Mathematics
Advanced
50 mins
Teacher/Student led
+65 XP
What you need:
IWB/Projector/Large Screen
Multilink cubes

Volume of Cubes and Cuboids

Learn to find the volume of cubes and cuboids using length × breadth × height, connect it to the area of the base multiplied by height, and work backwards to find a missing dimension from a known volume.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at the picture on the board: an empty box, with a pile of little centimetre cubes beside it.

    Roughly how many of those little cubes do you think would fill the box right up to the top? Have a good look before you guess.

    2 - Watch and Notice ~9 mins

    Three boxes in the picture, each already filled with little cubes. Take the length, breadth and height of each one from the teacher notes, and notice how the cube count grows.

    For each box, count one flat layer of cubes first. Then count how many layers are stacked up. One layer, times the number of layers, gives the whole box.

    The last box is a plain cube: every side is the same length. Together, tell me what happens to the count when all three sides are the same length.

    3 - Try It Together ~8 mins

    We build and measure at the board together. Whoever is at the board drags the sliders while the whole class works each answer out loud.

    First set the box to 3 × 2 × 2. Then grow it to 5 × 4 × 2. Then raise the height to 3 cm.

    Each time, work out the base layer first, then how many layers high the box is, and call out your prediction before we read the volume off the tool.

    Shape Measurer

    4 - Sketch the Cuboids in Your Copy ~2 mins

    COPYBOOK MOMENT

    In your maths copy, sketch these three shapes: the 5 × 3 × 2 box, the 6 × 4 × 3 box, and the 4 cm cube.

    Label the three dimensions on each one, then write the volume formula and the answer in cm³. Underline the unit on every one.

    5 - Class Challenge ~8 mins

    We work through these volumes together. First a 3 cm cube. Then a 7 × 2 × 2 cuboid. Then a 5 × 5 × 4 cuboid.

    Last of all comes a puzzle that turns it around: a box has a volume of 48 cm³ and a 4 cm × 3 cm base, so how high is it? Work each one together and confirm the answer before moving on.

    Find the volume of each box in cm³. Last of all, a box holds 48 cm³ and its base is 4 cm by 3 cm — work out how high it is.

    1. A cube with every side 3 cm — find its volume.
    2. A cuboid 7 cm long, 2 cm wide, 2 cm high — find its volume.
    3. A cuboid 5 cm long, 5 cm wide, 4 cm high — find its volume.
    4. A box has volume 48 cm³ and a 4 cm × 3 cm base. How high is it?

    Ways to start:

    • Start with the base layer: length × breadth. How many cubes in one flat layer?
    • Then multiply by the height: how many layers high is the box?

    Stretch:

    • For the last box, the volume and the base are given. What must you divide by to find the missing height?
    Answers & strategies (teacher)
    1. A cube with every side 3 cm — find its volume. — 27 cm³ (3 × 3 × 3)
    2. A cuboid 7 cm long, 2 cm wide, 2 cm high — find its volume. — 28 cm³ (7 × 2 × 2)
    3. A cuboid 5 cm long, 5 cm wide, 4 cm high — find its volume. — 100 cm³ (5 × 5 × 4)
    4. A box has volume 48 cm³ and a 4 cm × 3 cm base. How high is it? — 4 cm (48 ÷ 12)
    • 3 cm cube: 3 × 3 × 3 = 27 cm³
    • 7 × 2 × 2 = 28 cm³
    • 5 × 5 × 4 = 100 cm³
    • 48 cm³ ÷ (4 × 3) = 48 ÷ 12 = 4 cm high
    Pupil practice
    Module 5 · Measures: Length, Area, Volume, Mass and Capacity Measures
    Lesson 54 · Volume of Cubes and Cuboids
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