February 25, 2018

M: AREA, PERIMETER AND VOLUME

Our focus for the next week is to focus on mass, capacity and volume.
BIG IDEAS (taken from “Big Ideas by Dr. Small”):
  • The length of an object is a one-dimensional attribute. Length can be the measurement of a single measure of an object or a combined linear measure, like perimeter.
  • The area of an object is a two-dimensional attribute. Area can be a single measure of a 2-D shape on an object or a combined measure of a 3-D shape, like surface area.
  • The volume of a 3-D object tells how much material it takes to build the object and the capacity of an object tells how much it will hold.
STUDENT LEARNING GOALS:
  • I can determine the area and perimeter of a rectangle
  • I can create a rectangle given the area and/or perimeter
  • I can determine the volume of a rectangular prism.
CURRICULUM EXPECTATIONS:
  • estimate and measure the perimeter and area of regular and irregular polygons, using a variety of tools (e.g., grid paper, geoboard, dynamic geometry software) and strategies
  • create, through investigation using a variety of tools (e.g., pattern blocks, geoboard, grid paper) and strategies, two-dimensional shapes with the same perimeter or the same area (e.g., rectangles and parallelograms with the same base and the same height) (Sample problem: Using dot paper, how many different rectangles can you draw with a perimeter of 12 units? with an area of 12 square units?);
  • determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software, grid paper) and strategies (e.g., building arrays), the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area = length x width; Perimeter = (2 x length) + (2 x width)];
  • solve problems requiring the estimation and calculation of perimeters and areas of rectangles (Sample problem: You are helping to fold towels, and you want them to stack nicely. By folding across the length and/or the width, you fold each towel a total of three times. You want the shape of each folded towel to be as close to a square as possible. Does it matter how you fold the towels?);
  • determine, through investigation, the relationship between capacity (i.e., the amount a container can hold) and volume (i.e., the amount of space taken up by an object), by comparing the volume of an object with the amount of liquid it can contain or displace (e.g., a bottle has a volume, the space it takes up, and a capacity, the amount of liquid it can hold) (Sample problem: Compare the volume and capacity of a thin-walled container in the shape of a rectangular prism to determine the relationship between units for measuring capacity [e.g., millilitres] and units for measuring volume [e.g., cubic centimetres].);
  • determine, through investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume = area of base x height) (Sample problem: Create a variety of rectangular prisms using connecting cubes. For each rectangular prism, record the area of the base, the height, and the volume on a chart. Identify relationships.);

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