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.

Face-Off! An Integer Card Game

By Brigid Del Carmen

One way to help your child increase his speed and accuracy when solving integer problems is by playing “Face-Off." In five minutes, you and your child can make the game together and begin an enjoyable “study session”—one that may include prizes!

What You Need:

• 3" x 5" notecards (50)
• Markers
• Scissors

What You Do:

1. Cut the cards in half. Divide equally so both players have 50 cards.
2. Quickly write integers from 0 through 20 on each set of cards (remember to use positive and negative numbers).
3. Shuffle both decks.
4. Now it’s time to “face-off.” Player 1 should lay down the top 2 cards from his deck face up. Player 1 adds the 2 cards, paying attention to positive and negative signs. Player 2 should do the same with her 2 cards. Compare answers. The player with the highest answer keeps all 4 cards (place in a separate pile).
5. Continue playing until all integer cards are used. The player with the most cards wins!

Tips:

• Next time around, play “Face-Off” to practice subtraction of integers.
• Emphasize speed and accuracy when making and playing the game. The point is for addition and subtraction of integers to become automatic.
• Decide on a fun “prize” for the winner (the winner could choose what to have for dinner, for example, or what to watch on T.V). Never underestimate the motivational power of a small reward!

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.

Exploring Technology in the Elementary Classroom

Time Math by Recession Apps LLC

Reference

            Time Math is targeted to children in the second grade.  I could see this app used for students beyond second grade if they were still struggling with telling time.  This app is free and can easily be found on the app store for Apple products.  The specific math area of this app is the concept of time.  This app provides five different levels that can be explored.  The first level provides information on how to tell time.  The user learns what the hour and minute hands are used for.  The next level consists of asking the user “What time is it?”  The user then has the choice to select the intervals that will be asked.  These include: easy (hours), medium (fifteen minutes), hard (five minutes), harder (hours and five minutes), and hardest (hours and minutes).  The user is asked this each time they select one of the four levels.  The app generates a clock with a set time in relation to the difficulty selected and the user is asked to pick the correct answer out of three options.  The next level is “Set the Time” and asks the user to drag the hour and minute hand on the clock to the time that is indicated.  The last two levels are “What time will it be?” and “What time was it?”  Both of these levels require students to drag the hour and minute hand around the clock to reach the requested time. The graphics and design of this app is aesthetically pleasing.  The app is also very easy to navigate and allows for some many different difficulty levels, which is great for users who are just being introduced to telling time all the way through students who are more advanced.  When teaching a lesson about time, I think having this app projected on the board and/or giving each student an iPad to use with this app would be a great way to demonstrate time and walk through some problems together.  Instead of doing a worksheet, students could spend some time going through problems on their own. 

Academic Skill Builders http://www.arcademics.com/games/

Reference

            Academic Skill Builders is a free website with a plethora of fun math games.  The great thing about this website is that the user can select whatever grade level and subject they would like.  The grades range from first to sixth and the subject levels include shapes, counting, addition, subtraction, multiplication, division, integers, money, time, decimals, fractions, ration and proportion, and algebra.  Therefore, this website is great for all elementary students.  For the most part, the grade levels are on point.  This website appears to be set up to allow students the chance to practice math skills through fun and competitive games.  Parents, teachers, and administrators can also be at ease when having students online because the designers of this website were conscious about online safety. “Private” games can be set up with a password, so a student and his or her friends could organize games to play against each other in a private game.  “Public” games can be joined by anyone at anytime but there is no contact between the outside players and the student. The website also monitors player names and blocks inappropriate ones.  One of my favorite games I stumbled across while exploring this website was Jumping Chicks.  This game would be perfect for kindergarten and first grade students because the purpose of the game is to match the number to a pile of leaves that has the same number.  Your chick then jumps to that pile of leaves and the player is asked to complete the same steps again to keep your chick moving forward.  This is a fun and easy way to practice counting from one to ten. If ever in the computer lab or near computers and students finish their work before others, this would be a great website to have students visit until everyone was completed.  Having a math station in the classroom could also promote the use of this website.  Students would be able to select this math website, as opposed to a math worksheet, and have fun while still practicing their math skills.  This website, and the other website and apps I chose, provide visual learners with engaging animations to look at and allows game-based learning in a fun and interactive way.

Funbrain Math Arcade http://www.funbrain.com/brain/MathBrain/MathBrain.html

Reference

            Funbrain Math Arcade is intended for students in grades one to eight; however, after playing through this game at multiple grade levels, I feel that this game should really only be applicable for students in third grade and higher.  The reason I say this is because I do not think that students in second grade or below would have the proper hand-eye coordination and reading skills that are necessary for this game.  I had a hard time doing it myself so I have a feeling that very young students would struggle with the ability to select the right answer and figuring out how the game works.  Regardless, this website is great because it allows students to play in the format of a board game and has 25 different math games for them to play.  I think this would be great to use as a mini math activity maybe once a week.  Students could login with their saved password and complete five rolls on the game board, which means five games.  I would guess this would take around fifteen minutes. Depending on the grade level entered, the games ask students to add, match, adjust height and distance, subtract, multiply, divide, etc. A few things that I wish could be changed about this game is that the levels do not provide a lot of feedback for students who struggle and may need assistance or a hint.  However, the student is allowed to start that game level again after so many attempts.  I do like that the each game is fairly short and keeps the student motivated to win and unlock the next game.  Each game level also provides so much variety that could be tied into lessons.  For instance, one game level takes place inside a pyramid tomb and has images of Egyptian sarcophagi.  This could tie in nicely with a geography and social studies lesson on Ancient Egypt, as well as, reading aloud or independently reading books about mummies, pharaohs and pyramids.  There are a lot of options for using this website within the classroom. 

Todo Math by Enuma Inc.

Reference

This free app is by far the best math app I came across.  I love this app because the logistics and layout are fantastic.  Additionally, this app is perfect for student just beginning math, as well as for students who are up to second grade.  This app covers many specific math areas, such as: counting and cardinality, number operations, mathematical reasoning, time and money, and geometry.  The intended purpose of this app is to allow students to trace numbers and shapes, practice patterning, subtraction, adding, multiplying, and so much more.  I think the number and shape tracing is a great addition to this app; it’s probably my favorite part about the app because it would be such a huge help for students who are just learning how to write their numbers and drawing their basic shapes. I can easily see this app being used within the classroom because of all the great features it has.  The teacher could demonstrate how to use the app and then the students could follow along and complete each number and shape together.  A lot of the levels seem to follow the same order; therefore, it would be easy to have the teacher and young students complete the lower levels together to make sure that every student understands the process and the content.  This app seems like such a great tool to use because of the way it asks students to select the numbers and then draw them as well.  I feel like it reinforces their learning and knowledge. One downfall to this app is that although it says it is free, there are limited levels that can be played on the free version and buying this app is incredibly expensive.  However, I could justify buying this app for $24 each because it is so comprehensive and of high quality.  It also changes displays according to the seasons, which is cute, but could also be integrated into learning the new season each time it changed.  Lastly, this app was built with the classroom in mind.  If teachers do not have the budget to buy Todo Math, teachers may qualify for the school year’s Todo Math Grant Program.  Additionally, this app has a web-based teacher dashboard that tracks progress, students can play Todo Math at home on parents' iPhone or iPad and their progress is synched to your teacher dashboard, and school level management allows for supporting device sharing between classrooms (cart system) and multi-teacher management of school account. 

Reference