**New Zealand Curriculum: **Level 2

**Learning Progression Frameworks:** Measurement Sense, Signpost 2 to Signpost 4

#### Target students

These activities are intended for students who have experience ordering objects by length and weight using direct comparison. This method of measuring length involves bringing the objects together or ‘hefting’ (placing one object in each hand).

Students should also know how to apply either counting on or back, or skip counting to find totals in addition, subtraction, and simple multiplication problems.

The following diagnostic questions indicate students’ understanding of, and ability to compare the capacity of containers and the volume of cuboid shaped boxes. Allow access to pencil and paper and to a calculator if students need it. (show diagnostic questions)

The questions should be presented orally and in a written form so that the student can refer to them. The questions use a variety of containers and boxes that are easily found at home. In preparation, gather the following materials.

- Plastic measurement jug
- A bag of rice
- Plastic containers labelled as follows: Container A (300 mL), Container B (600 mL), Container C (150 mL), Container D (1 L), Container E (750 mL). Try to use containers that are close to cylinders.
- Five different grocery packets of different sizes, such as cracker biscuits, toothpaste, tea bags, muesli bars, milo, baking powder, sugar cubes, etc.

(A and B).**Here are two containers**(Let the student predict)**Which container holds the most water?****Check which container holds more using this water.**__Signs of fluency and understanding:__

Uses visual comparison to correctly decide which container holds more. Pours water from one container to another to verify which container holds more.__What to notice if they don’t solve the problem fluently:__

Gets confused by the height of the containers. May think that ‘taller containers hold more water. Unsure of how to compare the capacity of the containers by pouring from one to the other. This may indicate that the student would benefit from water play to learn how to compare the capacity of containers.__Supporting activity:__

Comparing capacities

(C, D, E , including A and B).**Here are three more containers****Put the containers in order from smallest to largest by how much water they hold.**

Let the student order the containers.**Use this water to check the order you have is correct. Explain what you are doing.**__Signs of fluency and understanding:__

Orders the five containers by visual comparison with indication that both cross-section and height are considered when comparing two containers. Organises the containers logically by comparing them two at a time.

Tests containers by pouring from one to the other, in sequence. Ideally the student begins with the container that they believe is largest. Explains what each pair comparison shows.__What to notice if they don’t solve the problem fluently:__

Attends to height only, rather than both cross-sectional area and height, when ordering the containers. This may indicate that the student needs more experience with directly comparing the capacities of containers with varying heights and cross-sectional areas.

Unable to order five containers logically by comparing them two at a time. This may indicate that the student needs support organizing the results of paired comparison of objects into a sequence when more than two objects are involved. This is also likely to apply when comparing lengths, areas, and weights.__Supporting activity:__

Ordering capacities

(Long and narrow, and short and broad, e.g. toothpaste and baking powder)**Here are two packets.****Which box do you think holds the most rice? Explain how you know.**(Provide the students with a container of rice.)**Use this rice to check which packet holds the most.**__Signs of fluency and understanding:__

Compares the boxes by volume correctly attending to visual appearance. The student may align the boxes by height or compare base areas. Pours from one box into the other to check the comparison is correct. Explains that there is some rice left over when they pour from the largest box to the smallest or there is not enough rice if pouring from the smallest to the largest.__What to notice if they don’t solve the problem fluently:__

Attends to one dimension, such as height, when comparing the boxes. Incorrectly thinks the taller or longer box holds more. This may indicate that the student needs experience comparing boxes of different heights and widths by pouring from one to the other.

Unable to check the comparison by pouring rice from one box to the other, or is unsure what the pouring shows, particularly if the result is inconsistent with their previous view. The student may benefit from pouring from each box into containers with identical cross-sections.__Supporting activity:__

Comparing boxes by volume

(Three other boxes as well as those used for Question 3).**Here are three more boxes****Put the boxes in order from smallest to largest by how much rice they hold.**

Let the student order the boxes.**Use this rice to check the order you have is correct. Explain what you are doing.**__Signs of fluency and understanding:__

Orders the five boxes by visual comparison with indication that all three dimensions are considered when comparing two boxes. Organises the boxes logically by comparing them two at a time.

Tests volumes of boxes by pouring from one to the other, in sequence. Ideally the student begins with the box that they believe is largest. Explains what each pair comparison shows.__What to notice if they don’t solve the problem fluently:__

Attends to one dimension only, such as height, rather than both cross-sectional area and height, when ordering the boxes. This may indicate that the student needs more experience with directly comparing the volumes of boxes with varying heights and cross-sectional areas.

Unable to order five boxes logically by comparing them two at a time. This may indicate that the student needs support organizing the results of paired comparison of objects into a sequence when more than two objects are involved. This is also likely to apply when comparing lengths, areas, and weights.__Supporting activity:__

Ordering boxes by volume

**How many cubes will it take to completely fill this box?****Explain how you worked the number out.**

Choose one of the boxes used for Question 4.__Signs of fluency and understanding:__

Makes a tower of cubes and works out how many towers will fit into the box. May use repeated addition or multiplication to find the total number of cubes.

Makes a layer by creating a rectangle that matches one face of the box. Works out how many layers fit into the box. Uses skip counting, repeated addition, or multiplication (ideally) to calculate the volume.__What to notice if they don’t solve the problem fluently:__

Fill the box with cubes, tips them out, and counts the number of cubes. This may indicate that the student needs experience with structuring units of volume in three-dimensional arrays.__Supporting activity:__

Measuring volumes using cubic units