gr8_fractions

= Fractions =

//It is expected that students will://
 * **Prescribed Learning Outcomes**

A6 Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically. [C, CN, ME, PS] || 1/4 x 3/5 = 3/4 x 1/5. (Note that the numerators of the fractions have been "switched" on one side of the equation.) Have students choose two other pairs of fractions and perform this "switching" procedure again. Discuss the results.
 * **Planning for Assessment** || **Assessment Strategies** ||
 * Have students use fraction strips and/or an area model (grid) to demonstrate the following:

Remind students that when applying the order or operations it does not matter if multiplication or division is applied first and that it may be easier to reduce the fractions first before multiplying. Extend the "switching" idea to explain why you are allowed to cross reduce fractions first before multiplying. These ideas may be reinforced by asking students to evaluate questions like the following by multiplying and then reducing and then by reducing and multiplying and discussing which method is easier. a) 24/15 x 7/35 b) 12/25 x 45/10 c) 32/16 X 27/9 || In assessing, look to see whether or not students can do the following: Look for misconceptions that students may have, such as needing to change to common denominators for multiplication. Students should be able to explain in writing and with representations why common denominators are not necessary. || Interview students to assess the logic (and possible mental math) of a solution. Alternately, you may wish for students to write about their thinking in a journal. For instance, 3/4 x 8/5 can easily be calculated by a student thinking, "3/4 of 8 parts is 6, so 3/4 of 8/5 is 6/5. ||
 * model multiplication of a positive fraction by a positive fraction and justify their reasoning.
 * generalize and apply rules for multiplying positive fractions
 * Have students use words and representations to do the following:
 * Explain why dividing two fractions less than one (e.g., 5/6 divided by 1/4) can give a quotient greater than 1.
 * Demonstrate that multiplying a fraction by 1/2 (1/3, or 1/4) is the same as dividing the fraction by 2 (3,or 4 respectively).
 * Explain using fraction multiplication why 2.4 x 0.3 = 0.72.
 * Estimate these answers: (a) 11/12 x 3/5 (b) 15/16 divided by 7/8. Describe your thinking process. || In assessing, look to see whether or not students can do the following:
 * model multiplication and division of a positive fraction by a positive fraction
 * make connections [CN] to decimal fractions
 * estimate the product of two given positive proper fractions to determine if the product will be closer to 0, 1/2, or 1.
 * estimate the quotient of two given positive fractions and compare the estimate to whole number benchmarks.