Content Area: Math

 

Index: 4.2E Grade 8 CPI 3

 

Standard: 4.2 - Geometry and Measurement

 

Strand: E - Measuring Geometric Objects

 

Cumulative Progress Indicator: 3 -  The student will develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.

·        Volume - prism, cone, pyramid

·        Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)

·        Impact of a dilation on the surface area and volume of a three-dimensional figure

 

Grade: 8

 

Framework Activities

 

·        Students use a paper fastener to connect two models of rays to form angles of different sizes. They estimate the correct position, then measure their guess with a protractor to see how close they were.

 

·        Students are given a parallelogram-shaped piece of oak-tag and asked to cut it apart and arrange the parts so that it is easy to find its area. Their solutions are expressed verbally and symbolically. This same process is repeated for a trapezoid.

 

·        Students bring cans from home, arrange them by estimated volume from smallest to largest, determine the actual volumes by measuring and computing, and compare these results to their estimates.

 

·        Good conceptual assessment items designed to measure students' understanding of area frequently ask the students to find the area remaining in one figure after the area of another figure has been removed. One sample item from the New Jersey Department of Education's Mathematics Instructional Guide, for example, asks students to find the area of a circular path that surrounds a circular flower garden (MG1). Problems like this one are not only good practice for tests like the Early Warning Test but can also be used as informal assessments by teachers who listen carefully to their students' discussions about them.

 

·        Students work through the Rod Dogs lesson that is described in the First Four Standards of this Framework. Students determine the effects of increasing the dimensions of an object on its surface area and volume.

 

·        Students use pattern blocks to see how the area of a square changes when the length of its side is doubled. They repeat the experiment using equilateral triangles.

 

·        Students use cubes to explore how the volume of a cube changes when the length of one side is doubled, then when the lengths of two sides are doubled, and, finally, when the lengths of all three sides are doubled.

 

·        Students use graph paper to draw as many rectangles as they can that have a perimeter of 16 units. They find the area of each rectangle, look for patterns, and summarize their results. 

 

·        Students trace around their hand on graph paper and count squares to find an approximate value of the area of their hand. They use graph paper with smaller squares to find a better approximation.

 

·        Students work in groups to find the surface area of a leaf. They describe the different methods they have used to accomplish this task. Some groups are asked to go back and reexamine their results. When the class is convinced that all of the results are reasonably accurate, they consider how the surface area of the leaf might be related to the growth of the tree and its needs for carbon dioxide, sunshine, and water.

 

·        Each group of students is given a mixing bowl and asked to find its volume. One group decides to fill the bowl with centimeter cubes, packing them as tightly as they can and then to add a little. Another group decides to turn the bowl upside down and try to build the same shape next to it by making layers of centimeter cubes. Still another group decides to fill the hollow 1000-centimeter cube with water and empty it into the bowl as many times as they can to fill it; they find that doing this three times almost fills the bowl and add 24 centimeter cubes to bring the water level up to the top of the bowl.

 

Vignettes (PDF Format)

 

·        Rod Dogs