# Math Art & The Right Side of Normal

I’m currently purging the schoolroom, starting to prepare for our move this summer. While cleaning out, I found these pictures I created long ago with my oldest daughter.

Ten years ago she was almost 7 years old.  To say she was struggling with math is an understatement; no matter how much we worked on math, especially facts, the next day all would be forgotten.  Zero retention.  I began doubting my ability to teach her, especially since she was also struggling with reading.

Fortunately for both of us, around this time I also stumbled upon a yahoo group run by Cindy Gaddis at The Right Side of Normal.  I learned so much from her and the other moms on the group.  (The yahoo group has pretty much died out, but the Facebook page is still active, and her book and website contain wonderful information.)  My child was absolutely a “resistant learner,” and thanks to Cindy this was the beginning of learning to work with my daughter, rather than against her.

We dropped all formal math curriculum and began to play.  These pictures are the very first thing we created, a treasure for me as they mark the beginning of my journey as a teacher of (and learner with) my children, not just an instructor.

# Math Art Week 4 – Division Facts

This “division tree” is similar to the multiplication leaves from last week. The first step in this project is to cut circles of different sizes from varying types of paper.  If the student struggles to cut circles, circle punches can be used, or they can be cut ahead of time by the instructor.  (Some of my students wanted to make their shapes more like leaves than circles.) Next, arrange the circles in stacks; use the term “divide” as much as possible: “Divide your circles into 3 stacks?  What about 4?  How many circles are in each stack? Can you divide them evenly without any leftover?”  Once the student grasps the concept of dividing, proceed with the project.

#### Materials

• various colors and types of paper*
• scissors and/or circle punches
• glue or mod podge

*We used scrapbook paper for the background, colored paper for the tree and circles, and some origami paper for the decorative bits. In the picture above, origami paper is used for the top 2 layers, which makes it difficult to distinguish that there are 2 layers!

#### Directions

1. Cut and divide circles as describe above.
2. Decide on a permanent arrangement / number of stacks.
3. Cut a tree to match the number of stacks.
4. Glue all parts to a heavy piece of paper.
5. Create a label to show which division fact is being illustrated.

# Math Art Week 3 – Multiplication Facts

This week in Math Art we created an art panel to illustrate a multiplication fact. Our plants had leaves broken into 2 sections; each section was doodled differently.  The students multiplied the 2 sections by the number of leaves they created to figure out their math fact.

#### Materials

• cardboard pieces from boxes
• gesso
• various paintbrushes
• acrylic paint
• plain colored paper for leaves and stem
• decorative paper
• mod podge
• fine tip permanent ink art marker, such as a Sharpie Fine Point Pen*

*It is important to use a permanent ink pen, or the doodles will smear when mod podge is applied.

Directions

1. Paint cardboard with gesso to prime it.  Let dry.  (Use hairdryer to speed up drying time).
2. Paint a background color on cardboard with acrylic paint.  Let dry.
3. On colored paper, draw leaf shapes.
• Divide each leaf shape into sections.  You may choose 2, 3, 4 or more sections.  Each section will be doodled differently.
• If you are working on a specific math fact, instruct the students to divide their leaves into that number of sections. For example, if you are creating, 6×4, you may have 6 leaves each with 4 sections, or 4 leaves each with 6 sections.
4. Decorate the leaves by doodling each section with zentangles.
5. Cut out a slightly larger leaf from the decorative paper to mount under the doodled leaf.
6. Cut out a stem shape.
7. Use mod podge to apply all shapes to the dried cardboard.
8. Write out the math fact and mod podge it on the cardboard.

# Math Art Week 2 – Fractions

Our project this week was based on the book “Picture Pie” by Ed Emberley.  Picture Pie helps the reader create simple pieces of art based on the fractions of a circle.   While these look simple, the execution can be quite tedious.  Below are the details for a simple bookmark.

“Fraction Fish Bookmark”

#### Materials

• black construction paper, cut in 2″ strips for bookmarks
• colored or patterned paper for circles
• 1″ circle punch
• scissors
• glue
• laminator (optional)

#### Directions

Teach a short lesson on the fractions of a circle.  Have kids use the circle punch and scissors to cut up and sort fractions.

Choose pieces for the Fraction Fish bookmark. This project requires 12 quarters and 2 eighths.

Arrange pieces in desired configuration.  Glue onto bookmark.

Let dry.  Laminate if desired.  (If you choose not to laminate, press the dried bookmark until all pieces are nicely flattened).

# Math Art Week 1 – Number Bonds

This summer we are hosting a small “Math Art” class for a few of our friends.  Each week we will create a math-themed art project (or an art-themed math project!).

Ways to Make “10”

For Week 1 we created a mixed media board that illustrated a Number Bond.  Each student picked a Number, then cut numbers out of newspaper and magazines to show at least 4 “ways to make” their chosen Number.   The ages of these kids were from 7 to 11 years old.

#### Materials

• cardboard
• various paintbrushes
• Mod Podge
• papers to create a background (scrapbook paper, newspaper, old worksheets)
• acrylic paint
• small container to mix paint with water
• wax paper
• old magazines and newspapers
• scissors
• pencils

#### Directions

1. Cut pieces of cardboard from old boxes.
2. Use a paintbrush & Mod Podge to paste on a background.  We used old math worksheets & tests. Tear paper to fit. (If you haven’t used Mod Podge before, just paint the cardboard with a thin coat, place your piece of decorative paper, then paint another thin coat on top.  Continue layering.)
3. Let dry, about 15 minutes if the Mod Podge is a thin coat.  Trim edges.
4. Paint the background with watered down acrylic paint.  If the paint is too thick to see the background, wipe some off with a towel.
5. Let dry.
6. Have each student choose a Number.  On a piece of paper, have them list at least 4 “ways to make” that Number.  Provide magazines, newspapers, and scissors to hunt for numbers.  (The weekly ads are a great source!)  They can keep track of the numbers they have found by laying them on the paper where they wrote their answers.
7. When the background paint is dry, use a pencil to sketch the body of a dragonfly.
8. Paint the dragonfly body with acrylic paint (NOT watered down!).  I place a dab of red, yellow, blue, and white paint on a piece of wax paper for each child, and let them mix colors as they wish.
9. Let dry.
10. Have each student look through magazines to find a pretty pattern for wings.  Cut wings and set aside.
11. Once the paint is mostly dry, use Mod Podge to attach the numbers and wings.
12. After all paint is completely dry, you can Mod Podge over the entire piece as a finish coat.

# Learning Fractions Through Art

One of my areas of frustration with early math learning is fractions.  There’s only so many times we can break a candy bar into pieces, or cut a pan of brownies, or slice a pizza.  Why are all the fraction activities based around food?

The Idea

Explore fractions through art projects.

The Execution

Last week we completed two art projects where we incorporated fractions as a natural part of what we were creating.  The first project was based on Ed Emberley’s Picture Pie book.  I used a large 1-inch circle punch and punched a pile of circles in different colors.  The kids helped me cut some of the circles into halves, quarters, and eighths.  First, we made some of the animals in Picture Pie.  I made sure to use “fraction speak” when asking my kids for pieces: “can you hand me three eighths in orange for the bird’s wings and beak?”

Bird from “Picture Pie.” Age 5

A few days later my daughter asked to do some more Picture Pie.  We looked at some of the fancy mosaic pictures, and she decided to create her own “Christmas Picture.”  Note that after she glued her mosaic, she embellished her picture with some fraction-esque drawings.

Age 7

Later in the week we incorporated more of fourths and eighths into our daily Doodles.  I taught the kids a new pattern we called “Flying Saucers.”

Flying Saucers is in the bottom right quadrant.

We practiced Flying Saucers on scrap paper before starting our Doodles.  Even my 5 year was able to “draw an oval, then draw one line down, draw one line across, and draw four lines from the center out,” breaking the oval into eighths.  Before I even mentioned it, the kids had a collective light bulb moment where they shouted out that we were drawing eighths!  None of them chose to use the new pattern in their daily Doodles, but I later discovered this picture that had been created during free time:

The Extension

We will be returning to these projects later in the year to learn twelfths.  We will also add in fractions from squares and rectangles.

I would like to create some mixed media pieces (cut and paste, markers, pencils, etc) using the ideas we learn from Picture Pie and our Doodles.  Kandinsky is a good inspiration for these pieces.

Composition 8 by Kandinsky

This is one of the first math activities I do with my children, usually starting around age 4 or 5.  It is simple enough for little ones, but is easily customized for older kids as well.  (See The Extension below).

The Idea

Use things found in the natural world (or the child’s world!) to expose him to early addition.  We memorize all the “doubles” math facts early on.  Later they can move to “doubles +1,” “doubles-1,” etc.

The Execution

Print pictures that show doubles addition.   If you are artistic, draw a picture.  If your child is artistic, let him draw a picture.  (To find pictures on the internet, search Google > Images.  Then choose Search Tools > Type > Line Drawing.) You can use paint, handprints, stamps, or any other medium your child enjoys. Label and write the math fact on the paper.  (See picture above).  In the early years I will usually label and write for my kids.  As they get a little older and better at numerals they can do it if desired. Display the picture for reference, or slide it into plastic protectors and make a “math fact book.”

Examples:

2+2=4

Any 4 legged animal.  Label the legs “1, 2, 3, 4.”  Others ideas: car.

3+3=6

Insects, like this Bumblebee.  Label the legs “1, 2, 3, 4, 5, 6.”
Other ideas: construction vehicle, train, flowers.

4+4=8

Spiders, like this one.  Label the legs, “1, 2, 3, 4, 5, 6, 7, 8.”
Other ideas: trains, flowers with 2 layers of 4 petals.

5+5=10

Trace 2 hands or 2 feet. Label the fingers/toes “1, 2, 3, 4, 5, 6, 7, 8, 9, 10.”
Other ideas: flowers with 2 layers of 5 petals.

6+6=12

A dozen eggs.  Label the eggs, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.”
Other ideas: flowers with 2 layers of 6 petals.

10+10=20

Trace 10 fingers and 10 toes. Label.

The Extension

Teaching strategies using “doubles.”

Once the child knows the “doubles” facts well, she can practice them on worksheets using doubles.

This same method can be used for older children to investigate multiplication facts.

# Drawing Spirolaterals

This activity can be done with any young child who can count and draw a straight line.  However, the math behind it is quite advanced, for the curious student who wants to dig deeper.

The Idea

Learn to draw spirolaterals, or “square spirals,” to explore the intersection of pattern and numbers.  A spirolateral starts with a segment of length 1, then turns to create a segment of length 2, then a turn and length of 3, etc.     End results vary based on the length and number of segments.

Spirolateral of 1,2,3,4,5,6,7,8,9.  The black dot is the starting point for the square spiral.

The Execution

Supplies

graph paper
pencil & eraser
markers

Read through this tutorial on How to Draw Spirolaterals.  Draw with pencil until you get the hang of it and start seeing the patterns.

Older children can start with regular graph paper.  Younger ones benefit from larger squares, such as this 1/2″ grid paper from Print Free Graph Paper.

The triangular spirolaterals are best for older children, or in pencil … it took me a few tries to get them right!

Some questions to explore:

Why do the spirolaterals based on multiples of 4 not work out? (Because you are making a square with 4 sides, and thus ending back where you started).

What other patterns do you see?

What happens if you skip numbers? (1, 3, 5 instead of 1, 2, 3, for example)

The Extension

Online software that can plot basic spirolaterals

Mathematical Definition:

From Wolfram: Spirolaterals as a subset of Mathematical Images

Inspiration for further exploration (from Robert Krawczyk, the spirolateral expert)

Curved Spirolaterals

# Hundred Board Math

There are two schools of thought concerning early math.  One is to teach memorization early and allow understanding to dawn later.  The other is to teach understanding first and allow memorization to occur naturally through use.  We tend to fall in the second camp, although I will say that it likely depends on the child.  Most of our Math Activities create an environment where the child has a chance to explore and make connections naturally.

The Idea

Use Hundred Boards, coins, and counters to allow children to explore numbers.

The Execution

Counting From 1 to 100

Place pennies on numbers from 1 to 100. As simple as it seems, this activity seriously entertains my kids for a good 15-20 minutes or more. You can start this activity as soon as the child understands not to eat the coins! It’s not important they do it in order at first, but at some point you may wish to model it that way. As my children have done this activity (from ages 3 to 6) their knowledge of number sequencing has grown. Not only do they learn to count to 100, but they notice the transitions from 9-10, 19-20, etc. They practice ending a row, then moving down and left to start a new row. They start to understand that “12” is not the same as “21,” and have a concept of the 20s, the 30s, etc.

Fill the board with pennies. Have the child count out 10 pennies from a row, and trade it in for a dime. Place the dime on the 10, 20, etc. This activity is a great pre-concept for regrouping (carrying and borrowing).

Skip Counting

Use transparent plastic counters instead of pennies.  Place counters on 1 to 20.  Remove every other counter.  Count out loud the numbers that are covered.  Practice evens, odds, count by 3s, 4s, 5s, etc.

Example: Using the transparent counters, place 3 counters on 1-3.  Ask the child to add 2 more counters.  On what number do they end?

Free Play

Bring this activity out occasionally without instructions.  Let them explore and discover.  My kids like to put pennies on all the numbers that have a 5, have a 2, etc.  They also like to make patterns.

The Extension

After spending a few months playing with the board, start to translate the concepts to paper.  We will perform the activity on the board (like Simple Addition) and then write it on paper as we go.  If the work on paper is confusing, go back to just the manipulatives, and try again in a month.

Trading Pennies for Dimes is an activity you will want to pull back out when you start regrouping with addition (I’ll post an example of this activity at a later time).

# Mixing & Measuring

The Idea

Free play with different measuring equipment to learn (1) how liquid measurements are related to each other and (2) the technical parts of accurate measuring.  One child of mine is very much into precision.  He had a grand time figuring out that 5 mL=1 tsp, 3 tsp=1 Tbsp, 1 Tbsp=15 mL, etc.

We also threw in the Floating Paper Clip Experiment for fun.

The Execution

Supplies:

• measuring spoons
• small measuring cups (from liquid medicines)
• large measuring cups
• water
• food coloring
• thick towel on the table
• optional (if you have it):  chemistry glassware

Add food coloring to the water to make it easier to see.  Mix, measure and pour.  Add more water to the colored solution when too much gets spilled.  We spent about 2% of the time actively discussing measuring points, and 98% of the time gleefully pouring and spilling.

The Extension

To continue exploration, mix several solutions with different colors and allow color mixing.