Stage 2 - Maths - Measurement - Volume and Capacity
Term
Week
Outcome:
MS2.3 Unit 2 (litres and cubic centimetres)
Estimates, measures, compares and records volumes
and capacities using litres, millilitres and cubic
centimetres
Key Ideas:
Estimate, measure, compare and record volumes and
capacities using litres and millilitres
Convert between litres and millilitres
WORKING MATHEMATICALLY OUTCOME/S
Questioning
Asks questions that could be explored using mathematics in relation to Stage 2 content
Applying Strategies
Selects and uses appropriate mental or written strategies, or technology to solve a given problem
Communicating
Uses some mathematical terminology to describe or represent mathematical ideas
Reasoning
Checks the accuracy of a statement and explains the reasoning used
Reflecting
Links mathematical ideas and makes connections with existing knowledge and understanding in relation to Stage 2
content.
Knowledge and Skills
Students learn about
 recognising the need for a unit smaller than the litre
 estimating, measuring and comparing volumes and
capacities using millilitres
 making a measuring device calibrated in multiples of 100
millilitres
 using a measuring device calibrated in millilitres
eg medicine glass, measuring cylinder
 using the abbreviation for millilitre (mL)
 recognising that 1000 millilitres equal one litre
 converting between millilitres and litres
eg 1250 mL = 1 litre 250 millilitres
 comparing the volumes of two or more objects by marking
the change in water level when each is submerged in a
container
 measuring the overflow in millilitres when different
objects are submerged in a container filled to the brim with
water
Working Mathematically
Students learn to
 explain the need for a standard unit to measure the volume
of liquids and the capacity of containers (Communicating)
 estimate and measure quantities to the nearest 100 mL
and/or to the nearest 10 mL (Applying Strategies)
 interpret information about capacity and volume on
commercial packaging (Communicating, Reflecting)
 estimate the volume of a substance in a partially filled
container from the information on the label detailing the
contents of the container (Applying Strategies)
 relate the millilitre to familiar everyday containers and
familiar informal units eg 1 teaspoon is approximately
5 mL, 250 mL fruit juice containers (Reflecting)
 estimate the change in water level expected when an object
is submerged (Applying Strategies)
LEARNING ACTIVITIES (Volume 8)
LEARNING ACTIVITIES (Volume 9)
COUNT THEM
DISPLACEMENT
Students build models using unit blocks, eg boxes, blocks,
Cuisenaire rods. Ask students to count how many of the units
were needed to build their individual or group model.
Students can make two types of displacement containers for
classroom use. One is the “overflow” type: it requires a container,
eg ice cream container, to be placed inside a large tray. Fill the
container to the brim with water. Place the object to be measured
into the container and collect the overflow in the tray. Measure
or
compare the amount of overflow.
Another displacement container is a “rising level” type: it requires
a clear container, large enough to allow objects to be fully
submerged without the water overflowing. Students should make
and investigate both types of displacement containers.
Commercially-produced “overflow” type displacement containers
are also available.
COPY THIS
One student makes a model using one type of unit block, eg a
garage using Multilink. A partner or others in a group copy the
model using a different building block, eg Centicubes. Discuss
difficulties and discoveries.
TOWERS
Make a collection of ten rectangular prisms, ten cubes and ten
triangular prisms. Ask students to build three towers, using a
different unit for each. Compare the towers. Discuss with
students the ability of each type of block to stack.
Discussion may also focus on sides and edges of the blocks.
WHICH TAKES UP MORE SPACE?
Students work in groups using the same kind of unit blocks to
build their own models. They then choose two or three partners
from the group and compare constructions. Students estimate
which construction has the larger volume and then check by
counting the unit blocks in each model. The group can report their
findings back to the class or make pictorial records.
GUESS AND CHECK
One student makes a model from unit blocks, eg Lego bricks,
Duplo bricks, Multilink or Centicubes. Their partner estimates the
number of blocks used in the model. Check by dismantling the
model and counting the blocks. Students should be encouraged to
draw their models before taking them apart.
ARE THEY THE SAME?
Students investigate the number of different models that can be
made using one, two three or four cubes. Results can be recorded
in tabular form. Some students may like to try to draw their
models on grid paper or isometric dot paper. Models may also be
represented on pegboards.
PENTACUBE PROBLEM
Pentacubes are formed from five cubes. There are many possible
model variations. Students experiment to find how many
pentacube models they can make.
OVERFLOW
Students have an overflow displacement container filled to the
brim with water. Ask them to predict what will happen if an
object
is placed in the container. Experiment to find out. Discuss the
results. Consider important factors such as splashes, arms and
fingers taking up space, measuring the overflow accurately, etc.
WATER LEVEL
Students partly fill a clear, plastic container with water and mark
the level with a rubber band or a felt pen. Tie a stone to the end
of
a piece of thread or fishing line. Suspend the stone in the water.
Mark the new level with another rubber band or felt pen. Discuss
what happened. Remove the stone and observe the water level.
Discuss what happened and why.
FLOATER
Repeat the “Overflow” and “Water Level” activities with a variety
of objects including some large objects that float, eg beach ball,
lunch box. Investigate ways of holding floating objects just below
the surface without immersing fingers or hands, eg pushing the
object underwater until the fingertips are just wet, filling the
object
with water or some other heavy material.
COMPARING STONES
Use an overflow displacement container, two identical clear jars
and two stones of distinctly different size. Immerse one stone
and
collect the overflow. Pour this into one of the jars. Refill the
displacement container and immerse the second stone. Pour the
overflow into the second jar. Compare the amount of water in the
jars and discuss. Use a partially filled “rising level” container and
the two stones. Mark the water level. Immerse one stone. Mark
the
new water level. Remove the stone. Refill to the original water
level. Immerse the other stone. Mark the new water level.
Compare
the marked water levels to determine which stone occupied the
most space. Repeat using other objects. Discuss which method is
more suitable/accurate in finding the difference in volume of two
objects? Practise ordering a variety of objects by volume.
CONSERVATION
Students investigate conservation concepts using either type of
displacement container by immersing and measuring
- a long, thin plasticine shape/a remoulded shape
- a ball of plasticine/the ball cut into pieces
- ten loose Centicubes/the Centicubes formed into a model.
LEARNING ACTIVITIES (Volume 10)
LEARNING ACTIVITIES (Volume 11)
DIFFERENT CUPS
MAKING AND FINDING ONE LITRE CONTAINERS
Collect sufficient cups of different shape, size and capacity for
each student to have one. Ask students to fill a bucket, large ice
cream container or bowl, using their cup. Count the number of
cups used to fill the container. Students work in groups to
construct graphs showing results for each person. Discuss results
with the group and the whole class. Repeat the activity using
other informal units. For example, use teaspoons to fill cups.
NUMBER OF
FULL CUPS TO
FILL BOWL
MISHA IRENE VLADO
Have students pour materials from a 10 cm x 10 cm x 10 cm
container into an empty 2 L juice carton. Mark the level. Cut the
carton to make a “standard” 1 L container. Pour materials from the
“standard” 1 L container into familiar litre containers of various
shapes, eg cordial bottles, milk cartons, ice cream containers.
Label the containers “Holds 1 Litre” (l L). Discuss variations in the
general shape of the containers in relation to the different uses
for which they are intended. Discuss why the containers are not
filled to the top when holding 1 Litre. Examine and use standard
measuring jugs, beakers and cylinders calibrated only in litres.
Find the number of cups required to fill a one litre container.
Repeat using familiar informal units, eg egg cups, spoons, yoghurt
tubs, mugs. Record results in a table or graph.
STANDARD CUPS
Collect sufficient cups of the same shape, size and capacity for
each pupil in a group to have one. Repeat the “Different Cups”
activity. Discuss the results obtained in the two activities.
Graduate a larger container using the cups collected. Use this
container to find the capacity of other containers.
FILLING WITH RECTANGULAR PRISMS
Find the number of blocks required to fill a suitable box.
Record the result. Repeat the activity using different sized,
uniform blocks. Record the result. Compare the number used in
each investigation and discuss outcomes.
FILLING WITH SPHERES
Find the number of tennis balls required to fill a container. Repeat
the activity using golf balls, marbles, cricket balls, etc. Record
the results each time, then compare numbers used and discuss
reasons for the differences in the answers.
IDENTICAL SETS
Collect sets of identical items to use as standard units for
measuring the capacity of rectangular containers. Suitable units
are: matchboxes, chalk boxes, small sultana packets, chocolate
packets, juice cartons. Fill rectangular containers with the
selected units. Compare the capacity of two containers using the
same units. Display results in a table or graph.
LARGER CONTAINERS
Have students calibrate large clear containers in graduations of
one litre by repeatedly pouring water from a one litre measure
and marking the new water level each time.
ESTIMATE AND CHECK
Collect a variety of containers, eg a plastic jar, jug, teapot, beach
bucket, juice bottle, saucepan, lunch box, ice cream container.
Have students estimate the capacity of each container to the
nearest litre, then use a one litre measure to check. Record the
measure. Calculate the difference between the estimate and the
measure.
FINDING CONTAINER CAPACITIES
Have students find the capacities of containers frequently used in
daily life, eg kitchen sink, hand basin, laundry tub, baby bath, fish
tank, rubbish bin, wheelbarrow, bath. Have students record their
findings in a table, graph or diagram.
HALF LITRES
Discuss the need for a measuring unit smaller than one litre. Have
students pour a litre of water into a pair of identical clear
containers to the same level. Mark the levels and label as “half
litre” or “1/2 L”. Check that one of these containers, filled to the
marked level twice, will fill the litre measure or other one litre
containers. Using the 1/2 L measure, sort and classify a variety of
containers under the headings: less than 1/2 L, about 1/2 L,
between 1/2 L and 1 L.
Resources
Blocks, Lego bricks, Duplo bricks, Multilink, Centicubes,
cartons, chalk boxes, dice, match boxes, timber offcuts, Base 10 materials,triangular prisms, grid paper,
isometric dot paper.
Technology
Links
Language
immerse, submerge, partially, raise, litre, half litre, millilitre, half
full, calibrated, decimal, measuring cylinder
Assessment
Ask students to
• order three objects by the displacement method
• demonstrate understanding of the idea that changing
the shape of a particular object makes no difference
to the volume of water it displaces.
Evaluation
• Have students had sufficient background experiences and discussion to be
able to carry out the planned activities successfully?
• Did I organise sufficient equipment for all students to be actively involved
in group work?
• Did I encourage students to make use of the playground for these water
activities?