Extending our mathematical thinking!

We are working hard at building number sense and problem-solving skills here in 5th grade! The mathematical concepts that we teach are CHALLENGING and RIGOROUS, but if we have a strong number sense and willingness to persevere, we have found out that we can feel successful! 

We work a lot with fractions in this grade and, at first, students often feel intimidated by fractions. Part of that intimidation is that they see fractions differently than they do whole numbers. We have been building their comfort level with fractions by using manipulatives and always relating the concepts back to operations with whole numbers first. 

Today we are working on multiplying fractions. We introduced this concept by asking the kids what they notice in the visual below. What could this visual represent? 

So many of the students said that this is representing the area model and that they notice 1 yellow counter out of a total of 4. This is exactly what we wanted them to notice! 

Then we reviewed what the area model of multiplication represents and how we work through the area model with whole numbers. This is what the kids showed as a review. 

Once we reviewed the purpose of the area model of multiplication, we transferred that understanding to multiplying fractions. We went back to the same visual and asked the same questions. Now the students saw the visual representation of 1/2 x 1/2 = 1/4! 

This is the concrete way to show the multiplication of fractions so that the students can physically SEE the math happen!