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Teacher Tool of the Month: Adding and Subtracting with Tens on the Open Number Line

Each month we will be featuring one of our FREE Teacher Tools for interactive whiteboards. Ready for use in elementary classrooms with any type of interactive whiteboard, these high-quality virtual manipulative tools help teachers connect students with great ways to make sense of math. Use these tools to create an environment for students to explain, discuss, and defend their mathematical thinking.

This month we are featuring “Adding and Subtracting with Tens on the Open Number Line “ for 2nd grade students.

Numbers to Twenty on the MathRack

This lesson provides an open number line virtual manipulative for teachers to use in a variety of instructional contexts. In contrast to number lines where all the counting numbers are visible, the open number line displays only starting points, change amounts, and resulting values. Teachers can use it to represent student strategies such as skip counting, adding on, or removal. Research shows this tool helps students move away from counting by ones.

Sample Lesson

Add and Subtract Landmark Numbers:  Students add or subtract two numbers by first jumping by 10 or a multiple of 10 or to the nearest multiple of 10, then adding or subtracting additional tens and leftovers (53+21 becomes 53+10+10+1 or 53+7+10+4 or 53+20+1)


In the jumps-of-ten strategy, one number is kept whole and jumps of ten are added to it.  This thinking is easily represented on an open number line.  Children often begin by adding only one ten at a time, although later all the tens are added at once.


1. Begin by listing the math string below one expression at a time. Ask students to find the sum in their head (mental math). Call on individual students to discuss their strategies before the subsequent problem is presented.
– 63+10
– 43+10
– 123+10
– 143+10

2. Next, draw a number line on the chart paper to illustrate these “jumps”.  See the example below.

3. Show the DreamBox open number line on the interactive white board and write that problem on the chart paper. Ask, “How can we use a mental math strategy to solve this problem? Discuss your strategy with your partner and draw your own open number line.”

4. After students have discussed the strategy, ask for a volunteer for a starting point. That student types the number in the open number line. Ask, “Why did you start with that number?”

5. Ask another student, what would you do next?” You can ask that student as she is demonstrating, “How far would do we need to jump on the number line from 53? Are we going to go forward or go back? Why?”

Sample Responses:

  • “2 jumps of 10 forward because we are adding.”
  • “Jump 20 forward because we are adding.”
  • If a student responds “jump back”, have students discuss that idea with their partner.  Have pairs report out to explain whether they think that strategy will get closer to the sum.
  • Some students may move back on the number line from 53 to the landmark 50 and then add the 10s.  This strategy is valid, and will require adding another jump of three later.

6. After the student has either made two jumps of 10 or one jump of 20, ask, “What should the next tag on the number line read?” Invite individual students to respond, and then ask them to describe how they arrived at an answer. Discuss their strategies.

Possible Responses:

  • “I skip counted by 10s from 53 like this:  53, 63, 73.”
  • “I know 5+2=7 so 50+20=70 and then I added 3.”
  • “I added 20 to 53 and got 73.”
  • “I added one 10 to 53 and got 63, then I added another 10 and got 73.”
  • “I jumped back 3 to 50.  Then I added two tens to get 70, etc.”

7. Invite a student up to the board to label the tag.

8. Ask students, “Are we finished?” If anyone says, “Yes,” ask the class about the leftover ‘1’ from 21. “What do we do with this 1?” Call on students to explain, and invite one student to demonstrate the last jump on the number line.

9. Call on another student to fill in the last tag with the answer and transfer it to the algorithm.

10. Click the “Next” button on the DreamBox open number line tool and begin a new problem. Engage all students in using the open number line to solve the problem and ask them to explain their thinking and justfy their answers. Use the questions above when appropriate to scaffold as needed.


Common Core State Standard
Grade CCSS ID Domain Cluster Standard
2 2.NBT.5 Number and Operations in Base Ten Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
2 2.SMP.2 Mathematical Practices Reason abstractly and quantitatively.

Try the lesson in your classroom today!


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