Google+ Badge

Tuesday, February 03, 2015

Comparing Fractions: Lesson Language

Today students will study how to compare fractions with greater skill and depth.

First, I'll introduce the process with the lesson language below.

Then students will apply that process as they work on their fraction compare posters.

Later students and I will review the concept using this worksheet.

During the explicit teaching time, students will be seated at desks with notebooks. I will be at the front of the room leading the learning activity. My student teacher will walk around helping students follow the lesson.

Then during the project time, students will spread out in the room and next-door computer lab to continue working on their compare posters. At that time I'll coach individual and small groups of students as needed.

Take a look at the language below. Is this how you would teach this concept? How would you change the language or progression? What would you add?

Tomorrow, I'll work backwards a bit, and explore the concept and skill of simplifying fractions.

Learning Language

  1. Let’s compare ⅞ and ⅚.
Take a few  minutes to draw and compare these fractions in your notebooks.

2. Let’s examine these fractions?
What do we know about these fractions?
  • names?
  • simplest form?
  • closer to 0 or 1? How do you know?
  • where do they fall on the number line?
  • how far away from ½?
  • what do they look like as a bar model?

3. Let’s compare the fractions using a number line.
Some fractions are easy to imagine and compare. We can easily place ½ and ¾ on a number line. ½ is less than ¾. Where do you think the fractions above belong on the number line?

4. Finding a common denominator.
  • When fractions are not easy to compare, we can find a common denominator to compare those fractions. A common denominator is in a sense “splitting each fraction amount into the same number of parts.”
  • A common denominator is a multiple that is common to each denominator.
  • What is a common multiple for 6 and 8? 
  • We can multiply the numbers by each other to find a common multiple. So 6 X 8 = 48, and that would be a common multiple, but that’s a big number and more difficult to work with. 
  • Is there a multiple of less value that is a common multiple of 6 and 8? This number would be the Least Common Multiple (LCM) or Lowest Common Denominator (LCD)
  • We can count up by the largest number and stop when we reach a number that is also a multiple of 6 like this 8, 16, 24! 
  • 24 is a multiple of 8 and 6.
  • We can change our images to fractions with 24 parts. That would look like this.

Even with a good tool, it’s difficult to work with only models when converting fractions to fractions with common denominators. There’s an easier numerical way to do this.

We know that when we multiply or divide any number by one, we get an equal number. The same is true for fractions when we multiply or divide any fraction by a fraction that equals 1 (1/1, 2/2/, 3/3, 4/4. . .), we will get an equal fraction.

Now with common denominators the fractions are easy to compare, add, and subtract.

What is the difference between these fractions?

If we add these fractions together, what is the total?