In the lesson on skip counting in basic 7, we learnt that skip counting is a way to perform addition and/or subtraction on the real number line.
We also leanrt that movement to the right on the number line implies addition while movement to the left on the real number line implies subtraction.
In this lesson, we will learn how to skip count forwards and backwards in intervals of 10,000s, 100,000s, 500,000s etc.
The interval is the distance between any two numbers on the number line. For instance, the interval between the numbers 2 and 5 on the number line is 3, which is obtained by subtracting 2 from 5.
It can also be said that 3 is the number of steps you will count when moving forward from 2 to 5 (addition), or when moving backwards from 5 to 2 (subtraction).
Remember
In skip counting, your starting point (position or number) is said to be your first term.
To skip count forward in a particular interval simply means to add the interval value onto each term to get the next term.
Example 1
Skip count forwards up to the 5th term in intervals of \(10,000\)
200,000, 210,000, ...
Solution
\(n^{th}\) term \(\Rightarrow 5^{th}\) term
Number of skips \(\Rightarrow n - 1\)
Number of skips \(\Rightarrow 5 - 1 = 4\) skips
Interval, \(\left(d\right) \Rightarrow 10,000\)
First term \( \left(a\right) \Rightarrow \mathbf{200,000}\)
Second term \(\Rightarrow\) \(200,000 \ +\) \(10,000 =\) \(\mathbf{210,000}\)
Third term \(\Rightarrow 210,000\) \(+ 10,000\) \( = \mathbf{220,000}\)
Fourth term \(\Rightarrow 220,000 + 10,000 = \mathbf{230,000}\)
Fifth term \(\Rightarrow 230,000 + 10,000 = \mathbf{240,000}\)
\(\therefore\) the terms are \(\{200,000, \ 210,000, \ 220,000, \ 230,000, \ 240,000\}\)
Example 2
Skip count forwards in 500000s up to the 5th number.
200,000, 700,000, ...
Solution
\(n^{th}\) term \(\Rightarrow 5^{th}\) term
Number of skips \(\Rightarrow n - 1\)
Number of skips \(\Rightarrow 5 - 1 = 4\) skips
Interval, \(\left(d\right) \Rightarrow 10,000\)
First term \( \left(a\right) \Rightarrow \mathbf{200,000}\)
Second term \(\Rightarrow 200,000 + 10,000 = \mathbf{210,000}\)
Third term \(\Rightarrow 210,000 + 10,000 = \mathbf{220,000}\)
Fourth term \(\Rightarrow 220,000 + 10,000 = \mathbf{230,000}\)
Fifth term \(\Rightarrow 230,000 + 10,000 = \mathbf{240,000}\)
\(\therefore\) the terms are \( \{200,000, \ 210,000, \ 220,000, \ 230,000, \ 240,000 \} \)
Example 3
Find the value of the 5th term when skip counting in intervals of 100,000 from 300,000.
Solution
\(n^{th}\) term \(\Rightarrow 5^{th}\) term
First term, \(a\) \(\Rightarrow\) 300,000
Interval, \(d\) \(\Rightarrow\) 100,000
let the last term \(\Rightarrow \ l\)
Using the formula: \( l = a + (n - 1)d \)
\( \Rightarrow l = 300,000 + \left( 5-1 \right)100,000 \)
\(\Rightarrow l = 300,000 + \left( 4 \right)100,000 \)
\(\Rightarrow l = 300,000 + 400,000 \)
\(\Rightarrow l = 700,000 \)
\(\therefore\) the last term is 700,000.
Example 4
Skip count forwards up to the 4th term in intervals of \(10,500\)
200,000, 210,500, ...
Solution
Example 5
Skip count forwards up to the 5th term in intervals of \(100,500\)
200,000, 300,500, ...
Solution
To skip count backward in a particular interval simply means to subtract the interval value from each term to get the next term.
Example 1
Skip count backwards up to the 6th term in intervals of \(100,000\)
1,800,000, 1,700,000, 1,600,000, ...
Solution
Example 2
Skip count backwards up to the 7th term in intervals of \(100,500\)
1,800,000, 1,699,500, 1,599,000, ...
Solution
Example 3
Skip count backwards up to the 5th term in intervals of \(10,000\)
1,800,000, 1,790,000, ...
Solution
Example 4
Skip count backwards up to the 4th term in intervals of \(500,000\)
1,800,000, ...
Solution
Example 5
Skip count backwards up to the 7th term in intervals of \(100,000\)
2,000,000, 1,900,000, ...
Solution
Test yourself on what you have learnt so far. Click on the link below when you are ready.
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