Fractions are such an abstract concept, and children need lots of concrete and representational (pictorial) experiences to really understand the meaning of a fraction. Concrete learning also allows students to explore concepts and build understandings of their own, rather than having information delivered to them from a teacher.
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I just developed this activity for exploring equivalent fractions for my third-grade teachers. The students have already learned about fractions as parts of wholes, as parts of sets, and on a number line. In exploring those concepts, some students have already noticed and commented on fractions that show the same amount. In other words, they have already discovered that equivalent fractions exist on their own! This activity will be used in a workstation.
Now, think about how the Standards for Mathematical Practice are embedded in this activity. Students are using tools (manipulatives) and models (sketching the fractions) to represent and explore the fractions. They are looking for structure when asked to make observations about what all the fractions equivalent to one-half have in common. At the conclusion of the activity, they will discuss their ideas with fellow mathematicians, so they will be justifying their solutions and critiquing the reasoning of others. And, since it’s building on what they already know about fractions and the teacher is not doing a direct teach, I’d say it also incorporates problem-solving. That’s a lot of Practices packed into one activity!
After exploring fractions equivalent to one half, students go on to explore additional fractions–there are four of these sheets in all.
The sheets are sized to be used with Learning Resources Fraction Tiles, but I realize everyone doesn’t have that resource, so I made a fraction strip kit that you can print (in either color or B&W), cut out, and use with the activity.