Using fraction strips or models, students are given the task of ordering fractions in reverse from greatest to least. The fractions they are ordering include halves, fourths, and eighths. The students are recording the fractions on a number line on their whiteboards. I have chosen this order because our lessons have focused on ordering fractions from least to greatest. I want the students to be flexible with their use of fractions in a reverse order to improve their efficiency in understanding different values. This is similar to students learning to count forwards and backwards. Once the students have ordered the fractions and have built a model showing greatest to least, they record it in their math journals.
Because this is a review lesson, the students will work with a model from the fraction lesson, Plant the Garden to 3/4. This model required students to determine how much more needed to be planted so that the entire garden was planted 3/4 full.
For today's lesson, I show them the same model, and I explain that they will be harvesting and clearing the garden, so that it only planted to 1/3. Changing the unit fraction to one that was different than the first task created the challenge as well as reducing the garden to the given fraction. Additionally, it allowed the students to feel comfortable with a challenging task because of the familiarity of the diagram and similarity to the previous lesson.
Here is how to show the garden planted to 1/3.
During this portion of the lesson, the students engage in solving and determining how to change the image of the garden to be 1/3 planted. In the image, the green sections are the planted sections, and the tan sections are bare land. I choose to have the students work together in partners, as they had for the lesson earlier in the year. This also allowed for the students to have a meaningful discussion about fractions and problem solving.
Because this lesson was presented approximately 3 months after the original lesson, the students review the diagram to determine the beginning fraction amount represented with the green sections. It is possible some students will focus on the tan sections and work on increasing those to 1/3. However, because the warm up focused on working in reverse, and the mini lesson also referenced reducing the planted area to 1/3, the students are focused on the green sections.
The students have used many of the same strategies from the original lesson with creating separate sections and folding the diagram into thirds. This strategy gives them a defined section of how many green squares and triangles will be needed to reach 1/3.
To close this lesson, the students are sharing their solutions strategy in small groups with other students. I want the students to be able to share their strategy and be able to communicate their thinking. This is also an opportunity show how students analyze the thinking of another student and also to consider how their own strategy is similar or could be improved. These solution strategies are key in this lesson, and something that I allow for extra time within the lesson.