Upleveling Missing Part Activities to Build Deeper Mathematical Thinking

Transcript

Welcome fellow Recovering Traditionalists:  Upleveling Missing Part Activities to Build Deeper Mathematical Thinking

I was looking through the book Putting Essential Understanding of Multiplication and Division into Practice in Grades 3–5 by NCTM when I came across something that is actually going to be the focus of three episodes, this one being the first: Upleveling Missing Part Activities.

Missing part activities are where students work with incomplete information. They’re given a whole and part of that whole, and they need to figure out the missing part.  Missing part activities are often used to help students build connections between inverse operations. If 3 plus ?? equals 8, that’s connected to asking what is 8 minus 3. Or 6 times ___ = 12 helps them see the connection to 12 ÷ 6.

A typical Missing Part Activity is when students know that 8 is the whole and 5 is one part, they need to determine that 3 is the missing part. Or in a more visual scenario, if you count out 10 objects with your students, then hide some of them and ask how many are hidden based on what’s still visible.  Inside the Build Math Minds PD site we have a slide deck with over 100 slides of animated visuals just like that.  A set appears, part of it disappears, and then you ask students how many disappeared (we call it the Disappearing Act). BUT, after reading a part of the Multiplication and Division into Practice book, I want to encourage you, and myself, to go beyond the typical Missing Part activity.

Here’s one example from the book that made me stop and think about our typical Missing Part Activities:

It made me imagine ones for addition & subtraction as well, like 8 + 7 is the same as ___ + 10

The reason problems like this are such an important addition to put into your Missing Part activities is that you are building a more cohesive sense of what equality is in mathematics and you are helping them build big mathematical ideas through the properties of numbers they are developing while thinking through these types of problems.

A lot of students think the equal sign means “the answer comes next” because they see problems like 5 + 6 = __ or the missing part version of that is 5 + __ = 11.  It gets ingrained that the answer always comes after the equal sign, even if you aren’t saying that, the kids are seeing it.  So you need to do lots of activities that help students see that the equal sign actually means “is the same as” and these examples are exactly that type of activity.

When thinking through these types of problems, they are essentially developing the Associative Property.  If you’ve forgotten which one that is, the Associative Property is when there is more than 2 numbers being added or multiplied together you can group them any way you want and the answer will stay the same.  So if you have 3 + 8 + 7, I could group the 3 and 7 together and then add the 8 and it would be the same answer as if I had just added them in the order they are given.

When solving a problem like 8 + 7 is the same as ___ + 10 they may not know it but their brain is taking apart numbers and associating them in a different way.  8 + 7 becomes 5 + 3 + 7 and then the 3 and 7 combine to make the 10 needed to figure out how to complete the missing part problem.

Then when solving 18 x 6 is the same as ____ x 12, they can use their understanding of double & halving but also the associative property.  18×6 becomes 9x2x6 because the 2×6 gives the 12 we need.  

Now even though I’m explaining them with the associative property, do NOT go teach that to your students.  The idea is to give them problems like these but allow them to solve it anyway they can.  They should have manipulatives out and modeling these problems.  I’m only sharing the formal associative property strategy with you so you get an idea of the big mathematical ideas these types of problems are helping your students build.  Remember the Lesh Translation Model?  

Kids need to be doing all 5 of the different types of representations and if you only do the associative property you are just doing the Abstract/Symbolic model.

In the next episode I’m going to be sharing how to write problems like these in a real-life context (one of the models in the Lesh Model), which I also got from the Essential Understandings book.  But for this week, I want to encourage you to use these missing part sentences as a Number Talk.  Put one problem on the board, have your students work on it, then take 5 – 7 minutes sharing a few different ways students determine the missing part.  

Number Talks are a great routine to get your students talking and looking at how different strategies work to solve the same problem. Remember that it’s important to focus on the reasoning process rather than just the answers. The value is in how students think about the problems, not just whether they get the right answers.  So during the Number Talk, it’s about sharing their thinking processes and discussing how they are similar and different. 

If you don’t know already I believe every day in math your students should be doing a Number Routine, Contextual/Word Problem, and a Game.  So, this episode was a Number Talk for upleveling your Missing Part activities.  Next episode will be an uplevel to word problems that have a missing part and then the final episode on missing part will be a couple of games I love.

Missing Part problems are probably already in your repertoire, but if you are like me they are probably just the standard “here’s the WHOLE and one of the PARTS, what is the missing part,” and those are good but let’s uplevel them to encourage more thinking, a better understanding of mathematical equality, and the properties of numbers.

Until next week, my fellow Recovering Traditionalists, keep letting your students explore math, keep questioning, and most importantly, keep Building Math Minds.