**Name** |
**Description** |

Running to School, Variation 2 | Students are asked to solve a distance problem involving fractions. |

Making Hot Cocoa, Variation 1 | Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context. |

Making Hot Cocoa, Variation 2 | Students are asked a series of questions involving a fraction and a whole number within the context of a recipe. Students are asked to solve a problem using both a visual model and the standard algorithm. |

Running to School, Variation 3 | Students are asked to solve a distance problem involving fractions. The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution. |

Traffic Jam | Students are asked to use fractions to determine how many hours it will take a car to travel a given distance. |

Video Game Credits | Students are asked to use fractions to determine how long a video game can be played. |

Baking Cookies | The purpose of this task is to help students get a better understanding of multiplying and dividing using fractions. |

Cup of Rice | The purpose of this task is to help give students a better understanding of multiplying and dividing fractions. |

Dan’s Division Strategy | The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division. Students are asked to explain why the quotient of two fractions with common denominators is equal to the quotient of the numerators of those fractions. |

Drinking Juice, Variation 2 | This task builds on a fifth grade fraction multiplication task, "Drinking Juice." This task uses the identical context, but asks the corresponding "Number of Groups Unknown" division problem. See "Drinking Juice, Variation 3" for the "Group Size Unknown" version. |

Drinking Juice, Variation 3 | Students are asked to solve a fraction division problem using a visual model and the standard algorithm. |

How Many _______ Are In. . . ? | This instructional task requires that the students model each problem with some type of fractions manipulatives or drawings. This could be pattern blocks, student or teacher-made fraction strips, or commercially produced fraction pieces. At a minimum, students should draw pictures of each. The above problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them. |

How Many Containers in One Cup / Cups in One Container? | The purpose of this problem is to help students deepen their understanding of the meaning of fractions and fraction division and to see that they get the same answer using standard algorithm as they do just reasoning through the problem. These two fraction division tasks use the same context and ask "How much in one group?" but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division. |

Models for the Multiplication and Division of Fractions | This site uses visual models to better understand what is actually happening when students multiply and divide fractions. Using area models -- one that superimposes squares that are partitioned into the appropriate number of regions, and shaded as needed -- students multiply, divide, and translate the processes to decimals. The lesson uses an interactive simulation that allows students to create their own area models and is embedded with problems throughout for students to solve. |