LessonnotesGH

SHS2 Mathematics · Semester 2, Week 10

Measurement

Lesson notes

Learning Objectives

Indicator: 2.3.2.LI.2 - Solve problems that involve SI and imperial units in volume and capacity measurements.

By the end of the lesson, learners can:

  1. Distinguish between volume and capacity of a solid object using appropriate mathematical language.
  2. Convert between SI units of volume (cm³, m³, litres, millilitres) and between SI and imperial units (gallons, pints, cubic inches).
  3. Calculate the volume of prisms, cylinders, pyramids, cones, spheres and composite solids using the correct formula.
  4. Convert a volume expressed in one unit cubed into another unit cubed (for example, m³ to cm³) and use this to state the capacity of a container in litres.
  5. Solve practical problems involving volume and capacity of everyday containers using both SI and imperial units.

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Curriculum details

Strand
Geometry Around Us (Strand 3)
Sub-strand
Measurement (3.2)
Content standard
2.3.2.CS.3 - Demonstrate conceptual understanding of the measurement of surface area, volume and capacity of solid shapes. 2.3.2.LO.3 Determine the volume and capacity of solid shapes and Solve problems that involve SI and imperial units in surface area, volume and capacity measurements.
Indicator
2.3.2.LI.2 - Solve problems that involve SI and imperial units in volume and capacity measurements.
Suggested placement
Semester 2, Week 10 (Week 30 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

  • exemplars - p.259: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference
NaCCA curriculum document, p. 256

Exemplars (from the NaCCA curriculum) 

Using Talk for Learning strategy, engage learners to explain, using examples, the difference between volume and capacity. Bring learners' attention to the fact that as differences exist between volume and capacity, which are two close concepts, it is the same among humans and, therefore, the need to appreciate these differences and respect each and everyone irrespective of their background.
Examples: i. The total amount of any substance which is contained in a particular space is called the volume. The total potential amount of any substance that can be contained in a space is called the capacity of that space. Thus, the amount of space that a substance takes up is known as volume. The maximum amount of a substance that an object can contain is known as its capacity.
A container part filled with blue liquid, beside a note distinguishing volume from capacity.
A small drawing of a cylindrical container part filled with blue liquid, beside a note explaining that the liquid in the container is its volume while the capacity is the amount that could fill the whole container. 
 The container here holds some amount of liquid. The total amount of liquid in the container is the volume of the liquid, but the capacity of the container is the potential amount of liquid that can be contained in the entire space of the container.
ii.
Table contrasting volume and capacity by meaning, units, which objects have them and examples.
A two-column table headed "Volume" and "Capacity". It contrasts the space an object covers in three dimensions with the amount something can hold; gives units of cubic centimetres and cubic metres against litres, gallons and pounds; notes that both solid and hollow objects have volume while only hollow ones have capacity; and gives cube, cuboid, cone and cylinder against cone, cylinder and hollow hemisphere as examples. 
 Volume Capacity Volume indicates the total Capacity refers to the ability of amount of space covered by something (like a solid substance, an object in threegas or liquid) to hold, absorb or dimensional space. receive by an object. Common units (units of Common units (units of measurement) - cm 3 , m 3 measurement)- litre, gallons, pounds Both solid and hollow Only hollow objects have the objects have volume. capacity. Example - Cube, Cuboid, Example - Cone, Cylinder, hollow Cone and Cylinder hemisphere
iii. Find the volume and capacity (in litres) of a cylinder whose radius is 7 cm and height is 20 cm.
Solution: Given, r = 7 cm and h = 20 cm We know that, Volume of cylinder = πr 2 h = (22/7) × 7 × 7 × 20 = 22 × 7 × 20 = 3080 cm 3 Capacity of the cylinder = 3080/1000 litres (1000 cm 3 = 1 litre) = 3.08 litres
Note: We can also represent capacity in terms of cm 3 . Hence, in the above example, volume will be numerically equal to capacity.
Experiential Learning: In mixed-gender groups, task learners to identify and compare referents, then estimate volume and capacity measurements in SI and imperial units. Encourage learners to see the need to embrace technology in solving problems in surface area measurements while appreciating the need to use them appropriately.
Examples: Practical Activities for Learners
- How will you help Adzo use a 1-L milk carton to estimate 750 ml of water?
- Estimate the number of cubic metres in the classroom. Explain how you determined this estimate. Find the actual measurement. Use this information to help you estimate the volume of another differently sized room, such as the library.
- I need a box with a volume of 4000 cubic centimetres to hold a gift I have purchased. Describe what the box might look like. What is an example of a gift that would fit into this box?
- A container holds 1.5 litres. Is it large enough to make a jug of orange juice if the concentrate is 355 ml and you have to use the concentrate can to add three full cans of water? Explain your thinking.
- Investigate the capacities of various beverage containers to determine which size container is found most often. Record your findings in a graph or table and present this to the class.
Experiential Learning: Engage learners in pairs to identify a situation where a given SI or imperial volume unit would be used.
Example: I would measure water in a bath using L, but I would measure liquid in a baby-food bowl in ml.
Collaborative learning: Learners discuss and solve problems that involve the volume of 3-D objects and composite 3-D objects using formulae. Then, write the volume measurement expressed in one SI/imperial unit cubed in another SI/imperial unit cubed.
Example 1: Determine the volume of the following shapes (It should also include pyramids and all available solid shapes)
3D Object Formula
Table of volume formulas: cylinder pi r squared h, cone one third pi r squared h, cube s cubed, prism lbh.
A table headed "3D Object" and "Formula". An oblique and a right circular cylinder with radius r and height h give pi r squared h; an orange cone gives one third pi r squared h cubic units; a pink cube of side s gives s cubed; and a prism gives Base Area times Height, written l b h. 
πr 2 h
1 πr 2 h cubic 3 units.
s 3
Base Area × Height (lbh)
A sphere with volume four thirds pi r cubed and a hemisphere with two thirds pi r cubed.
Two solids with their volume formulas. A yellow sphere of radius r is paired with four thirds pi r cubed, and a pink hemisphere of radius r with two thirds pi r cubed. 
4 πr 3 3
2 πr 3 3
Table of volume formulas for triangular, square, rectangular, pentagonal and hexagonal pyramids.
A table headed "Pyramid" and "Volume" with five coloured pyramids down the left: triangular, square, rectangular, pentagonal and hexagonal. Each row works one third times base area times height down to a boxed result for that base. 

            
        
          
              

                Four green composite solids, each made of joined blocks and labelled with its edge lengths.
                

                  "Example 2: Determine the volume for the following composite shapes", with four green composite solids drawn beneath. Each is made of two joined rectangular or triangular blocks and carries its edge lengths in inches or centimetres.
                

              

          
        
          
              
 Example 2: Determine the volume for the following composite shapes:
Composite shapes
Teaching and Learning Resources:
- Mathematical sets.
- Technology tools such as computers, mobile phones, etc.
- * Computer software applications like GeoGebra
Assessment (2.3.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.

            
        
      

    

  


  

    
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