Before beginning your lesson, share the video from the following website: http://www.flocabulary.com/pemdas/
It is a great video showing the order of operations, one that your students will be able to sing along with since the words appear on the screen. PEMDAS is an acronym for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction; it serves to remind your students how to approach an expression containing more than one operation.
(I would recommend viewing the PEMDAS video a few times before engaging the following lesson.)
1. Show the following equation on the whiteboard/interactive whiteboard:
4 + 6 * 5 =
2. Ask the students to complete it on their own paper. Have a volunteer come to the board to complete it.
4 + 6 * 5 = 34
3. Say, “This is correct because we follow the order of operations, going left to right when adding/subtracting.”
4. Write the same equation on the board:
4 + 6 * 5 =
But this time put the answer as 50:
4 + 6 * 5 = 50
5. Ask, “How can that be?”
6. After responses from students, if nobody suggests adding first, then the teacher will suggest it. Say, “We’re supposed to multiply the 6 and the 5, and then add the 4, getting 34. But what if we add the 4 and 6 first, then multiply by 5? What do we get?”
7. After acknowledging that this is out of order, say, “Sometimes mathematicians need to go out of order. When we do, there is a way to do it! It’s called using parenthesis.”
8. Place parenthesis in the equation like so:
(4 + 6) * 5 = 50
9. Say, “Parenthesis mean ‘Do what’s inside me first!' So, looking at the parenthesis, what does it tell us to do first?”
10. After responses, reinforce, “Yes, add the 4 and the 6! So if I do that, I get 10, and if I multiply that by 5, what do I get?”
11. After correct responses, move on by writing the following on the board:
6 – 1 * 4 = 2
12. Say, “This is correct, right? But what if I write this?”
6 – 1 * 4 = 20
13. Tell students to write this equation on their paper and ask if they can place parenthesis to make this equation correct. Ask for volunteers to come to the board and write their answers. Be sure they write:
(6 – 1) * 4 = 20
14. Say, “What does the parenthesis tell us to do? That’s right! ‘Do what’s inside me first!’ Let’s try another one.” Write the following on the board:
10 - 4 / 2 = 8
Say, “This is correct, right? But what if I write this?”
10 – 4 / 2 = 3
15. Tell students to write this equation on their paper and ask if they can place parenthesis to make this equation correct. Ask for volunteers to come to the board and write their answers. Be sure they write:
(10 – 4) / 2 = 3
16. Say, “So, what does the parenthesis mean? That’s right! ‘Do what’s inside me first!’ Okay, just so you know, sometimes it doesn’t make a difference. For example (write on the board):
6 + 2 – 1 =
6 + (2 – 1) =
17. Will both students get you the same answer? Ask students to finish these two equations, asking for volunteers to come to the board and tell you the steps they followed for each one. Say, “These will also get you the same answer, regardless of the parenthesis.”
8 * 2 – 1 =
(8 * 2) – 1 =
18. Ask students to finish these two equations, asking for volunteers to come to the board and tell you the steps they followed for each one.
19. At this point, do a few more examples together, getting students to do the following samples at their desks, placing parenthesis to make the equations true.
8 + 4 / 2 = 6
9 + 5 / 2 = 7
1 * 2 + 2 *10 = 40
20 / 2 + 2 / 1 = 5
20. Walk around, fielding questions and clarifying. Get volunteers to put the corrected equations on the board.
(8 + 4) / 2 = 6
(9 + 5) / 2 = 7
1 *( 2 + 2) *10 = 40
20 / (2 + 2 )/ 1 = 5
At this point, see if any students want to try to create some similar equations on the board. When you feel your students are ready, there is a ten problem attachment you can use to assess your students, or you can have them all create their own problems, using the guideline that the placement of parenthesis makes a difference regarding the answer.
After your initial assessment of their understanding of how to use parenthesis, it's time to have all your students collaborate on these equations. Have students work in small teams to create five to ten equations that require proper placement of parenthesis, but make sure these collaborative groups leave the parenthesis out for another group to work on. Have groups exchange equations and work them, calling on several to share their finished equations with the class on the white board.