It's springtime in Everyday Math Land, and fractions are all over the place. In our lessons, we're talking about understanding fractions, comparing fractions, fractions on a number line, area models for multiplying fractions, simplifying fractions, even subtracting and dividing fractions. And when the topic is fractions, there is SO much to talk about.
Take this problem, for example, from a fifth grade, Unit 5 math box:
Gwen is 7/8 of the way through a race. It is important students recognize that means Gwen is almost finished with her race. It's an essential piece of information, and it needs to be understood.
Next, we learn that he family was cheering for her when she was 2/3 of the way through the race. It is important for students to know what that means as well. At 2/3 of the race, is Gwen almost finished? Is it as close to the finish as 7/8?
Each of the above two pieces of information could be discussed in a turn-and-talk. It's likely many students will assume this is a multiplication problem (because of the theme of the lesson), so they need to be given the opportunity to justify that, to prove that the operation is multiplication. They won't be able to, because it is a subtraction problem.
Through meaningful discourse, students should be able to explore the information given to realize what is being asked. First we are given one value, 7/8 of the whole (of the race), and then we are given another value, 2/3 of the whole (of the race) and we are asked to identify how much of the whole (of the race) is in the difference (the distance between 2/3 of the race and 7/8 of the race).
So the number model is: 7/8 - 2/3 = X.
The key here is the meaningful conversations, the discourse we want our young friends to experience so we can allow them to form their understanding of the problem. Encourage debate with problems like these; see if students can justify or prove why they chose the operation they chose.
Fractions are really hard for children to grasp, especially for those who have not become fluent and automatic with multiplication, and/or have not mastered the concept of division. It is essential they have these conversations to build their conceptual understanding of what fractions are, and what happens when we add them, subtract them, multiply them and divide them.
We need to do what we can to avoid those fraction immersion blues that come in March and April. It affects students when they are struggling with understanding fractions, and then things just progress too fast. It seems like one minute they were identifying fractions on a number line, and the next they were dividing mixed numbers. The fraction immersion blues affects teachers when they find themselves having to explain fractions to frustrated learners a lot, and having to watch their students suffer through the pain of doing math they don't understand for weeks at a time.
Allowing maximum time for students to collaborate and communicate their thinking around fractions is essential this time of year.
Make room for more collaborative work and meaningful math talk by jigsawing journal activities and spot-checking their journal work and math boxes as they work on them. And let me know if there are ways I can help.