Measurement and geometry– volume and capacity

A student:

• measures, records, compares and estimates volumes and capacities using uniform informal units MA1-11MG
• describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM
• supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM

Content

Volume and capacity

• Measure and compare the capacities of pairs of objects using informal units
• Compare and order several objects based on volume and capacity using appropriate uniform informal units

National Numeracy Learning Progression mapping to the NSW mathematics syllabus

When working towards the outcome MA1‑11MG the sub-elements (and levels) of Understanding units of measurement (UuM3-UuM7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

Materials

• Three different sized containers, for example, cup, jug, saucepan (Ensure that two of the containers are of similar size and one is different)
• Water, sand or rice
• Pour and order (DOCX 70.5)

Teacher instructions

The purpose of this task is to gauge students’ understanding of initial capacity concepts such as:

• estimating the capacities using uniform informal units
• checking their estimate by measuring
• comparing the capacities of three containers using appropriate uniform informal units

Students compare and order the capacities of three different containers (for example, cup, jug, saucepan. Select two containers of a similar size and one that is different). Students are encouraged to use their own methods and may fill one container and pour the contents into another container or may fill both containers and then need to think further about their strategy. Provide sand, water or rice for students to measure.

Students estimate and draw the objects in order and then draw them again after they have measured how much each container will hold. Ask students to tell you why the put the containers in that particular order. If students are able to write, ask them to record their explanations.

Record observations about how students fill the containers, do they use another cup or container to measure and count as they go? Do they pour the sand/water/rice into all of the containers and not know how to compare them? Do the students fill one container and use that fill the other containers?

Option to take photos as the students are working to record their actions.

Student instructions

Estimate the capacities of these 3 containers. Draw them in order from the one which will hold the least to the one which will hold the most.

Describe how you made your estimate.

What do you know that is helping you work it out?

Measure how much each container will hold.

Draw the 3 objects in order from the container that held the least to the one that held the most.

After you have measured how much each container holds, draw the 3 objects in order from the container that held the least to the one that held the most.

Write or tell your teacher how your estimate was the same or different from when you measured the containers?

Possible areas for further exploration

Students may need further exploration of the language used in capacity, such as least, most, amount, order.

Observe how students fill the containers and whether or not they know how to compare the different containers.

Where to next?

Extend the task to include 5 containers so that students have the opportunity to compare more than 3 objects.

Make and use a measuring device for capacity that is calibrated in uniform informal units. Eg. Calibrate a jug by adding cups of water and marking the new level as each cup is added. (See next capacity task)

Adapted from Mathematics K-6 Sample Units of Work p. 74