Crazy Huge Puzzle

My freshmen, as you may have read in a previous post, really like puzzles.  They say that puzzles are way better than worksheets.

So I decided to make a crazy huge puzzle.  (Note:  I noticed when I ran this sheet a second time that it is kind of small.  The first time it was a full page.  You may need to play around with it.)  Then I made a sheet to explain the rules and to record answers on.  There are four given angle measures, along with some 90 degree angle markers.

What I like about this activity is that they need to use what they know about special angle pairs, triangles, exterior angles, etc. in order to do this.  There are also multiple ways to get the measures of many of the angles, so they can check their work.  But the very best part about this activity is that there is not enough given information to complete the puzzle!

I gave each group 5 chips (each group got a different color).  These allow them to buy an angle (or a hint) from me.  They had to choose a banker who would come to my desk to make a purchase.  Here is the answer key.  If I have any wrong answers, please leave a comment!

The minimum I had to "buy" in order to complete this was 2 angles.  I tried it several different ways, and each time I got stuck and need to buy 2 angles, but not always the same angles!

Kiddos were totally engaged for a full 45 minutes.  They begged for more time to complete it tomorrow.

Some great things I overheard:

"No!  Don't buy anything yet!  We need to be sure there is nothing else we can do on our own!"

"Wait: yesterday we did that exterior angle thing.  I think we could do that.  Y'know, add up the 2 far away angles?"

"Are you SURE about that?  How come?  Where did you get that number?"

Things I would do differently next time:

• reduce the number of chips to 3
• make sure the groups are no more than 3 people.  (I had one group of 4, and it just seemed the 3 person groups had all members engaged, where the 4 person group had one that just sort of sat back....maybe just the dynamics?  He was totally able to do the work, just chose to do more watching than doing.  I think 2 groups of 2 would have worked better.)
• Allow a little more time.  We have 80 minute classes.  If I had given a whole hour, they could have finished it.

Addition Number Talks and a Missed Opportunity

This week was a short week, because Veteran's Day was celebrated on Wednesday.  I had to really push to get what needed to be 5 days' worth of work into 4.  AND it is my policy to never give homework on a holiday, so whatever practice I wanted them to do on Tuesday, had to be worked into the class time.

The result was only one number talk this week, and a missed opportunity to point out how frequently they used the commutative and associative properties.

Here is the board shot of the problem 37 + 49:

The first student used the strategy of starting from the left, which I misnamed as the break apart method.  This is definitely the strategy most students (who didn't use the traditional algorithm) used.

The second is the traditional algorithm.  I asked her how she kept track of what she had and she said she could just mentally do this by looking at the numbers on the board and picturing them one above the other.

The third used the take and give strategy.  He took some from the 37 and gave it to the 49.  What amazed me is that he took 7 to give to the 49, not just 1 to make it 50.  This led to a number talk inside a number talk when I asked him how did he add 7 to 49 so quickly!  He said he could just do it: "I'm weird like that!"  Others begged to share how they did it (the favorite way was to add 1, then add 6 more), then got back to one more strategy.

This is the round and adjust strategy.  As I started to record what this student was saying, she said it might be easier if I showed it on that "number line thing you do".  Ah yes. It is getting through!

It was the third strategy where I really missed a great opportunity to discuss how breaking it apart and giving a piece to the second addend is really just the commutative and associative properties in action!  I am very disappointed in having missed this chance since this is an Algebra 1 class and we have been talking about the properties.  Sigh.

I will have to do another with them and hope for the same chance.  Next time:  3 digits plus 3 digits in the hope of them discovering that other strategies can serve them better than the traditional algorithm, or at least that they have a better understanding of what "borrowing" means.

Number Talks Chapter 5 reflection

We did some multiplication number talks this week.  I suppose it should not come as a surprise that a few students did the algorithm in their heads.

The problem was 13 times 12.

"I put the 13 above the 12.  Then I multiplied 2 times the 3 and got 6.  Then I multiplied the 2 times the 1 and got 2.  I put it next to the 6.  (Note: I put the 2 to the right of the 6, since she said 'next to the 6') .  In FRONT of the 6, I mean.  Next I put a 0 under the six."

"Can you help us understand why you put the 0 here?"

"I put it there because you are supposed to.....um,....., as a place holder."

"Ok, thank you."

"After that I did 1 times 3 to get 3 and put it in front of the 0, and last I multiplied 1 times 1 to get 1 and put it in front of the 3.  When I was done with multiplying I added up and got 156."

First of all, I was impressed that anyone could keep all that in her head.

Second, I asked if anyone wanted to share another strategy.
Thankfully, the very next strategy perfectly mirrored what the algorithm girl was trying to do.

After the students were done sharing, we went back and noticed how the two strategies were related.  I wanted them to see that the 0 isn't just something that you put there as a place holder.  I wanted them to notice what they were really multiplying by.  I didn't do any of the talking.  Other kids pointed out how the one related to the other.

All in all, a good talk.

For the next one, I want to pick a problem that will work nicely with the halving and doubling strategy.

"Way Better Than Doing a Work Sheet!"

We have been studying special angle pairs in my freshmen Geometry class. Yesterday I told them I LOVE puzzles and I gave them this homework.

For each angle they had to give a specific reason for the angle measure ("vertical angles with <1", etc).

When they came in this morning, they were all abuzz!  "Did you get angle 12?  yeah, but I got stuck on angle 15...." and other such snippets of conversation were overheard.

Finally one kid turned to me and said:  "This took me a long time, especially coming up with a reason for each angle, but it was cool!  I can see why you like puzzles:  they are WAY better than doing a work sheet!"

Gotta love 'em!!