A pile of cubes can be drawn in 3D or as top, front and side views. A front or side view shows only the tallest pile in each column; a top view with numbers shows every pile.
An architect shows a building from above, from the front and from the side. Why not just one drawing?
An isometric drawing shows a solid in 3D on isometric (triangle) paper. Views are flat drawings seen from one side: the top view (also called the plan), the front view and the side view (together called elevations). A view shows what you can see; cubes hidden behind others do not show.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
One view
Picture a tall tower with a short pile directly behind it.
TryTry it on the board and compare the result with your prediction.
Three views
Press a cell in the grid to add a cube to that pile. After the tallest, it goes back to 0.
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Change the piles so the top view has 4 squares and the front view has 5. Which piles did you change?
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InvestigateWork out why it happens, one step at a time.
What a view shows
How tall is the tallest pile?
Read Noor's working. What does the view show?
A column has piles of 3, 1 and 2 cubes, one behind another. How many squares does the front view show for that column?
Noor works out the front view of a column of piles. Click the line where her reasoning goes wrong.
ModifyChange the problem on purpose and see what happens.
Build to a description
Both views must be 3 squares.
Need a hint?
Piles of 1 cube only.
Another hint
Use six of the nine cells, with at least one in every row and every column.
Need a hint?
The top view has 4 squares, so 4 piles.
Another hint
The tallest pile is 3, so every pile can be at most 3.
Need a hint?
Press a cell until its number matches.
Another hint
The numbers are back row 2 1 0, middle row 0 3 0, front row 0 0 1.
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Build a shape with 6 cubes whose front view and side view each have 3 squares.
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Build the fewest cubes that give a top view of 4 squares.
Use the board. This ticks when you get there.
Build the most cubes you can with a top view of 4 squares and no pile taller than 3.
Use the board. This ticks when you get there.
The top view of a solid has these heights. Back row: 2, 1, 0. Middle row: 0, 3, 0. Front row: 0, 0, 1. Build it. How many cubes?
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Views
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Look at the stack on the board. How many squares does its side view show?
A top view with heights is 3 1 on the top row and 0 2 on the bottom row. How many cubes are there?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Two designs
Write one advantage and one disadvantage of nets and of 3D drawings.
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Need a hint?
A top view of 5 squares needs 5 piles.
Another hint
Some piles must be 2 cubes tall, or the front and side views are too small.
Build a solid whose top, front and side views each have 5 squares.
Use the board. This ticks when you get there.
For teachers
Students build piles of cubes and compare the isometric drawing with the top, front and side views, finding what each view hides (AC9M7SP01, nodes 2 and 3). About 40 minutes.
I can draw or read the top, front and side views of a pile of cubes.
I can say what a view hides.
I can say one advantage and one disadvantage of a net and of a 3D drawing.
Before class
Do the Run board yourself first. Build a small pile from linking cubes to hold up.
The one idea: a view shows only what you can see from one side, so the front and side views show the tallest pile in each column and hide the rest. The common mistake is adding the piles (Noor's mistake).
The board's rows run from the back (top of the grid) to the front. The front view looks from the front; the side view looks from the right. The top view puts the back row at the top.
The view orientation is the hinge for this node: students who mix up front and side cannot compare representations.
Running the lesson
Predict: ask what could be hiding behind the front pile.
Run: ask students to say which view they think will change before they press.
Investigate: ask Noor's question again with a column of 1, 3, 1.
Modify: ask for the fewest cubes first, then the most.
Make: ask which drawing they would give a builder.
The hard part (on purpose)
Knowing which side is which. Turn a real pile of cubes round on the desk beside the board; the side view is seen from the right.
When students get stuck
A student adds all the piles to find a view. Ask: If you stand at the front, which cubes can you see in one column? Fix: Only the tallest pile. Lower piles are hidden behind it.
A student confuses front and side views. Ask: Which way are you looking? Which row is nearest you? Fix: Front looks from the front row; side looks from the right.
A student thinks the isometric drawing shows every cube. Ask: Can you see the cube hidden behind the tall pile? Fix: No drawing from one direction shows everything; the top view with numbers is the exception.
Stretch and support
Stretch: Two different piles can have the same top, front and side views. Can you find a pair?
Support: Use a real pile of linking cubes and look at it from each side before using the board.
Where it leads
This completes AC9M7SP01.
Where it leads: building solids from their views, and surface area and volume of prisms (Measurement); drawing in perspective in Year 8.
What each step is for
one view: Committing to whether the front view gives the number of cubes shows whether they know a view hides cubes.
three views: Changing cubes and watching the three views shows what each view reveals and what it hides.
what a view shows: A view shows only the tallest pile in each column (Noor adds the piles); the top view with numbers shows the most.
build to a description: Building to a description uses the views to reason about hidden cubes: the fewest, the most, and the trade-offs of each drawing.
views: Reading views and counting cubes, mixed; adding the piles is the planted slip; the cube net review keeps nets fresh.
two designs: Building a solid whose three views match, then judging nets against drawings, brings the lesson's representations together.
Now you can
Draw or read the top, front and side views of a pile of cubes.
Say what a view hides.
Say one advantage and one disadvantage of a net and of a 3D drawing.