Lesson type: Property investigation — describing 2D shapes and 3D solids by what is countable and certain.
Stepping Stone: analyse the properties of 2D and 3D shapes; describe a solid by its faces, edges and vertices, and recognise the structure a family of solids shares.
NEO Cornerstones: Connection · Movement · Reflection · Creativity · Rest · Nutrition
45-minute shape: Connect 15 · Move 8 · Reflect 10 · Create 5 · Rest/Nourish 4 · Evidence 3
Choose only the support that helps now. Every route returns you to this lesson.
Every solid can be described with three words:
Face — a flat surface of the solid.
Edge — a straight line where two faces meet.
Vertex — a corner where edges meet. (More than one are called vertices.)
Keep these three words handy — you will count them for every solid in this unit.
What to do: choose a base for the prism, then predict how many faces, edges and vertices it will have before you reveal the counts.
What you are trying to notice: a prism is built from its base — change the base and the whole structure changes with it in a predictable way.
Change the base polygon. The picture and the counts update together. Try to see the rule that links the base to the faces, edges and vertices.
Predict for this prism, then check:
Carry this forward: the base decides everything about a prism. Next you will see that same base sweeping through space to build the solid.
What to do: use the slider to sweep the base polygon through space. Watch a flat shape turn into a solid prism.
What you are trying to notice: a prism is a base carried a certain distance — the flat cross-section is the same all the way along.
Carry this forward: because the cross-section stays the same all the way along, later we will measure a prism by its cross-section — for its surface and its volume.
What to do: read the clues one at a time. Decide which solid fits — or reveal another clue first. Each clue is a property, so you are reasoning, not guessing.
What you are trying to notice: a few well-chosen properties are enough to identify a solid exactly.
Which solid is it?
Carry this forward: the properties you used — faces, edges, vertices, curved or flat — are exactly the language you will use to describe every solid in this unit.
What to do: choose a set of flat faces and see which solid they would make. Then invent your own on the Scratchpad.
What you are trying to notice: a solid is decided by which faces meet, and how many.
Pick the faces, then check what they build:
Make it your own: on the Scratchpad, sketch a solid of your own and label its faces, edges and vertices — then challenge someone to name it from three clues.
Naming what stays the same is quiet, patient work. Before moving on, take a slow breath and let one idea settle.
Notice one thing: of everything you have looked at, which single property did you find most useful for telling two solids apart? There is no right answer — just the one that helped you.
You can jot it on the Scratchpad, say it aloud, or simply hold it in mind. You can pause here and return whenever you are ready.
Mode: intellectual. This lesson does not sit in a food or body context, and we will not pretend it does. What it feeds is your spatial reasoning — the ability to see structure, to describe it precisely, and to trust a property you can count.
Carry one idea forward: "A shape's properties stay true however I turn or draw it." That steadiness is what makes measurement possible later in the unit.
Which felt stronger for you today — seeing the structure, or describing it in words? Noticing that helps you choose how to show your thinking next time.
Your task: describe three different solids by their properties, and state the rule linking a prism's base to its faces, edges and vertices.
Submission choices: an annotated Scratchpad image, a short written table, a labelled poster, or a spoken/video walkthrough with a labelled sketch.
Filename pattern: NEO_MATH_SHAPES_PROPERTIES_FirstName_Date
| Criterion | Approaching Proficiency | Developing Proficiency | Proficiency | Refining Proficiency |
|---|---|---|---|---|
| Understanding | Names some properties of a solid. | Counts faces, edges and vertices with some support. | Describes a solid fully and correctly by its properties. | Explains the structure a family of solids shares and why it holds. |
| Application | Identifies a solid from a picture. | Uses the prism pattern for a familiar base. | Uses the n-sided rule to predict counts for a new base. | Generalises and justifies the rule for any base polygon. |
| Communication | Records an idea with limited labelling. | Uses some correct property language. | Communicates a clear, well-labelled description. | Writes clues precise enough to identify a solid uniquely. |
| Reflection | Names one thing noticed. | Identifies one property that helped. | Explains which properties best distinguish solids. | Reflects on how seeing and describing supported each other. |
Use support in this order: 🤔 Socratic prompt → 💡 hint → ✅ check → 👀 worked solution. The worked solution unlocks separately for each question, once you have used the prompt, used the hint and checked two answers.
Use the Scratchpad to predict, sketch, test and revise.
You can use this board, paper or another way of recording your thinking. The Scratchpad is optional.
Angles are in degrees. Examples: 9 × sin(37) = 5.42; sin⁻¹(0.5) = 30