To introduce our new topic, I asked the kids to write the following math problem on their desk (using dry erase markers):
3 + 3 x 4 + 2 x 3 + 3
Most students solved from left to right getting an answer of 81. Other students are in UIL Number sense and had a better idea. They grouped the multiplication problems together and got an answer of 24. However, when I added in the parenthesis in the correct position:
3 + (3 x 4) + 2 x (3 + 3)
We found that the answer was 27. This lead into my lesson objective:
We will understand the need for a standard order of operations by investigating the impact that changing the order has when performing a series of operations.
I explained to the kids that there is an agreed upon order of operations: parenthesis, exponents, multiply/divide, then add/subtract. Knowing that just telling them one time would have little to no effect on their long term memory, I employed a tactic I had seen on one of my favorite blogs, Runde's Room. The link will take you to the day she chose to teach the order of operations using the game of hopscotch!
I decided to try this myself! I planned to take the kids outside and make hopscotch boards using sidewalk chalk and then doing all kinds of equations.....but then the cold front came through.... 38 degrees may not be cold to many people, but to Texans, you would think it just snowed! So, instead, I made hopscotch boards on the floor of my classroom with masking tape.
Then we played some hopscotch calling out the order of operations as we proceeded. To make it more entertaining (for me especially), we kept increasing the speed at which we played the game!
After playing hopscotch, we recorded our new learning in our journal. I found another blog whose teacher used the hopscotch method in her classroom and then created the PEMDAS graphic organizer that we used in class today. The video with information is at: Order of Operations: PEMDAS
I discussed that they need many different ways to help them remember the Order of Operations. My kids told me that they would never forget hopscotch, but I explained that they needed something that would not allow them to mix up the order of the multiplication/division, and addition/subtraction. At this point, I mentioned the acronym PEMDAS. I also encouraged them to use a mnemonic device to remember the steps such as:
To complete the day, we worked with a page from Mailbox Magazine called "A Skeleton of My Former Self." This page allowed us to work with the order of operations while finding answers to interesting facts about the body!
We did not quite finish all of the facts today, so we will do that tomorrow.
Since there was new learning today and I wanted the kids to showcase their understanding the knowledge gained today, I assigned an Order Of Operations Math Concepts Poster. This poster was created by Jen Runde, the author of the blog Runde's Room (I have attached the link for any interested in purchasing).
It was a busy class, but fun!
HOMEWORK: xtramath.org and Math Concepts Poster
Nice lesson and well presented but with one proviso which I hope that you explained to your students.
ReplyDelete3 + 3 x 4 + 2 x 3 + 3 = 24 This is CORRECT for the expression as written.
However, adding the parentheses "in the correct position" CHANGES the expression!!! That is why the result is 27. There is NOTHING in the original expression that indicates that your placement of the parentheses is correct. The CORRECT placement to get 24 is 3 + (3 x 4) + (2 x 3) + 3 = 24
Now, showing them that a different result can be achieved by grouping the expression DIFFERENTLY. 3 + (3 x 4) + 2 x (3 + 3) = 27
Here are some other ways that the numbers can be grouped to get a different result? 3 + 3 x (4 + 2) x 3 + 3 = 60; or (3 + 3) x 4 + 2 x (3 + 3) = 36. This is a precursor to their understanding of TERM which is separated by + or -
I really liked the hopscotch game. Nice reinforcement.
These are just my thoughts for a model lesson study on Order of Operations:
Start with 3 + 3 x 4 + 2 x 3 + 3, as you did by asking the kids what result do they come up with.
Then have kids with different results present their methods. Ask the kids who is right or wrong. Take a vote, mark the count on the board.
Then introduce parentheses as grouping symbols and allow kids to group the original expression and see what result they get. Again have students present where they placed the parentheses and how they derived their result. Again, take a vote on the correct result. Some kids might even say that they are all right. :)
Now ask the kids WHY? This can result in a lively and terrific discussion leading to them even volunteering that RULES are important and that there has to be an ORDER (because that is what the lesson is about ;)
Now, summarize their discussion and conclusion that there have to be rules to follow so everyone gets the same result every time. Mathematicians decided on a convention (explain vocab meaning) a long time ago. That is what we now call Order of Operations.
Now practice various problems followed by 5 key ones as a formative assessment.