The photo below is courtesy of Robert Yu, Head of Lego Education China, as shared by Jonathan Rochelle, Director for Project Management at Google.
The use of Legos shown here is a classic (and wicked clever) example of manipulatives.
Before writing the actual fractions students can use drawings as shown below. The sequence of manipulatives, drawings then the actual “mathy” stuff constitutes a Concrete-Representational-Abstract (CRA) model. Concrete = manipulative, Representational = picture, abstract = symbolic or the “mathy” stuff.
Fractions is one of the most challenging math topics. Many high school and college students struggle to some degree with fractions. The Common Core of State Standards (CCSS), despite all the criticism, includes components to address the conceptual understanding of fractions. Below is a photo showing a 4th grade Common Core standard regarding fractions along with an objective for a class lesson I taught at an elementary school in my district. I subsequently presented on this at the national CEC conference in 2014. Notice the bold font at the bottom, ¨justify…using a visual fraction model.¨ The photo above shows an example of a model I used in class.
The photo below shows a handout I used in the lesson. The first activity involved having students create a Lego representation of given fractions. These would eventually lead to the photo at the top with students comparing fractions using Legos. The students were to create the Lego model, draw a picture version of the model then show my co-teacher or I so we could sign off to indicate the student had created the Lego model.
The Lego model is the concrete representation in CRA. In this lesson I subsequently had students use fractions trips (on a handout) and then number lines – see photos below.
The photos below are used to introduce length and area as part of a CRA approach. First a student is asked to build a Lego garage. He first builds the bottom row of a wall and the teacher asks for length in terms of how many Legos are lined up. After building a wall the teacher asks for area in terms of how many Legos are used in the wall. Then the student is given a handout with the following photos. Following this handout the student finds length and area of tiled floor and walls made up of cinder blocks, if available. Eventually a ruler is introduced and multiplying to find area is presented at the end.
For the photo above the student is asked to count Legos to compute length. In the photo below the student is asked which is longer and to explain.
In the photo above the student is first asked to determine the area of the red wall in terms of number of Lego squares. Then the student is asked which wall has more area. This is followed by the photo below. This allows a different perspective of area.