Order of Operations Four

What is Order of Operations Four?

This activity allows two users to play a game of order of operations where each player tries to connect four game pieces in a row before his or her opponent does. The players can choose to answer problems which use addition / subtraction, multiplication / division, exponents, and parentheses. They can also choose the difficulty level.

Depending on the order in which the operations are evaluated, answers may be different. To avoid different answers to the same problem the order in which the operations are evaluated must be consistent. Examine the expression

^- 3 ² - 5 * 2

For instance, if you square the 3 before negating it, that changes the expression to

^- 9 - 5 * 3

whereas if you negate before you square then the expression is

9 - 5 * 3.

The order in which operations are evaluated has been standardized to:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right) and where negation is viewed as multiplication by ^- 1
4. Addition and Subtraction (from left to right)

Related Resources

• Activity Order of Operations Quiz
• Discussion about Distributive Property
• Discussion about Order of Operations
• Worksheet Order of Operations Four
• Worksheet Order of Operations Four (doc)
• Worksheet Order of Operations Quiz (doc)

How Do I Use This Activity?

This activity allows the user to practice order of operations with addition / subtraction, multiplication / division, exponents, and parentheses.

In this applet, questions are categorized by a combination of level (which determines the difficulty) and by types of problems listed. For more information on how questions are generated and what each level and problem type means, see Question Types for Order of Operations Quiz and Order of Operations Four.

Controls and Output

• This activity is similar to Connect Four, and is designed for two players. The goal is to have four pieces of the same color connected either horizontally, vertically, or diagonally. One player uses red pieces, while the other player uses black pieces.
• Before you start the game, you can set several options. You can choose how much time each player will have to answer the questions, you can choose the problem difficulty (Level 1, Level 2, Level 3) and you can select the types of arithmetic problems you want to see. Once you have all of the settings as you want them, click the Start Game button.
• After clicking the Start Game button, a new screen appears. Towards the left of the screen is a table that lists the types of questions selected along with the difficulty level.
• To earn a piece, you need to answer an arithmetic question. Enter your answer, rounded to three decimal places if necessary, into the answer textbox:
• After you have entered your answer, you need to click on the Answer button to find out if you are correct.
• The timer on the right-hand side of the board shows how much time you have left to answer. Once the timer turns all gray, the time is up. If you chose "No Time Limit," the timer will simply be gray, and it will not count down.
• If a player answers a question correctly, the player will be able to place one of their pieces on the board. To place a piece, simply click on the column that you want to drop the piece into. The piece will fall into the lowest available slot in the column. If a player answers incorrectly or if time runs out, the other player will have a chance to answer. If neither player is correct the answer appears in a pop-up window.
• If a player -- player Red for instance -- answers incorrectly, the other player -- Player Black -- will be asked to answer the question. If Black also answers incorrectly, the answer will be displayed in a pop-up window and the game will continue with a new question for Black. Note that whether or not player Black answers correctly, it will be Black's turn again, because Black just attempted Red's question.
• If you want to restart the game or change options selected on the beginning screen, you can do so by clicking on the New Game button:
• To change the font size of the question displayed you can, at any time during game play, select one of the three radio buttons on the left side of the screen:
• This activity will automatically record how successful you are at answering the questions. To view the score, press the Show Score button at the bottom of the activity and a pop-up window will appear with the scoreboard. To close this pop-up window press the Close button or click back on the main window.
• To pause the scoring, press the Active button at the bottom of the screen and it will change to a Paused button. To resume scoring, press the Paused button.
• To reset the scoreboard, open the scoreboard using the Show Score button and then press the Reset button.

Description

This activity allows two users to play a game of order of operations where each player tries to connect four game pieces in a row before his or her opponent does. The players can choose to answer problems which use addition / subtraction, multiplication / division, exponents, and parentheses. They can also choose the difficulty level. This activity would work well in groups of 2 for about 15-20 minutes.

Place in Mathematics Curriculum

This activity can be used to:

• Give students practice with basic math skills.
• Develop students mental math skills.

Be Prepared to

• Explain how to apply the order of operations.
• Encourage students to try more difficult problems and decrease the allowed time.
• Prevent any disputes and taunting between winners and losers.
• Explain why an exponent takes higher precedence than a negation.
• Explain why negation is considered to be an operator.

Related Resources

• Activity Order of Operations Quiz
• Discussion about Distributive Property
• Discussion about Order of Operations
• Worksheet Order of Operations Four
• Worksheet Order of Operations Four (doc)
• Worksheet Order of Operations Quiz (doc)