This lesson builds strategies for learning fundamental addition and subtraction facts using story problem contexts. To aid in computation, a number line is employed. It is encouraged for students to present and talk about their solutions in a variety of ways. Students are going to: 
- Select the right operations to address story problems. 
- Use a number line to illustrate addition and subtraction techniques. 
- Count sentences to demonstrate their work. 
- Make use of counting techniques, both forward and backward.

- What mathematical representations exist for relationships? 
- What are some applications for expressions, equations, and inequalities in the quantification, modeling, solving, and/or analysis of mathematical situations? 
- How can the study of mathematics aid in clear communication? 
- How are relationships in mathematical contexts described by patterns? 
- How can identifying regularity or repetition help with problem-solving efficiency? 
- How are numbers represented, compared, quantified, and modeled using mathematics?

- Addition: To join two or more numbers (or quantities) to get one number (called the sum or total). 
- Subtraction: To take one quantity away from another.

- number line (0–20) for the floor, large enough for students to walk on, or masking tape to create one (number lines at www.jumpingjoeysnumberline.com/products/ ) 
- sets of 7 beans (lima beans work well) prepared in advance, each with a “+” sign on one side and a “−” sign on the other. (Plastic chips could be used instead of beans.) You will need one set per pair of students (or only one set if you play the Number Line game as a class). 
- small cups, one for each set of beans 
- paper and pencils, or dry-erase markers and a whiteboard 
- copies of Number Line (M-1-3-2_Number Line), one per pair of students for the Number Line game (none if playing as a class) 
- game markers, one per student if playing the game in pairs (none if playing as a class) 
- Number Line 0–30 (M-1-3-2_Number Line 0-30)

- Assessing students' understanding during the story problem exercise will be made easier with observation.
- Determine which students would benefit from extra instruction by keeping an eye on them while they play the Number Line game.

Explicit instruction, modeling, scaffolding, and active engagement 
W: Create a number line on the ground that is large enough for students to walk on and move forward or backward following the related story problems. 
H: After reading story problems, assign students to ascertain the problem's beginning and, depending on the situation, proceed suitably forward or backward. For further reference, write the corresponding number sentences on the board. 
E: If students are working in pairs, use small number lines; otherwise, use one number line for the entire class to play a game. Students use beans that have a "−" on one side and a "+" on the other to mark where they move on the number line. To view all of the rules, refer to the lesson details.
R: Watch the students play and make sure they are writing the right numbers in their sentences and moving in the right way. Go over ideas with students who need a refresher or clarification. 
E: Conduct a group conversation about the sequence in which the students wrote their number sentences and performed addition and subtraction while playing. To show that the outcome is the same regardless of which operation is carried out first, ask some students to model what they wrote. 
T: You can add more beans, lengthen the line, or make a line that doesn't begin with zero to make the Number Line game more challenging. Ask students to write a number sentence that matches the number line solution regularly. You can also write a number line on the board with a starting point, and minus signs. 
O: The main goal of this lesson is to teach you how to solve addition and subtraction problems using a number line. 

Students familiarize themselves with the use of a number line as a tool for addition and subtraction problems in the first exercise of this lesson, which involves working with story problems. It is expected of them to listen to problems and decide which operation to apply. To find the answer, they must then choose which direction to go on the number line. This activity precedes the Number Line game. Students start to realize that subtraction can result in differences between numbers on the number line as they keep an eye out for a distance of ten spaces or more between their game markers.

Make a big, horizontal number line (0–20) on the classroom floor to start. Throughout this exercise, discuss the motions needed for each of the numerous story settings and number phrases. This gives the spaces on the number line more attention and gives the meaning of addition and subtraction a mental picture.

"To assist us in solving a few story problems, we will utilize this number line. To determine the starting number, whether to add or subtract and the number of spaces to move, carefully listen to each story. We will play a game with the number line after using it to solve story problems."

Select a student to move a marker or walk on the number line. Every new story has the power to transform students.

"Malia has twelve eggs in her fridge. She makes breakfast with four of them. How many does she have left?"

"Geoffrey, which number should you begin with?" (Twelve.)

"All right, feel free to stand on the 12 (or place your marker there). Are we subtracting or adding right now?" (She is deducting since she uses the eggs and they run out.)

"All right, so do you move forward or backward on the number line?" (I go back because we're going to take away the eggs she used, meaning she will have less.)

"How many spaces will you move?" (Four, as she utilized four eggs.)

"Yes. Give us an example of that, and count aloud for us."

When counting backward, Geoffrey should move four spots back on the number line, making the sequence "11, 10, 9, 8."

Give Geoffrey a thumbs-up from his classmates if they support his move and a thumbs-down from those who disagree once he has taken four steps backward on the number line. Allow him to reconsider his action or ask a friend for assistance if he makes a mistake. Select a student to act out the story if he is right and some others don't.

Select a student to write the following number sentence, which indicates the story's solution:

12 – 4 = 8.

Proceed with stories that offer a framework for considering the significance of addition and subtraction. Provide an example of how to count both forward and backward. Share tales like these:

"Sadie's aquarium is home to nine fish. She purchases six more after saving up her money. How many fish will she have in total when she adds the new fish to her aquarium?"

"Jon observes five birds consuming food from his feeder. Five more fly up to the feeder and begin to eat as he watches silently through the window. Now, how many birds can Jon count?"

"I got ten cards in the mail yesterday. I got eight more today. "How many cards do I have?"

"In August, Mr. Reed's class consisted of 20 pupils. Three of his pupils transferred to new schools during the year. At the end of the academic year, how many students were enrolled in his class?"

"While strolling along the beach, Tad collected eighteen rocks. He returned nine of them to the beach. He pocketed the remaining amount for his collection of rocks. How many rocks did Tad keep?"

"Gail went to buy fruit at the store. She purchased 3 plums, 5 bananas, and 4 apples. "How many fruit pieces did she have in her shopping bag when she left the store?"

Number-Line Game

Introduce the following game once students have shown they understand how to model addition and subtraction on a number line and have successfully chosen the appropriate operations to perform. Pairs or the entire class divided into two teams could play.

Create or hang a number line on the wall big enough for students to stand under each number if you're playing in teams. You'll need dry-erase markers and a set of seven beans in a cup. To serve as the game piece, or "marker," each team should select a student. Taking turns, teammates reveal information and instruct their "marker" on where to go beneath the number line.

If the game is played in pairs, provide two game markers (any small object), a set of seven beans in a cup, a small number line (M-1-3-2_Number Line), paper, and a pencil for writing number sentences.

While describing the rules, play a practice round or two:

1. Each player places his or her marker at 7.

2. It's a turn for each player to dump and shake the beans. The first to go is whoever has the most "+" beans. Alternate turns for the rest of the game.

3. Place the beans in the cup, shake, and then remove them after each turn. Count the number of "+" and "−" signs you currently possess. For every + and −, move your marker one space to the right and left, respectively. For instance, you would move your marker from 0 to the right 4 spaces and stop on 4 if you rolled 4 "+" beans and 3 "-" beans on your first turn. You would then stop on 1 after moving three spaces to the left. To demonstrate your movement, write a number sentence, or number sentences. You would write 0 + 4 – 3 = 1 in this scenario. You will begin at the "1" on your subsequent turn and proceed from there. Thus, a "1" will begin your number sentence.

4. The winner is the first person on the number line to reach 20.

5. After ten turns, if there is a tie, the game is over.

As time permits, engage in a couple of games. Observe students' work while they play, making sure their movements on the number line and their number sentences match the set of beans they shake.

Once the class is back together, ask them if it made a difference which way you moved during your turn. For instance, you shake the two "+" and the five "−" after starting on the 6. Write the numerical sentence on the board and pose the question, "Is 6 + 2 – 5 equal to 6 − 5 + 2?" (Yes, they are equal and equal 3)

Give students ample time to react and clarify their ideas. Ask students to model some number sentences they wrote during the game for the class to show that they would have stopped on the same number regardless of which operation they completed first.

Extension:

To address students' needs all year long, use the following activities in your classroom:

Expansion: You could increase the difficulty of the Number Line game by adding one, two, or three more beans and extending the number line from 0 to 30 (M-1-3-2_Number Line 0-30).

Make a number line that doesn't begin with zero for students who are prepared for a more difficult task. Establish a number line with any range of 20 numbers, for example, 10–30 or 25–45. Utilize the initial batch of seven beans.

Routine: Require students to keep a math journal on their desks. As soon as the students arrive, encourage them to write answers to the problems you post on the board in their journals as part of their morning routine. Draw or hang a number line (0–20) on the board occasionally, and underneath it, draw seven bean shapes to practice using a number line for addition and subtraction. Mark some of the shapes with "+" signs and the remaining ones with "−" signs. Mark the beginning number on the number line by circling that number. Students should be asked to write the number they would land on and the number sentences that would demonstrate how they could move on the number line in their journals. Select students to present their solutions.

Workstation or Small Group: Keep an eye out for students who are interval or discrete counters. It might take some time to help the students who are exceptions comprehend that they should begin counting forward or backward on the subsequent space, not on the first one they land on. Arrange a two-player Number Line game at a workstation. Give each player two game markers, a number line, and whiteboards or paper to record on. The game follows the same rules as the one used in this lesson.
This game could be used for guided practice in a small group setting. Assign players to two- or three-person teams and have them follow the team rules while playing.