Performance Task: Order of Operations Treasure Hunt by Tabatha Burcher In this lesson students will review order of operations. Students will solve numerical expressions using order of operations. Students will write a simple expression to share with a partner. Students will explain in their journals how to solve a simple expression that they have created. STANDARDS FOR MATHEMATICAL CONTENT Write and interpret numerical expressions. MCC5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. MCC5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. STANDARDS FOR MATHEMATICAL PRACTICE 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE Understanding the correct order of steps when performing order of operations problems is important in completing this task. These skills help us to build our understanding of numerical equations with the use of parenthesis, exponents, multiplication, division, addition, and subtraction. COMMON MISCONCEPTIONS Students work the problem from left to right. Utilizing the correct order is imperative. The acrostic Please Excuse My Dear Aunt Sally helps students remember to use parenthesis first, then exponents, then multiplication and/or division and finally addition and/or subtraction. Once completing the exponents step, students work all multiplication and then all division. Multiplication and/or division are one step. Students should work from left to right solving whichever multiplication or division problem arises. Students work all addition and then all subtraction. As with multiplication and division, addition and/or subtraction is one step. They should be worked out from left to right. ESSENTIAL QUESTIONS How can an expression be written given a set value? How can expressions be evaluated?
How can I effectively explain my mathematical thinking and reasoning to others? How can I use cues to remind myself of the order of steps to take in a multi-step expression? How can we simplify expressions? Why is it important to follow an order of operations? MATERIALS Answer/Question cards in varying colors Problem solving sheets in varying colors Answer keys in varying colors Treasure Journals Pencils School or classroom map Parents/volunteers GROUPING Individual/Partner/Small Group task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION In this task students will work with order of operations to solve numerical expressions. COMMENTS This activity can be contained to the classroom or be spread out at locations around the school that will not disturb other teachers or students. To introduce this task review as a large group the correct order when using order of operations, reminding students of the acrostic, Please Excuse My Dear Aunt Sally to help students remember to use parenthesis first, then exponents, then multiplication and/or division and finally addition and/or subtraction. Before starting this task o Draw a map of your classroom or school, labeling important features such as door, window, teacher s desk, classroom numbers, cafeteria, etc. o Hide the treasure somewhere in your classroom. It can be anything you like. o Place answer/question cards around the classroom or school. TASK Each student will receive a colored worksheet. The colors will allow for the differentiated questions. The color of the worksheet will match the color of the question cards the students will look for. Students will solve the first expression on their own. If questions are posted in the classroom, students will choose a partner with the same color worksheet to work with. If questions are posted around the school, students will work in small groups with all students who have the same color card. They will be supervised by a parent/volunteer who will carry the map and an answer key. Students will compare their solution with peer(s) to verify that their answer is correct. They will discuss and correct any mistakes before moving on to find the next clue (which is their answer). Once the answer is verified, students will move on to find the card or room number that matches the answer.
Continue solving until question #7. Question 7 says to write your own expression for 335. Answer 335 is where they will find the treasure. If they are moving around the school, make the solution for #7 be your classroom number. That is where they will find the treasure. The answer to question #8 is whatever you decide to have for your treasure. Once each student has a piece of treasure, have them take out their journals and answer the following: o Write the expression you created for question #7. Explain how to solve using order of operations. Show each step. FORMATIVE ASSESSMENT QUESTIONS Why did you do the parenthesis first in the task? What will you do to try to figure out if the answer given is correct? How will you demonstrate that it is correct? How will you convince your partner when you think her answer is incorrect? What strategies are you using to analyze the given problems? What cues are you using to recognize the correct order of operations? DIFFERENTIATION Extension Have students use the worksheet with question #1: 3 + (12 2 + 6) + 5 2 x 2 + 28 =. Questions on this sheet are more advanced. Intervention Have students use the worksheet with question #1: 10 2 + (4 x 5 + 6) =. Questions on this sheet are less difficult. Parent/volunteer for this group can help guide problem solving as needed.
START: Group 1: We will now begin our Pirate Treasure Hunt! Good Luck! 20 2 (75 x 2) + 2 = On Level Difficulty 252 2 (4 x 5 2 ) + 90 3 = 230 119 6 + (8 2 2 x 3) 2 3 + (50 2) = (2 x 10 2 ) + 5 2 + 6 =
231 10 2 2 (48 24) + 5 2 + 1 = 126 2 x 11 2 (48 2) = 218 Write an equation that equals 335. Have your partner solve it! 335 (or homeroom teacher s room number) What kind of bootie does a pirate steal from a pilgrim?
Name Order of Operations Treasure Hunt Directions: 1. Solve the Start question and write the answer in box 1. 2. To find the next question, you have to hunt for the classroom number that matches the answer in box 1. Hint: If you get to the classroom and there s not another clue there, you need to re-work the problem. 3. Write down each question and answer in the boxes below then go on to the next stop in your hunt. 4. You will know you ve found the last answer when you reach the Pirate s Treasure! Start A pirate has stolen your treasure! Quick! Go find it! 20 2 (75 x 2) + 2 = Question 2: Answer 1: Question 3 Answer 2: Question 4: Answer 3: Question 5: Answer 4: Question 6: Answer 5: Question 7: Answer 6: Question 8: Answer 7: Answer 8:
START: Group 2: We will now begin our Pirate Treasure Hunt! Good Luck! Intervention 126 10 2 + (4 x 5 + 6) = 50 x 4 + (5 x 4) 2 = 218 (2 x 10 2 ) + 5 2 + 6 = 231 8 ( 20 + 5) + 45 15 =
230 252 20 2 (75 x 2) + 2 = 23 4 + (20 x 5) = 119 Write an equation that equals 335. Have your partner solve it! 335 (or homeroom teacher s room number) What kind of bootie does a pirate steal from a pilgrim?
Name Order of Operations Treasure Hunt Directions: 1. Solve the Start question and write the answer in box 1. 2. To find the next question, you have to hunt for the classroom number that matches the answer in box 1. Hint: If you get to the classroom and there s not another clue there, you need to re-work the problem. 3. Write down each question and answer in the boxes below then go on to the next stop in your hunt. 4. You will know you ve found the last answer when you reach the Pirate s Treasure! Start A pirate has stolen your treasure! Quick! Go find it! 10 2 + (4 x 5 + 6) = Question 2: Answer 1: Question 3 Answer 2: Question 4: Answer 3: Question 5: Answer 4: Question 6: Answer 5: Question 7: Answer 6: Question 8: Answer 7: Answer 8:
Extension START: Group 3: We will now begin our Pirate Treasure Hunt! Good Luck! 3 + (12 2 + 6) + 5 2 x 2 + 28 = 231 10 2 2 (48 24) + 5 2 + 1 = 126 2 x 11 2 - (48 2) = 218 6 + (8 2 2 x 3) - 2 3 + 50/2 =
119 5 + 15 2 = 230 2(5 3 ) + 2 = 252 Write an equation that equals 335. Have your partner solve it! 335 ( or homeroom teacher s room number) What kind of bootie does a pirate steal from a pilgrim?
Name Order of Operations Treasure Hunt Directions: 1. Solve the Start question and write the answer in box 1. 2. To find the next question, you have to hunt for the classroom number that matches the answer in box 1. Hint: If you get to the classroom and there s not another clue there, you need to re-work the problem. 3. Write down each question and answer in the boxes below then go on to the next stop in your hunt. 4. You will know you ve found the last answer when you reach the Pirate s Treasure! Start A pirate has stolen your treasure! Quick! Go find it! 3 + (12 2 + 6) + 5 2 x 2 + 28 = Question 2: Answer 1: Question 3 Answer 2: Question 4: Answer 3: Question 5: Answer 4: Question 6: Answer 5: Question 7: Answer 6: Question 8: Answer 7: Answer 8:
Order of Operations Treasure Hunt Answer Key Intervention On Level Extension Question 1 10 2 + (4 x 5 + 6) = 20 2 (75 x 2) + 2 = 3 + (12 2 + 6) + 5 2 x 2 + 28 = Answer 1 126 252 231 Question 2 50 x 4 + (5 x 4) 2 = 2 (4 x 5 2 ) + 90 3 = 10 2 2 (48 24) + 5 2 + 1 = Answer 2 218 230 126 Question 3 (2 x 10 2 ) + 5 2 + 6 = 6 + (8 2 2 x 3) 2 3 + (50 2 x 11 2 - (48 2) = 2) = Answer 3 231 119 218 Question 4 8 ( 20 + 5) + 45 15 = (2 x 10 2 ) + 5 2 + 6 = 6 + (8 2 2 x 3) - 2 3 + 50/2 = Answer 4 230 231 119 Question 5 20 2 (75 x 2) + 2 = 10 2 2 (48 24) + 5 2 + 1 = 5 + 15 2 = Answer 5 252 126 230 Question 6 23 4 + (20 x 5) = 2 x 11 2 (48 2) = 2(5 3 ) + 2 = Answer 6 119 218 252 Question 7 Write an equation that equals 335. Have your partner solve it! Write an equation that equals 335. Have your partner solve it! Write an equation that equals 335. Have your partner solve it! Answer 7 335 335 335 Question 8 Answer 8 What kind of bootie does a pirate steal from a pilgrim? What kind of bootie does a pirate steal from a pilgrim? What kind of bootie does a pirate steal from a pilgrim? Whatever the treasure is Whatever the treasure is Whatever the treasure is