Definition of Modelling
Modelling is a way to represent number quantities using mathematical concepts and ideas. In this lesson, we will learn how to model number quantities using multi-base blocks, graph sheets and token currency notes
We will also learn how to use multiples of 10s, 50s, 100s and 200s to representnumbers in various ways.
Multi-base Blocks
The Components
The components used in building a model for any given number are as follow:
1. cube
2. rod
3. flat
4. block
Remember
The cube is the unit with which all the other components can be built. Hence, you can easily find the value of all the other components by first knowing the the value of the cube and using the relation below.
The Rod
\[ 1 \ \text{rod} = 10 \times 1 \ \text{cube} \]The value of 1 rod is equivalent to the value of 10 cubes.
The Flat
\[ \begin{eqnarray*} 1 \ \text{flat} & = & 10 \times 1 \ \text{rod} \\ 1 \ \text{flat} & = & 10 \times 10 \ \text{cubes} \end{eqnarray*} \]The value of 1 flat is equivalent to the value of 10 rods or 100 cubes.
The Block
\[ \begin{eqnarray*} 1 \ \text{block} & = & 10 \times 1 \ \text{flat} \\ 1 \ \text{block} & = & 10 \times 10 \ \text{rods} \\ 1 \ \text{block} & = & 10 \times 100 \ \text{cubes} \end{eqnarray*} \]The value of 1 flat is equivalent to the value of 10 rods or 100 cubes.
Practice Exercise
Question 1
If a cube represents 1,000, what is the value of a rod?
Watch the video below for a clearer understanding of the question.
Question 2
If a cube represents 10,000, what is the value of a rod?
Watch the video below for a clearer understanding of the question.
Question 3
Using multi-base blocks \((1 \ cube = 100,000)\) model the number 1,500,000.
Watch the video below for a clearer understanding of the question.
Question 4
Using multi-base blocks \((1 \ cube = 100,000)\) model the number 21,500,000.
Question 5
Using multi-base blocks \((1 \ cube = 100,000)\) model the number 100,700,000.
Ready for more challenges?
Full Practice SetGraph Sheets
Main Idea
We can also use the graph sheet to model number quantities. We can first initialize a perfect square, say \((1 \ \text{cm} \times 1 \ \text{cm})\), and give it the value we gave to the cube (100,000) in the multi-base block.
Relations
We can therefore relate the value of the other components as below:
\[ \begin{eqnarray*} 1 \ rod & = & 10 \times 1 \ cm^2 \\ 1 \ rod & = & 10 \ cm^2 \\[0.5em] 1 \ flat & = & 10 \times 1 \ rod \\ 1 \ flat & = & 10 \times 10 \ cm^2 \\ 1 \ flat & = & 100 \ cm^2 \\[0.5em] 1 \ block & = & 10 \times 1 \ flat \\ 1 \ block & = & 10 \times 100 \ cm^2 \\ 1 \ block & = & 1,000 \ cm^2 \\ \end{eqnarray*} \]
Practice Exercise
Question 1
Using a graph sheet, model the number 4,200,000.
Question 2
Using a graph sheet, model the number 13,300,000.
Ready for more challenges?
Full Practice SetUsing Multiples
Main Idea
Another way we can represent numbers is by using multiples of 10s, 50s, 100s and 200s. We can use the multiples of these numbers to expand larger numbers like 5,560.
Here, we will use only multiples of 10s, 50s, 100s and 200s to model numbers, but remember that you can use multiples of any other numbers to model.
Practice Exercise
Question 1
Represent 5,560 using multiples of 10s, 50s, 100s and 200s.
\(\therefore\) 5,560=(200 \(\times\) 20)+(100 \(\times\) 10)+(50 \(\times\) 11)+(10 \(\times\) 1)
Ready for more challenges?
Full Practice SetUsing Token Currency
Main Idea
Sometimes when we are given a particular amount of money, we may wish to know how many of each currency note make up the total of the money we are given.
In this lesson, we are going to learn how to combine different notes from token currencies to get any given amount. We will use the idea of modelling with multiples in the previous lesson to model given amounts using token currency notes.
Remember that you can adjust the multiples to get different combinations of each note.
Practice Exercise
Question 1
Represent Gh₵5,560 using token notes of Gh₵10.00, Gh₵50.00, Gh₵100.00 and Gh₵200.00.
Make sure each note is used.
Question 2
You are depositing Gh₵504,670 at the bank. Using token currency notes find how many Gh₵10.00, Gh₵50.00, Gh₵100.00 and Gh₵200.00 make up the total amount you are depositing. Make sure each note is used.
Question 3
You are depositing Gh₵1,000,000 at the bank. Using token currency notes model how many Gh₵10.00, Gh₵50.00, Gh₵100.00 and Gh₵200.00 make up the total amount you are depositing. Make sure each note is used.
Ready for more challenges?
Full Practice SetMath Challenge
Timed Test in 7 Levels
Test your math skills through progressively challenging levels