1) Identify fractions using concrete materials that represent the area model.

2) Identify fractions using concrete materials that represent the measurement model.

3) Identify fractions using concrete materials that represent the sets model.

1) When teaching this concept, it is very important that you use several “fraction models.” Using more than one fraction model to teach fraction concepts provides students a foundation for generalizing their understanding of fractions to other math concepts/skills. This teaching plan emphasizes three fraction models, the Area Model, the Measurement Model, and the Sets Model. Both the Area Model and the Measurement Model teach fractions as parts of an established “whole” measurable area (e.g. a one-fourth fraction piece is actually one-fourth of the area of the whole circle; a three inch piece of a 12 inch rod represents one-fourth of the whole length of the rod). For most children, especially students with learning difficulties, the Area Model and Measurement models are easier models to grasp compared to the Sets Model which is a third Model for teaching and understanding fractions. Using multiple models to teach fractions is important because it assists students to generalize their understanding of fractions later on. In this teaching plan, the Area Model is taught first, followed by the Measurement Model. The Sets Model is included in the concrete level plan only since drawing solutions using sets can be cumbersome for children, particularly children with written expression difficulties.

2) If you are working with first or second graders, it is recommended that you carefully decide whether your students are ready to understand fractions using the Sets Model (e.g. a set of 12 unifix cubes can be put into groups of three and one group represents ‘one-fourth.’) before implementing the part of the teaching plan that teaches fractional parts through the Sets Model. Some math experts believe this model is best introduced during third grade when students have a better understanding of both number sense including whole numbers and fractional parts.

3) Initially, each fractional part should be taught separately. As students demonstrate understanding of one fractional part, then move to the next, then the next. In this teaching plan, “one-half” is taught first using the Area Model. You will see that descriptions of the various instructional strategies address “one-half” first. You should “stay with” one-half all the way through to scaffolding instruction, then move to “one-fourth,” etc. You will probably notice that students will “catch on” more quickly each time you move through a different fractional part. When you have modeled each fractional part and scaffolded your instruction for each fractional part within the Area Model, then move to student practice (“Acquisition to Mastery”). When you move to the Measurement Model, follow the same process. You may discover that your students will “catch on” more quickly with this model since you have built a solid foundation with the Area Model. However, do not rush this if your students are not ready. Use the same process for teaching understanding with the Sets Model. Remember, you are laying a very important foundation for later understanding of fractions and without this solid foundation, students will be negatively affected later in their mathematics development.