Number Patterns
continue this pattern for 3 numbers
36,41,46,
51,56,61
Imagine a number machine that doubles the input and then adds 3. If you input the number 4, what would be the output?
For the given number machine, doubling the input (4) and then adding 3:
2×4+3=8+3=112×4+3=8+3=11
So, the output is 11.
Consider a reverse function that adds 6 to the input and then divides the result by 3. If the output is 4, what is the input?
6
Continue this pattern for 5 numbers
72,75,78
81,84,87,90,93
Consider a number machine that subtracts 5 from the input. If you input the number 12, what is the output?
For the given number machine, subtracting 5 from the input (12):
12−5=712−5=7
So, the output is 7.
Consider a reverse function that subtracts 5 from the input and then adds 7. If the output is 12, what is the input?
10
Continue this sequences for 5 numbers
90, 84,78
72,66,60,54,48
Consider a number machine that triples the input and then subtracts 4. If you input the number 6, what is the output?
Certainly! Here are five questions related to number machines for Year 7 Track 1 math students along with their answers:
Question 1:
Imagine a number machine that doubles the input and then adds 3. If you input the number 4, what would be the output?
Answer 1:
For the given number machine, doubling the input (4) and then adding 3:
2×4+3=8+3=112×4+3=8+3=11
So, the output is 11.
Question 2:
Consider a number machine that subtracts 5 from the input. If you input the number 12, what is the output?
Answer 2:
For the given number machine, subtracting 5 from the input (12):
12−5=712−5=7
So, the output is 7.
Question 3:
Imagine a number machine that squares the input and then adds 2. If you input the number 3, what would be the output?
Answer 3:
For the given number machine, squaring the input (3) and then adding 2:
32+2=9+2=1132+2=9+2=11
So, the output is 11.
Question 4:
Consider a number machine that triples the input and then subtracts 4. If you input the number 6, what is the output?
Answer 4:
For the given number machine, tripling the input (6) and then subtracting 4:
3×6−4=18−4=143×6−4=18−4=14
So, the output is 14.
Imagine a reverse function that multiplies the input by 3 and then subtracts 4. If the output is 14, what is the input?
6
Look at the sequence of numbers below:
2, 6, 10, 14, 18, ...
What is the rule or pattern that governs this sequence? What are the next number in the sequence?
The pattern is adding 4 to each number to get the next one.
The next number in the sequence is 22, 26,30.
Imagine a number machine that adds 7 to the input and then divides the result by 2. If you input the number 10, what would be the output?
For the given number machine, adding 7 to the input (10) and then dividing the result by 2:
(10+7)2=172=8.52(10+7)=217=8.5
So, the output is 8.5.
Consider a reverse function that doubles the input and then subtracts 10. If the output is 16, what is the input?
13
Investigate the following decreasing pattern:
64, 32, 16, 8, 4, ...
Identify the rule that defines this numerical pattern. What is the next number in the sequence?
The pattern is dividing each number by 2 to get the next one.
The next number in the sequence is 2.
Consider a number machine that multiplies the input by 4 and then subtracts 6. If you input the number 5, what is the output?
For the given number machine, multiplying the input (5) by 4 and then subtracting 6:
(4×5)−6=20−6=14(4×5)−6=20−6=14
So, the output is 14.
Imagine a reverse function that subtracts 3 from the input and then multiplies the result by 4. If the output is 20, what is the input?
8