The Measuring Cups is a set of five nesting, polygonal containers with flat bottoms and tops. These measuring containers hold, and are labeled with, common US customary volume units (1 tsp, 1 tbsp, and fractional cups). Additionally, all containers feature the equivalent metric volume measure (e.g., 5ml, 15ml, etc.). Finally, the largest measuring container features the mass equivalencies (grams and oz) of 0.5 cups (120ml) of three common baking ingredients (flour, sugar, butter). The model can be printed without support structures in most 3D printers.

**Big Idea**

The Measuring Cups manipulative are a useful tool for exploring several volumetric and density relationships. In their most basic use, the cups allow for the exploration and comparison of US customary and metric volumetric units. Three of the cups can be used to directly compare fractional relationships with US customary units (½ cup, ⅓ cup, ¼ cup) while all of the cups’ metric volumetric sizes can be used with advanced learners to determine ratios and relationships. Finally, material density can be explored using materials listed on the ½ cup (120 ml) container and extended with the use of other materials and a scale.

Students engaging with this basic manipulative can first build an understanding of volume while using a single material and then density when using multiple materials.

**Purpose**

Students can use the Measuring Cups to make sense of different unit standards used to represent the same quantity (e.g., US Customary vs Metric), in addition they can use the manipulatives to visualize various ratios and fractional relationships between a single material source, and finally they can use these manipulatives to investigate the density relationship between various materials of the same volume.

**Sample Tasks and Explorations**

- Using the smallest measuring container (2 tsp, 5ml), how many of the container are required to fill each of the other containers? Repeat the exercise for each of the containers except the ⅓ cup (80 ml).
- Show that the ⅓ cup (80 ml) container is the equivalent volume of all the smaller containers.
- Using water as a source material along with other lab equipment (e.g., graduated cylinders) check and record the actual volume of the volume of the measuring cups. Extension : compute the error and/or difference in measures.
- Verify that
**two**of the largest containers (½ cup; 120ml container) are equivalent to**three**of the 2nd largest (⅓ cups;80 ml container). Are there other container equivalencies that can be found? - Using several easily accessible materials and a single measurement cup, plot and compare the weights of the materials. How do the weights differ given the constant volume?
- Extension: Repeat the experiment with different measurement cups. Plot the volume and weight for each material in a different color.