 My third graders have been studying fractions for the past few weeks.  Last week, students represented fractions as multiples of a unit fraction.  In one of the lessons they  broke apart 4/5 into four 1/5 pieces.  They used number lines to show all the different unit fraction pieces.

Afterwards, students represented fraction as multiples of a unit fraction.  They showed how addition equations and multiplication equations are related.  Students reviewed how repeated addition is similar to multplication. Students are becoming better at understanding how to multiply a whole number by a fraction and show the progression on a number line.  I had some students want to jump to multiplying the numerators and denominators , but these students had trouble when explaining why they used that process.

The next task really seemed to stretch their thinking.  It also showed me how well students grasped the idea of combining fractions with similar denominators.  The students were asked to create a three-fruit salad.  They were given fruit and the typical weight for each item.  Students needed to combine three of the fruits to total exactly five pounds. Students needed to create two different recipes for this task. Students needed to also show how they combined the fruits withe  a visual model and display a number model.  For the most part, students were able to combine the fruit accordingly.  An interesting tidbit was that many of them overemphasized one fruit over another.  For example, I had a few students that took 16 cups of grapes to get a total of four pounds.  Then they just found two items that totaled one pound.  I asked the students what those types of fruit salads would taste like.  They didn’t have a response, so I’m assuming we’ll have to look at the context a bit more next time.  This could also be used for a ratio/proportion lesson somewhere down the road.

Later on in the week, I gave a similar task related to a four-fruit salad with a weight of exactly six pounds.  This time the weights weren’t unit fractions. Students first noticed the strawberries 7/8 weight.  A few students were pretty sure that the 7/8 might not be compatible with the rest of the fractions.  Others disagreed with this idea and said that the 1/3 didn’t fit.  Students worked out this task and needed some help along the way.  Students moved towards creating just number models, as some decided to not go the visual model route.  Overall, I’m impressed with how they tackled this problem.  We’ll be discussing it tomorrow afternoon.