When it comes to gaining an understanding of the count sequence for fractions, there are fewer more powerful tools than asking students to place fractions on a number line. For primary students, it is important for students to not only know how to count from 1-10 but to also understand the count sequence. I have written on this in the past and suggested number path activities for our youngest students.
Once our students enter 3rd grade and begin to explore fractions on a number line, I recommend similar activities! For some students, transferring their understanding of whole number number lines to fractions will be quite simple but, for others, there are common misconceptions that arise.
Misconception #1: Confusing “Lines” and “Spaces”
Students who have number line misconceptions will often label this dot 3/4 instead of 2/3. We can support students in overcoming this misconception about fractions on a number line at the concrete, representative, and abstract level.
- Hands-On (Concrete): Give your students a strip of paper the SAME LENGTH as the number line they are working with. As them to fold the paper so that the segments match the number line. You may have to give your students multiple strips of paper so they can experiment and play around- give them the chance to persevere in figuring it out! They can then label the unit fractions on the paper strip and lay it against the number line.
- Representative: Ask your students to color each segment of the number line in a different color. How many colors did it take to represent the different sections of the number line? Ask your students to label the unit fractions within the number line.
- Abstract: Once your students have had a bit of time to explore the number line through concrete and/or representative means, ask them why this line could NOT represent 3/4. Allow your students to use math language think about and explicitly explain their misconception away.
Misconception #2: Thinking a Number Line Needs Numbers
It may be difficult for students to label this dot without any lines or delineations across the number line. That being said, there are things we know about the placement of this dot and we want our students to be critical thinkers when it comes to math! There are a number of questions you can ask your students to help them realize all that they can reason about fractions. Ask your students questions such as:
- What do we know about where this dot is on the number line?
- The dot is just past the half way point.
- The dot is not very close to either end of the number line.
- What fractions could NOT be represented by this dot?
- The dot can’t be a fraction that is equal to or less than 1/2
- It couldn’t, for example, be 9/10… the dot is too far away from 1 whole.
- Giving your students multiple choice options also allows them to think critically about fractions on a number line.
Misconception #3: Not Seeing The Connection Between Whole Numbers and Fraction Numerators
When we label a number line that has been broken into, for example, fifths, the number line would show 1/5, 2/5, 3/5, 4/5 and 5/5 or 1 whole. If your students can accurately space and place numbers 1-5 on an open number line, they should be able to use that knowledge to accurately space and place 1/5 through 5/5. Students do not always make this explicit connection!
To help that connection, try this activity:
- Provide your students with an open number line. Have available number tiles from 0-5 and from 0 – 5/5
- Ask your students to place the 0 at one end of their line and 5/5 at the other end.
- Ask your students to place “2” on the number line. Ask your students why they placed the 2 where they did. What numbers are they leaving space for? What other considerations did they make?
- Next, ask your students to place the number 4. Again, ask about the considerations they made.
- Finally, ask your students to place numbers 1 and 3 into the number line.
This first task should be very simple for your students! You will then repeat the activity with the tiles 0 – 5/5. As your students place their tiles again ask what types of considerations they are making. Additionally, ask “How is placing fifths on the number line similar to placing whole numbers on the number line? Make the connection and similarities explicit for your students!
Try using number lines in your classroom to explore fractions and clear up fraction misconceptions!
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