I chose this problem because it could be solved differently. The problem requires the students to understand how to add fractions, however, if they use benchmark fractions they will be able to answer the yes or no part of the question. To pry further into their understanding, you could ask the students if he met his goal and by how much or if he didn’t meet his goal then how far off was he. Students should be able to use a visual to support their reasoning.
I’m going to use a website that allows the teacher to visually represent area models and how they work with fractions. I chose this web page for a couple of reasons. First, drawing area models can be difficult to do especially when working with multiplication and the parts get very small. Second, this internet page shows the students how the area model works, then you can go to the try it tab and work with any fractions. I’m going to show the students first how the area model works, then I will take them to the “try it” tab and have them give me some fractions to watch and see what happens when they are multiplied. Students will NOT be taking notes at this time. I want this to be pure instruction which means they are watching only. They won’t be answering questions nor will they be writing anything down. I would take several examples from students before I move on to letting them try some on their own.
During this time the students will be working on multiplying fractions and applying what they just saw from the internet page about using area models to multiply. Students will be modeling the problem, finding the solution, and simplifying if needed for each problem.
I’ve chosen 4 problems that students will come across when multiplying: fraction by fraction (no simplifying), fraction by fraction (simplifying), whole number x fraction, and mixed number by fraction. Students will struggle with multiplying the mixed number by a fraction. As students are working on this problem, ask them if there is another way to represent that mixed number to simplify their problem? Encourage students to make a mixed number and model it this way to help simplify the problem. Students should be able to model for each of these to get their answer.
As students finish one problem, I want them to do a HUSUPU to check solutions with another partner. This will work out well because students that know what they are doing can check with other high functioning students because they will be done faster. Struggling students will need help and this will give me time to support those students.
Before moving on to the next section, place one of the problems on the board (preferably a fraction by fraction without simplifying) and ask students if they notice anything about the expression and its answer? It will be interesting to see if the students notice the algorithm for multiplying fractions.
This is a problem out of the math series book Number Tools (Britannica, 1997). The students will be multiplying and adding with fractions to reduce and expand the recipe. The table works like a ratio table in that they can multiply or add columns together to get to the next column. If students are having difficulty remind them they can use the area model, used from earlier in the lesson to help them find a solution. (SMP 1, 2,5,6)
Encourage students to share strategies with tablemates as the finish each column. Sharing strategies means to explain how they got the answer, not just the answer (SMP 3)
I’m giving this problem to the students to work out on their own. I want to see if they recognize this as a multiplication problem and if they can reason out, through modeling, what their solution is and how they know their solution is correct.
Allow students time to work out this problem. As students are working on the problem, you can walk around looking for different strategies or visuals used to support their answer. Use these students to demonstrate their understanding while working it out on the board. It is good to let students see that there is more than one way to solve a problem. While at the board, students should talk out loud their thinking so students can understand their thought process.