Hello Fourth Grade Families,
Your Fourth Graders are exploring solutions to a problem that is intended to deepen and extend their understanding of the properties of multiplication. The context for this investigation is a cardboard factory. When companies design a box that is needed to ship a product there are many factors to consider; What are the possible dimensions of the box? What dimensions use the least and most cardboard? Can we assign an actual cost to each box if we know the cost of producing one square unit of material? All these questions are explored as students use manipulatives to build various rectangular solids.
Greater efficiency in working with numbers emerge as students uncover new strategies. For example, students are often intrigued by the “double and halve” approach to multiplication. When confronted with multiplying mixed numbers such as 2 ½ x 24, students can double and halve the factors to get 5 x 12 and again to get 10 x 6 (a fact most 4th Graders know). Many are also surprised to learn that the dimensions of two very different boxes, such as a (3 x 6) x 2 and a (6 x 2) x 3, hold the same volume due to the associative property of multiplication.
Another mathematical goal is that students continue to learn to communicate and reason as they create posters that model their thinking and have opportunities to share their thinking in front of peers. As models are built, pictures are drawn and charts created to organize their thinking, students learn from each other’s discoveries and come to their own realizations. Ask your child how many ways there are to make a box that holds 24 cubic units or what kinds of boxes hold the most volume with the least surface area. These can be launchpads for great at-home investigations as well.
Take Care,
Tracy Arensberg
LS Math Specialist
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