How to Add and Subtract on a Number Line

I've been using Mathematical Reasoning (Level B/1st grade) with my preschooler. (I LOVE Mathematical Reasoning. Best math books ever! We used half of Beginner 1, all of Level A, and are now using Level B.)

Mathematical Reasoning teaches children how to add and subtract using a number line. This is also something my public school fourth graders need to be able to do to meet Common Core standards, except instead of whole numbers, my fourth graders are adding and subtracting fractions.

The problem? When I surveyed my class, half said they'd never explicitly been taught how to use a number line. So, I taught my students how to use a number line the way I taught my daughter to use a number line...

Put your pencil on zero. That's the "starting line."

Make a BIG JUMP to the first number. (For example, in 4 + 3, the BIG JUMP is from 0 to 4.)

Next, make TINY HOPS (to the right for addition, or to the left for subtraction). (In the example 4 + 3, from the number 4, you make 3 TINY HOPS to the right.)

The number you land on is your answer. (In the above example, you land on 7.)

...BIG JUMP & TINY HOPS. That's all there is to it. (You can even do this on the sidewalk with sidewalk chalk and make it like hopscotch for your kinesthic learners.)

The half of my class that hadn't known how to use a number line smiled and made comments like, "Oh, now I get it!"

Here is yet another problem with Common Core: We roll out new standards, with the "expectation" that students in all grades will be able to meet those standards with the teaching they receive that school year.

But let's talk Charlotte Mason for a minute... Let's say you hadn't been a CMer with your child for grades 1 through 3, and then, in year 4, you made the switch. You had never taught your child to narrate, and - all of a sudden - you ask your child to narrate. Would your brand-new-at-narrating student narrate with the ease of a child who had been practicing this skill for three years? Or would your student find it difficult to organize their thoughts and give you more than a one sentence answer to "Tell me about the story."

I'll tell you that, from my own experience, it's work to teach fourth graders who aren't accustomed to narration how to narrate. Public school students are horribly used to being asked questions with single sentence answers, or being told how many sentences a paragraph must have, or being told what page they will find the answer to the question, or being given the answer "Yes" when asked "Is my work/answer good enough?"

We cannot expect students who do not have a foundation in New Program X to be successful in New Program X. It would be less unfair to start New Program X with a group of kindergarteners, and the next year have the first graders continue New Program X, and the year after that have the second graders continue, etc.

But to anyone just reading this because they were never taught to add or subtract using a number line - I wasn't - and is just curious as to an easy, fun way to teach it, I give you BIG JUMP & TINY HOPS. Happy hopping.