# Class Activities

# Free Printable Random Grouping Cards For Math Class

[UPDATED – January 2019]

In my class, most often, I pair students up to work through math problems. I also, most often have less than 24 students. I’ve updated the cards to include a version for ONLY 24 cards and groups of 2. This will make it easier to create different groupings within the same class period without having to give students new cards.

Ready to download these **free printable random grouping cards**?

There are three copies of the cards.

**ONE DESIGNED FOR ONLY GROUPS OF 2, One with equations/expressions and one without (groups of 2 or 3 – 36 cards). **

# Chocolate Mania [3 Act Task]

This post and task was written and created by both Jon Orr and Kyle Pearce.

For about a year now Kyle Pearce and I have been travelling to schools and districts across North America sharing our techniques on how to Make Math Moments That Matter for our students.

In those live workshops we’ve been using a task without a name. On the first anniversary after creating that task we wanted to share it here with you and give it a name.

We’re all about creating tasks and then thinking about how they might be modified for use across a variety of grade levels. With a few modifications, you can successfully run this task in classrooms from K through 10. In particular, you could address the following expectations:

- building estimation skills;
- building multiplicative thinking and proportional reasoning using arrays;
- building multiplicative thinking and proportional reasoning using double number lines;
- making connections to the inverse relationship between multiplication and division;
- connecting double number lines and ratio tables to creating and solving proportions through algebraic reasoning;
- highlighting the value of the constant of proportionality (i.e.: unit rates) so students can “own” every problem possible in a proportional relationship;
- determining rates of change;
- representing linear relations in various ways;
- solving problems using the four representations of linear relations; and,
- many more.

Here is Chocolate Mania:

## Act 1: Sparking Curiosity

Ask students to create a notice/wonder table or you can use one that we built for our online workshop Making Math Moments That Matter.

Ask your students to write down anything they notice and anything they wonder while viewing this video:

Note: There is no audio. Can’t see the video because you’re viewing this post in a rss reader? Click here to go to the post page.

Here are possible notice and wonders from our workshop participants and also some from our students:

- They’re both wearing plaid.
- The video is in reverse.
- How many chocolates will they eat?
- Did they get sick?
- How long did it take to eat all the chocolate?
- It looks like they’re spitting it out.
- Kyle is eating Kisses.

At this point the students’ responses are listed on the board during the class discussion.

After capturing all the notice and wonders on the board steer the class to working on the problem:

### “How many chocolate did Kyle eat? How many did Jon eat?”

Have your students estimate how many each of us ate. What is too high? What is too low? Your students may be feeling uneasy about their estimates; that’s okay! The point here is we don’t have enough information. To help with estimates at this stage we disclose that all the wrappers of all the chocolates we ate are showing in the image above.

We encourage you to record many of the estimates in a chart as a class. This will put some pressure on making those estimates carefully.

## Act 2: Revealing Information to Fuel Sense-Making

To avoid rushing to the algorithm we’ll push down the curiosity path some more. Instead of just handing over all the necessary information to solve a problem ask the students what they want to know more about. This process is key; student anticipation of what is needed is a gold mine for understanding where they are in their thinking. By having them ask for information they have to start problem solving!

Students may ask for the time it takes for the whole video and you as the teacher can then say, “And what would you do with that if I gave it to you?” Listen to how they answer this. You’ll gain valuable information about where that student is on this problem solving journey. You will know after that answer if the student is thinking proportionally or not.

Here is some information to share:

Ask students to share what this series of photos tells them. What do they notice? What do they wonder? Then share this photo. It reveals the total amount of ml each of us consumed.

At this point students will have enough information to determine how many pieces of chocolate each of us ate. Let them go at it!

## Fuel Sense-Making to Consolidate Learning.

Note: You or your students may want to work with more familiar numbers compared to what you see above. For example, to get a close prediction to the actual number of chocolates each of us ate a student may round the 111.8 ml to 110 ml and similarly round the 17 ml for 3 chocolates to 20 ml.

Depending on the grade level or skill level of your students we can expect to see some of these strategies

- Counting with familiar numbers;
- Using arrays;
- Number line counting;
- Tables of value counting;
- Long division;
- Unit rates;
- Solving Proportions;
- Creating and solving equations.

Here are some of those strategies:

### Counting Up Chocolates and ml.

Students may count up 17 ml every 3 pumpkins until they reach close to the total amount of ml. If they go over the total amount they may want to subtract a cup of chocolates so they can get more accurate.

Here’s that strategy in action

### Working with Fractions:

To get more precise answers we can encourage students to work with parts of chocolates in decimals or fractions. Many teachers would be inclined to stay away from fractions because they feel it may “de-rail” the lesson. We say use this context to reinforce fraction work and understanding.

### Counting/Multiplying/Dividing Using Arrays:

Students may organize their counting strategy in a double array model. Simultaneously counting in groups of 3 pumpkins and 17 ml will allow them to see that they will need just over 6 cups of pumpkins, while showing the proportional relationship between the pumpkins and volume.

### Double Number Line:

Students who solve the problem with a proportion will benefit from seeing it laid out on a double number line. By showing how to solve a proportion on a double number line we take a familiar concept (counting on the number line) and extend it to work multiplicatively. Students who solved the problem with an additive strategy will see the benefit of greater precision of using a scale factor.

### Unit Rates:

Many students may use a unit rate to help solve this problem.

Note: This student will benefit from a conversation on notation, units and order of division.

### Linear Relations:

You may choose to use this problem to either introduce or practice linear relations. I used this task to link the idea of finding the unit rate to determining the rate of change (slope) in a linear relation and then use it to build an equation to help solve the problem.

### Reveal the Answer:

After consolidating the learning goals you wanted to bring out into the open for discussion with your class show them this reveal video of the actual number of chocolates each of us ate. Be sure to go back and validate those students who estimated the closest early in this task.

## Is there a Volume relationship?

We want to leave you with some thinking here. We chose these chocolates for a very specific reason. In fact we hunted down the spherical chocolate that has the same height and diameter of that Hershey’s Kiss.

**Your Task:** What volume relationships can we pull from this image?

Did you notice the relationship between the amount of chocolate by volume Jon ate versus Kyle?

Look for an upcoming post on how we used this task to teach volume. But before we do that we want to know how you see a lesson on volume forming with this information. Use the comment section below to share your ideas, questions, comments, or even just snippets of what a lesson could look like.

# Hour Glass Multiples

## Sparking Curiosity & Fuelling Sense-Making with the Least Common Multiple.

In this 3-Act Task students will be presented with a puzzling video of 3 “hour glass” sand timers. They’ll solve a brain-teaser like problem while ultimately learning about common multiples and the least common multiple (LCM).

In this particular, this task can be used for

- estimation;
- spacial sense;
- volume;
- counting in multiples;
- least common multiple;

## Act 1: Sparking Curiosity

Ask students to create a notice/wonder table or you can use one that Kyle Pearce and I built for our online workshop Making Math Moments That Matter.

Ask your students to write down anything they notice and anything they wonder while viewing this video:

Then have them share with elbow partners and then finally with the entire class.

Some possible notices and wonders:

- I see three different colour timers.
- Is that sand?
- Whose house is that?
- Are they timing the same amount?
- What times will they time?
- Will all three timers ever end at the same time? If so, when?
- Is the timer in minutes?
- I think the yellow timer times for 3 minutes.

After capturing all the notice and wonders on the front board steer the class to working on the problem

**“Will all three timers ever run out of sand at the same time? If so, when? If never, why not?” **

Assume that we will keep turning over a timer after the sand runs out.

Take a few minutes to have your students estimate when the timers will all run out at the same time –> “Predict with reasoning”.

## Act 2: Reveal Information to Fuel Sense-Making.

To avoid rushing to the algorithm push down the curiosity path some more. Instead of just handing over all the necessary information to solve a problem ask the students what they want to know more about. For example student 1 might say “I’d like to know the times of all the timers”. As a teacher your next question should be: “I see, and **if I gave you that information what would you do with it?**” We can learn what our students understand and are thinking with their response to one prompt. By asking them to anticipate what they need forces them to develop a problem solving strategy.

After hearing a few students out, give them this information: But make them guess first. What time does each timer time?

Reveal the timers:

After this reveal send students to their vertical spaces to explore the strategies they began in the anticipation stage to determine when the timers will run out of sand at the exact same time.

Strategies you may see:

- Drawings that show how much time is left every time one timer runs out.
- lists of the multiples of 2, 3, and 5.
- tables that track minute by minute.

## Fuel Sense-Making to Consolidate Learning.

Depending on your grade range and student ability you’ll want to frame your consolidation so showcase your target learning goal.

I’m sure most learning goals will include a triple number line showing how multiples of 2,3, and 5 overlap.

Clearly show using the lines how the 2 and 3 minute timer will be turned over at the same time at the 6 minute mark. Then show them all the common multiples between 2 and 3.

Finally bring in the multiples of 5 to the mix.

As part of your consolidation show this video which overlays the common multiples as they occur in the reveal video. Students can clearly see that when the timers are turned over at the same time we have a common multiple.

Here is a reveal video without the number line overlay.

Try this lesson out in your class and report back here in the comments to tell us how it went.

Are you new to 3-Act Math problems? Grab our guide to running these problems in your classroom. Learn tips, suggestions, and avoid common mistakes of using these types of tasks.

### Acknowledgements.

I want to thank Michael Jacobs for turning my thinking towards thinking about the least common multiple. The creation story of the above task comes from this hour glass timer I bought from David’s Tea

I just bought this triple “hour” glass timer! I think we can pull some math from it. What do you wonder? What do you want to know more about? Let’s build some math lessons together. What can we do with this? #iteachmath #mtbos #mathchat pic.twitter.com/6FCz8ivpsO

— Jon Orr (@MrOrr_geek) November 6, 2018

Mike said,

if you flip it over every time the sand runs out from one timer, how many times will you flip it over before all the timers are empty at the same time?

— Michael Jacobs (@msbjacobs) November 6, 2018

Bryan also was thinking it was screaming LCM.

Doesn’t this scream LCM to you??🤩

— Bryan Penfound 🌐 (@BryanPenfound) November 7, 2018

Which made me start thinking about how that couldn’t work with all three timers attached. So I set off to buy some new timers. I found the ones you see in the problem above.