Hula hoops, bean bags, and a room full of children. What does your mind go to? Is it missing addends? Probably not! If you didn’t go to unknown addends, I want you to visualize teaching this complex concept to your students. What does it look like? What does it sound like? How many students master this skill by the time your unit is over?
By the time we get to unknown addends, students have typically had experience with addition and subtraction through 10, sometimes exposure through 20, and how those operations relate to one another with fact families. These are all building blocks that prepare them for unknown addends. This is a hard skill for students to grasp and you might have felt before that you didn’t have enough time to spend on it for students to truly master it. What if I told you that I could help you teach ALL of your students this complex math skill and that almost all of them would master it or be on their way to mastery? Missing addends is tricky but if you keep it fun and focus on a few things, I promise you, you’ll have kids leaving your class experts on this concept!
There are some key components in helping students master unknown addends. Using the CRA model, coupled with a math workshop, are two of them. With these two models, students are given ample opportunities to practice this complex skill in a way that works for them.
The CRA model breaks down math into three components: Concrete, Representations, and Abstract. This is where the power lies. All students start with concrete practice. As we practice our concrete skills together, THEN drawings, or representations (R) and mental math, or A-abstract, concepts are introduced. With all of these components, not only are students given choices on how to interact with the skill, it also is differentiating for their needs. Learn more in depth details about the CRA Model HERE. The math workshop model is an amazing combination of hands-on learning activities and direct instruction. It embodies differentiation and student choice and children stay engaged and learning. There are many different ways to implement a math workshop but it generally consists of direct instruction in the form of a mini lesson, followed up with ample time for practice in a student centered setting. The workshop is ended with a debriefing that includes a recap and reflection on student learning. You can learn more about implementing a guided math workshop HERE. But before we get our students started with the content, let’s intrigue their little minds!
Set Up Those Hoops!
I bet you’re wondering, “What the heck are these hula hoops for?” I pull out these amazing tools every single time I introduce this concept to students because they have the exact same reaction: What is this and how is it math?
We look at missing addends like a mystery that needs to be solved. With this information and your hula hoops, you know your students are engaged. This hands-on learning is not only exciting, but we’ve also now made this concept more concrete for them. We add in more concrete components, such as bean bags and equation symbols. Since students have already had lots of exposure to equations, adding the plus and equal sign helps students understand that we are working to fill an equation together.
Here we’ve used the example question of “4 + _____ = 9” Since the standard is using subtraction to solve unknown addend equations, we use the bean bags to build our subtraction equation together. Then it’s as easy as using a strategy to solve for subtraction. This introductory lesson is a great hook for students and gets them really excited to learn more about how to solve unknown addends.
Using Math Workshop, we start with our mini lesson. A typical mini lesson with unknown addends looks like most other math lessons… pretty messy. It’s us working on the carpet together with tons of manipulatives, white boards or ipads, and an anchor chart or one displayed on the SMART Board. I am a HUGE proponent of gradual release (I do, We do, You do) so we follow that model.
While going through our lessons I heavily model for students. This looks like A LOT of thinking aloud to explain what I’m doing and why I’m doing it. Students watch as I work through an unknown addend equation and listen to me explain every single step of the way. I usually start modeling with manipulatives so they feel comfortable doing it too. I do this a few times while having students notice my strategies that I use and how I check my work.
After I’ve modeled for students, now it’s time for US to practice. This is where they get really excited! They get to use their manipulatives and it has taken away so much of the burden of heavy math. This concrete phase is SO important because it gives students a better foundation for those representations and abstract thinking of math to stand on. I also introduce drawings and mental math strategies for those students who are ready to move away from the concrete. This is where your differentiation comes in. Students are given those choices on how best to begin solving their problems. In the pictures below, you’ll see that reflected in the student work displayed. During this whole group time together after our mini lesson, we work hard to solve problems, model, and even more importantly, make mistakes. We work through them together and learn strategies that help us grow.
Practice Makes Progress
Independent and center practice are both crucial workshop pieces to help your students thrive. When it comes to this practice that makes progress, remember that targeted practice is going to give you the most bang for your buck. Providing students with more targeted practice to see what they know and how we can continue to support their learning. This means that your centers and independent work must be differentiated which may equal a little extra prep work behind the scenes but it’s worth it. This is because there is power in targeted questions. They can quickly show you: what students know, how they are doing with the targeted skill, and what support you can give them the next day and week to get them to mastery.
Being able to flexibly cater to your students’ needs is one of the most beautiful things about workshop. You are able to provide all these areas and opportunities to support students and help them thrive. And over here center time is NEVER boring! Take a look at some of the fun, engaging, and differentiated activities students can use below! Not only are they super exciting, it also covers ALL the targeted practice for YOU to get your students to mastery.
Small Group Time is a BIG Deal
While your mini lesson and whole group time provides a strong base, and center time provides ample practice, your guided group time is really where all the magic happens. When I’m planning my small group sessions, I like to use the standards from the grade directly above me and below me to see how best to differentiate for students.
Lower grade standards help me to close the gap for students that are struggling, whereas higher grade standards provide me with skills to challenge students who have mastered the concept. We might have students working on basic addition and subtraction before going into unknown addends, while some students are stepping up their skills with numbers within 20, 100, or even 1000 depending on the needs. No matter where students are, we ALWAYS start out concrete before representations and abstract concepts. They are given ample strategies, materials, and proper scaffolding to help them be successful. Students are given the tools they need to thrive with the skills they need to work on. Those could include two sided counters, equation stems, open number lines, and more.
Check out what our small group table has looked like for students on all levels!
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Tackling Story Problems
It’s so exciting when students are really starting to get unknown addend equations! However, now it’s time to throw a wrench in and add word problems. No worries though! By using a simple game-changing strategy, in addition to the CRA and workshop model, students can absolutely master those too!
Let’s think about what usually happens when you introduce missing addend word problems. How many times have you seen students read a story problem for unknown addends, add the total and the addend together, and then have no clue why that’s wrong? This is where the simple game-changing strategy comes in.
Take a look at the images below. What do you notice?
The numbers are still there but they are covered. Why? Because if you provide a story problem to a student, most times they will immediately look at the numbers and begin trying to do something with them. What we really want though, is for students to ignore those numbers and try to figure out what the problem is asking us to do. This strategy helps students so much because they can ignore those numbers and focus solely on the problem solving. Teaching them those key vocabulary words can help support their understanding and learn how to problem solve successfully… even with those tricky unknown addends. Would you like to see what this looks like in action? If you subscribe, you’ll have exclusive access to a video of me teaching how I work through numberless word problems just like this one.
So are you ready to tackle this tricky concept? I promise by using these strategies, not only will your students master this complex task, but they will also deeply understand this skill and of course have FUN! Check out this bundle that includes everything you need for a jam packed engaging unit on unknown addends!
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