• Observe students as they complete the Adding and Subtracting by Jumping Worksheet (M-2-2-3_Adding and Subtracting by Jumping Worksheet and KEY.docx).

• Observe student responses during Instructional Procedures.

• Observe students as they play Top-It, Beat the Calculator, and/or games listed in Related Resources.

Begin by having students do some choral counting as follows:

• “Start at 145 and count forward by 100s until I tell you to stop.” Stop students at 945. (145, 245, 345, 445, 545, 645, 745, 845, 945)
• “Start at 279 and count forward by 100s until I tell you to stop.” Stop students at 1079. (279, 379, 479, 579, 679, 879, 979, 1079)
• “Start at 932 and count backward by 100s until I tell you to stop.” Stop students at 32. (932, 832, 732, 632, 532, 432, 332, 232, 132, 32)
• “Start at 1064 and count backward by 100s until I tell you to stop.” Stop students at 164. (1064, 964, 864, 764, 664, 564, 464, 364, 264, 164)
• “Start at 264 and count forward by 10s until I tell you to stop.” Stop students at 344. (264, 274, 284, 294, 304, 314, 324, 334, 344)
• “Start at 321 and count backward by 10s until I tell you to stop.” Stop students at 281. (321, 311, 301, 291, 281)

“In the last lesson we added and subtracted three-digit numbers splitting each number into hundreds, tens, and ones. Today I am going to show you another strategy we can use to add and subtract numbers. It is called jumping. When we use the jumping strategy, we use an empty number line to record our jumps. We jump forward or backward by 100s, then 10s, and finally 1s. I will model this for you.”

Write 545 + 178 = on the board. Draw a line, put a dot on the left side, and label the dot 545. Say, “My second addend is 178. In 178 there is one hundred so I am going to jump 100 from 545.” Draw an arrow from 545 forward on the number line and write +100. “If I jump 100 from 545 I will land on 645.” Put a dot on the number line and write 645. “In the number 178 there are 7 tens. 7 tens is 70 so I am going to jump forward 70.” As you are counting the jumps, record them on the number line by drawing arrows, writing +10, dotting the number line, and writing the number you land on. “655, 665, 675, 685, 695, 705, 715. In the number 178 there are 8 ones, so now I will jump forward 8 from 715. I know 8 can be decomposed into two parts. I will decompose the 8 into a 5 and a 3 because I know I can jump 5 to get to 720. Then I can jump 3 more to 723.” Write 723 after the equal sign.

Write 268 + 237 = on the board. Guide students through the above process. Be sure to model on your number line what the students should be doing on theirs.

“What number is your empty number line going to begin with?” Students write a line on their whiteboard, put a dot on the left side, and label it 268.

“How many hundreds will you jump?” (2) Students jump 100, draw an arrow, write +100, put a dot on the number line, and label it 368. Students jump another 100, draw an arrow, write +100, put a dot on the number line, and label it 468.

Continue this process by asking the following questions and guiding students through the work on their number line:

“How many tens will you jump?” (3)

“How many ones will you jump?” (7)

“What will you decompose your ones into to get to the next decade (or set of ten)?” (2 and 5)

Next, model this subtraction problem, 645 – 257 =, using an empty number line. Follow the same steps you did when modeling the addition problem. Make sure you begin on the right of the number line so you are making jumps backward.

Write 762 – 325 = on the board. Guide students through the process of jumping backward on their empty number line by asking the following questions about the work on their number line:

• “What number will you write on the number line to begin with?” (762)
• “What side of the number line will you write that number on?” (right)
• “How many hundreds will you jump back?” (3)
• “How many tens will you jump back?” (2)
• “How many ones will you jump back?” (5)
• “What will you decompose your ones into to get the decade (or set of ten) before?” (2 and 3)

“Now you are going to use an empty number line to help you solve addition and subtraction problems.” Distribute a copy to each student of the Adding and Subtracting by Jumping Worksheet (M-2-2-3_Adding and Subtracting by Jumping Worksheet and KEY.docx). Move around the room observing and asking clarifying questions to evaluate which students can add and subtract three-digit numbers using an empty number line and which students need additional exploration.

Extension:

• Routine: Students play Top-It and/or Beat the Calculator (M-2-2-1_Top-It Directions.docx and M-2-2-1_Beat the Calculator Directions.docx). Students can use an empty number line to help them compute. Students can play games listed in Related Resources.
• Small Group: For students who need additional exploration, guide students through additional addition and subtraction problems using the empty number line. Ask the questions you did in Instructional Procedures to guide them. If students are having trouble with three-digit numbers, practice the jumping concept with two-digit numbers.
• Expansion:
  • Students write number stories (addition and subtraction) using three-digit numbers.
  • Students play the suggested Extensions for Top-It and/or Beat the Calculator (M-2-2-1_Top-It Directions.docx and M-2-2-1_Beat the Calculator Directions.docx).
  • Students add four-digit numbers and show their thinking.