Continue decimal patterns using models

If numbers increase or decrease by a regular amount, we can describe this as a number pattern. You've already seen number patterns with whole numbers here. Now, we are going to look at number patterns with decimals.

Number patterns can be increasing or decreasing. We will look at both possibilities.

Increasing

If numbers rise by a regular amount, we can describe these as increasing number patterns. We could use addition or multiplication to make numbers get bigger. We are going to focus on increasing number patterns using addition.

Let's consider an example:

$0.2$0.2

$0.5$0.5

$0.8$0.8

$\editable{}$

$\editable{}$

$\editable{}$

As the numbers rise by a regular amount, we have an increasing pattern. How much do they increase by every time?

Let's consider the first two terms, $0.2$0.2 and $0.5$0.5. The difference between these two numbers is $0.5-0.2=0.3$0.5−0.2=0.3. This means it goes up by $0.3$0.3 between $0.2$0.2 and $0.5$0.5, as shown below.

$+0.3$+0.3

$\nearrow$↗

$\searrow$↘

$0.2$0.2

$0.5$0.5

$0.8$0.8

$\editable{}$

$\editable{}$

$\editable{}$

It seems the pattern is going up by $0.3$0.3 each time. Is the pattern always going up by $0.3$0.3?

Let's check. Let's look at the second and third terms, $0.5$0.5 and $0.8$0.8. The difference between these two numbers is $0.8-0.5=0.3$0.8−0.5=0.3. This means it goes up by $0.3$0.3 between $0.5$0.5 and $0.8$0.8, as shown below.

$+0.3$+0.3

$+0.3$+0.3

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$0.2$0.2

$0.5$0.5

$0.8$0.8

$\editable{}$

$\editable{}$

$\editable{}$

As it goes up by $0.3$0.3 on both occasions, we've found the pattern, and can continue adding $0.3$0.3 to finish the pattern.

What is $0.8+0.3$0.8+0.3? $0.8+0.3=1.1$0.8+0.3=1.1. This means we can write $1.1$1.1 in the first empty box.

$+0.3$+0.3

$+0.3$+0.3

$+0.3$+0.3

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$0.2$0.2

$0.5$0.5

$0.8$0.8

$\editable{1.1}$1.1

$\editable{}$

$\editable{}$

We can apply the same rule to the last two boxes.

$1.1+0.3=1.4$1.1+0.3=1.4 and $1.4+0.3=1.7$1.4+0.3=1.7.

$+0.3$+0.3

$+0.3$+0.3

$+0.3$+0.3

$+0.3$+0.3

$+0.3$+0.3

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$0.2$0.2

$0.5$0.5

$0.8$0.8

$\editable{1.1}$1.1

$\editable{1.4}$1.4

$\editable{1.7}$1.7

Decreasing

If numbers reduce by a regular amount, we can describe these as decreasing number patterns. We could use subtraction or division to make numbers get smaller. We are going to focus on decreasing number patterns using subtraction.

Let's consider an example, this time using two decimal places:

$0.86$0.86

$0.79$0.79

$0.72$0.72

$\editable{}$

$\editable{}$

$\editable{}$

As the numbers reduce by a regular amount, we have a decreasing pattern. How much do they decrease by every time?

Let's consider the first two terms, $0.86$0.86 and $0.79$0.79. The difference between these two numbers is $0.86-0.79=0.07$0.86−0.79=0.07. This means it goes down by $0.07$0.07 between $0.86$0.86 and $0.79$0.79, as shown below. Notice that there is a minus sign in front of the $0.07$0.07 to show that it is going down, and that we need to subtract as we move along the pattern.

$-0.07$−0.07

$\nearrow$↗

$\searrow$↘

$0.86$0.86

$0.79$0.79

$0.72$0.72

$\editable{}$

$\editable{}$

$\editable{}$

It seems the pattern is going down by $0.07$0.07 each time. Is the pattern always going down by $0.07$0.07?

Let's check. Let's look at the second and third terms, $0.79$0.79 and $0.72$0.72. The difference between these two numbers is $0.79-0.72=0.07$0.79−0.72=0.07. This means it goes down by $0.07$0.07 between $0.79$0.79 and $0.72$0.72, as shown below.

$-0.07$−0.07

$-0.07$−0.07

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$0.86$0.86

$0.79$0.79

$0.72$0.72

$\editable{}$

$\editable{}$

$\editable{}$

As it goes down by $0.07$0.07 on both occasions, we've found the pattern, and can continue subtracting $0.07$0.07 to finish the pattern.

What is $0.72-0.07$0.72−0.07? $0.72-0.07=0.65$0.72−0.07=0.65. This means we can write $0.65$0.65 in the first empty box.

$-0.07$−0.07

$-0.07$−0.07

$-0.07$−0.07

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$0.86$0.86

$0.79$0.79

$0.72$0.72

$\editable{0.75}$0.75

$\editable{}$

$\editable{}$

We can apply the same rule to the last two boxes.

$0.65-0.07=0.58$0.65−0.07=0.58 and $0.58-0.07=0.51$0.58−0.07=0.51.

$-0.07$−0.07

$-0.07$−0.07

$-0.07$−0.07

$-0.07$−0.07

$-0.07$−0.07

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$\nearrow$↗

$\searrow$↘

$0.86$0.86

$0.79$0.79

$0.72$0.72

$\editable{0.65}$0.65

$\editable{0.58}$0.58

$\editable{0.51}$0.51

 

Worked Examples

QUESTION 1

QUESTION 2

QUESTION 3