Year 2 Lesson Plan 4 - Canceling Like Factors in Fractions

  1. (5 min) Mental Math
    1. What is 3/4 as a decimal? [.75]
    2. Which is larger, 23 or 32? [32]
    3. What is 60% of 60? [36]
    4. Start with 2500; subtract 400; now divide by 7 [300]
    5. Start with 8.4, multiply by 10, now divide by 4 [21]
  2. (5 min) Review of selected problems from lesson 3 (no more than 3 problems)

    When we simplify fractions, we are really canceling like factors. We look for a number that divides, with no remainder, into both the numerator and the denominator of the fraction. Sometimes, the numerator will divide with no remainder; but sometimes the numerator and the denominators are both multiples of the same number which can be "canceled" out. Here is an example of how the canceling works.

    This works because 3 divided by 3 = 1.

    I hope you remember from last year that when we multiply two fractions we multiply the numerators to get the new numerator, and we multiply the denominators to get a new denominator. Sometimes this can result in large numbers that may be difficult to simplfy, such as:

    We can make the problem above a lot easier to multiply and to simplify if we cancel before we multiply. For every factor we cancel in the numerator, we must cancel the same factor somewhere in one of the denominators.

    In the problem above, we can make the job easier by noticing that 5 goes into 15. We cross out the 5 and replace it with a 1. We cross out the 15 and replace it with a 3. Also, we cancel the 7 and 14: 7 becomes 1 and 14 becomes 2. Now we multiply the tops and multiply the bottoms to get a fraction which is already simplified. Here's how it works:

    In the following example, we cancel the 3 in the first denominator with the 6 in the last numerator, leaving a 2. Then we cancel the 2 in the second denominator with the 2 in the last numerator, leaving 1 on the top, and 10 on the bottom. Another way of thinking about this is noticing that 3 x 2 = 6 on the bottom which cancels with 6 on the top. Pretty soon you will get to the point that you can do shortcuts.

    In the following example, you see the 2 in the first fraction canceling the 2 in the last fraction. They do not have to be on top of, or even next to, each other!

  6. WHOLE NUMBERS...... are fractions!

    It even works to cancel units. Here is an example:
    5 feet   x  3600 seconds  =  18,000  feet
      second         hour                hour
  8. In-class exercise. If students finish, check their answers and hand out homework. Let students start working in class.