Multiplication Model (Integer/Fractions)

thingiverse

This is created in response to a math teacher's request for a 3D printable model that teaches multiplication to students in grades K-8. It allows users to model both integers and fractions, based on how they define the whole unit. Example 1: What is the result of multiplying 3 by 5? Example 2: What is the area of a rectangle measuring 3 cm by 5 cm, expressed in square centimeters? Example 3: If we consider each board section as one square unit, what is the area of a rectangle that measures 3/12 units by 5/12 units? Print Settings Printer: FlashForge Finder Rafts: No Supports: No Resolution: 0.2mm Infill: 25% Notes: Use a higher infill rate for the slider to improve strength. Post-Printing Place the two sliders carefully on the board, noting that one is slightly taller than the other for proper overlap. If sliding becomes difficult, remove either the right or bottom end of the slider. Design Process I created this design using 123D Design software. Standards CCSS Overview and Background Multiplication models have multiple interpretations. For integers, it can be represented as repeated addition, division (tree), or area calculation. For fractions, it can be viewed as area or a sequence of steps for partitioning. The 3D model allows both integer and fractional multiplications to be modeled. Lesson Plan and Activity Clearly define units (non-dimensional, linear, two-dimensional, or three-dimensional) before starting the activity. To demonstrate integer multiplication, use the small square as a non-dimensional unit for counting. For an area model, use the small square as a 2D unit (unit square). To model fraction multiplication, define the entire board as a two-dimensional unit (square unit). Each small square is equivalent to 1/144 of this unit. Alternatively, you can view the small square as a non-dimensional unit and model fraction multiplication as a sequence of actions. For example: John has 144 toy cars; he gives 3/12 of them to Mary, who then gives 2/12 of what she received to Katie. How many toy cars does Katie receive? The model can be used in various ways depending on the context. Materials Needed N/A