to numbers when learning number values.Possibly use lemon glue for two objects and vanilla for three objects.

Maybe when learning math facts we could use scented markers or using pudding with fingers.

Certainly graphing likes and dislikes of certain smells.

We could make patterns of nice and awful smells.(rose, rose, dirty sock, rose, rose, dirty sock)
Scientific Investigation: Math and The Sense of Smell
The Effects of Fragrances on Memory and Mental Performance in School Children

Drs. Rodionova and Minor have investigated the effects of peppermint and lavender odors on the performance of elementary and middle school students in math and spelling. Odors were presented in the classroom while students were working on verbal and math tasks.

Get on the Math Train Track

Train Station MathSubway Math

Photo Credit: Wooden Train
on Flickr, Creative Commons.


Children love playing with wooden trains and trains are a wonderful way to explore numbers. You can count the cars on a train. You can compare prices of tickets or you could move millions of people. Check out the video below.
Business & Commerce Movie - The New York City Subway
Watch a video of how New York City subway moves millions of people every day, thanks to the skills of a team of remarkable people.

Using all five senses makes learning come alive...

No matter what lesson you are teaching, think of the five senses and find ways to incorporate each of them. For example if you are learning addition facts:

1. Write them in frosting mixed with peppermint and then sprinkle on candy sprinkles. (sight)

2. When they are dry run your finger over them. (touch)

3. Scratch along the surface and smell the words (scent)

4. Listen to the sound of the scratching (hearing)

5. Eat your facts (taste)

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Math and Phonics Rods for Hands-On Learning

Jumbo Cuisenaire Rods Class Set



Since these Jumbo Cuisenaire Rods are bigger it is easier for children to use these in the Skyscraper game explained in Math-u-see.

Engage your younger students with easy-to-handle large wooden Cuisenaire Rods that range in size from a 2-cm cube to a 2 cm x 2 cm x 20 cm rod. Includes 3 Jumbo Cuisenaire Rods Mats and 154 Cuisenaire Rods.
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Lenses with more Hands-On Learning ideas

More Fun Hands-on Math Activities

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Cuisenaire Rods make Hands-On Learning Fun

Cuisenaire Rods Intro. Set Wood

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Mastermind

Mastermind Board Game



Mastermind - Use inference and logic to play a game and guess a hidden pattern of pegs.
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Mastermind teaches Hands-On Math Skills

Mastermind is Hands-On Logical Thinking


Mastermind Wooden Brain Teaser Game
Available on Amazon



Mastermind or Master Mind is a simple code-breaking board game for two players.

The modern game with pegs was invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert, but the game resembles an earlier pencil and paper game called

that may date back a century or more.

Cows and Bulls

On a sheet of paper, the players each write a 4-digit secret number.

The digits must be all different. Then, in turn, the players try to guess their opponent's number who gives the number of matches.

If the matching digits are on their right positions, they are "bulls", if on different positions, they are "cows".

-Wikipedia
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Hands-On Math for 4-6 Graders

Family Math (Equals Series)



Children learn and enjoy mathematics by working on challenging and engaging tasks.

They learn algebra, probability, statistics, estimation, logic, geometry, and measurement by developing problem-solving skills and building a conceptual understanding of mathematics with hands-on materials.

The materials can be found in the home.

Hands-on Methods should be used at all grade levels to promote true understanding of mathematical concepts.
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Three Bean Salad Math Problem

Three Bean Salad Math
Sample Problem: Second and Third Grade

I have a three bean salad, made up of lima, pinto, and garbanzo beans. (We'll use dried beans!) They are mixed together to make a salad. Here are three clues that tell you how many beans of each type are in my salad:

There is one lima bean in my salad.

There are half as many garbanzos as pintos.

The total number of beans is odd and less than 20.

How many beans in my salad?

One beauty of good problems is that they can be easily modified to suit the children's interests and abilities. For example, the problem above has three answers. Can you make up clues to another salad that will yield just one answer? No answers? How about an infinite number of answers?
Henri Ducharme.com
Henri Ducharme offers classes to children 2nd to 5th grade in Oakland, Ca. Teachers like Henri Ducharme make learning come alive. If you live in the area check out his classes.

Contact Henri Ducharme

Hands-on Pre-Algebra

Middleschool Hands-on Math Games and Activities

Yahtzee



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Math Journals

Of Course you believe in writing across the curriculum, but in Math Class?

You would be amazed at what this simple activity can do to cement your student's knowledge of the skills being taught.



Don't forget that if you are using Math Journals in a Kindergarten you need to model, model, model. If you are working in a First Grade modeling is still important but should become a more independent activity. Using Word Walls is especially important for making this an independent activity for journal time or as a center.

The students in my class write in their journals after math centers and just before recess. They leave their journals open to the page they have just finished (some may have glue that needs to dry) on a large table. As they finish they can quietly check out each other's journals. After recess we all stand around the table to talk about our journals before putting away our journals and beginning the next activity.



We keep our journals in a bin with the library books. Some children love to read them during Silent Reading Time.

Rather than using prompts I feel that it is important to have children write about the concept in their own words. As they a write, children can raise their hands and I will write words on the board as needed. Often these words are added to Word Walls or to a child's Personal Office.



If you do use prompts, duplicate them and allow the children to glue the prompt into their journals

You will really notice the impact of writing in Math Journals daily as the year progresses. These journals are great for sharing on Grandparent's Day or to occasionally take home to share with parents. You might make them into a Literacy Bag occasionally for homework.

The daily Math Journals are perfect for portfolio assessments, conferences and report card documentation for both classrooms and homeschoolers.
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Why Math Journals?

                                                                The math journal to the right was make by Integer Jim.

Math JournalIn her article Why Math Journals? by Deb Russell she writes...

Journal writing can be a valuable technique to further develop and enhance your mathematical thinking and communication skills in mathematics. Journal entries in mathematics provide opportunities for individuals to self-assess what they've learned. When one makes an entry into a math journal, it becomes a record of the experience received from the specific math exercise or problem solving activity. The individual has to think about what he/she did in order to communicate it in writing; in so doing, one gains some valuable insight and feedback about the mathematical problem solving process. The math no longer becomes a task where by the individual simply follows the steps or rules of thumb. When a math journal entry is required as a follow up to the specific learning goal, one actually has to think about what was done and what was required to solve the specific math activity or problem.

Math instructors will also find that math journaling can be quite effective. When reading through the journal entries, a decision can be made to determine if further review is required. When an individual writes a math journal, they must reflect on what they have learned which becomes a great assessment technique for individuals and instructors.

If math journals are something new, you will want to use the following strategies to assist the implementation of this valuable writing activity.

Procedure:

A journal should be written at the end of a math exercise.
Journal entries should be in a separate book, one used specifically for mathematical thinking.
Math journals should contain specific details about the areas of difficulties and areas of success.
The math journal entries should take no more than 5-7 minutes.
Math journals can be done with children and adults. Younger children will draw pictures of the concrete math problem they have explored.
Math journals should not be done daily, it's more important to do math journals with new concepts in areas specifically related to growth in mathematical problem solving.

Be patient, math journaling takes time to learn. It is critical to understand that math journaling is an entry of the mathematical thinking processes. There's no right or wrong way of thinking!

Math Journal Prompts To Get You Started:

I knew I was right when......

If I missed____________ I would have to__________________.

The thing you have to remember with this kind of problem is........

Tips I would give a friend to solve this problem are.........

I wish I knew more about......

How many times did you try to solve the problem? How did you finally solve it?

Could you have found the answer by doing something different? What?

What method did you use to solve this problem and why?

Was this hard or easy? Why?

Where else could you use this type of problem solving?

What would happen if you missed a step? Why?

What other strategies could you use to solve this problem?

Write 4 steps for somebody else that will be solving this problem.

What would you like to do better next time?

Were you frustrated with this problem? Why or why not?

What decisions had to be made when solving this problem?

What do you like about math? What don't you like about math?

Is math your favorite subject? Why or why not?

"When one has to write about problem solving strategies, it helps to clarify thinking. We will often discover solutions to problems when we write about the problem".

Math Journals BOOST REAL LEARNING



Marilyn Burns is my hero. She showed me how reading and writing relate to math. She writes in such an inspiring way that you can't help but implement her ideas immediately and when you do, you will see an incredible difference in your student's understanding and retention of the concepts that your are teaching.



Marilyn Burns says that, "words can help your students work with numbers

A math journal is one of the best ways to introduce writing into your math class. It helps students stretch their thinking and make sense of problems that can sometimes leave them confused or frustrated.

When children write in journals, they examine, express, and keep track of their reasoning, which is especially useful when ideas are too complex to keep in their heads. By reading their journals, you can evaluate their progress and recognize their strengths and needs. The math journal thus becomes a great learning tool for your students--and you. This is why we think it's good practice to incorporate journal writing in math class."

This is an article from Instructor (1990), published by Scholastic, Inc. on April 1, 2001.

This article is available on Amazon
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Using Art Projects to Create a Math Adventure...

Learn about Integer Jim's Math Journals

Math Journals

When you want to be truly inspired you need to check out the Math Journals created by Integer Jim. I can't imagine children leaving his class who would not maintain a love of math for a lifetime after creating one of these Math Journals.
The Math Squad - using art to make math fun
The Math Journal is a comprehensive and in depth project. It requires a lot of time and effort on the part of the students. For that reason, I use it as the centerpiece of my curriculum; the textbook that I taught from previously, Integer Jim (aka Jim Bennett) now uses as a resource book for problems and homework assignments. As he observes the students were never enthusiastic about the textbook anyway. Now they definitely have something that they are enthused about.

This project is most successful when it is used either as the core of the curriculum or in a situation where there is additional (lab) time. Integer Jim does not recommend that the Math Journal be used as a supplementary project with a class that meets just 5 periods a week. Having tried it he found there just isn't enough time! There are other projects described on his web site that are more suitable as supplementary projects.

Write Your Own Math Book

Write your own Math Text

Most educators now use the Writing Process to teach children how to write.
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Mini Offices for Math

A Mini Office is easily adapted for any child whether in a classroom or homeschooling. You might want to include math vocabulary words that your child would like to spell when journaling about math. You might include the times table, unit measure equivalents, or a clock with movable hands. Think about what skills your child is learning and include these in the Mini Math Office.
Mini Offices
A mini office is a particular application of lapbooks. Each child can make his own mini-office -- a lapbook filled with reference pages for his own learning. The sky is the limit on what you can include. Fill the mini office with the charts that your child needs -- maps, state abbreviations, penmans

Lapbooking and Mini Math Offices

When I look for great ideas for recording the work we do as homeschoolers I look for lenses by one of my favorite lensmasters, Jimmie.

Mancala on eBay

Classic Wooden Mancala Game Board



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Rules for Mancala

Mancala Rules
Additional rules for mancala

Life Size Geometry



Look what you can make with triangles and squares. Check out the angles. Put all that math to work to make a fort that you can really play in.
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Hands-on Learning Books

Hands-On Math!: Ready-To-Use Games & Activities for Grades 4-8



These books are full of Hands-on ideas. I use these books to come up with ideas for centers all around the room where 2 or 3 children can work independently while I work with small groups.

The ideas in this book also are great activities to add to the Take Home Literacy Bags which help parents stay connected to what their children are learning in class.
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Math in the News!

Wolfville School Math Fair
Photos of the math fair projects done by grade nines and graders including games, puzzles and art.
Math teacher takes sensory approach
Lisa Scott, developmental math instructor, loves to teach. Scott has taught at Wesleyan for three years but has taught math for a total of 14 years.

"After working with kids individually for so long, I think they all have kind of the same problem with math," Scott said. "Most kids that struggle with math, it's because they're visual learners. Algebra is not something most teachers teach as visual. It's just-here's a series of steps, just do them."

Everyday Math

Card Game Math

Card Game Math

Photo Credit: Card Game Math
on Flickr, Creative Commons

Math curriculum earns an 'A' :: Beacon News :: News
Oswego's elementary school math curriculum is declared a winning formula. They praised the amount of learning, discussion and engagement in math classes. They have been using the "Everyday Math" program for the past 14 years.
Mathwire.com | Addition & Subtraction Games
Addition & Subtraction Games
Featured Game: Face Off! Students place markers on the numbers 2-12. &nbsp Students toss two 6-sided dice, find the sum and remove a marker from that number, if there is still one. The first player to remove all mar
Students Nationwide Improve Math Skills With Everyday Mathematics' Online Games
Everyday Math games reinforce concepts in a valuable and enjoyable way. They are designed to help children practice their basic facts and computation skills and develop increasingly sophisticated problem-solving strategies

Everyday Math Games

The Everyday Math program was designed to teach math in classrooms using games. The children play simple games using dice, spinners, workmats and everyday objects to practice math concepts at independent learning centers. In a classroom setting these are set up as rotation stations. Homeschoolers might use these in workboxes where children can work independently while siblings are working at different levels.

Because of the game format, these math games can be played together by children of different ages and abilities.
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Bridges in Mathematics

I have just discovered a new and exciting math curriculum with fun, creative, hands-on learning activities that keep kids busily working on math at activity centers. The activity centers are introduced in the math corner. Using imagination and real-life examples children learn math in a naturally playful manner. This curriculum is designed for classrooms but could easily be adapted for homeschoolers.
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Links to great Math Resources for Hands-On Learning

Math U See
I used the Math U See program with my 1st graders. Math U See teaches games to make learning math fun and intuitive. The rods included in the Math U See program resemble Cusainre Rods. My children especially liked a game called Sky Scraper where each of the supporting beams had to be a certain number of units high. They needed to add 3+2 for example to make a beam 5 units high.
Activity Resources
A book publisher and distributor dedicated to Mathematical manipulatives for over 25 years!

Algebra in the Concrete

Activity Resources is a company created by a mathematics teacher for mathematics teachers. Mary Laycock has been a mathematics educator for 60 years. Her goal throughout her life has been to provide real understanding of mathematics through hands-on (manipulative) activities.

The products of Activity Resources are a compilation of the supplementary materials that Mary Laycock has found can help a teacher build this type of understanding in students. Mary has written or edited well over 100 of the products. The ones she did not write or edit are products from many other authors and publisher who meet her criteria for quality teaching content.

Mary believes that a concrete (hands-on) approach produces the best understanding at any level from learning to count through calculus.

I ran across Activity Resources and books by Mary Laycock when I was homeschooling my oldest. She was starting Algebra 1 and needed a more concrete was of learning. We did "Algebra in the Concrete" by Mary Laycock which uses Cuisenaire Rods to teach Algebra. I spoke with Mary on the phone about this time. She is a wonderfully kind and gentle person.

Hands-on Learning in the Kingdom

Family Multiplication Study

From Classic Function Machines to Mirror Books and Hundreds Boards, this blog makes learning multiplication come alive.
Natural Math
Have you created any mathematics lessons today?

Pi Day

What is Pi Day

Pi Day is a day to discover and celebrate Pi, the ratio of the circumference to the diameter of a circle.

It is a day to help children learn the true meaning of Pi through hands-on activities rather than just memorizing a series of useless numbers.

Make circles. Find their diameters. Use the diameter to measure around the circumference of the circle.
File:Pi-unrolled.
Pi Unrolled
TeachPi.org
This page is the heart of TeachPi.org. It's where you've come to find more than 50 ideas for ways to make Pi Day entertaining, educational, tasty, and fun. And the list will continue to grow

crafts » contests » eats » songs & arts » donations
» fun with digits » events » projects » lessons » misc.
What does pi mean?
Pi

Pi is the ratio of the circumference to the diameter of a circle

National Pi Day - March 14

A Day to Celebrate Math

Jigsaw Puzzle Pi- Pie 81 Pieces in Tin

National Pi Day? Congress makes it official
The U.S. House of Representatives designates March 14 (3/14) as National Pi Day, in a bid to draw attention to improving math and science education. Read this blog post by Declan McCullagh on Politics and Law.

Math Manipulatives for Hands-On Algebra

I used this method to teach algebra to my daughter when we homeschooled. Because of this method my daughter is now minoring in math in college and was always able to explain math concepts to other students throughout high school and college when their teachers were unable to help them.
Algebra in the Concrete
Activity Resources is a company created by a mathematics teacher for mathematics teachers. Mary Laycock has been a mathematics educator for 60 years. Her goal throughout her life has been to provide real understanding of mathematics through hands-on (manipulative) activities.
Algebra for Homeschoolers
Methods and materials to make algebra come alive. Homeschoolers will love these delightful hands-on math resources...

Donald in Mathmagic Land

Math Video
Donald in Mathmagic Land (Disney) [VHS]
Available on Amazon


From the golden rectangle, golden ratio, and the proportions of the pentagram to learning angles by playing pool, Donald Duck introduces higher level mathematics in a fun and easily understood format.

Children love to watch this movie over and over. Donald in Mathmagic Land focuses on the non-arithmetic aspects of math. I have heard of a math professor and Physics PhD, who likes this movie so much that he shows it on the first day of every class he teaches. This movie can start a real love of math. It shows that, in the words of Donald himself, "Mathematics is a lot more than two times two!"

Donald in Mathmagic Land is the only Disney product that I will recommend.
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Movie Math Duel

Can Movies be considered Hands-On Math Materials?

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dlcass says:

Absolutely. I can still sing the songs from School-House Rock that I watched when I was a kid. .I hope this winds up on the right side (yes/no) as I can't see the choices next to the buttons.

Vicky says:

"Tv disengages the brain" .... that is the most ridiculous thing I have ever heard. There is a reason why there are more and more Interactive Whiteboards in schools these days. Technology is engaging, it grabs their attention and draws them in. The 21st century learner is used to fast moving images and sounds. It IS what they know. The movie is not the bad guy. The teacher is. A movie should be used as supplementary material, integrated with multiple KLA's to provide a comprehensive and meaningful learning experience. A movie is not a hands-on piece of concrete material, however it could be used as inspiration for activities which include concrete materials.

brandy says:

it depends on how you use it. If you are simply watching and not engaging in any part of the activities or putting to use the ideas set forth then it is like any form of knowledge that is merely passed before the eyes but not put into concrete motion. If you though, are using it as a tool to encourage new ways of thinking and experimentation and thus engaging thoughts created by the movie into an action developed by those watching; you can be creating whole new hands on avenues that you may not think of on your own and they may not think of on their own. In moderation and with the proper preperation and encouragement to experiment, they can be a valuable hands on tool.

_Joan_ says:

Let's see . . . you could measure the diameter of the DVD and then calculate the circumference and surface area, OR you can note the total playing time of the movie and calculate the number of times you can watch it before dinner time, OR you can calculate how much each minute of movie-watching is costing you (based on the price of the DVD) and then decide if the movie was really worth what it cost.

Yes, I think movies can be great hands-on math materials!

marsha32 says:

we have some math lessons on DVD that come with worksheets to print out to follow along with the teacher and then more to print off to do on their own. So, in that way I would think of it as hands on as they work with the teacher.

goatlover_and_pescetarian says:

well only if they are about maths... but you dont put ur hands on anything!!

definitely not handson.i guess they show u how to do ur own handson stuff though...

Asinka says:

Nope

Kailey says:

no, i tink that you soulg teach them yourself!!!!!

onefineham says:

I really don't think movies are typically good studies for math because Tv disengages and pacifies the brain. Hands on math learning is a terrific concept as it dramatically increases the parts of the brain being engaged. I've lensrolled your page to my guitar lesson lenses. There is a HUGE correlation between proficiency in music and math... and having read your lens it occurs to me that the child is intuitively learning math concepts playing guitar (string numbers and fret numbers) and learning to associate them with SOUND as well as visual stimulus. Your lens was a surprising eye opener for me this afternoon! Kudos!

 

Teaching Math with Classic Board Games

The Mathematics of Classic Board Games

What can be learned from classic board games? There is an amazing amount of math that is picked up by playing board games. Read the discriptions below which only hint at the many, many ways in which math is used in playing board games.
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Blogs about manipulatives

The Best Learning Equipment May Be in Your Own Home
Manipulatives are those things that crowd our schoolrooms; they teach in a hands-on manner and they usually spill over the bins and buckets that try to contain them ? but most of all they are fun. Manipulatives can be homemade or store bought, ...

More Hands-on Math

Fun Math with Hands-on Learning

Each of the following articles offer fun math games and activities to use with your math manipulatives. Make math fun for your children. Help your children truly understand the mathematics you are teaching. Play games with math manipulatives today!
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Math Manipulatives or Textbooks

How do you children learn math best?

Many people think that math can only be taught by assigning pages and pages of math problems. Often children using this method find that they do not understand what they are doing and are incapable of applying math to everyday situations. There is another way. By teaching with math manipulatives, children experience the math with multiple senses. They are then able to apply the concepts to situations in everyday life.

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Results of Hands-on Math!

Does Hands-on Math Work?

Graduating Outstanding Senior with High Honors

Where did all this get us you may ask? When my daughter entered school for the first time starting in 7th grade she was ready to start Algebra II. She is now a graduating senior at the top of her AP Advanced Calculus class. Her understanding of math is so deep that she is able to explain how to do problems to the children that are having difficulties when the teacher's explanations don't make sense to them.


Photo Credit: Math Degree
on WPClipart


I promote hands-on mathematics because it works, it's fun and it promotes true understanding of the fundamental concepts of math that just pushing numbers does not.

PS: Just a quick update: She is now about to graduate from college with a degree in Mechanical Engineering with minors in Math and Theatrical Costume Design. She has now taken all the math courses offered at the University and still finds that the solid foundation in hands-on math she learned as a homeschooler is what makes understanding the highest levels of math come easy to her. She was chosen one of two students to tutor those needing help at a college math major's level. She often finds that by going back to the hands-on methods we used as homeschoolers is what makes math understandable for these math majors as well.

Hands-On Math is in the Stone Soup Homeschool Network

Stone Soup Internet Directory of Unit Studies
Unit Studies: Stone Soup Homeschool Network - Stone Soup Homeschool Network
A free Unit Study Database, featuring unit studies on nearly every subject!

How do you encourage Hands-on Learning?

How do you have fun with math?

Tell me about your messy project or teaching idea. Take lots of pictures showing how your children use their math manipulatives so that you can share your ideas with us. Please let me know if you would like to learn how to make a page like this one. In the meantime, have fun with math...

  • poldepc May 19, 2012 @ 1:41 pm | delete
    great lens you posted
  • rachelscott May 7, 2012 @ 1:02 am | delete
    Math is my favorite subject.
  • dariameister Apr 18, 2012 @ 11:53 am | delete
    Give them a realistic scenario with a mathematical problem or puzzle :)
  • NinaLouder Apr 18, 2012 @ 6:15 am | delete
    Great lens.
  • Keeah Apr 14, 2012 @ 9:07 pm | delete
    I use whatever, toy, food or activity the child is currently fascinated with turn it into a math activity.
  • TutorAgency Apr 9, 2012 @ 9:02 am | delete
    Thanks for another excellent lens. Where else could anyone get that kind of information in such a perfect way of writing?
  • Pangionedevelopers Feb 18, 2012 @ 7:43 pm | delete
    great info source
  • hntrssthmpsn Feb 10, 2012 @ 9:39 pm | delete
    My son had some initial difficulties with the concept of postitive and negative numbers and the number line. We tried examples using money, beans, drawings... finally, we found ourselves on a staircase with a landing in the middle and inspiration struck. We declared the landing to be zero, and he had the concept down pat in under three minutes. I love the variety of hands-on approaches you lay out here! That "eureka moment" is accessible via such a wide range of paths!
  • jimmyworldstar Feb 4, 2012 @ 11:58 pm | delete
    Hands on math is great for kids who have trouble with numbers. I remember as a kid I used objects and analogies which made it easier for me to comprehend division and multiplication when I started elementary school.
  • gonzalezdenise Jan 30, 2012 @ 8:31 pm | delete
    Loved your lens.
  • OhMe Jan 30, 2012 @ 6:24 am | delete
    I love Math Activities! Great lens.
  • Brite-Ideas Jan 29, 2012 @ 11:42 pm | delete
    fantastic lens!
  • Ramkitten Jan 29, 2012 @ 10:20 pm | delete
    I can't offer anything to answer your question here, but I will say ... another amazingly comprehensive lens on learning. Excellent! *Blessed*
  • Blessedmombygrace Jan 29, 2012 @ 9:46 pm | delete
    Great lens. We have currently hit the Algebra wall in our homeschooling, I will have to check out the resource you mentioned using with your daughter.
  • Donnette Jan 11, 2012 @ 2:05 am | delete
    Another fantastic lens. You are such an inspiration!
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About the Author of this Lens

Check out what else I'm up to when I'm not adding up all the ways to teach math.

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Hands-on Math on Wizzley

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Come write about your experiences learning and teaching using math manipulatives on Wizzley, a fun and easy place to express your opinion:
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Evelyn_Saenz

Hello world. I am a teacher and homeschooling mom. I love to help others find exciting ways to help children learn.

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