The purpose of the warm up today is to get students thinking logically about math. I want them to make sense of the problems and decide if the answer could be correct by thinking about what is a reasonable answer (MP1). I put the following problems on the board:
81 + 19 = 910
54 - 17 = 43
70 - 58 = 2
45 + 45 = 90
I ask students to copy the 4 problems into their math journals. Now I ask them, without actually doing the math, to put a smiley face next to the problems whose answers look about right, or logical, and a frown next to those that do not look logical.
I give them several minutes to do that and then I ask them to show with a thumbs up if the first one is logical or not. I count the number of yes and no's and write it on the board. I do the same for the other 3 problems.
Next we discuss why the answers I have given may or may not be logical. What can I do to get an idea of what the answer might be close to? What might have caused me to get the answers I did?
We solve each problem together and then check to see if our assertions about logical and not logical were correct.
I invite students to move to the rug for the next part of the lesson.
Once students have gathered around the outside edges of the rug, I ask how many have ever played or watched soccer, football, basketball, softball, t-ball , or baseball? Most students have played or seen at least one of these sports.
I tell them that today our rug is like a playing field. What sport would we like it to be? I let students vote on one of the above sports to create the playing field for. I draw the field quickly on a piece of large paper on the floor.
Now, what happens if the ball is on field? (We can play the game). I bring out a small ball and place it in the center. What happens if I kick (throw, hit depending on the sport), the ball out of the field? (There is a penalty, play stops, there is no point, etc.) I push the ball off my field.
Math is a lot like playing a sport. You need to keep the ball on the field. (In other words you want your answer to make sense to the problem you are given (MP1). For example if I said 1 + 1 = 11 you would all laugh because that does not make sense to the problem. I didn't add the two numbers together, I wrote them next to each other, so I would say my ball is no longer on the field because my answer isn't logical. If my ball (or answer) goes too far off the field, you can't find the answer. If the ball rolled too far off the field it would get lost and you couldn't play anymore.
We want to find a way to keep the ball on the field when we do math and to start that idea, we are going to play a new game today.
There will be 4 players in the game. The first player will draw a card and read the math problem. The second player will use smiley face numbers (review these as numbers rounded to the nearest 10 - thus ending in a zero that could have a face drawn in them) to solve the problem. The third player will solve the problem using a calculator and the 4th player will use a different strategy to solve the problem. Each player will keep their own score. Once everyone has solved the problem, the smiley face person announces his/her answer. The calculator person announces his/her answer. These 2 should be close to one another. If they are not, play stops here for everyone to check with calculators. Now the other player tells his/her number. If it is on the playing field (within 10 of the smiley face or the calculator answer), that person gets a point for scoring and keeping the ball on the field. If it is not within ten, no point is given. Everyone gets a point if the numbers are all on the field.
At the end of the round, players switch jobs to the left.
Play continues for about 15 minutes, or until everyone has had several turns with each job in the game.
Now that students have had practice with using the playing field to check their answers for how logical they are, I want them to try the exercise individually.
I hand out a practice page to each student. (I have several sets with different problems to accommodate different learning levels within the classroom. ) In this activity I am asking students to reason more abstractly and quantitatively as they make sense of their problems and try to use the playing field as a model for what they are trying to do. (MP2, MP4).
Students work independently and I circulate around to support students who may be struggling, or to listen to student thinking.