Students are going to develop their understanding of place value. Students are going to: 
- Employ their knowledge of how to make ten to add single- and double-digit numbers. 
- Utilize a blank number line to assist them in seeing the jumps they make.

- How are mathematical representations of relationships made? 
- How can the study of mathematics aid in clear communication?
- How can identifying regularity or repetition help with problem-solving efficiency?
- How do we represent, compare, quantify, and model numbers using mathematics? 
- What does it mean to analyze or estimate a numerical quantity? 
- What qualifies a tool or approach as suitable for a particular task?

- Compose: Putting numbers together (addition). 
- Decompose: Breaking numbers apart (subtraction).

- open/empty number line drawn on a class whiteboard (line with two arrows on the ends)
- copies of Open Number Line Activity Sheet (M-1-2-2_Open Number Line Activity Sheet)

- Throughout the lesson, observations of the students and their partners will be used to gauge the student's progress. 
- The Open Number Line Activity Sheet (M-1-2-2_Open Number Line Activity Sheet) can be used as a formative assessment as well as a review of the strategies covered in Lesson 2.

Explicit instruction, modeling, scaffolding, and active engagement 
W: Show the class the blank number line. Get comfortable writing numbers on the line. 
H: Put the number 30 on the line and ask how you can get to 35 in one hop. 
E: Ask students to keep making one hop before adding two more to complete the decade. 
R: Give students the chance to plot off-decade numbers on number lines and practice hops and jumps. 
E: Use class discussions or small-group work to assess students, and give them the chance to ask questions and get clarification when needed. Reiterate that any approach is appropriate as long as it helps the student and provides the right response. 
T: Assign students who are having trouble to either start at single digits and jump to ten, or jump from decade numbers and add single digits. After mastering addition across decades, students can proceed to subtract. 
O: The class works together for the first part of the lesson before moving on to solo projects. 

On the board, draw an open number line. Demonstrate to your students the versatility of an open number line by using it to represent any range of numbers. Put a 32 on the number line, and plot the location of 40 by counting by ones. Tell students that reaching the closest ten is the aim of the game. Proceed with this procedure until students appear to comprehend how the number line functions.

Plot the 35th number on the numerical line. "How can I hop to 40 in just one hop?" ask students.

Solicit suggestions. On the number line, draw the hop and indicate it with "+5" above the jump. Next, note that 35 + 5 = 40 is a number sentence. On the number line, plot the number 48. "How can I hop to 50 in just one hop?" poses a question to the class. Ask students to discuss their thoughts with a companion. Next, select a student to distribute. When you have finished, ask the students how to hop to the next decade using the other off-decade numbers.



Plot the 35 once more on the number line after that. Ask the class, "How can you add 6 to 35 using two hops?" Ask students to discuss possible solutions for the problem with a partner.

Invite volunteers to participate. Students may claim that they would add 5 to get to 40, then add 1 more.


Let's try another problem, starting with 46 this time. Ask the class: "How can you use two hops to add eight?" Continue doing this until the students fully grasp the material.



After that, give each pair an Open Number Line Activity Sheet (M-1-2-2_Open Number Line Activity Sheet). Give the students some time to practice the number-line hops together.

As the class gathers in your designated meeting place, request that volunteers demonstrate the jumps they performed for a few of the issues on their worksheets.

Extension:

Routine: You can use the date's number to advance to the following decade or to move daily between decades when you're following a calendar routine.

50 jump back 6

60 jump back 4

63 jump back 6 in two hops

72 jump back 5 in two hops.

Small Group: Give students practice on the blank number line, adding single-digit numbers to decade numbers. After that, you can begin with one digit and increase to reach ten.

Expansion: Students can start working with subtracting from a decade number and subtracting across decades if they are comfortable jumping between them. As an illustration: