Hopping Backward on the Number Line

• ## Hopping Backward on the Number Line

Periods: 1
Author: Grace M. Burton

### Instructional Plan

Inform the students that they will find differences using the number line model. Make a number line on the floor with numbered carpet squares or by drawing on a shower curtain. Display a subtraction problem, such as 9 – 5 = ___. Ask one student to stand on the number line at 9. Ask the rest of the students which way the student would hop to subtract. When students answer that the student should hop to smaller numbers, have the volunteer hop back 5 spaces. Encourage children to count aloud as each backward hop is made. Describe the action this way:

If you start at 9 and take 5 backward hops, you land on 4.

Allow other students to demonstrate additional subtraction sentences.

After several examples, model how to record counting back on a number line. Display a number line on the board or overhead projector. Write a subtraction sentence, such as 10 – 3. Use a counter to act out this problem, asking students where to place the counter and how many backward hops you should take. After acting this out, record it by circling the number 10 on your number line and drawing 3 backward hops.

Put the children into pairs, and give each pair a counter and an individual number line (or a 12‑inch ruler that they can use as a number line). Have students work in pairs to solve subtraction problems on their number lines and share their answers. Optionally, have students record their action using the Number Line Hopping Activity Sheet before sharing the difference. After some practice, encourage the students to predict the differences and verify their predictions by moving a counter on the number line.

Discuss the order of numbers in subtraction by asking questions such as, "If I start at 9 and hop backward 5 spaces, will I get the same answer as if I start at 5 and hop backward 9 spaces?" Encourage the students to conclude that the order property, which works for addition, does not work for subtraction.

### Assessments and Extensions

Assessment Option

Have students answer the following prompt in their math journals: "How would you tell a friend to find the difference between 2 and 5 using a number line?"

Extensions

1. Pose such puzzles as, "I am the number you land on when you a take a hop of 5 and then hop back 1. Who am I?" Have children create and share similar problems. They can write their puzzles on file cards and give the cards to students in other classes to solve.
2. Move on to the next lesson, Finding the Balance.

### Questions and Reflections

Questions for Students

1. What number will you land on if you start at 5, then hop back 3?

[I landed on 2.]

2. When you hop backwards on a number line, how do you know where to start? How do you know when to stop hopping?

[The first number in the subtraction problem tells me where to start. The second number tells me how many hops to take.]

3. If I start at 9 and hop backward 5 spaces, will I get the same answer as if I start at 5 and hop backward 9 spaces?

[No; if I start at 5, I cannot hop backward 9 spaces.]

4. If I want to find the difference between two numbers, how will I know which number to start with?

Teacher Reflection

• Which children counted as they took hops, and which moved directly to the number?
• What activities would be appropriate for children who have met all the objectives?
• Which children had trouble using the number line? What instructional experiences do they need next?
• Do students need additional experiences to understand the order property?
• Were the numbers used appropriate for the age of your students?
• What adjustments would you make the next time that you teach this lesson?

### Objectives and Standards

Students will be able to:
• Use the number line model to find differences.
• Investigate whether the order property holds for subtraction.

Common Core State Standards – Mathematics

Pre K to 2nd

• Kindergarten
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.

Pre K to 2nd

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.

Pre K to 2nd

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.
Common Core State Standards – Practice
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.

### Related Resources

 Counting Back and Counting OnGrade: PreK to 2ndCreate concrete and symbolic representations for subtracting one. Taking Away SetsGrade: PreK to 2ndSubtract sets of concrete objects and record differences. Finding the BalanceGrade: PreK to 2nd, 6th to 8thModel subtraction equations using pan balances. Finding Fact FamiliesGrade: PreK to 2ndGenerate addition and subtraction fact families. Practice Makes PerfectGrade: PreK to 2ndMatch addition and subtraction facts in the same fact family. Looking Back and Moving ForwardGrade: PreK to 2ndReview subtraction with concrete and symbolic representations.