Primary 5 · Measurement & Geometry

P5 shapes and spatial reasoning

Spatial reasoning, or spatial visualisation, is not a P5 chapter of its own, but P5 papers set it, mostly in volume questions. Your child counts the unit cubes in a solid, the hidden ones too, reads its views, and works out how many more cubes would fill a box.

Taught in
Term 2
Syllabus
Exam skill
Usual slip
Counts what shows

A stack of 6 unit cubes: 4 below and 2 on top

What your child learns in P5 shapes and spatial reasoning

Three skills, each with what it looks like on a worksheet.

Not a chapter of its own in the MOE syllabus. Schools test it as problem sums.

Count layer by layer

Count a stack of unit cubes one layer at a time, starting at the bottom. Include the cubes you cannot see: a cube sitting on top needs a cube under it, even when the drawing hides it.

4 in the bottom layer and 2 on top: 6 cubes

Views from the front and the side

Papers ask your child to draw a solid as it looks from the front or the side, on a square grid. Each column of cubes shows as squares as tall as the column, whatever is hidden behind it.

frontside
The solid, with the two views marked
Its front view: one square per cube face you see

How many more to fill it

Another common question asks how many more cubes would fill a box or make a cube. Find the full count first, length × breadth × height, then take away the cubes already in.

The box holds 3 × 2 × 2 = 12; 5 are in, so 7 more

Key facts and formulas

Term 2
  • Count cubes layer by layerCount each layer, from the bottom up.bottom to top → 6+4+2=6 + 4 + 2 = 1212
  • FrontSideFront viewSide view
    Front and side viewsLook straight at one face. Draw only the squares you see.
  • Cubes to fill a boxCubes the full box holds − cubes already in it4×3×2−9=4 \times 3 \times 2 - 9 = 1515

Words to know

Unit cubes
Equal cubes a solid is built from, often 1 cm along each edge.
Layer by layer
Counting one level of cubes at a time, from the bottom up.
Hidden cubes
Cubes the drawing cannot show, behind or under the ones in front.

The sentence that costs the mark

This solid is built from unit cubes. How many cubes are there in total?

Two cubes in the bottom layer sit under the top layer, out of sight.

What the working usually does

countvisible=8

Counts every cube the drawing shows from the front. A careful count, just of the ones you can see.

What the question asked

countall=10

Counts layer by layer: 6 below and 4 on top. The 2 hidden cubes must be there to hold up the top layer.

The visible count is not careless. It is an accurate count of every cube in view. The slip is trusting the drawing: two cubes hold up the top layer from the back, under and behind cubes you can see.

The same P5 shapes and spatial reasoning question, worked properly

Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.

Find the volume of the solid, which is made of centimetre cubes.

Step 1 of 5▌
  1. Count the cubes layer by layer, starting at the bottom.
  2. The bottom layer has 5 cubes. Two of them are hidden, because each holds up a cube on top.
  3. The top layer has 3 cubes.
  4. Altogether that is 5 + 3 = 8 cubes. Each cube is 1 cm³, so the volume is 8 cm³.
  5. So the volume of the solid is 8 cm³.

Every question in StudyLah comes with a walkthrough like this one.

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Three quick P5 shapes and spatial reasoning questions

Try them together, then tap to check.

Question 1

The figure is a solid made of 1-cm cubes. How many more cubes are needed to make its volume 28 cm³?

Show answer

Answer13. Layer by layer the solid has 7 + 5 + 3 = 15 cubes, hidden ones included, and 28 − 15 = 13.

Question 2

The solid below is made up of 1-cm cubes. What is the least number of 1-cm cubes that must be added to the solid to make it a cube?

Show answer

Answer17. The longest edge is 3 cubes, so the smallest cube is 3 × 3 × 3 = 27 cubes. The solid has 10, and 27 − 10 = 17.

Question 3

A rectangular tank is partly filled with 1-cm cubes as shown below. How many more such cubes are needed to fill the tank completely?

Show answer

Answer31. The full tank holds 4 × 4 × 3 = 48 cubes. 17 are in, hidden ones included, so 48 − 17 = 31.

Helping at home

How to tell it has clicked

Ask your child to count the cubes in a drawing, then ask: are there any you cannot see from here? That question is the whole lesson.

If they add the hidden ones and can point to where each must be, they have it. If they stop at the visible count, that is the habit to change.

Try this tonight

Build a small stack with real blocks or sugar cubes. Look at it from one side and ask how many there are, then walk around it.

Ask which cubes are holding others up. Every one of those must be there, seen or not.

Before and after P5 shapes and spatial reasoning

  1. Builds on

    Primary 4 Nets

    Unfolds the solids into nets

  2. You are here

    Primary 5 Shapes and Spatial Reasoning

    Counts every cube, even hidden ones

The methods your child will use here

More in Primary 5

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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