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

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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

 

Order of Operatiosn (PEMDAS)

By Brigid Del Carmen

In middle school math, students are required to memorize many formulas and processes, and using acronyms can be very helpful with these tasks. One such acronym, PEMDAS, can be used to remember the steps for Order of Operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, which is the order students must follow when finding the value of expressions. Here's how to practice PEMDAS, and help your middle schooler complete her homework in half the time!

What You Need:

• multi-colored markers
• paper/pencil

What You Do:

1. At the top of the paper, ask your child to write the acronym PEMDAS, using a different color marker for each letter. Next to the word, write the symbol for the operation. Parentheses ( ) Exponents n² Multiplication • Division ÷ Addition + Subtraction -
2. Write a simple expression: 20 - 2² + (4 • 2)
3. Help your child find the value of the expression one step at a time.
   • Start with P.
   • Say: “Are there parentheses?” (yes) Solve what is in parentheses first, rewrite expression: 20 - 2² + 8
   • Put a check next to P.
   • Say: “Are there exponents?” (yes) Compute the exponent, rewrite expression: 20 – 4 + 8
   • Put a check next to E.
   • Say: “Is there multiplication or division?" (no)
   • Put a check next to M and D. (Note that if both of these operations did occur in the expression, they would be computed in order, from left to right. Multiplication and division stand on equal footing, as do addition and subtraction, and are always computed in order of appearance.)
   • Say: “Is there addition or subtraction?” (yes)
   • Solve, computing from left to right. In this case, subtraction (20 - 4) would come first, followed by 16 + 8.
   • The answer is 24.
4. Continue writing simple expressions, encouraging your middle-schooler to use PEMDAS as a checklist.

Tips:

1. Once your child has mastered simple expressions using PEMDAS, ask her to find the value of one expression two different ways. Compare the answers and note how important it is to follow PEMDAS.
2. Post PEMDAS on the fridge or bulletin board to be sure your middle-schooler doesn’t forget this very important acronym.
3. Come up with a phrase, such as "Please Excuse My Dear Aunt Sally" to help with remembering this important acronym!

Set Up Shop with Algebra!

By Brigid Del Carmen

One way to make variables and expressions more concrete for middle school students is to use real-world examples. Using items around your house, create a “store” and set up expressions to represent the cost of the items. It takes just a few minutes to set up, but this activity will have lasting effects. Those once abstract and confusing variables and expressions will now represent real-world thinking – and real-world shopping!

What You Need:

• Sticky notes
• Black marker
• Household items, such as books, playing cards, paper clips, cucumbers, apples
• Paper and pencil
• Clipboards (optional)

What You Do:

(b) book = $10.00

(n) napkin = $.25

(y) playing cards = $1.00

(a) apple = $.90

(p) paper clips = $.10

(s) spoon = $2.50

(f) forks = $3.50

(w) water = $1.75

(d) soda can = $1.50

(c) cucumber = $3.50

2(10.00) + 3(3.50)

20.00 + 11.50

31.50

1. Set out several household items (1 of each) and label each with a variable and a price (on sticky notes). For example:
2. Begin the activity by explaining to your child that every time you are shopping, especially at the grocery store, you write expressions “in your head”. It’s really simple if you think of writing expressions as just writing out what you are thinking as you shop.
3. Explain how you would set up a simple expression to represent the cost of one item.
4. Say: “I want to buy 3 apples.
5. First, I set up an expression to represent the cost of the apples: 3a
6. Next, I calculate the cost of the apples by filling in the price of each apple: 3(.90) = $2.70
7. Now, demonstrate how you would set up an expression with 2 terms.
8. Say: “I want to buy 2 books and 3 forks.
9. First, I set up an expression to represent the cost of both items:
10. 2b + 3f
11. Next, I calculate the total cost of the items by filling in the price of each item:
12. Continue providing examples, each time adding another item. Once you feel your child has an understanding of the process, it’s time to send him shopping! Give your middle-schooler lists of items and the quantity for each. Ask him to set up expressions and calculate a total for each shopping list. Extend the activity by asking him to predict which list will be the most/least expensive before solving.

Tips:

Review by asking your child what each expression means. For example, 2f + 8s + 3p means: the cost of 2 forks, 8 spoons, and 3 paper clips.

Take your child to the grocery store. Give him a notepad and, as you shop, have him write expressions to represent the cost of what is in the cart. For example, if you are buying 4 cans of tomatoes, the expression is 4t. If each can costs $.80, he should evaluate the expression: 4(.80) = $3.20. Ask him to estimate the total cost of the items in your grocery cart before you check out. Challenge him to come as close to the actual total as possible.

Simplify Fractions GAME

Race to simplify fractions in this fast-paced game! Simplifying fractions is an essential skill for every math student from fifth grade onward. Students need continual practice with simplification in order to successfully be able to add, subtract, multiply and divide fractions. Play this game again and again and work towards mastering this important concept!

What You Need:

• Deck of playing cards (with face cards removed)
• Even number of players
• Paper
• Pencils

What You Do:

1. Create a fraction bar sheet by drawing a line across a piece of paper. 
2. Set up the game so that the players face one another. For each pair of two players, you'll need to create a separate fraction game board.
3. Shuffle the deck of cards.
4. Distribute the deck evenly between the two players.
5. Have the players place their decks face down in front of them.
6. Players should begin by simultaneously turning over a card from their decks and place it on the fraction bar sheet. Each player should place one card above the fraction bar. The cards above the fraction bar represent the numerator.
7. Then, players should place one card below the fraction bar. The card below the bar represents the denominator.
8. There should be a card above the bar and a card below the bar, giving you four cards total.
9. The first player to correctly simplify the fraction shown by the cards wins all four cards. If a tie results, split the cards evenly.
10. If the fraction can't be simplified, each player should collect the card that the other player put down and position it at the bottom of his deck.
11. Play continues until one player has accumulated all of the cards.
12. Alternatively, you could set a time limit on the game. When time is up, the player with the most cards wins!

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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!"

Mayflower Math

By Julie Williams

Okay, it’s true: the Mayflower is generally a social studies topic, not a math one. But if you’ve got an elementary school math maven, we think the historical record also contains some great opportunities for number practice!

Here’s an activity to pull out for Thanksgiving, as everyone talks about the history of the holiday. You’ll notice that some questions are much easier than others, and that’s on purpose. We think that sixth graders should be able to handle the whole thing; but younger kids may also be able to do parts (and feel very proud of themselves in the process!). Of course, parents, you’re also welcome to “hop on board” as well!

What You Need:

• “Mayflower Math” worksheet (download here)
• Pencil
• Scratch paper for working out the problems (Psst: parents, you may be tempted to use a calculator, but we recommend some old fashioned pencil and paper figuring to help kids reinforce the math behind their answers.)

What You Do:

1. Before you even put out worksheet or pencils, try engaging your child on the topic of the Mayflower. Remember: elementary classrooms almost always include Thanksgiving books and activities, and your child may know more than you think. For example, does anyone in your family know how many days the ship sailed? How many people were on board? How many were women, men, or kids? How big was the ship?
2. After guessing, download our “Mayflower Math” worksheet and get to work. Don’t worry if your kids skip around—as we’ve noted, these problems vary widely in difficulty. Encourage your young mathematician to try lots of strategies, and to ask for help along the way, too.
3. When you’re done, talk about your answers. You may all be impatient to check right and wrong, but an important math standard is “reasoning”—the ability to track your thinking and explain it. Your math teacher will thank you for the extra care.
4. Want to check your work? Download our answer sheets here: Answer Sheet 1, Answer Sheet 2.

Algebra Tic Tac Toe

By ChristianMiller

Once students hit Algebra, math gets a lot more tricky. In order to build a strong foundation for higher-level math, practice is essential. Try a new approach to working with variables and equations by playing this tic-tac-toe game and watch your kid's math confidence increase exponentially.

What You Need:

• 9 sheets of white paper
• Markers
• A friend

What You Do:

1. Help your child draw a nine square tic-tac-toe grid on each of the sheets of white paper with the black marker.
2. Next, have your child arrange the sheets of paper into a 3 x 3 grid with the tic tac toe grids facing up.
3. Then, take over duties and write a random algebraic equation in each of the 81 spaces. For example: 3x+5= ?  x=8.
4. Have your child and another player take turns trying to solve the various problems contained within the grids.
5. If either player can successfully solve a problem, they can put either an X or an O in the square. 
6. Whoever gets tic-tac-toe on a given sheet by solving three problems in a row on a given grid can turn the sheet over and mark it with an X or an O. 
7. To win, a child must successfully get three sheets in a row.

Helpful Tip: Want to play this game multiple times and really solidify your kid's algebra knowledge? Laminate the sheets and play with dry or wet erase markers.