August 2023 - Down River Resources | Your Elementary Math Guide
At the beginning of the school year, there is a lot of hype decorating classroom. After the new borders are up, teachers begin thinking about the students on their class list. (If they're lucky enough to have it!) There will be different levels of math understanding in the classroom, especially number sense. Pre-assessment in math is tricky. But… why is that? Teachers want to see where mathematicians are in their understanding WITHOUT having to print and pass out a daunting paper test. Listen, I get it. No one gets excited about math when a thick packet of white copy paper is placed in front of them! How can we pre-assess students’ math thinking without using a paper test? I have a fun and pain-free task that will engage your mathematicians and leave you with lots of knowledge about your students’ math thinking! Don’t worry, I’ll explain!

# Use Mystery Bags as a Quick and Effective Pre-assessment of Number Sense

I recently did this activity with first grade, second grade, third grade, and fourth grade mathematicians. I think you could do it with kindergarten and fifth grade too, you just need to alter the number of objects. More about that in a minute!

Each mathematician was given a brown bag with a quantity of objects inside of it. Mathematicians were asked to make a sign for their bag to show many objects they had. I promise I’ll explain how this simple activity will give you tons of helpful information about your students’ number sense. But, first…

1. I grabbed a pack of brown paper lunch sacks, or brown paper bags, from my local grocery store. You can find this in the aisle with Ziploc bags, usually placed towards the bottom of the shelf.
2. I printed some simple labels to identify each bag, more for my sake. (I used letters to identify each bag since we are working with numbers.) I wanted to have a log of the contents of each bag.
3. I grabbed a variety of objects that I use as math manipulatives in my classroom, such as colored squares and linking cubes, or connecting cubes. (Since I was doing this activity with first grade and second grade mathematicians, I counted out assortments of objects that totaled in the teens. I also repeated this activity with third grade and fourth grade mathematicians and used objects that totaled in the 20s.)

You might be wondering how long this took? I prepped the bags quickly. As a busy wife and mom to three, ain’t nobody got time to spend hours prepping lessons. I got all my supplies and just made rows of objects. I did include three colors in each bag. I’ll tell you why later.

Before I introduced the activity, we talked about how signs, posters, and billboards used to advertise something use words and pictures. Their signs could include words and pictures too!

It sounded something like this:

Have you seen a billboard out your window? I keep seeing the one with big chicken strips on it. The picture makes me interested in trying the chicken. On the sign, there are words that tell me what it is and where to get it. The words give me more information about the picture. I see posters that get me interested in different movies at the movie theatre too. There is usually a picture from the movie and words to tell me the title of the movie and the date that it is being released.

After a few minutes of exploring their bags, mathematicians worked quickly and quietly on their sign.

I kept thinking, “How are my students developing mathematical notation?” As I observed each mathematician diligently working, I was curious how and why they were making choices as to what to include on their sign.

Some drew pictorial representations matching the color and quantity of objects inside of their bags. This is why it’s important to have more than one color in each bag. Others drew iconic representations; instead of drawing the exact objects, they drew a shape to represent the object. Most of the mathematicians, after drawing something on their sign, added numerals to represent the quantities too.

I asked clarifying questions to each mathematician, such as:
• “How did you lay out your objects to count?”
• “Tell us how you counted.”

If a mathematician gave me a blank stare, I asked some closed questions, for example:
• "Do you need a word to describe your object?"
• “Did you count by ones, such as 1, 2, 3…?”
• “Did you count how many objects you had altogether? How many objects were inside your bag?”

After one mathematician shared their poster and their math thinking with the classroom, they dumped the bag out so the others could see. Revealing the mystery for their classmates was so exciting for them!

Now, let’s make this simple.

### Examples of Mathematical Thinking using the Mystery Bag Activity

We will take a look at a few real examples from the classroom, so you can practice looking at a mathematician's number sense. There’s a lot of good information that you can glean from this simple math investigation.

 Bag E

The mathematician who received Mystery Bag E attended to the color and quantity in her bag. Her bag was filled with linking cubes that were blue, white, and green. She drew an iconic representation; instead of drawing cubes, she drew squares to represent each cube. She used different colors in an unstructured, or random, arrangement. If you look towards the top of her sign, there is a key she drew noting that there were 4 cubes in each color. Though she knew there were four in each color, she miscounted and wrote "11" to represent how many cubes were in her bag.

 Bag F (note the towers the mathematician made prior to drawing)

 Bag F

The mathematician who received Mystery Bag F also attended to the color and quantity in her bag. Her bag was filled with linking cubes that were yellow, green, and red. She drew a pictorial representation and drew the two-dimensional face of a cube. She used different colors in a structured, or organized, arrangement. If you look towards the top of her sign, there is a key she drew noting that there were "14" to represent how many cubes were in her bag.

There are a few cubes that she crossed out on her paper. She explained that when she was drawing, she got carried away and was not attending to the number in the tower. She double-checked her work and noticed the error.

NOTE: This representation was interesting because it was the only one where the cubes are linked together to form a tower which matched how the mathematician organized her cubes to count the quantity.

 Bag B

 Bag H

Both of the mathematicians who received Bag B and Bag H drew a more abstract pictorial representation, unlike the previous examples. Neither mathematician drew the unitary representation, or each object in the bag. They drew one representation of each color and wrote a number to represent the quantity. Each of them wrote the total quantity on their poster too. While their representation looked different, each of them attended to the color and quantity in their bag.

 Bag C

The mathematician who received Mystery Bag C also attended to the color and quantity in her bag. Her bag was filled with linking cubes that were blue, red, and white. She drew a pictorial representation and did not have a word for the objects in her bag. She could not explain what was in her bag nor how many was inside of it. I asked her to look at her sign to help her remember. She immediately responded, "14."

It appeared by looking at her poster that she had 1 blue, 2 red, 3 blue, 4 red, and 5 white cubes, which would total 15 cubes. She also wrote a number expression "8 + 8." While there is no equal symbol, she wrote "16" next to the expression and then the number "14." Everything on her sign is "math" and does represent quantity and color but it is not an accurate representation.

She used different colors in a structured or organized arrangement. If you look towards the top of her sign, there is a key she drew noting that there were "14" to represent how many cubes were in her bag.

## What did I notice about my class using this Mystery Bag activity?

As you can see, there are varying levels of math thinking in this classroom, which is great! I am eager to build each mathematician's number sense but I need to know where to begin. This activity was a great way to pre-assess their number sense.

So, let me give you the gist I got from these examples and several others I did not include here. Overall, I noted that:

• Most mathematicians can count objects up to 20.
• All mathematicians can attend to quantity using a unitary, or counting by ones approach.
• They were paying attention to the different colors and used the colors, or smaller parts, to compose the total number.
• Some mathematicians attended to quantity more accurately.
• There were a couple of mathematicians who counted their quantity by twos.
• When counting their quantity later as a class in the same way, many mathematicians dropped off after the strong 2, 4, 6, 8... thus, we will work on rote counting by twos.

This is definitely a number sense investigation that I will be using for years to come in my elementary math classroom and I might even replicate it mid-year to see how their math thinking and representing has changed over time.