3 Act Math: Pretzel Cut

This task is a little different than most, but I really think it has some good exploration built in and it lends itself to more of an open task.  The standards that I think best fit this task are Math Practice 1, 3, and 4.  If you think there is a good fit with a content standard, please comment below.  There is definitely some partitioning of the whole which could be a good application of 3.GA.2.

Act 1

What did you notice?  What do you wonder?

Focus Question: How will the bread be cut?

Act 2

I made 7 cuts.  Number of Pretzels

Act 3

3 Act: Ho Ho Ho

I happened upon some Little Debbie snacks at the grocery store a few days ago and got some ideas for some new tasks.  This task is meant to show fractions as division by dividing the number of Ho Ho’s by the number of plates (or people).  The common core standard this best fits is 5.NF.B.3.

Act 1

What do you notice?  What do you wonder?

Focus Question: How many Ho Ho snacks will each person (or plate) get?

Act 2

More Information

Act 3

Making Sense of 5 x 3/8

I wrote this blog post last year and somehow never finished it:

My youngest son is in the fourth grade.  He is a good student and loves math, but I wasn’t sure if he was truly understanding fractions.  I decided to ask him how he would solve 5 x 3/8.  He started by trying to use an algorithm (which he did not understand) but luckily saw the mistake and was able to reason about the answer to determine that the algorithm did not produce a reasonable answer (The entire video is at the bottom of this post).

After he was unsuccessful with the algorithm he just looked at me and said,  “but 9 is more than 5” with a puzzled look on his face.  He knew something went wrong but he wasn’t sure how to figure out what.  I asked him if there was a different way he could represent the problem to make sense of it and he said he could draw a picture or a diagram.  I said, okay what would that look like.  He struggled a little with trying to visual 3/8 so I asked him what 1/8 would look like.  He went to a number line.  However, when he labeled his number line, this is how he labeled it:

First attempt

I asked him to show me where 1 was and he quickly erased a line and was able to tell me that one was the same as 8/8.  I asked him to show me where zero was and he corrected the number line to look like this:

Second attempt

He then was able to plot 3/8 on the number line like this:

three-eighths

When I asked him what two 3/8 would look like, he was stumped.  I said, where would you put the dot to show another 3/8?  He was able to produce this number line and we discussed that this was two groups of 3/8.  He proceeded to extend the number line to show five groups of 3/8 which landed him at 15/8.

2 groups of 38

I asked him if he had a way he could teach this to someone else who didn’t know how to complete this problem and he produced this scenario and drawing:

Five times 38

Skylor: “There was a chocolate chip cookie and eight children.  They only had one chocolate chip cookie and they all wanted it and they needed an equal share.  So they broke the cookie into eight pieces and then let’s say five of the kids wanted to save theirs for later because they had just had food and they weren’t that hungry. 

So only three children had their cookies at that time.  And then I will shade in the cookie pieces that those children ate. Those pieces would be ⅜ of the cookie. But if there were five cookies, then you would take this and there would be five of these (five cookies all split up so the children could have their pieces of the cookies).  

Five of these ⅜ would be ate at one time. So that would be…let me just draw that…so that is five split up cookies. And then three children had their share of the cookies (that represents ⅜ of the one cookie). There was five cookies so then there was that much. These were the pieces that were ate, but the total of those pieces that were ate were 3, 6, 9, 12, and 15.  

Me: “So 5 x ⅜ equals…”

Skylor: “So five times ⅜ equals fifteen eighths.”

We know how important it is to allow students to make sense of a mathematics, yet many times we feel rushed to teach.  If I would have tried to “teach” Skylor the algorithm for this problem, would he have been able to internalize the concept?

If I would have switched to teaching mode and given him steps to complete or a specific diagram to draw (my diagram) what might have happened?

Will Skylor be able to make sense of the algorithm now?

As a Math Recovery Intervention Specialist, one of the most important things I learned was the importance of wait time and the practice of questioning instead of telling.  When we stop leading students thinking and start allowing them to make sense of their own learning (MP1) it is amazing what they can accomplish.

3 Act: Dart Throw

One of my youngest son’s favorite party games is the balloon dart throw.  Each year for his birthday party I come up with some way to incorporate the game.  I fill them with party favors such as mini lego sets or minifigs and his friends get to keep the prize and put it together when they pop them.

When I was brainstorming next year’s theme, I realized this would make a great task!  I have filmed several of these for different grade levels.  This is a great one for 1.OA.A.1, 1.OA.B.4, 1.OA.C.5 for adding within 20 and missing addends.  It also could be used for the second grade fluency standard, 2.OA.B.2.

Act 1

Possible Question: How many balloons were popped?

Act 2

12 total balloons

I threw 10 darts and missed three times.  On my ninth throw I popped two balloons with one dart.

OR less challenging: there are 4 balloons left.

Act 3