This page is an overview and menu page for all the information you need to do these Grade 5 activities.
About the Activities
In the activities How Many Cubes? and Discussion: Sharing Ways of Predicting pairs of students do the following: they look at pictures or written descriptions of rectangular boxes and predict how many unit cubes will fit inside the boxes; they check their predictions by building the boxes and filling them with cubes; and they then describe their method for making predictions and try to convince their classmates that their method will always work. Their work focuses on:
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determining the number of cubes that fit in a box by examining pictorial and written descriptions of the box
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developing, describing, and justifying a strategy for determining the number of cubes that fit in a box
To do these activities, you, the teacher, will need:
(These files are provided in Portable Document Format (PDF) and can be read using Adobe's free Acrobat Reader. If you don't have this application, you can download it at Adobe's web site.)
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Instructions for How Many Cubes? and Discussion: Sharing Ways of Predicting PDF
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Overhead projector
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Transparency of the Packaging Factory Teacher Resource PDF
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Transparency of Student Sheet 1, How Many Cubes? PDF
Your students will need:
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Interlocking cubes, 70 per pair
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Graph paper to match your cubes, 3-5 sheets per pair
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Scissors and tape for each pair
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Student Sheet 1, How Many Cubes?, 1 per pair
About the Unit
Containers and Cubes is the fifth grade unit in the Investigations curriculum focusing on 3-D geometry: volume. Volume is an essential concept in students' learning of three-dimensional or solid geometry. In this unit, students develop viable strategies for visualizing and enumerating cubes in 3-D arrays, and then apply these strategies to determine the volume of various rectangular containers. They then extend their thinking to nonrectangular containers such as pyramids, cylinders, and cones. Throughout the unit, students further develop their visualization skill, their knowledge of 3-D figures, and their understanding of relationships between two-dimensional and three-dimensional objects.
"Often kids are learning to copy...but (not really) to explain what they are doing. Being able to explain has to carry over to other things; it's a way of thinking about learning and acquiring new information that is very important. It carries over to science and social studies and all area of the curriculum." -- Grade 4 Teacher
"[With] this type of math, everybody at one time during the year rises to the surface. I've found this every year that I have taught Investigations.If they are having problems in multiplication, then in geometry they will be the star. If they're having problems with division then in fractions they will be the star. Everybody can find a place in that curriculum where you can be a star and feel really good about yourself. That is the power of Investigations--everybody can be such a part of it and can feel so successful, from the kids that have LD right up to the brightest kid that walks into the school. Everybody has success with it." -- Grade 5 Teacher
"I believe that this Investigations way of thinking is the levellest play field that we can have. It's easy to pick up who is having difficulty, but it's not always the same kids having the same difficulty all the time, so the issues of tracking go away. There are so many ways for kids to come into the process. There is so much allowance for the time it takes to do the thinking. Because the emphasis is on thinking instead of speed or automatic recall or memorization which a lot of math previously seemed to be." -- Grade 4 Teacher
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