Bansho – 3D Geometry and Measurement
Bansho – 3D Geometry and Measurement
Overall:
✓ Compare and sort 3D figures
✓ Identify and construct nets of prisms and pyramids
✓ Volume of a rectangular prism
Specific:
✓ Distinguish among prisms, right prisms, pyramids, and other 3D figures
✓ Identify prisms and pyramids from their nets
✓ Construct nets of prisms and pyramids using a variety of tools
✓ Determine the relationship between capacity (amount a container can hold) and volume (amount of space taken up by an object) (ml to cubic cm – size vs amount of liquid)
✓ Determine the relationship between the height, the area of the base, and the volume of a rectangular prism (stacking base 10 blocks), to arrive at a formula (V=area of base x h or V = l x w x h)
Order of information:
• Naming prisms/pyramids
• Counting faces / vertices / edges
• Naming faces
• Drawing nests
• Identifying nets
• Building models using cubes (volume)
• Base 10 blocks to find formula for volume
• Volume questions
Lesson 1
Do You Remember, page 301 text
Lesson 2
Activate: Name shapes and where they are found in the real world.
Discuss meaning of words, face, vertices, and edges.
Problem: In groups of 4, using a chart, count the faces/vertices/edges of a variety of shapes. See if you can find a pattern in the chart.
Consolidation: 3D shapes are organized by their attributes.
Prisms
Patterns: Number of faces = number of sides of shape + 2
Number of edges = number of sides of shape X 3
Number of vertices = number of sides of shape X 2
Pyramids:
Patterns: Number of faces = sides of base + 1
Number of edges = sides of base X 2
Number of vertices = Number of Faces
HW: Ontario Math workbook pg 56, 57
Lesson 2B
P: Using cube interlocking blocks, explore the relationship between 2 and 3 D objects. Students create a building and draw the front, side, top (possibly rear) views. Also they can include a hint, the number of cubes used.
Rules:
• Base no larger than 2X3.
• No holes in building
• No higher than 3
Answer cards are created by using a top view and writing down the number of cubes in each square:
|1 |3 |
|1 |3 |
|1 |1 |
C: Are there shapes that cannot be solved using the 3 views?
Lesson 2C
P: Using yesterday’s views, have the students go around and try to re-create each others buildings.
Lesson 2D
Teach children how to use dot paper to re-create 3D models
Lesson 3 (possibly skip)
A: Using information from last lesson…
P: Create riddles for different 3D figures.
C: See if the students can solve the riddles. What must a riddle have (what information) in order to distinguish it from all other shapes?
Lesson 4
P: How many nets can you make for a given 3D figure?
• Everyone can work on the same shape?
• Have 2 or 3 groups working on the same shape?
HW: identifying nets sheets
Lesson 5
A: What would you call a unit of measurement that is a cube? What does it measure?
P: Using snap cubes, make a robot, but describe each part on a table in volume.
HW: sheet 52 (OWB)
Option 2 – review ‘buildings’ lesson. Using pre-made sheets with isometric drawings, predict the number of cubes used.
Lesson 6
A: What is a unit of volume? How many in a base 10 flat?
P: If you stacked 17 flats, what would the volume be?
Lesson 7
P: What is the volume of a shoe box that is 25 cm long 50 cm wide and 20 cm tall?
Lesson 8
Task: Find a book or a box in the class. What is the volume?
Questions/assignments to explore:
• Use Google SketchUp to create your dream house. You are only allowed to import vegetation. You must write up a description of the house using 3D geometry vocabulary.
• Prove or disprove, if you double the dimensions of a cube, you will double the volume.
• Prove or disprove, if you double the length of a rectangular prism, you will double the volume.
• If you have a container that is 20 x 10x 12, that is completely full of water, and you drop in a stone block that is 5 x 5 x 5, how much water will remain in the container?
• How big a container (rectangular prism) do you need to hold 3500 L of juice? What if the container had to be a cube, what would the minimum size be? What about 2 containers? ]
• A group of students are trying to fill up a rectangular tub with detergent for a science experiment.
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