Outcome: Outcome: WA20.5 Extend and apply understanding of 3-D objects including:
- top, bottom, and side views
- scale diagrams.
- When sides of an object are equivalent, only one of the sides needs to be drawn.
- A drawing of an object can be shrunk down or enlarged to fit on paper by using a scale. The scale between sides must be the same.
- An effective drawing of the side views of an object means that the 3-D object can be constructed from its diagram easily.
Task/Problem/Question: Find an object in the classroom with two or more sides that are different. How could you represent the object in 2-D drawings on a piece of paper so that a person can see what all the sides look like?
Alternative: Create a 3-D object using Lego. How can this object be shown in 2-D space?
Lesson Expansion: Students will give their side views to a classmate and the classmate will construct or draw what they have inferred the 3-D object looks like. The completed 3-D objects will be handed back to the original student, who will look for any discrepancies with their object and determine what errors in their drawing led to the discrepancies (the object wasn’t drawn to scale, they didn’t indicate a depression on the front side view, etc.)
- What do you think students might do?
- Student grabs an object that is smaller than the paper, but larger than their hand.
- The student traces each side of the object onto the paper. Questions to ask: What are the lengths of the sides of the object? Are all of the sides useful to draw? What would you do if the object had a more complex shape to trace?
- Student measures the sides of the object and records them exactly on to the page. Questions to ask: Are there any other details of the shape that are important to record, or is it just the side lengths? Does anyone creating this object need more information?
- Student grabs an object that is larger than the paper.
- The student measures the sides and then puts several pieces of paper together to construct views. Questions to ask: Is there a way to fit the pictures all onto one page? How do you make the object smaller on the paper? How do you make the side lengths smaller?
- Student decides that in order to fit on the page, the longest side length must be changed to ____. All other sides are adjusted to be scaled. Questions to ask: Why did you choose that size for the longest side? How did you change the other side lengths?
- Student divides the side lengths by the same number to make the drawing smaller. Questions to ask: Why did you divide by that particular number? Is there a number you could multiply by that would give you the same result?
- Student grabs an object that is smaller than their hand.
- Student draws tiny side views Questions to ask: How detailed can you get with a tiny drawing? Is there another way to draw the side views so that the drawing is more detailed? How do you make a number bigger? How would you make all the numbers bigger?
- Student multiplies all of the side lengths by the same number. Questions to ask: Why did you multiply by that number?
- What barriers might the students encounter?
- Added or subtracted to the side lengths to make them fit. Questions to ask: How do we make equivalent fractions? Do you think that the same idea could apply to the side lengths?
- Misunderstand the question, as in, draw one ‘3-D’ picture instead of the side views. Questions to ask: Does a person know what the bottom of the object looks like from this picture? What does each side look like if you look at it head on? Do you think you could draw a flat picture of just one side?
- Pick a more difficult object to draw. Questions to ask: Are any of the sides similar to any shapes you already know? Is there a good place on the object that you can use as a starting point (a stretch of straight line, or a definite corner)? Without looking at the detail, and just looking at the outline, do you think you could draw the outline?
- Multiply or divide all the sides by different numbers. Questions to ask: Are the differences between all the old side lengths and the new side lengths equal? Is that important? How do we know that our picture is accurate?
|Tracing the Object|
|Measuring the sides and drawing them exactly||
|Shrinking the object by dividing by a number or multiplying by a fraction||
|Deciding what the length of the longest side should be and changing all other sides to be proportional||
|Making an object larger by multiplying by a positive whole number||
Selecting and Sequencing:
- Start with most common and then work towards least common
- Most to least sides drawn
- Begin with objects that are paper sized, move to smaller objects and then larger objects or vice versa
What are you going to say or ask the students to get them to connect their work to the learning goals?
- Which side lengths didn’t need to be drawn? Why were they not important?
- When do you need to draw all side lengths?
- What do you multiply a number by to enlarge it? To shrink it? How does that change the object you drew?
- What is necessary for someone to construct a 3-D object from a 2-D drawing of its sides?
- Do all sides need to be multiplied by the same number? Why?
- Why is scale factor important?
- How does one know the size of the original object if the diagram is resized?
- Can you draw ****’s object from their pictures?
- What was ****’s object?
- What details need to be included in the pictures?