Welcome to the third and final post in this series of examples of math from the real world – specifically the Halloween aisle at Target. In the first post we looked at packages of 4 party favors, and in the second post we looked at packages of 6 or 8. Today we’re going to move into estimating using packages with larger quantities, and I’ll wrap up by sharing a few bonus images that didn’t fit anywhere else.
If you aren’t familiar with Andrew Stadel’s website Estimation 180, that’s what gave me the inspiration for taking and sharing the pictures in this post. He has a great Ed Talk from this summer’s California Teachers Summit that you should check out.
Here’s a quick rundown of Andrew’s main points:
- Students often lack the access to opportunities to strengthen their number sense.
- Estimation is a gateway to better number sense.
- Estimation is important because it’s an opportunity to take numbers and make sense of things around us.
- Have students estimate by giving them a visual, asking them a simple question, avoiding guesses, and justifying estimates with reasoning and context clues.
- Make estimation accessible by having students create their own estimation activities.
When you visit Estimation 180, you’ll see that every estimation activity asks a simple question that fall into three categories:
- How long…?
- How many…?
- How much…?
Then he guides students to estimate using reasoning, not guesses. He always asks students to make an estimate that is too high and an estimate that is too low before asking them for their actual estimate. Finally, students have to provide a reason they chose their estimate.
I say all of this because if you want to get the most out of the pictures I share in this post, then you’ll want to follow this same structure or something similar to ensure students are truly processing the activity and not randomly guessing. And with all that said, let’s get to the pictures! (Click a picture to see and/or save a larger version of it.)
Halloween Estimation 1
Before you look at the reveal, you may want to answer the following questions:
- What’s too LOW?
- What’s too HIGH?
- What is your estimate?
- What is your reasoning?
Okay, here’s the reveal:
Halloween Estimation 2
I suggest asking the same questions that you did for the fingers. It may seem redundant, but what we’re going for is repeated reasoning through repeated questioning. What regularities will students begin to notice the more they estimate using those guiding questions?
I’d also like you to think about these two questions:
- Do you think the number of skull erasers in the bag is greater or less than the number of fingers that were in the previous bag?
- What is your reasoning?
And here’s the reveal:
Halloween Estimation 3
What strategies would you use to estimate here? Technically, your students could slowly count every eraser, so you may want to mesh this estimation with a quick images routine – show the picture long enough that students can get a mental image, but not so long that they can count one by one.
Here’s the reveal:
Halloween Estimation 4
This is another picture that could benefit from the quick images routine of showing the picture just long enough for students to get a mental image. You may even want to show it a second time to give students a chance to revise their thinking, but still keep it short enough that they can’t count one by one. I especially like how students can use color to help estimate with this picture.
Here’s the reveal:
Halloween Estimation 5
In order to make a better estimate, you might like some additional information:
How does the side view help you make a more reasonable estimate?
I can give you a bit more information:
How could the measurements help you estimate the total number of stickers?
And, finally, the reveal:
If you want to make your own estimation activities for your students, it’s really that easy. Find something that comes in a pack, cover or hide the total quantity if it’s written on the pack, and provide something for students to use as a benchmark. In the case of the previous pictures you could see all or some of the items in the pack to help get a sense of the size of each object.
As promised, I have some bonus pictures to share before signing off. These pictures didn’t fit with the other sections I wrote about, but I still wanted to share them.
I like this picture because there are so many different ways students could find the total number of pumpkins. I also like that some students may notice the tall white pumpkin while others may only see the 3 by 3 array of pumpkins. It reminds me of a similar visual prompt Joe Schwartz shared in a post he wrote about the Notice and Wonder strategy. Scroll down to the section in his post that says “Grade 1.” What I liked was all the different number sentences the teacher recorded to show all the different ways students saw the quantities in his picture.
We saw several examples of arrays in the previous two posts. This is a much larger total than those examples. I like how the rows are spread apart from each other to draw attention to them. However, the columns also stand out because the color of gem is the same within each column. So much to talk about structure here, along with multiplication and fractions.
I considered putting this final image in with the estimation pictures. I didn’t hide how many bubble sticks are in each package, but that doesn’t necessarily tell you how many bubble sticks are in the whole box! I like that there are 10 packs in the two left columns and 1 pack all by itself. It’s such a natural way to show 24 × 11 broken apart into 24 × 10 and 24 × 1. (And I didn’t even plan it. This is how the box was arranged.)
That wraps up my blog series on finding math in the world around us. In addition to getting a slew of pictures you can use in your classroom, I hope it sparks your curiosity the next time you’re out and about, or even hanging around close to home. Maybe something will catch your mathematical eye. if so, snap a picture to share and discuss with your class. Then come back here and leave a comment to let me know about it. I’d love to hear your stories.