# 3 Act: Gotta Count ‘Em All

Recently I’ve been reading the book Counting Collections and I got really inspired to create some three act tasks that played on the counting collections structure. I particularly liked the sections about recording student work and I thought this would be a really great visual for students to take back to their work with counting collections to think about different ways that they could record their work but also different ways that they could group and organize numbers when counting large collections.

My son is a huge Pokemon fan and had this great little assortment of Pokemon.

This task can be used for assessing multiple standards and practices, but I settled on 2.NBT.B.7.

### Act 1

What do you notice?  What do you wonder?

How many Pokemon altogether?

Make an estimate that is too low, one that is too high and one that is about right.

### Act 2

There were 4 cups of 25 Pokemon and 20 more.

### Act 3

Act 3 Final Count

# 3 Act: Be There or Be…

This three act task is based on the Jo Boaler task that she shows in her Ted Talk video where the different color tiles are falling and people see the pattern emerge in different ways,  Although this shows only one way of the colors being added, it’s a great visual representation of how a pattern grows and and looking at perfect squares I just thought this was such a great task for students to grapple with in this way.   Although this task is great for many standards, I have chosen to link it to numeric patterns 4.OA.C.5.

### Act 1

What did you notice? What do you wonder?

Focus Question: What will the 5th shape look like? or How many tiles will be in the 5th shape?

# 3 Act: Star Pattern

We play a game in stations to practice skip counting called “Cross the Creek” or “Cross the Galaxy.”  Basically we rename it based on the shape of the foam tiles.  The way the game works is that you write multiples of a number or a counting pattern on one side of craft foam pieces.  You then lay it out face up so that students can practice seeing and counting.  Students take turns walking across the numbers and saying them as they walk.  After they cross, they can choose one number to turn over and then the next person goes.  It’s a really great kinesthetic way to get kids to practice counting patterns after they have had time to conceptualize the pattern.

I say all of that to set up this next 3 Act task.  I thought, a predictable sequence would be fun, but I want to start out with a number pattern that encourages students to think about the nature of patterns.  For that reason, there will be two different videos for Act 2 based on student responses to what information they need.  The first will give them just the second number and the next will give them the first three numbers.  The goal is to get them to see that patterns cannot be discerned by simple looking at two numbers (or three in cases like the Fibonacci sequence – but that will be explored at a different time:).  There are many standards this task addresses, it can be used at any grade for MP 8.  Or for content standards in several grades in Operations and Algebraic thinking.  Specifically 2.OA.A.1.

Star Pattern Google Slide Deck

### Act 1

What do you notice?  What do you wonder?

What is the number on the yellow star?

Estimate.

### Act 2.0

What do you know?  What do you need to know?

### 2.1

Are you confident in your answer after seeing this new information or would you like to revise?

# 3 Act: Jump Drive

While at the NCSM Conference in San Diego, I wanted to see as much of the city as I could after sessions were out.  I walked along the bay and as I continued to walk, I kept seeing scooters and bicycles parked at random intervals.  I decided to check it out and ended up renting one.

CCSS 5.NBT.B.7

### Act 1:

What do you notice?  What do you wonder?

Focus Question: How much did it cost to rent the bike?

# 3 Act Math: Butter Believe It

This task best fits 3.NF.A.3.a-b as an introduction to equivalent fractions.

## Act 1

What did you notice?  What do you wonder?

Focus Question: How many will go on each plate so that everyone gets the same amount?

## Act 2

How many full bars were there?

## Extension:

What if the bars were cut in fourths and eighths?

# 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

# 3 Act: Broken Heart

This task is meant to emphasize partitioning on a line of symmetry.  Common Core Standard 4.G.A.3.

## Act 1

What did you notice?  What do you wonder?

Focus Question: Where will I need to cut the heart for it to be symmetrical (or to cover itself)?

## Act 2

Use this recording sheet for students.

# 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?

# 3 Act: Dart Throw (Structuring to 5)

You can switch up Act 2 pretty easily to meet your goals.  This is a great activity for structuring to 5 and best fits standards K.OA.A.1-3 and fluency standard K.OA.A.5.

You might choose to use this recording sheet to provide some support for students.

### Act 1:

What did you notice? What do you wonder?

How many balloons popped?

How many didn’t pop?

# 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:

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:

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

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.

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:

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.