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:
- Each player puts his/her marker at 7.
- 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.
- 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”.
- The first person to reach 20 on the number line wins.
- 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.
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.