Activity: Symmetry of Shapes

Let's find symmetry in shapes! You will need some shapes. You could buy some, or make your own like this: Print out Shapes (In Color) or Shapes (black and white) and cut them out.

Folding Test

You can find if a shape has a Line of Symmetry by folding it.

When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.

Here I have folded a rectangle one way, and it didn't work.

So this is not a Line of Symmetry

But when I try it this way, it does work (the folded part sits perfectly on top, all edges matching):

So this is a Line of Symmetry

An Octagon

Let us try the Octagon (the 8-sided shape)

Is this a Line of Symmetry?

Let's try folding it:

Yes! When folded over, the edges match perfectly

So let us draw it on:

I found another way too::

Tried this	It works!	Draw it on

In fact I found 8 Lines of Symmetry:

Triangles

How about this Triangle?
I tried this fold, but it didn't work:

Can you find any Lines of Symmetry in that triangle? I couldn't.

But how about other types of triangle?

Your Turn

Now it is your turn ... pick a shape and find its Lines of Symmetry.

In fact, try them all! See what you discover.

Final Note: The Circle How about the Circle? Did you find any Lines of Symmetry? In fact the circle has infinite Lines of Symmetry, how about that! Click here for original source!

Math Meets Art: Symmetry Self-Portraits

Click here for original source!

Symmetry is one of my favorite parts of our geometry unit. We always begin by looking for symmetry in the world around us. The perfect book to begin my lessons on symmetry is Seeing Symmetry by Loreen Reedy. It opens my students’ eyes to symmetry that surrounds them in letters, words, nature, and even architecture.  After reading this book, my students love to design their own geometric animals, flowers, and buildings.

Beyond drawing the symmetrical butterfly, however, I like to show my students exactly how symmetrical they are. In order to do this we create symmetrical self-portraits, an activity that uses precise measurement to get beautiful results. Below, you’ll find the directions I had my students follow to create their “other half.”

Materials

• Closeup photo of each student
• 8.5 x 11 white paper for printing
• Paper cutter
• 9 x 12 white construction paper
• Glue sticks
• Rulers
• Shape templates (optional)
• Crayons and colored pencils for coloring.

Step-by-Step Directions

Step One: First, I took a closeup photo of each student. It’s best to take it straight on, making sure the head isn’t tilted to the left or right.

Step Two: Next, I downloaded the photos from my camera and resized them in Microsoft Word so that they took up most of a full page. Once they were resized, I printed them in color.

Step Three: Using scissors, I cut out each head. Having the head trimmed makes it easier to find the line of symmetry for the next step.

Step Four: Using the paper trimmer, I cut each photo in half, straight down the middle. I used the middle of the student’s nose to help me find the halfway mark on each student’s face.

Step Five: Students glued their half-heads onto a piece of 9 x 12 white construction paper.

This next part involves some modeling. Once you show the students how to measure, most can do it with ease.

Step Six: Using the ruler, students pick a starting point and measure how far it is from the line of symmetry. Then they measure that exact same distance on the opposite side, marking the spot with a dot.

For example, Eiki started with his eye. He measured and learned that the inside corner of his right eye was 1.25 cm from the line of symmetry. This helped him know that his left eye must also be 1.25 cm from the line of symmetry. So he measured 1.25 cm and made a dot there. Next he measured the distance from the center to the outside corner, making a dot on the opposite side.

Step Seven: Students continue to measure and mark dots all around the perimeter of their heads. Once they have generated a good amount of dots, I tell the class that they have made themselves into a dot-to-dot drawing and it is time for them to connect the dots! Once the dots are connected, they can really start to see their image emerge.

Step Eight: Next, students began coloring their portraits.

Step Nine: For the final step, students added a background of their choosing. Many used shape templates or rulers to draw symmetrical shapes and patterns. Getting the background symmetrical proved to be the trickiest part for my students, and I will definitely model this step more next time.

 

Symmetry Meets Technology

My class loves the free app Symmetry Lab Basic. This app quickly became a favorite during all the indoor recess we had over the cold winter months. Students use the touchscreen on the iPad to draw creative, symmetrical, kaleidoscope-like works of art.

On the desktop computers, my students enjoyed all the features of Polygon Playground that not only allowed them to create symmetrical shapes, but also introduced them to tessellations.

One of the easiest ways to show symmetry is through snowflakes. My students enjoy making them out of paper, but it is much faster (and neater!) to make them on the computer with Make a Flake.

Books to Try

 

1.G Grandfather Tang's Story

Alignments to Content Standards: 1.G.A.2

Student View

Task

Materials

• A copy of Grandfather Tang's Story by Ann Tompert
• One set of tangrams for each student (see note in commentary)
• A set of tangrams for the teacher (magnetic for the whiteboard or colored to use on a document projector)
• Character worksheet
• Crayons

Actions

• The teacher reads Grandfather Tang's Story to the class. As the teacher comes to each character in the story, note the picture of the animal that is an outline of a shape that can be made with tangrams. Students may need to spend some time looking to see how these outlines represent the animals since they are somewhat abstract. Ask the students if they see familiar shapes as components of the animal outlines--for example, the tail of the fox is a trapezoid and the wings of the hawk are triangles.
• After the class has read the story, the students choose animals from the story to make with the tangrams. The worksheet shows the tangram animals, and when they have made an animal, they color the corresponding shape on the worksheet.
• The teacher can demonstrate for students how to turn and place the tangram shapes as needed to support the students.
• After the students have worked on making 2 or more animals from the book, they can make their own animals.

IM Commentary

The purpose of this task is for students to compose two-dimensional shapes to create a composite shape using the 7 tangram pieces. It is essential that the language the teacher uses during the task is precise to support students' academic vocabulary development. For example, "turn the square so one side is lined up with the shorter side of the rhombus to create the tail of the squirrel."

Trying to make the animals without the internal lines is very challenging, so the worksheet shows how the pieces are composed for each animal. This helps students see the shapes both as a single figure (consisting of the outline and a single region filled inside it) and as a composite shape that can be decomposed into smaller shapes. If the teacher wants to challenge the students, then they can try to make the animals just looking at the outline shown in the book.

As an extra challenge, see if the students can combine their tangrams into the original shape of a large square.

Note: The tangrams can be plastic machine-made sets or students can make them in a preceding lesson. There is a template for creating tangrams attached to this task. If the students create their own tangrams, they will see that the 7 pieces originate from a large square. Making the tangrams for themselves also helps students develop the ability to compose and decompose figures.

Not all of the characters are included on the character worksheet. The students can build these as time permits.

Attached Resources

Character worksheet

Tangram Template

Solution

• If the student completes the fox fairy, hawk, and squirrel, then they will color those three figures:

• There is no single solution for each of the students' own pictures

Click here for original source

Personal Pie Chart

By Chris McAllister

For many kids, the best way to learn about fractions is to represent them visually. Visual learners in particular can get bogged down by multi-step word problems. This activity will help your child tackle those tricky fraction word problems by way of a hands-on method.

What You Need:

• Construction paper
• Piece of cardboard
• Scissors
• Compass or large tin can for tracing
• Index cards
• Pencil or pen

What You Do:

1. Prep for this game by making the playing cards. On each index card, write out a fraction word problem. These are pretty easy to write once you get the hang of it. Here are four to start with. Refer to your child's math textbook for more ideas. Note: Start playing this game with eight as the constant denominator. You can change this up as your child gets the hang of it.
   • Theresa baked an apple pie and cut it into eight pieces. She ate one, and gave one to John. What is the fraction of the remaining pie?
   • Peter has eight pieces of candy. He gave Julie three, Tracy three and Dan one. What is the fraction of the candy that he gave away?
   • Natasha bought eight cookies. She gave two to her brother, two to her dad, and two to her mom. What is the fraction for the number of cookies she has left?
   • Rose has eight baseball cards. She gave two to Tom and two to Michael. How many cards did she give away?
2. Now, help your child to make her own Personal Pie Chart. Use a compass or trace a large coffee can on a piece of colored construction paper. Cut it out. This will be your base. Repeat this step with a piece of white paper. Evenly divide the circle into eight pieces, or wedges. Now, have your child color each of the eight pieces a different color and cut them out. It's fun to play this game with your child, so feel free to make your own Personal Pie Chart!
3. Review fractions with your child using the Personal Pie Chart. Discuss numerators and denominators. Give her a couple of practice runs: ask her to use the chart to show 1/2, 2/6, 3/8, 7/8.
4. Tell your child that you are now going to play a game with her Personal Pie Chart! Drawing from the pile of playing cards, challenge your child to solve the word problem and show you the answer on her Personal Pie Chart. You may need to do the first few together. Take turns drawing cards, and, as your child gets more comfortable, set up a point system for every correct answer.

After your child has mastered denominators of eight, create new wedges for your Personal Pie Chart and playing cards for other denominators. The possibilities are endless!

Collage of Fractions

By Erica Loop

Break out the ruler and brush up on a little elementary math. Don't despair if numerators and denominators seem like a bore to your child. This colorful collage is sure to show him the brighter side of fractions. This is a great activity for kids having a hard time grasping the concept; being able to see and touch fractions helps kids understand fractions more clearly.

What You Need:

• Construction paper in a variety of colors
• Thick black marker
• Scissors
• Ruler
• Pencil
• Glue stick

What You Do:

1. Choose a fraction to start with. It's better to start simple even if your child is confident in his fraction skills.
2. Have him write the chosen fraction on a sheet of construction paper with the black marker. Ask him to point out the numerator (top number) and the denominator (bottom number).
3. Select a shape to represent the fraction, such as a rectangle or triangle. Help him draw the shape on another sheet of construction paper (preferably in a different color) using the pencil and ruler. Make sure the dimensions of the shape are in whole inches, ideally in a multiple of the denominator so the shape will be easy to cut up. For example, if your fraction is 3/4, you could make a rectangle that is 8 inches long, since 8 is a multiple of 4.
4. Still using the ruler, divide the shape up into a number of segments equal to the denominator of your fraction. Using the example from step 3, you would divide the rectangle into 4, 2-inch segments.
5. Have him cut out the whole shape from the construction paper.
6. Flip over the sheet of construction paper that you wrote the fraction on and glue the shape onto the other side.
7. Now have him choose another sheet of construction paper in a different color than the shape. Using the same measurements you used in step 4, draw a number of segments equal to the numerator of the fraction. Using the same example again, you would cut three 2-inch wide segments.
8. Cut out the segments and glue them on top of the shape within the lines.
9. You're done! Go back to step 1 and repeat with a different fraction.

Try attaching all your fraction collages to a large piece of poster board, overlapping them and arranging them in different directions for artistic effect.

What Remains? BINGO

By Ellen Dean

This board game focuses on the art of finding remainders. With a few simple materials you can find around the house, you can create a fun new way to work on an important concept. Your child will start out by creating a bunch of division problems, then he'll solve them and, finally, he'll turn the remainders into a game of bingo.

What You Need:

• Index cards or white paper cut down to size
• Pencil
• Paper
• Ruler
• Counters (plastic chips, pennies, beans)
• Scratch paper

What You Do:

1. Have your child and all other players write a unique division problems on 24 index cards. Distribute the cards evenly among the players and figure out the answers on scratch paper. Double check the answers to make sure they are correct.
2. Write the correct answer on the back of the index card.
3. Create a bingo card by making a grid on paper. The grid should be 5 squares across and 5 squares down, with the center square being the "Free" square. Write B-I-N-G-O at the top of the grid.
4. Read aloud all of the answers on the back of the index cards. Have the players write down the numbers inside the squares on their bingo cards. They should choose which square they wish to write each number in and continue writing numbers in the squares until each square has a number in it.
5. Shuffle the index cards and place them face up in a stack in the middle of the table, so the answers cannot be seen.
6. All players should place a counter on the "Free" space.
7. Read aloud the division problem on the first card and let all the players work out the answer on their pieces of scratch paper. The first player to call out the correct answer gets to use that number on his bingo card.
8. Continue playing until the first player to make a full row on his card shouts, "Bingo!"

Magnetic Division

By Mary Anne Edwards

The mere mention of long division may make your kid cringe. But there's no getting away from it: it's an important fourth grade math skill, and one he needs to know well. The key to conquering long division is lots of repetition and practice, but that doesn't have to mean all worksheets and scratch paper. Make this hands-on game, and explore the fun side of division.

What You Need:

• Roll of blank magnetic strips (with a white surface on one side)
• Magic markers
• Pencil
• Lined paper
• Scissors
• Large baking sheet (or use side of refrigerator)

What You Do:

1. Have your child grab the pencil and a sheet of lined paper and review his multiplication facts by completing the following problems:
   1. 3 x 2=____
   2. 4 x 5 = ____
   3. 6 x 7= ____
   4. 8 x 9 = ____
   5. 9 x 9 = ____
   6. 7 x 4=____
   7. 8 x 3 = ____
   8. 5 x 8 = ____
   9. 9 x 5 = ____
   10. 10 x 10 = ____
2. When he's done, check his answers. If he's a little shaky on certain multiplication facts, it doesn't hurt to try a few more problems.
3. When he’s ready, create the number tiles by writing the following numbers and symbols on the magnetic roll:
   • 2 sets of  numbers 0-9
   • 1 division sign
   • 1 set of numbers 10-100
   • 1 decimal point
4. Snip the numbers into individual tiles with the scissors.
5. Use the baking sheet and magnetic numbers to complete the following division problems:
   1. 250 / 2
   2. 1075 / 50
   3. 6728 / 46
   4. 9258 / 71
   5. 3478 / 62
   6. 8120 / 89
   7. 9671 / 34
   8. 754 / 12
6. Remind him to use the decimal point when needed. When he's done, help him check his answers. As he gets more confident, encourage him to try problems with larger numbers.

Need to practice addition, subtraction, or multiplication instead? No problem: just make plus sign, minus sign, and multiplication signs, too.

Mary Anne Edwards is a freelance writer with teaching experience in Preschool, First, and Fourth Grades. She has also taught Second Grade Title One reading groups.

Graham Cracker Division

By Melissa Dianda

Are you looking for a fun way to teach your child important math concepts? Start with this quick and simple activity that will teach him the concept of dividing whole numbers by fractions—using one of his favorite snacks! Graham crackers are perfect for this activity, since they're easily divided into equal parts…and they make a great tasting reward!

What You Need:

• Graham Crackers (whole can be divided into 2 parts)
• Lined paper
• Pencil

What You Do:

1. First, have your child predict what he thinks 1 divided by ½ is. With a little help from a graham cracker, invite him to find out if he's correct.
2. Hand over a whole graham cracker to your child. Explain that this is one graham cracker, so it represents the number 1.
3. Then, have him divide the graham cracker in half by bending it down the middle. After it splits, ask him to count how many graham cracker pieces there now are.
4. After he responds that there are two, say “That's correct. 1 divided by ½ is 2.” He may looked puzzled, since most division problem answers or quotients are usually smaller than the dividend, which in this case was 1.
5. Now, ask your child to predict what 2 divided by ½ is.
6. After your child responds, have him set the broken graham cracker aside and hand him two more. Explain that now he has two graham crackers, representing the number 2.
7. Then, have him divide the graham crackers in half by bending them and splitting them down the middle. After they split, ask your child how many pieces there are.
8. After he responds that there are 4 pieces, say, “That's correct. 2 divided by ½ equals 4.”
9. Next, explain how to divide whole numbers by fractions without using graham crackers. Multiply the whole number by the fraction that has been reversed. 1 divided by 1/2; 1 X 2/1 = 2, or 1/1 x 2/1 = 2/1, which equals 2. Remind him that any whole number is equivalent to that number, over 1.
10. Have your child try a few problems on lined paper. For example, 3 divided by 1/4 is 3 X 4 = 12. 4 divided by 1/4; 4 X 4 = 16, 5 divided by 1/3; 5 X 3 =15.

Finally, celebrate your child's new math concept with a yummy snack of sweet graham crackers! Try practicing some more math during snack time.

Hula Hoop Times Tables

By Alicia Danyali

If you’re finding it painful to get your child to practice math lessons learned throughout the school year and her skills are slipping, try this mental and physical multitasking game to get your child back into the swing of things. This physical coordination reinforcement activity uses a hula hoop to get the mental juices flowing. It's especially fun with two or more players taking turns and keeping score, but it works just as well with one.

What You Need:

• Hula hoop
• Pad of paper
• Pencil
• Bowl or hat
• Timer

What You Do:

1. Make a list of the multiplication tables your child has learned during the school year. Your child will be reflecting on and reinforcing these lessons as she looks back on what she’s learned. Space these out on the page so that you will be able to cut each item into a separate strip of paper. Once the list seems substantial, cut up the paper, fold it in half, and place it in the bowl or hat.
2. Now let the hula thinking begin! Start by having one person pick a piece of paper from the bowl, read the category out loud and get ready with the hula hoop. The other player will be the note taker, and should write down the times table category and name of the Hula Hooper for score-keeping purposes. Put the paper back in the cup once read, so it can be picked it in the future.
3. The hula hoop player starts hooping, while reciting the times table category that she has chosen. For example, if she has chosen the 6 times table, she should recite "6, 12, 18, 24 ..." as she keeps the hula hoop up. Using a stopwatch or other kind of timer, the note taker keeps track of how long the hula hooper keeps the hoop going while still managing to recite the answers. The turn ends when the hula hoop falls to the ground and stops or the hooper can't come up with any more products.
4. Now the next player gets a turn, following steps 2 and 3, until everyone gets a chance to play and all of the multiplication tables are practiced by each player. If a player chooses a number they've already done, they should place the paper back in the cup and choose again.

Alicia Danyali, BS Elementary Education, taught primary-level students for four years at the International School of Amsterdam, The Netherlands. The last four years of her teaching career, she taught at the Washington International School in Washington, D.C. She recently completed writing a series of children's picture books and is a mother of one young son.