# Mound Math Excel Exercise Numbers and Operations

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3 You wonder if you can make a still smaller mound for your classroom, and a much larger one for the city park? Assuming you do a 1/20 scale model, and a 1/2 scale model-what are the diameter and heights of each of these mounds, and how do the volumes change? 1/20 scale model: ½ scale model Diameter height volume What is the ratio of your scale model replica to the original mound diameter? To the original mound height? To the original mound volume? What pattern do you observe in the way that the ratios for diameter and height differ from that for volume? How long would it take one person to build the 1/20 scale model? The ½ scale model? Math investigations How does the volume vary in relation to the diameter and height? In other words, in a 1/10 scale model, where height and diameter are 1/10 of the original, what is the ratio of the volume of the scale model to the original mound? How can you use ratios and formulas to calculate the volume of any scale model? Extensions: For your budget you need to know how many cubic yards of soil you will have to purchase? How does your 1/10 scale model mound volume estimate translate into cubic yards of soil?

4 Assessment framework topics addressed: Addresses use of fractions, decimals, and ratios, and addresses calculation of volume of irregular objects. Apply proportional reasoning to a variety of problem situations (eg comparisons, rates and similarities) Use all operations in everyday situations to solve single or multi-step word problems From Geometry: Identify, describe, and compare properties of 2 and 3 dimensional figures Determine perimeter and area of irregular shapes when given a reference tool such as a grid Draw similar figures in any shape using a scale factor (e.g. enlarge/shrink) Identify three-dimensional shapes from two-dimensional perspectives Use geometric formulas to derive lengths, areas, volumes of common figures

5 Cross-section of Nicholls Mound, as modified from Milwaukee Public Museum records, 1928 The above box is 90 feet from end to end (so you need to estimate just how big the mound itself is) The mound is 11 feet high Objects in mound are not to scale. (Wisconsin law protects all burials, regardless of religion or time of internment)

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