PEMDAS+Puzzle

PEMDAS Puzzle

 * Introduction: **

By completing this unit successfully, students will be able to create and solve equations. Students will deeply understand what algebraic equations are, and through this knowledge, will be able to solve algebraic equations on their own.


 * Previous Knowledge: **

The students will have already learned what an equation is and will have been introduced to the order of operations.


 * Learning Objectives: **

Students will meet the following standards:
 * 6.2.D: Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions.


 * Materials: **
 * Worksheets (to be determined) (1 for every student on days 1 and 3)
 * ‘PEMDAS Puzzle’ game board (1 for every 4-6 students)
 * ‘PEMDAS Puzzle’ note cards with numbers 1-9 and operations +, -, *, /,, and ^n (1 for every 4-6 students)
 * 20 piece puzzle (1 for every 4-6 students)

An example of a pocket board is shown above. This is the "game board" used in the PEMDAS Puzzle game.


 * Instructional Plan: **

Day 1: On the first day, we will review PEMDAS and the order of operations. To begin, we will play a version of ‘guess my rule’ where students will figure out what was done with the given number to get the given result. For instance, the numbers 2, 7, and 5 will be given and the desired result will be 33. A worksheet will be given at the end of the group discussion that will allow the students to practice 2-operation equations (ie 7*5-2) without exponents and parentheses.

Day 2: On the second day, we will go over the answers from the worksheet given the day before. The students will then play PEMDAS Puzzle using only two operations at a time. We will begin by explaining the rules of the game: groups of 4-6 students will race to create a number of different equations that result in a specific integer given by the teacher. The goal is to get 20 points by using different operations that represent different point values (addition and subtraction are 1 point, division and multiplication are 2 points). Each point will earn the group a puzzle piece. The faster they get to 20, the more likely it is that they will get the prize at the end. The students will then be split into groups of 4-6. The teacher will place an objective number on the board. The groups will come up with equations using two operations. There are two ways that the points can be distributed: 1. Each group chooses 2 people to be the point distributers' (giving out the puzzle pieces) while the other students play the game and then they switch when they attempt another equation. <span style="font-family: 'Comic Sans MS',cursive;">Or: <span style="font-family: 'Comic Sans MS',cursive;">2. The teacher monitors the groups progress and distributes the puzzle pieces accordingly.


 * <span style="font-family: 'Comic Sans MS',cursive;">PEMDAS Puzzle Game Instructions: **

<span style="font-family: 'Comic Sans MS',cursive;">- game board (pocket board) <span style="font-family: 'Comic Sans MS',cursive;">- white board <span style="font-family: 'Comic Sans MS',cursive;">- PEMDAS poster <span style="font-family: 'Comic Sans MS',cursive;">- cards w/ numbers 0-9 and operation symbols +, -, x, /,, and ^ (3 cards for each number and operation symbol) <span style="font-family: 'Comic Sans MS',cursive;">- Puzzle with 20-24 pieces
 * <span style="font-family: 'Comic Sans MS',cursive;">Materials: **

<span style="font-family: 'Comic Sans MS',cursive;">Rules and Overview: <span style="font-family: 'Comic Sans MS',cursive;">Students will race to create a number of different equations that result in a specific integer given by the teacher. The goal is to get 20-24 points by using different operations that represent different point values (when addition and subtraction are used they are worth 1 point, when division and multiplication are used they are worth 2 points, and when parentheses are used they are worth 3 points). Each point will earn the person a puzzle piece. The faster they get to 20-24, the more likely it is that they will get the prize at the end. <span style="font-family: 'Comic Sans MS',cursive;">1. Students are given a pocket board and set of number/operation cards (cards w/ numbers 0-9 and the operation symbols +, -, x, /, and ^ (3 cards for each number and operation symbol)). <span style="font-family: 'Comic Sans MS',cursive;">2. An ending number is written on the whiteboard, or placed on a piece of paper on the table. <span style="font-family: 'Comic Sans MS',cursive;">3. Students then use the instructed number and whatever kind of operations they choose to create equations that equal the ending number. They can used as many operations and numbers as they would like, as long as the ending number is the same as the given number. <span style="font-family: 'Comic Sans MS',cursive;">4. For each operation students use they receive points: + and - 1 point; x and / 2 points; and ^ 3 points. Each point is worth a puzzle piece. <span style="font-family: 'Comic Sans MS',cursive;">5. As students earn puzzle pieces, they should begin to build their puzzle. <span style="font-family: 'Comic Sans MS',cursive;">6. The first team to build their puzzle wins.


 * <span style="font-family: 'Comic Sans MS',cursive;">Pocket Board Instructions: **

<span style="font-family: 'Comic Sans MS',cursive;">- poster board <span style="font-family: 'Comic Sans MS',cursive;">- small manila envelopes <span style="font-family: 'Comic Sans MS',cursive;">- glue <span style="font-family: 'Comic Sans MS',cursive;">- scissors <span style="font-family: 'Comic Sans MS',cursive;">- ruler/yardstick
 * <span style="font-family: 'Comic Sans MS',cursive;">Materials: **

<span style="font-family: 'Comic Sans MS',cursive;">1. Cut the poster board into three pieces, so that the pieces remain 28 inches long. <span style="font-family: 'Comic Sans MS',cursive;">2. Measure and mark 1 inch up from the bottom across the entire length of each piece. <span style="font-family: 'Comic Sans MS',cursive;">3. Glue the envelope flaps closed, and then cut each envelope in half. <span style="font-family: 'Comic Sans MS',cursive;">4. Cut a 'v' into one open side of each envelope. <span style="font-family: 'Comic Sans MS',cursive;">5. Glue the envelopes across the bottom on the 1-inch line with the 'v' side up, creating pockets. There should be 8 pockets on each board. These boards can then be laminated.

<span style="font-family: 'Comic Sans MS',cursive;">Day 3: We will introduce exponents and parentheses to the students by first giving examples. Then, we will play ‘guess my rule’ with using 2 or more operations as well as exponents OR parentheses. Students will be given another worksheet to work on individually, getting help from fellow classmates as needed.

<span style="font-family: 'Comic Sans MS',cursive;">Day 4: The fourth day will be the final day of PEMDAS Puzzle as a class activity. Students will be able to use as many operations that they feel comfortable with as well as parentheses and exponents as they feel necessary. The teacher will explain that the rules stay the same; however, the use of parentheses and exponents will earn them 3 points each - making their chance of winning increase.

<span style="font-family: 'Comic Sans MS',cursive;">Day 5: Students will be given a small quiz that will include solving equations with multiple operations, as well as writing equations on their own.

<span style="font-family: 'Comic Sans MS',cursive;">BEFORE: What are components of an equation? What is PEMDAS?
 * <span style="font-family: 'Comic Sans MS',cursive;">Questions for Students: **

<span style="font-family: 'Comic Sans MS',cursive;">DURING: What symbol/operation could you change to make this work? What number could you substitute to make to get the specified number? Would changing these (show two things...) around help?

<span style="font-family: 'Comic Sans MS',cursive;">AFTER: What worked best? What problems did you run into? What didn't work for you? Did you have a strategy? What would you differently next time?

__<span style="font-family: 'Comic Sans MS',cursive;">Problem Solving: __ <span style="font-family: 'Comic Sans MS',cursive;">"Given the equation (3x4-2+7)/4, what step (first, second, third, etc.) is 3x4?"
 * <span style="font-family: 'Comic Sans MS',cursive;">Standard-Based Questions: **

__<span style="font-family: 'Comic Sans MS',cursive;">Communication: __ <span style="font-family: 'Comic Sans MS',cursive;">"Explain what the first step in the given equation is."

__<span style="font-family: 'Comic Sans MS',cursive;">Reasoning: __ <span style="font-family: 'Comic Sans MS',cursive;">"Why did you add first, instead of multiply? Why wouldn't you multiply first?"

__<span style="font-family: 'Comic Sans MS',cursive;">Connection: __ <span style="font-family: 'Comic Sans MS',cursive;">Where else/what other situation would you use the concept of order in?

__<span style="font-family: 'Comic Sans MS',cursive;">Representation: __ <span style="font-family: 'Comic Sans MS',cursive;">"Draw out or use symbols to represent your thinking when solving that equation."

<span style="font-family: 'Comic Sans MS',cursive;">Students can be assessed by the practice options provided below. Student comprehension may also be checked and assessed by having the students write out an explaination or verbally explain on how they solved the problems. By doing so the teacher is able to see if the students are grasping the correct concepts and solving problems as they should. The provided worksheets can also be used in partner work. For example, have the students pair up and take turns guiding each other through a problem. The students will tell their partner which steps to take until they get the answer. By doing this, the students will be able to enhance their communication skills and comprehension. If the students disagree on a step to be taken, they will have to talk through what the right action really is before continuing.
 * <span style="font-family: 'Comic Sans MS',cursive;">Assessment Options: **

<span style="font-family: 'Comic Sans MS',cursive;">Student understanding can be measured and checked through the use of the following: <span style="font-family: 'Comic Sans MS',cursive;"> With answer bank.

<span style="font-family: 'Comic Sans MS',cursive;">With no answer bank.

<span style="font-family: 'Comic Sans MS',cursive;">Although this lesson is on the order of operations, it omits the use of exponents in the equations. The document provided below is a practice sheet that includes the use of exponents, which are present in problems that require the use of the order of operations. This sheet can be used as an introduction to exponents in a follow up lesson. It may also be used as practice within a follow up lesson, or even as an assessment tool at the end of that lesson.
 * <span style="font-family: 'Comic Sans MS',cursive;">Extension: **

<span style="font-family: 'Comic Sans MS',cursive;">The order of operations can be taken a step further by implementing the use of exponents within the equations. <span style="font-family: 'Comic Sans MS',cursive;">

<span style="font-family: 'Comic Sans MS',cursive;">Look through the Instructional Plans for more possible lessons before and after using the PEMDAS puzzle game in class.

<span style="font-family: 'Comic Sans MS',cursive;">While we were at the Selah Game Night, we had to adjust our game to using just addition and subtraction. Each operation was then worth double its original value to make the game well paced and engaging. Overall, the students enjoyed the game and learned how to substitute 2x7 for 7+7.
 * <span style="font-family: 'Comic Sans MS',cursive;">Teacher Reflections: **