3 Mistakes You Need To Avoid When Teaching Missing Numbers in an Equation

I have made every single one of the mistakes that I am asking you to avoid. In fact, most teachers do.

A few years back I sat with a first-grade teacher. The day had ended and she was sitting at the kidney table, head resting on her hands out of pure exhaustion from the day.  She had called me down to meet because she had followed the math program to a T and yet more than a few of her students were still struggling to find a missing number in an addition or subtraction equation.

I could so clearly feel her frustration. I had been in her position a year prior when I was trying to support my intervention students and yet every attempt I made fell flat on its' face. My students consistently would add and subtract arbitrary numbers to find an answer. Any answer. Regardless of whether or not the answer made sense. 

We looked back at the instruction she had delivered and found that students had been asked to solve many story problems. The program had advocated for a lot of drawing and many of those drawings relied on the idea of counting on or counting up to find the unknown number.

These lessons weren't bad! Word problems and counting strategies are exactly the approaches we want to take when teaching missing numbers in addition and subtraction equations. A few tweaks were all that was needed to turn these flat lessons into lightbulb moments.

This activity asks students to manipulate the gems as they add or subtract to find a missing number. 

Mistake #1: Not Making The Lesson Hands-On

When we teach math skills and concepts, we want to give consideration to CRA. Your students will understand more clearly when they first experience at the concrete level. If your curriculum or lessons jump straight to equations without hands-on support, you are being set up for failure! 

When a number is missing from an equation we are either missing the start the change or the result. 

Giving the students two of these numbers and allowing them to experiment with manipulatives will help them to see why future counting strategies work. 

Mistake #2: Being Too Abstract

This was a mistake I made big-time. I was sure that if my students understood fact-families and the part-part-whole relationship that they should easily be able to find the missing number in an equation. "Just pop the numbers into a number bond and from there you can easily find the missing number!" 

<Face Palm>

6-year-old brains just don't work like that. I'm asking them to take one abstract idea (an equation), to pop it into a representative model with no inherent meaning (number bond) and then to *think* about that in a way that leads to either a new equation (abstract idea) or counting strategy (abstract idea). 

... It's a wonder that strategy didn't work! 

You may be surprised when I say that I think it's a great idea to use number bonds and equations. However, they need to be grounded in something more concrete first. You can avoid being too abstract by asking your students to use these representations ONLY AFTER they use concrete manipulatives first. Your students can then record what they did with their manipulatives as an equation or in a number bond. 

Which leads me to my last point. 

This simple activity practices missing numbers in a subtraction equation by asking students to start with a number of frogs and then find out how many need to jump away to get to the target result. 

Mistake #3: Ignoring Context 

The teacher I was working with was using an abundance of story problems as they were written in the curriculum. The problem was that the contexts provided weren't necessarily understandable to our students. Worse yet, the context kept changing! 

When you first introduce this skill, pick a context and let the students play with it over and over and over so that the context is supporting their ability to make meaning rather than hindering their ability to understand. 

Pair these simple contexts with hands-on tools and ask your students to record the results as equations. It will take time and practice but your students will soon gain the skills and confidence they need. 

Learn from my mistakes and skip straight to the lightbulb moment with your students. 

Research-Based Strategies & Exclusive Freebies In Your Inbox

The Ultimate Guide to 1st Grade Math Intervention

When I first became a math interventionist I'll admit, I was a bit over my head! I was set to plan for six different grade levels alongside interventionists who had been doing the job for much longer than I had. I was so, so excited for my new position but moving from the classroom into an interventionist role was like stepping into a whole new world.

Previously, I had been given a full year curriculum and all of the materials I needed to teach my students- now, I was flying solo. Previously, I had been given my class list with the students I was working with already determined- now, I was tasked with setting my roster. Previously, I had taught all subject areas- now I was somehow feeling like one was an even bigger job!

It wasn't long before I had settled into my new position and was loving every single minute. Over the years as an interventionist, I found the routines, lessons, and philosophies that resonated with me and helped my students to learn, grow, and close the gap between themselves and their classmates.

The 1st Grade Math Interventionist Bundle has everything you will need to walk into your classroom feeling calm and confident. You will know you are prepared to reach and teach every single one of your 1st-grade students. Let me walk you through what is included in this incredibly comprehensive resource.

5 Day Focus Lessons 

You will find 14 units of study, each including 5 lessons focused on one very specific topic. Each unit includes:
  • A pre and post assessment
  • Five days of incredibly detailed lessons
  • Independent practice activities
  • Daily tickets out the door
These units are the heart and soul of the bundle and will anchor your year. Because there are only 14 units (listed HERE) you are able to take your time. There is nothing more frustrating than a curriculum that is jam-packed so you feel like your students are chasing the pacing guide. The exact opposite is true here. Spend a day (or two) on a lesson if you need and at the end of a unit if you have any students who need more support you can take the time and give them the help they need. Don't worry, I have plenty of important work for your other students to do!

Seasonal Math Centers

You may think that in an intervention setting the idea of math centers goes out the window. For me, that couldn't be farther from the truth! Math centers will give your students the opportunity to practice, practice, practice until these skills become second nature. Each set of seasonal centers includes centers for every single 1st-grade math standard. This means no matter what month of the year you are in, you will have the perfect math center to meet any and all skills your students need to practice. 

Fact Fluency 

Fact fluency instruction is very much embedded in the skills 1st graders are learning in math. That doesn't mean that you should neglect fluency instruction as well. You will find 40 Print & Go math fact games (20 addition and 20 subtraction). When your students are playing math games they are practicing an abundance of addition and subtraction facts in a short period of time. They are applying the skills they have learned in their lessons and refined in math centers and they are moving their facts to long term memory. 

I have also included a Fact Fluency Strategy & Assessment Guide as a bonus file. This file gives you everything you need to understand how students learn math facts and to assess your students in an efficient and effective manner. 

Word Problem Notebooks 

Word problems are embedded in every 5 Day Focus Unit. You may wish to give your students more opportunities for practice with word problems and that's where the WP Notebooks come into play.

Each themed notebook comes with 25 word problems- that is 5 of each of the problem types in the Common Core Standards. 

I recommend using these notebooks as a warm-up, for assessment, in math centers or even as homework. 

The Planning Guide

I know I promised to help you feel calm and confident and then I described a HUGE bank of resources! No worries, I have also included a planning guide. Within an hour of starting the planning guide, you will have set your full year at a glance. You will have a plan for quick and effective monthly planning and you will set yourself up for success creating weekly plans in just minutes. I am a fan of systems that work for me and this planning guide helps you to take this bundle and use the pieces to "work smarter, not harder" when it comes to your math planning. 

Right now you may be feeling like you are flying solo but that won't always be the case. If you are ready to jump into your next school year feeling calm, confident and ready for your students, head over and grab the 1st Grade Math Interventionist Bundle

Research-Based Strategies 

& Exclusive Freebies In Your Inbox