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Math Unit 13

 

Study Guide

Unit 13: Area, Perimeter and Volume

 

Chapter 1- Examples of test questions:

  • Think about your living room.  When you try to figure out how much flooring you need to cover the floor space, you need to know the area of the room.  Area is the amount of flat space an object covers.
  • In class we have worked with square units.  If you have a 1-inch by 1-inch square unit the area is 1-inch.  If you add more 1-inch squares, you’d need to have four to make another square.  The area would be 4 inches.  Perfect squares have the same length as width.
    • To find the area of a perfect square or even a rectangle, multiply the length by width to find the area.
  • The 1-inch squares can be made into various shapes.  If you have six 1-inch squares, the area will always be the same even if shape is not the same.
  • Transition to shapes that have lengths and widths that aren’t based on 1-inch squares.  For example, a 6 cm by 4 cm rectangle.
  • Various flat figures will be drawn.  Squares are noted as 1 square unit.  Some squares are cut in half and placed in various places on the figure.  Students need to count the squares to find the area.
    • Which figure has the largest/smallest area?
    • Figure 1 is made up of ____ more/less square units than Figure 2.
    • Look at a figure and draw a figure that has the same area.
    • Seeing various figures, find the figure with an area of 5 square inches.
    • What is the difference in area between Figure 1 and Figure 2?
  • Various flat figures will be drawn.  Squares are noted as 1 square centimeter.  Some squares are cut in half and placed in various places on the figure.  Students need to count the squares to find the area.
    • Which figure has the largest/smallest area?
    • What is its area?
    • Draw a figure with an area of 14 square centimeters.
  • Word problem: The mosaic had 5-inch square tiles.  There were 16 such tiles.  What was the area of the mosaic?
    • Step one - find the area of the 5-inch square tile.  5x5 = 25
    • Step two - find the area of 16 such tiles - 16x25

 

Chapter 2- Examples of test questions:

  • Think about a yard that needs a fence.  You need to know the perimeter to know how much fencing to purchase.  The perimeter of a figure is the distance around the outside of the figure.
    • To find the perimeter of a rectilinear (figure that doesn’t make a perfect rectangle) figure, count up the units of length along the outside.  Be careful to count each unit length only once, and not to count a square corner as only one unit.  Idea: mark off the units as they are counted.
  • Different shapes may have the same area but different perimeters, or the same perimeter but different areas, or two shapes could have the same perimeter and area but be different shapes.
  • If the length of the sides is measured or give, we find the perimeter by adding up the lengths of the sides.
  • Have students practice finding the area and perimeter of flat objects in your home.
    • If you have a rectangular or square table, have students measure the length and width.
      • Area = multiply the length by width
      • Perimeter = add the sides together (length + length + width + width)
  • Figures with 1 cm squares in various forms.  Find both perimeter and area.
  • Compare various figures 1 cm squares.
    • Which ones have the same area and perimeter?
    • Which ones have the same area but different perimeters?
    • Which ones have the same perimeter but different areas?
  • Compare two figures of various shapes.
    • Which figure has a longer perimeter?
    • What is the difference in perimeter?
  • Figures will be given with the actual measurement of the sides in inches and centimeters.  Find the perimeter.
    • If a square is drawn and only one side of measurement is given, know that all sides are the same.  Remember that a square can be called a rhombus.
    • The perimeter is given and the length of three sides.  Find the missing length.
  • Two figures given.  One a square with one side labeled.  Find the perimeter of the square.  Then compare it to a rectangle.  The rectangle has one side labeled, but the other side needs to be figured out.  The perimeter of the square and rectangle are the same.

 

Chapter 3- Examples of test questions:

  • Two-dimensional representations of simple solids made up of unit cubes.
    • A rectangular prism has a box shape.
    • If the length of all three sides (in all three dimensions) is the same, then the rectangular prism is a cube.
  • Find the volume of solid figures by counting the number of cubes that would fill them.  Volume is the amount of space, flat as well as vertical, a solid occupies.
    • A cube that is 1 unit on the flat sides and 1 unit on the vertical sides is a 1 cubic unit.
    • Solids with 6 cubes would be 6 cubic units no matter how the 6 cubes were placed.  Solids with the same volume need not look the same.
  • Drawings with various amounts of cubes.
    • How many unit cubes are needed?
    • How many more unit cubes are needed for Figure 1 than Figure 2?
    • How many unit cubes are needed to make both solids for Figure 1 and Figure 2?
    • What is the volume of the solid?
    • Which figure has a volume of 7 cubic units?
    • Which figure has the greatest volume?
  • Two different solids are each made up of 4 unit cubes.  Do the solids have the same volume?
  • A drawing of cubes is given.
    • Figure A: Imagine that 9 cubes are removed.  What is the volume now?
    • Figure B: Imagine that 3 cubes are added.  What is the volume of the solid now?
    • Which solid has a greater volume now, Figure A or Figure B?
  • Various figures are drawn.  Find the volume of each.  Which of the figures has a greater/smaller volume than the answer to the question, “Which solid has a greater volume now, Figure A or Figure B” from above?

 

Unit 13 Cumulative Test:

  • Review all of Units 1 - 13
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