Hopping Backward on the Number Line
Unit: Links Away
PreK to 2nd
Grace M. Burton
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.
Number Line Hopping Activity Sheet
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.
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
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?
[I will start with the biggest number.]
Pre K to 2nd
Counting Back and Counting On
Grade: PreK to 2nd
Taking Away Sets
Finding the Balance
Grade: PreK to 2nd, 6th to 8th
Finding Fact Families
Practice Makes Perfect
Looking Back and Moving Forward