What on Earth is an open number line?

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After finishing our unit on skip counting and comparing three-digit numbers, we have moved into a lengthy addition and subtraction unit. Right now, we are focusing on equipping our second graders with a variety of subtraction strategies that they flexibly employ to solve different problems.

This unit focuses on a few main Common Core Standards:

CCSS.MATH.2.OA.A1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

CCSS.MATH.CONTENT.2.NBT.A.2: count within 1000; skip-count by 5s, 10s, and 100s.

CCSS.MATH.CONTENT.2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

CCSS.MATH.2.NBT.B.8: Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

Students are asked to subtract numbers within 1000. They need to read a problem and determine what the most efficient strategy would be depending on the problem. Then, they need to solve it and defend their thinking before their peers. Most of our second graders rely on some form of one-to-one counting to add and subtract. Many form stacks of tens and ones using unifix cubes to represent a number and then count the stacks to combine. Many are still stuck using concrete or pictoral operations.

Enter the open number line. We are nudging our second graders toward more efficient and abstract strategies that involve using friendly numbers, like tens, to add and subtract. They can use the open number line to explain their thinking.

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For example, there are many ways to figure out how many years eight-year-old Carlos has to wait to turn 33. Students who are still using one-to-one counting might start at eight and count up by ones until they reach 33, then counting how many jumps they made to get to 33.

As they become more efficient, they might try to get to a friendly number like a ten, jumping two to get to 10, then counting by tens to 30, and finally adding three more to get to 33.

Or they might count backward by tens to 33– 33, 23,13–and take three more away to get to ten, and two more to get to eight.

All of this hopping, jumping, and leaping is mental math. Students are breaking apart and recombining numbers in ways that make sense to them. Instead of following a rote pattern like many of us did as second graders, they are developing genuine number sense. It takes time and patience.

So if your second grader counts backwards by ones to figure out the difference in ages, it’s okay. Let it happen. She is developing her number sense.

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