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.
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| 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.
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| 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.
