If Not the Algorithm, Then What?

The summer before my school was implementing Common Core math standards, we all attended a 3-day training.  In 2nd grade we tackle “regrouping” (or borrowing and carrying) in addition and subtraction.  It’s a big deal for us, it’s our thing, and we’re proud to teach this critical skill.

I remember the trainer saying, “you don’t need to be teaching them the algorithms for addition and subtraction anymore.”  What?!?  I’m not sure what I was more uncomfortable with, the hard student desk I was sitting in, or the idea of not teaching the algorithm anymore!   Surely this trainer didn’t know what she was talking about.  Someone was brave enough to raise their hand and ask, “so, if we aren’t teaching the algorithm, how will the kids learn to add and subtract numbers that need regrouping?”

The trainer calmly said, “Well here’s one way, it’s called an open number line.”  I’m sure we looked just like our amazed 2nd graders as we watched her sketch outlines and jumps and solve problems on number lines that only contained a few landmark numbers.

Quick Start Guide

Here are some important things to know about the open number line strategy:

*used to model addition, subtraction, fractions, and time (these are just the ways I’ve used them)
*students start with a blank line and only write down numbers they need as landmarks
*jumps of any size can be taken, jumps of 10 are common because it’s an easy mental computation
*the same problem can usually be solved in more than one way on an open number line
*it’s a written strategy that can eventually be done mentally

Prerequisite Skills

The cool thing about open number lines is that they require (and give kids practice in) using number sense to truly understand what is happening when two numbers are added or subtracted rather than just crossing numbers out, writing a number one over here, and doing other steps because your teacher told you so.  To really use open number lines successfully, it helps if your students have these prerequisite skills:

Smaller numbers to the left, bigger numbers to the right – If students have had exposure to standard number lines, then they will probably understand this.  Having a standard number line posted somewhere in your class is helpful for students who get confused about this.

Counting by 10s – On an open number line, it’s efficient to make jumps of 10, rather than only jumps of 1.  If your students can count by tens starting from any number (both forward and backward) they will be ready to make jumps of 10 on an open number line.  If your kids aren’t quite there yet, here are some number sense routines to help them.

Decomposing numbers – To use an open number line, students will need to be able to break numbers apart.  At the simplest level, they need to be able to separate the 10s and the 1s in a number.  For more complex open number line strategies, they need to both decompose and compose numbers.  For example, in the problem 49 + 24, it would be efficient to break the number 24 into 20 + 3 + 1 so that the 1 can be combined with the 49 to make 50 (a nice, friendly number : )

The Concept of “Friendly Numbers” – “Friendly numbers” are just another way of saying “multiples of 10.”  I explain to my students that any time we can get to a friendly number it makes our lives so much easier because we’re only dealing with 10s, not 1s (“Awww, look how friendly it is kids, it doesn’t even have any ones!…ha, ha : )

Combinations that make 10 – This goes hand-in-hand with “friendly numbers.”  If you know ways to make 10, then you can make easier math problems for yourself, you can get yourself to a friendly number.  If kids know the combinations that make 10, they can look at a number like 37 and think, “I would need 3 more to get to the next friendly number because 7 + 3 makes 10.”

 Addition Strategies

You will find that there is more than one way to solve a given problem using open number lines.  Some strategies are more efficient than others.  These are all available on a FREE HANDOUT

 

Subtraction Strategies

Save Yourself Time

If you’re looking for an easy way to get your kids up and running with open number lines, I have a resource for you in my TpT shop.  It starts with a review of representing numbers, addition, and subtraction on a standard number line, then moves on to open number line basics like making jumps of ten, and continues with more complex problems and strategies. >>SEE MORE

Hannah Braun

Hannah Braun is a former teacher with 8 years of experience in the classroom and a master's degree in early childhood education. She designs engaging, organized classroom resources for 1st-3rd grade teachers.