Unit 7 Overview:

In this unit, students should master multiplying with fractions. They need to understand multiplication as a concept and fractions deeply so they can fully comprehend what happens to the product in fraction multiplication. They need to be able to use previous knowledge, a variety of strategies and models and be able to explain their thinking. Be sure to give students plenty of time to develop visual representations that make sense to them.

1. Students will apply and extend previous understandings of multiplication to multiply a fraction or a whole number by a fraction by interpreting the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q b. (For example, use a visual fraction model to show ⅔ x 4= 8/3 and create a story context for this equation and do the same for ⅔ x ⅘ ). (NF.B.4a)
2. Students will find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying side lengths and multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas (NF.B.4b)
3. Students will interpret multiplication as scaling (resizing), by: comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. (NF.B.5a)
4. Students will explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (nxa)/(nxb) to the effect of multiplying a/b by 1. (NF.B.5b)
5. Students will solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. (Students must create their own visual model). (NF.B.6)
6. Students will make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. (MD.B.2)
7. Students will solve problems where they need to interpret a fraction as division of a numerator by the denominator. (NF.B.3)
8. Students will explore dividing a unit fraction by a whole number or a whole number by a unit fraction and create a story context to model the expression. (Students must create their own visual model). (NF.B.7abc)