Quantity and Numbers
Activity - Quantity and Numbers
Objectives of the activity
- To develop an understanding that quantity is something we associate with objects and there are different ways of representing this and that different objects have different measures of quantity
- Represent quantity as numbers and express symbolically
- Understand the difference between the ordinal value of a number and the representation of a quantity
- Manipulate numbers, perform mathematical operations and express these operations symbolically in mathematical language.
This is not one period – but a lesson topic. There could be a few more lessons in this section. For example, for representing collections and making a distinction between 1 apple and a dozen apples. This idea could be explained later to develop fractions. Another activity that can also be used to talk of units of measure. Addition and subtraction have been discussed here – extend this to include multiplication and division).
Materials/ Resources needed
- Apples in two groups (or any other fruit)
- Small cards for writing down the numbers as well as for writing the operations
- Pencils, etc
- A collection of other objects – stones, sticks, notebooks
Prerequisites/Instructions, if any
Website interactives/ links/ simulations/ Geogebra Applets
Process (How to do the activity)
- This whole activity can be done in groups with different sets of objects
- Keep two group of apples separately.
- Keep them in physically different arrangements.
- Based on visual inspection and counting, determine the number of apples and which group is larger or smaller or if both are equal.
- Activity is in 2 parts
Developmental Questions (What discussion questions)
For initial activity
- How can you describe the two groups? [ Words – red, large, small, more, less]
- Which words are being used first – more or less, dozen, kilo
- What is the first thing you want to do when you see the two groups?
- The students may start counting – but ask them for other ways of understanding the quantity (trying to do a one-to-one correspondence between the two groups of apples)
- If for every apple in one group, I have one apple in the other group, then I do not need to count at all. Can this one to one be done with anything other than apples? [ children, ribbons, stones]. This can bring about the idea that quantity is something that is present in many different objects
- With this mapping can I say more or less or equal? Now represent this by numbers; and discuss the difference between the two comments below: “There are 6 apples in group 1” and “This is the 6th apple in the first group”.
- Can these numbers represent only apples or anything else? Does this number “2” mean the same thing when I am counting dogs or notebooks?
- Manipulating the quantities. By physically combining and representing them in numbers, introduce the idea of mathematical operations of addition and subtraction
For Part 1
- Bring the two groups of apples together. Add Group 1 to Group 2. Describe what happens [ Words – more, large, big, add]
- What did this process do? I had two groups and I mixed them? What happened?
- Can I mix them like this all the time? Why? Why not?
- If I have apples and notebooks can I mix them? Why? Why not?
- Introduce the idea of “+”. This process is called addition and is represented like this.
- Let us separate the two again. And count the number in each group. Add Group 2 to Group 1. Does it matter? Are the results the same?
This can be written as 5 + 6 = 11
The “+” is called a mathematical operator. The addition is called an operation. These operations have some properties and they always hold.
Separate the two groups again. Can I add only all of them together? Or can I add 1 at a time, 2 at a time, 3 at a time? The ideas to be introduced would be Skip counting and quantity increase is continuous.
For Part 2
- Now from the large group take away some apples. What happens to the number? What have we done?
- We have reduced the large group by 3 apples. This can be written as 11 – 3 =8. When I mixed two groups what did we do? And what are we doing when we are separating the two groups? This will introduce words like increase, decrease, subtract, opposite.
- Pose this question like this – “ I added 5 apples to six apples to make it 11 apples. What should I do to a bag of 11 apples to make it have 6 apples again”. I take away 5. This is called subtraction and is the inverse process of addition.
The “-” is called a mathematical operator. The subtraction is called an operation. These operations have some properties and they always hold.
Evaluation (Questions for assessment of the child)
- Create situations where children work in groups and compare collections of items without counting.
- Have groups work with 3 groups of fruits, sticks, pencils, etc. The idea that addition can be extended indefinitely can be discussed.
- Subtraction with quantities without getting into negative numbers.
- Children must orally and in a written form represent these operations.
- Create different sets of objects and ask the children to add [ to test for the legitimacy of addition]
- Adding to quantity in 2's, 3's - Combinations of 2 numbers that will give 10 as an answer. Can you guess the pattern for combinations of numbers that will give 20 as an answer? [ Subtraction is an inverse process of addition]
- In their community, street, what is their house number? What does this number mean?
- How will you count mustard, sand, apples and sugar? The children will discuss this in groups and discuss with the class
- Addition worksheet
- Subtraction worksheet
- Simple word problems - *Worksheets of simple problem solving – with word descriptions. Children can either draw these answers or write them in statements. Evaluate the ability of the child to process written instructions.
Addition, Subtraction, Counting
To link back to the concept page Numbers