Sunday, February 19, 2017

Addition Notations: Arrow Language

I absolutely love using arrow language! If you are not familiar with the term, arrow language is an addition notation similar to using a number line to solve problems. In terms of teaching different notations and ways to solve addition or subtraction, arrow language is the next step up from number lines.

Find it here!

Arrow Language falls under the partial sums or partial differences umbrella category. Students solve an addition or subtraction problem by completing smaller steps using friendly numbers.

After students are familiar with solving on a number line, using arrow language as a notation is more efficient and doesn't take up as much room on the page. The difference is that arrows are used instead of jumps on a number line and those arrows are not equivalent in size to the amounts being added and subtracted. On a number line, adding 70 results in a much larger jump on the number line compared to adding a 20. With arrow language, adding the 70 and adding the 20 would both be on the same size arrow. My students were able to adjust easily. If you have students struggling with place value, I'd stay with using number lines or base ten blocks before using arrow language as a notation.




Another thing I love about arrow language is that it is solved horizontally instead of the traditional stacked vertical line up. Why? Many higher level math concepts tend to be solved horizontally, such as order of operations, foil, and algebra. It's nice to have a tie in for higher level math. Also, I love that there is no borrowing or carrying in arrow language. Everything is nice and neatly combined and I feel that the students' grasp on place value is more strongly reinforced instead of remembering rules about borrowing or carrying.

I love it!! I really do!! I love it more than using number lines to add and subtract, though you wouldn't know based on how many number line resources are in my store. 😉 I create the resources I need and my students needed number line practice for the beginning of the year to branch from second grade into third. The transition to arrow language was fairly smooth since many of the place value or adding issues were addressed already using number lines.

My resource, Arrow Language,  has 5 worksheets and 3 notes pages that focus on different ways to solve addition problems using arrow language. Starting with counting up to friendly numbers, students solve problems by first adding up to the next tens place and/or hundreds in order to add easier.


Next, students practice separating the addend by place value to add. This is my favorite of the three and solves the problem fairly quickly. Students need to be able to add from different starting points other than friendly numbers as well as be able to add across the hundreds place successful to use this method.


Switching addends is useful to practice as well. The second addend may offer a better starting point than the first addend in terms of adding quickly and efficiently. It's also nice to reinforce the commutative property for addition. I like to compare the starting points of a problem to allow students to start thinking about which addend would be the better choice to start from instead of just mindlessly adding.


For the last 2 worksheets, students choose which way they'd like to add using arrow language. The 3 notes pages can be used for teacher notes, student binder notes, or as a print out to hang up in the classroom. For a video example with arrow language, you can check out my free video Decomposing: Addition Notations that includes printouts as well. The video focuses on a few other useful and handy addition notations as well.




What's great about using arrow language as a notation is that you can use it with regular traditionally stacked worksheets. I am a bit obsessed with the math color worksheets like the Math Line Designs below. My students solve the problems on a lined sheet of paper that they attach to their beautiful colored page when finished and just add the answers to the color page as usual. Math and art belong together! I try to sneak in as many colors, arts, and crafts into math as possible!

Find it at Amazon.

(Note: I just love using the Math Line Designs. I am not in cahoots or earning anything from my recommendation. ☺)


I hope you have a chance to try out arrow language for addition and subtraction. It is a staple in our math strategies toolkit of knowledge. Happy solving!

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