Tuesday, September 23, 2014

DIY Math Skip Counting Manipulative Tutorial

This very easily made manipulative for skipping count that I found on pinterest  has become a favorite with many parents on some of the Facebook group pages I post on.  So  I would like to share a DIY tutorial of it here on my blog. This manipulative is taken from a traditional Waldorf math lesson that is done with colored chalk on the board by a teacher while they tell the story of the relationships of patterns to numeracy.   My husband Mike, did this project it in about an hour and since I had some of the materials on hand like the dowels and number stickers the cost was only $1.75 for the wooden circle piece at the craft store.  I find self adhesive number stickers at the scrapbooking section but you could use a sharpie or craft paint. or even a water color vegetable based paint and polish it down with bees wax to seal and finish for a natural manipulative desire.  You could do it on paper as well.  I will share ideas about cheaper methods below.

The Manipulative being used to count by threes.


One Round wooden plaque  (size it for your learner's small motor needs)
10 Wooden peg dowels with the rounded nail head ends
Some kind of wooden craft glue
A drill with a bit
Number stickers 0-9 or paint or permanent marker
Small balls of colored yard
Ruler / Compass/ Protractor
Pencil/ Paper/ Scissors 
Husband that will completely take over project while you have a glass of wine (Optional)

 One of his 1st steps was to trace the circle on top of the wooden base to paper and cut out a circle as a kind of temp plate so as to get the dimensions of the fractions segments to be equal.  He did not want to draw the line segments out on the wood to get the dowels precisely right, so he did it on paper and scored through the paper onto the wood after he found the center and did the geometry of where the 0 though 9 numbers would be.
 Then he checked his work and followed his pattern's dimensions with the five lines through the middle of the circle.  This was as hard as it looks but he did get it precisely right.  An educator could easily turn this into a practical lesson of geometry.  How to find the center of a circle and how to divide that circle up into 10 equal parts. One of my favorite exercises to do with young children is to imagine how the 1st humans discovered and recognized a circle.  Was it a animal tied by a rope to a stake in the ground that made them see the circle shape the very first time?  How would an animal make a circle like this? String and stick circle making exercises could be incorporated to introduce how people solved problems of math with simple low tech tools and "how did they figure it out" discussions make math fun.  Imagining primitive people doing this is engaging for young learns.  A wonderful book to read aloud to learners on these subjects is "String, Straight-Edge & Shadow- The Story of Geometry" by Julia E Diggins HERE
So the way he did this was to take 360 degrees ( a circle) divided it by ten (10 segments) giving him 36 degrees for each segment from the center point.

 An extension of this geometrical problem solving exercises could be created as an open-end project on this of finding the center and dividing the segments for older children. You don't even need the wood manipulative if they can make a circle and divided it into 10 equal fractions you could do the patterns with colored pencils on paper circles. Create a 36% angled template and a circle and let younger learners trace on to the circle with their templates of the small angled fraction segments. They can label the numbers and then draw all the patterns the numbers make with different colored pencils.
After the math puzzle is solved and the 10 points marked it's time for drilling out the space under the marks
Mike says to figure out which drill bit to use he matches the wooden peg base to his drill bits till he finds one that matches.  He then practiced on a piece of scrap wood to see how it would work first.  He also recommends a trick of putting a piece of tape on the drill bit to mark how deep to drill and to make each hole uniform.

 He just used a wooden glue after he drilled out the holes.   He did end of tapping in the dowels with a rubber ended hammer just to make sure they were snugly in there.

adding the 1st peg

Stick on your numbers
Make sure you have the zero on top and wait for the glue to dry.  Then get your small ball of colored yard and start skip counting.

I like the three times lesson as it shows a wonderful star pattern and the kids love to see how their answers form patterns with this manipulative. Make sure you loop the string around the peg dowels. Also be aware and show the child, as they progress, how as they take the 3 string off, if they counted all the way up to 3 x 10 = 30, that they can then go counter clockwise and do the 7 times skip counting and the last digit of the skip counting series will be the number of they are taking the string loop off.  Its a fun a ha moment for kids to discover.  I think it is easier to see these patterns with skip counting by one and then taking off the yarn to skip count nine.  Most kids know number nine has some tricks and it may help them see the pattern.  I use multiplication labeled arrays or a times tables chart on the table so if my son gets confused on the numerical language or sequencing of what he is doing he can reference it with a visual aid near by and get back on track and self correct.  Again empowering and adjusting the learning lens to abstract thinking, using rhythmical language, visual cues and both hands activity across the midline all work together working together to mastery of the process. Retention of these math facts through visual recognition of the patterns they may help students who cannot memorize their math multiplication facts in traditional ways.  The best part is, it makes math fun while showing patterns in a simple inexpensive way.  Waldorf educators do this circled skip counting on chalk boards too and it is very beautifully rendered.  Go back to my link to Pinterest to see examples of this.

If you use different colored yarn for different numbers you can layer patterns too and see common denominators.

The green string is on the three's and the orange sting is marking the six's times.

My son is very serious here but he does like this work

This is a extension of using a knitting loom.

My son said it is like a trampoline and bounced his hand on it.

Just a note on some of my languaging used here and why I love manipulatives.  Skip counting is the pattern of numerical order of the multiplication tables.  If I count by twos or threes or fours I am skip counting. Using a manipulative to see an abstract concept of say counting by 7's helps the child see a pattern. Why use manipulatives? They work for us.  It's that simple.  Memorizing multiplication tables is usually done by drills, worksheets and rote memorization of the facts.  It takes effort and practice and for spatial learners, such as my son. A sensorial manipulative allows him to see a abstract relationship connection to what he is memorizing and create a visual road map to "the big picture" of what it could mean is crucial to his motivation to struggle through the tedious for the reward of where math can take his brain and what he can do with those basic math facts. Cognitive research shows not everyone learns the same way.  From my own math educational experience often I had no concrete understanding of what I was memorizing.  A manipulative or material that allows the child to visually see what they are counting has obvious benefits. Montessori classrooms are filled with math and other manipulative and these tools are consider the curriculum.  This wooden item is a Waldorf method to teach children the relationships between patterns and math.  The connection the learner makes with these manipulatives forms a bridge to more complexed conceptual thinking skills and hopefully a passionate enjoyment of geometry.  I also see my son learn that thinking requires effort, effort is worth the work and it can be fun along the way.  The process of  learning math can be joyful.   Just look at his smile below.

Another variation with pattern blocks my son created

 The most important part of why I do what I do is these looks from my son.  He loves learning this way.  He uses what he learns in his own studies of art, drawing spaceships and futuristic communities in space using these shapes and patterns.  He can synthesis what he learns and make it meaningful to him in his own learning and interest.  My goal is for him to be a lifelong learner and I think that making math enjoyable, practical and sensorially engaging is working at that goal.
Conor's hexagon space station drawing.
Here are some of our reference materials and supplemental lesson materials.

skip counting lesson