Early Addition and Subtraction With Part-Part-Whole Models
In this task, we will start with something for our kindergarten to grade 3 friends focusing on early addition and subtraction with a part-part-whole model. In the first task, we will take it Estimation 180-style to spark curiosity and build number sense through estimation. However, in the sequel, we will fuel sense making by diving into subtraction promoting visual models such as the part-part-whole model.
Act 1: Spark Curiosity
Let’s break this task down into the 4-part math lesson model. In order to get started, we are going to introduce a task that is contextual, visual and concrete.
Show this video.
Then, ask students:
What do you notice?
What do you wonder?
Give students some time (maybe 60 seconds?) to do a rapid write on a piece of paper. Then, ask students to share with their neighbours.
Then, allow students to share with the entire group.
Act 2 – Give Some Information
A question that I’m sure you’ll hear from the notice and wonder portion of act 1 is the following:
How many gummy worms are there?
Let’s give them an opportunity to make a prediction!
Consider using Dan Meyer’s “too low” then “too high” strategy to help them come up with a more reasonable estimate. Let them chat with their neighbours and challenge them to a prediction duel.
Act 3 – See Whose Prediction Is Closest!
After allowing students to share and writing them down on the whiteboard, let’s show them the act 3 video!
Celebrate the closest prediction in the way that you typically do in class. Also make a special note to congratulate some of the students who weren’t so close and ensure that they know that we are building our estimation skills through this process.
While it is great to do this Estimation 180-style task to spark student curiosity while also building their estimation skills, I’m always seeking out ways to extend tasks in order to fuel sense making.
Sequel Act 1 & Act 2: Fuel Sense Making!
Since we’ve already taken some time to set the context for this problem and student curiosity is already sparked, we have them in a perfect spot to help push their thinking further.
I also find that once students are already “into” the task, we don’t necessarily have to spend a ton of time building up the curiosity and anticipation that we did in the initial task.
Let’s give them an opportunity to inquire.
I might show them this video next where I put all of the gummy worms back into the jar and then I remove some.
The question we’ll try to figure out is:
How many gummy worms are left in the jar?
Alternatively, we could also ask:
How many gummy worms were taken from the jar?
Having students predict is always fun, but it might not be necessary to have them all share out as we did in the previous portion of the task. Play it by ear to see how into sharing they are at this stage.
Fuel Sense Making: Early Addition and Subtraction With Part-Part-Whole Models
To me, this portion of the task is the most important. I invest a lot of time sparking curiosity and making predictions in each of my lessons for the payoff of knowing I can dive into the sense making portion using the part-part-whole model for early addition and subtraction. The best part is, you could be using this model for the first time and introducing it in the consolidation of the task or revisiting if your students have already been actively using this model. The benefit of using a part-part-whole model for addition and subtraction is that they can quickly see that addition and subtraction are intrinsically related. They can also see that addition and subtraction word problems can be attacked by determining whether they have been given two parts or a part and the whole right from the start.
Assuming you’ve given students actual gummy worms or alternatively, concrete manipulatives (too much sugar!), you can walk around the room as they work to sequence how you’d like to make some connections using student work.
Here are a few animated gifs that might help when making these connections.
In the first, students might line up 25 gummy worms (or square tiles) and physically remove 8 before recounting.
Alternatively, if students have been exposed to a part-part-whole model, they might choose to go that route. If they haven’t, then you definitely want to include this model in the consolidation of the task as we press for understanding from conceptual to more procedural in nature.
After sharing out student solutions, you will want to consolidate the task as well as the key learning for the lesson. While there are many different consolidation possibilities depending on your grade level, student readiness and the time in the school year, I’d like to think that an anchor chart outlining the importance of a part-part-whole model would be a good possibility in this case.
If this is not the first time students have seen a part-part-whole model, you might consider using this task as a way to fuel sense making around the 4 types of addition and subtraction problems and maybe ask students to create their own problems to match each type:
- Join – I had 15 gummy worms in the jar and I added 10 more. How many gummy worms do I have altogether?
- Separate – I had 25 gummy worms in the jar. After removing some gummy worms, there were 10 left in the jar. How many did I remove?
- Part-Part-Whole – There are 25 gummy worms in the jar total. 8 are green the rest are red. How many are red?
- Compare – One jar has 25 gummy worms while another has 18 gummy worms. How many more gummy worms does the first jar have?
Importance of Concreteness Fading
If you haven’t read any of my previous posts that mention concreteness fading, be sure to give them a read.
You’ll notice that in the visuals I’ve posted above, I’ve shown visual representations of subtraction. It is actually really important that students have an opportunity to manipulate, experience and feel gummy worms or manipulatives that they can imagine are the gummy worms to build their fluency with numbers and operations.
In this case, students should have that concrete manipulative experience prior to having them draw the gummy worms visually on paper.
Then and only then should we move on to symbolic representations when they can build a visual in their mind of the math they are engaging in.
Hope you enjoyed the task!
Let me know in the comments how it went!
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