This task was developed to give students a real world application of multiplying fractions that would be engaging. It also allows students to take the concept of arrays, which they should have worked with extensively in their study of multiplication, and apply this familiar concept to another area of multiplication fractions. The relationships between factor sizes and products can be discovered and – generalized as students study partial products. Once students understand this relationship, they will be better able to attend to precision because they will know if their partial products are reasonable. Decomposition: Mixed Number = Whole number + Fraction (if fraction is a proper fraction) x Whole Fraction Number < whole # Whole > or = whole # > or = Fraction Number < whole # Fraction < both Fractions > or = Fraction Students should be allowed to draw representations of their thinking. This allows them to “talk through” their process which in turn enables students the opportunity to attend to precision as they explain and reason mathematically. Teacher Notes: Before the lesson, work with students on a number talk involving multiplication. Use the following problems, one at a time, giving think time and time to share after each one. Discuss strategies and give students opportunities to make connections to other areas in mathematics. Students should notice about the size of the product in relation to the factors. The use of maybe “of” helpful for students to visualize some of the problems. 2 x 4 x 4 or of 4 x or of x x or of x 4 or of 4 2 x 4 or 2 of 4
This task was developed to give students a real world application of multiplying fractions that would be engaging. It also allows students to take the concept of arrays, which they should have worked with extensively in their study of multiplication, and apply this familiar concept to another area of multiplication – fractions. The relationships between factor sizes and products can be discovered and generalized as students study partial products. Once students understand this relationship, they will be better able to attend to precision because they will know if their partial products are reasonable. Decomposition: Mixed Number = Whole number + Fraction (if fraction is a proper fraction) x Whole Number Fraction Whole Number > or = whole # < whole # > or = Fraction Fraction < whole # > or = Fraction < both Fractions Students should be allowed to draw representations of their thinking. This allows them to “talk through” their process which in turn enables students the opportunity to attend to precision as they explain and reason mathematically. Teacher Notes: Before the lesson, work with students on a number talk involving multiplication. Use the following problems, one at a time, giving think time and time to share after each one. Discuss strategies and give students opportunities to make connections to other areas in mathematics. Students should notice about the size of the product in relation to the factors. The use of “of” maybe helpful for students to visualize some of the problems. 2 x 4 x 4 or of 4 x or of x x or of x 4 or of 4 2 x 4 or 2 of 4
CCGPS_Math_5_Unit4Framework.docx