Story:Yesterday we got a lot of great practice saying, writing and drawing fractions! Let's put our new knowledge to use! In our new Read Aloud, The Invention of Hugo Cabret, our first setting is a train station. Did you know that a train can be divided into fractions? What if one train compartment was the whole?

Using the Cuisinaire rods, build a train compartment that is 18 units long. You can use tape to create your whole in the most efficient way since there is not an 18 unit-long block. Next, find out all the different ways you can break apart your train compartment into equal fractional pieces. Once you have found all the ways, check in with your teacher for an extension. Remember to use fractional numbers, drawings and words to show your work.

Inspired by The Invention of Hugo Cabret by Brian Selznick; Scholastic, 2007

Suggested manipulatives: Unifix cubes, multilinks, centimeter cubes, wooden blocks, Cuisenaire rods.

Prep time: 5 minutes to prepare the materials.

Classroom time: Asking children to do their best work for each Math Vitamin assumes that some children will need a longer time than others. Ideally you want to offer a block of time for Math Vitamin projects and have another task available (writing, free exploration etc.) for those students who finish work prior to their peers. For this project allow 40-60 minutes for students to work through all the steps.

How to individualize/stretch: Most likely you will have some students who are still exploring factors. Ideally for this Math Vitamin, your students will be comfortable with factors and ready to explore the fractional values of those factors. If not quite ready, change the manipulative. The Cuisenaire rods shown in the video are a more complex manipulative to use for students who are just beginning to see factors and/or work on beginning fractions. To begin, have students use Unifix cubes as they can break them into single units. Build a rod with 8 cubes of one color and then ask students find ways to make shapes of the same length with other colors that equal 8 (2+2+2+2, or 4+4). Then, have them try 12. Once students can see the factor relationship they are ready to explore the fractional values. To begin that work, stay with the unifix cubes, seeing the one-to-one relationship between the whole and the parts is important for this early exploration. Once ready, increase the numbers (36 is a great one!) and eventually ask students to solve with the Cuisenaire rods as seen in this video.

Story: Students have been learning to divide and label fractions. They began this work as detectives using pattern blocks to divide up an hour into equal amounts of time. With the understanding that an hour was equal to a yellow hexagon, they began their work. Today, they are extending that base of information by finding combinations for how they could divide up a three-hour time span. Students are required to discuss their ideas and models with their peers and teachers as they work. All Math Vitamins require students to build, draw and record their work as well as share their thoughts with peers and teachers. The strong UCDS math community within each classroom is developed through the process of peer and teacher conversations that focus on exciting mathematical tasks and engaging ideas about the various approaches to solve them.

Suggested manipulatives: Pattern blocks and base ten blocks are ideal for this particular math vitamin. The Pattern Blocks are visually easy to divide into equal parts and provide direction as to the number of groups needed that help students determine how many minutes each section would represent. Unifix Cubes are also a great way to begin division activities as unlike the Base Ten Blocks, you can separate the blocks into singular units.

Prep time: Adapting the vitamin wording to fit your specific story, putting manipulatives out in the room, creating the “fraction key” and copying the vitamin documentation forms will take about 20 minutes. Set up is always more fun and shorter on time if you do this activity with a colleague.

Classroom time: Asking children to “do their best work” for each Math Vitamin assumes that some children will need a longer time than others. Ideally you want to offer a block of time for Math Vitamin projects and have another task available (writing, free exploration etc.) for those students who finish work prior to their peers. For this project allow 45-60 minutes for students to work through all the steps.

How to individualize/stretch: Always begin by exploring the manipulatives before asking the students to solve tasks with them. For students just beginning to divide, have them find out how many ways they can cover the yellow hexagon with the same color pieces. Have them label their work. Next steps involve having students determine the value that goes with each of the colored pieces (60 divided into 3 groups means that each group is 20). Stretches include changing the value of the whole.