Dividing Shapes and Lines
Students will understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts. Students will understand a fraction as a number on the number line, and with guided instruction, represent fractions on a number line diagram.
Introduction (5 minutes)
- Explain to your students that they will use different models to identify fractional units and label these units on a line.
- Remind your students that a numerator is the top number in a fraction, while the denominator is the bottom number. Explain that equivalent fractions have the same value but different denominators and numerators.
- Tell your students that they will also work with these units to measure objects in the room.
Explicit Instruction/Teacher Modeling (5 minutes)
- Pass out index cards and scissors to students.
- Tell students that they will divide these cards into different fractions and use them to place fractions on a number line.
- As students fold and label their index cards, fold and label an example set for students to be able to see.
Guided Practice/Interactive Modeling (15 minutes)
- Instruct your students to place the first index card on their desks. At this point, this card can be used as a unit, or one length of measurement, to measure their desktops or any other object. The length of the object would be recorded as “4 cards” or however many cards long it is.
- Have students fold the second index card in half and open it back up. Ask them how many pieces they see and the size of the pieces.
- Now, have students draw a line on the fold and label each piece as ½. Remind the students that before they folded the card, the unit was the entire card. Now that the card has been divided in half, each half is a unit. Draw attention to what has happened to the size of the unit, explaining that it would take twice the number of these units to measure the same object.
- Have students fold the third index card in half twice before opening the card back up. Question the students again about the number of pieces they see and the size of the pieces.
- Direct your students to draw a line on each of the folds and label each piece as ¼. Remind the students that before they folded the card, the unit was the entire card. Now that the card has been divided into four pieces, each fourth is a unit. Draw attention to what has happened to the size of the unit, explaining that it would take 4 times as many of these units to measure the same object.
- Have students lay their cards vertically on their desks and compare the two folded index cards to the unfolded card.
- Direct the students’ attention to the line on the floor that represents the first index card (one unit). Measuring the length of a wall in the room could be represented as something similar to “6 lines”, rather than 6 feet or yards.
- Ask your students where they think the ½ cards will go on this line. Have them place these on the top of the line. The ¼ cards will go on the bottom of the line. Question them as to why they believe this would be correct. For example, ask why they would need two ½ cards.
- Repeat this process with the ¼ cards on the bottom of the line. Stop and explain if there are any corrections or interventions in understanding to be made.
- Ask for comparisons of the marks for ½ and ¼. These would be equivalent measurements.
Independent Working Time (10 minutes)
- Have students independently label the provided lines on their papers.
- Give them time to measure one object in the room with each unit and record their findings on the lines. Ask them if they notice the same pattern in the amount it takes to measure the same object.
- Enrichment: Have your students apply the concept from this lesson with 1/3 and 1/6.
- Support: Provide another model of this concept by showing students beakers with the respective portions filled. This will be a vertical representation of a fractional line.
Assessment (5 minutes)
- Instruct your students to draw a line with ½, ¼, and 1/8 represented on the Number Line sheet.
- Then, have your students draw a line with 1/3, 1/6, and 1/12 represented.
Review and Closing (5 minutes)
- Draw or illustrate how the measurements for the measured object in the room changed when different units were used to measure it. Then, write a number sentence to show this change.