Lesson Plan

## Up and Down the Line

### Objectives

This lesson uses story problem contexts to develop strategies for learning basic addition and subtraction facts. A number line is used as a tool for computation. Students are encouraged to represent and discuss their solutions in multiple ways. Students will:

• choose appropriate operations to solve story problems.
• demonstrate addition and subtraction strategies using a number line.
• record number sentences to show their work.
• use counting forward and counting backward strategies.

#### Essential Questions

How are relationships represented mathematically?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How is mathematics used to quantify, compare, represent, and model numbers?
• How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
• How are relationships represented mathematically?

### Vocabulary

• 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.

50–60 minutes

### Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

### Materials

• 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.doc), one per pair of students for Number Line game (none if playing as a class)
• game markers, one per student if playing game in pairs (none if playing as a class)
• Number Line 0–30 (M-1-3-2_Number Line 0-30.docx)

### Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

• 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.doc), one per pair of students for Number Line game (none if playing as a class)
• game markers, one per student if playing game in pairs (none if playing as a class)
• Number Line 0–30 (M-1-3-2_Number Line 0-30.docx)

### Formative Assessment

• View
• Observation during the story problem activity will help to assess student understanding.
• Observation during the Number Line game will help determine which students might benefit from additional instruction.

### Suggested Instructional Supports

• View
Scaffolding, Active Engagement, Modeling, Explicit Instruction W: Prepare a number line on the floor, big enough so that students can walk on it and move forward or backward depending on the associated story problems. H: Read story problems and have students determine the starting point for the problem and then move appropriately forward or backward, depending on the context. Write corresponding number sentences on the board for additional reference. E: Play a game using one number line for the entire class, or small number lines if students are working in pairs. Students use beans marked with a “+” on one side and a “−” on the other to determine whether they move up or down the number line. See the lesson details for all of the rules. R: Monitor students as they play to observe whether they are moving appropriately and writing correct number sentences. Review concepts with students who require some clarification or a reminder. E: Have a group discussion regarding the order of addition and subtraction students used as they played, and the order in which they wrote their number sentences. Ask some students to model what they wrote and demonstrate that the result is the same regardless of which operation is performed first. T: For additional challenges to the Number Line game, increase the length of the line, add more beans, or create a line that does not start with zero. On a regular basis, draw a number line on the board along with a starting point and a set of plus signs and minus signs, and have students record a matching number sentence and number line solution. O: The focus of this lesson is to use a number line as a tool for addition and subtraction problems.

### Instructional Procedures

• View

The first activity in this lesson, working with story problems, helps students become familiar with a number line as a tool to use with addition and subtraction problems. They are asked to listen to problems and determine which operation to use. They must then decide which way to move on the number line to find the solution. This activity leads into the Number Line game. As students watch for a distance between their game markers of ten spaces or more, they begin to see that subtraction can mean a difference between numbers on the number line.

To begin, create a large horizontal number line (0–20) on the floor of the classroom. During this activity talk about the movements required for each of a variety of different story contexts and number sentences. This focuses attention on the spaces on the number line and provides a mental image for thinking about the meaning of addition and subtraction.

“We are going to use this number line to help us find solutions to some story problems. Listen carefully to each story to decide which number we should start on, if we are adding or subtracting, and how many spaces we should move. After using the number line to solve story problems, we will use it to play a game.”

Choose a student to walk on the number line (or to move a marker). Change students with each new story.

“Malia has 12 eggs in her refrigerator. She uses 4 of them to make breakfast. How many does she have left?”

“Geoffrey, which number do you need to start on?” (Twelve.)

“That’s right, go ahead and stand on the12 (or put your marker there). Now, are we adding or subtracting?” (Subtracting, because she uses the eggs and they’re gone.)

“Okay, so which way do you move on the number line, forward or backward?” (I go backward because we’re taking away the eggs she used, so she’ll have fewer.)

“How many spaces will you move?” (Four, because she used four eggs.)

“Yes. Show us what that looks like and count out loud for us.”

Geoffrey should step back four spaces on the number line while counting backward, “11, 10, 9, 8.”

When Geoffrey has moved four steps backward on the number line, ask for a thumbs-up from his classmates who agree with his move or a thumbs-down if they do not. If he makes a mistake, give him a chance to rethink his move or ask a friend for help. If he is correct but some students disagree, choose one of them to act out the story.

Choose a student to write the number sentence that shows the solution to the story:

12 – 4 = 8

Continue with stories that provide a context for thinking about the meaning of addition and subtraction. Model the strategies of counting forward and counting backward. Tell stories such as:

• “Sadie has 9 fish in her aquarium. She saves up her money and buys 6 more. When she puts the new fish in her aquarium, how many fish will she have altogether?”
• “Jon sees 5 birds eating from his birdfeeder. As he sits quietly at the window watching, 5 more fly up to the feeder and start eating. How many birds can Jon count now?”
• “Yesterday I received 10 cards in the mail. Today I received 8 more. How many cards do I have?”
• “Mr. Reed had 20 students in his class in August. During the year, 3 of his students moved away and went to new schools. How many students were in his class at the end of the school year?”
• “Tad picked up 18 rocks while walking on the beach. He put 9 of them back on the beach. He put the rest in his pocket for his rock collection. How many rocks did Tad keep?”
• “Gail went to the store to buy fruit. She bought 4 apples, 5 bananas, and 3 plums. How many pieces of fruit were in her shopping bag when she left the store?”

Number Line Game

When students are successful at choosing the correct operations to perform and demonstrating an understanding of how to model addition and subtraction on the number line, introduce the following game. It could be played in pairs or as a class divided into two teams.

If you are playing with teams, hang a number line on the wall (or create one on a whiteboard) which is large enough that students can stand under each number. You will need a set of seven beans in a cup and dry-erase markers. Each team should choose a student to be the game piece, or “marker.” Teammates take turns shaking the beans and telling their “marker” how to move under the number line.

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

Play one or two practice rounds while explaining the rules:

1. Each player puts his/her marker at 7.
2. Each player takes a turn shaking and dumping the beans. Whoever has the most “+” beans goes first. Alternate turns through the rest of the game.
3. For each turn, put the beans in the cup, shake them, and dump them out. Count how many “+” signs and how many “−” signs you have. Move your marker one space to the right for each + and one space to the left for each −. So, for example, if you roll 4 “+” beans and 3 “–” beans on your first turn, you would move your marker from 0 to the right 4 spaces and stop on 4. Then you would move 3 spaces to the left and stop on 1. Write a number sentence (or number sentences) to show how you moved. In this case, you would write 0 + 4 – 3 = 1. On your next turn you will start at the “1” and move from there. So your number sentence will start with a “1”.
4. The first person to reach 20 on the number line wins.
5. If nobody wins after 10 turns, the game is a tie.

Play a few games as time allows. Monitor students’ work as they play by checking to see whether their number sentences match the set of beans they shake and their movements on the number line.

Bring the class back together and pose this question, “Did it matter which way you moved first during your turn? For example, you start on the 6 and you shake 2 ‘+’ and 5 ‘−’.” Write the number sentence on the board and ask, “Does 6 + 2 – 5 = 6 − 5 + 2?” (yes, both equal 3)

Allow time for students to respond and explain their reasoning. Have students model for the class some number sentences they wrote during the game to demonstrate that regardless of which operation they did first, they would have stopped on the same number.

Extension:

Use the following activities in your classroom to meet the needs of students throughout the year.

• Expansion: The Number Line game could be made more challenging by extending the number line from 0 to 30 and adding one, two, or three more beans (M-1-3-2_Number Line 0-30.docx).

For students who are ready for a greater challenge, create a number line that does not start with zero. Choose any expanse of 20 numbers such as 10–30 or 25–45 and create a number line. Use the original set of seven beans.

• Routine: Have students keep a math journal in their desks. As students arrive, ask them to take out their journals as part of their morning routine and write solutions to problems you post on the board. To reinforce using a number line for addition and subtraction, occasionally hang or draw a number line on the board (0–20) and draw seven bean shapes under it. Draw “+” signs on some of the shapes and “−” signs on the rest. Circle a number on the number line and designate it as the starting number. Ask students to record in their journals the number sentences that would show how they could move on the number line and write the number they would land on. Choose students to share solutions.
• Workstation or Small Group: Be watchful for students who are interval or discrete counters. The students who are one off may need some assistance in understanding that they do not need to count the space they start on, but to start counting forward or backward on the next space. Set up a Number Line game at a workstation for two players. Provide a number line, two game markers, and whiteboards or paper for recording. Rules for the game are the same as the version played in this lesson.
This game could be used with a small group for guided practice. Divide the group into teams of two or three players and play according to the team rules.

### Related Instructional Videos

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Final 3/14/14