Multiplying a Fraction and a Whole Number: Models

Lesson Frame

• We will represent and solve problems involving multiplication of a whole number and a fraction.
• I will represent and solve problems involving multiplication of a whole number and a fraction.

Lesson

Yesterday we began working with multiplication of a fraction and a whole number by finding fractional parts of a whole. Today, I wanted my kids to be exposed to models that will be coming their way as they work with multiplying fractions:

• Fraction Strips
• Area Models
• Circle Graphs

I also decided that we would solve problems that had a Halloween feel this week to make things a little more interesting. Here are some examples of problems we solved:

This model uses the idea of fractions strips.  Basically, you place two "wholes" together.  Then you have to divide the two wholes into four parts based on the denominator.  I had to be careful with this step, because my kids looked at the model at saw it at 2 wholes and four-fourths.  I had to block the second whole from view and ask my kids how many pieces each whole had.  It was at this point they understood that each section actually represented 1/2.  Finally, we colored in three sections and were able to see that the answer was 1 1/2.

As we worked through this models, it was important to remind students as we worked with each of the 3 "containers" that we were coloring in 1/2 of each of them, one at a time.  The black "x" represents our moving that 1/2 to the first containers to visually see the answer 1 1/2 

My students were most comfortable with this representation.  They have worked with it in many different ways.  Again, the black "x" show us moving pieces to fill in each circle to demonstrated 1 1/8.

Our last type of representation was based on our learning yesterday.  I wanted to remind students of the process and the fact that this is also a model of multiplying a fraction and a whole number.

I explained that this week we are spending the majority of our time taking notes of the multiple ways to show multiplication of a fraction and a whole number.  I also explained that we will be using our notes next week during our rotations in order to become more comfortable with the processes.

Assignment

We spent the final 20 minutes of class working on a Fifth Grade Builder.