Input/Output Machines
What is an input/output machine?
Input and output machines perform operations on a number (the input) to produce another number (the output)
List the first six multiple of the number 4
4, 8, 12, 16, 20, 24
What is the divisibility rule for the number 3?
The sum of the digits is divisible by 3.
Define the word equation. What makes a balanced equation?
An equation is a mathematical sentence with an equal sign.
A balanced equal has the same value and sum on both sides. Whatever you do to one side you must do to the other.
Define Integers:
Give an example
An integer is a whole number (not a fractional number) that can be positive, negative, or zero
examples: 2, 3, 4, -5, -6, 0
If the operation in the machine is (x6) determine the output for numbers 1-4
6, 12, 18, 24
Write the first 4 terms for this pattern rule: Start at 7. Add 4 each time: ______, ______, ______, ______,...
7, 11, 15, 19,
Explain why a number with a 0 in the ones place, is divisible by 10.
It has 10 as a factor.
Find the missing number:
____ - 91 = 33
58
What are the two types of integers?
Provide an example
Positive and negative
+35, -81
input column: output column
1 8
2 10
3 12
4 14
5 16
What is the pattern rule for the output column?
Start at 8. Add 2 each time.
Write the first 5 terms for this pattern rule: Start at 7. Multiply by 3, then subtract 2 each time: ______, ______, ______, ______, ______, ...
7, 19, 55, 163, 487
What are the divisibility rules for numbers 6 and 9?
6) if the number is divisible by 2 and 3
9) if all the sum of the digits is divisible by 9
Find the missing number:
96 + _____= 147
147-96= 51
List the opposite of the following:
a) 6
b) -52
c) 0
a) - 6
b) 52
c) 0
input column: output column
1 1
2 4
3 7
4 10
5 13
What is the pattern rule for the output column?
Start at 1. Add 3 each time
Which of these patterns are recursive? How do you know?
a) 3, 6, 12, 24, 48, 96, ...
b) 1, 4, 9, 16, 25, 36, ...
c) 1, 3, 9, 27, 81, 243, ...
All patterns listed are recursive patterns.
Three numbers divisible by 6, how do you know?
Making sure the ones digit is even and that the sum of the digits is divisibly by 3.
Balance the following equation:
32 x 2 = ______ x 16
32 x 2 = ___4___ x 16
32x3= 64
64/16 = 4
What integers are included in the situation?
+450 and -50
If the operations in a two-step machine are (x6) then (+1) determine the output for numbers 1-6
7, 13, 19, 25, 31, 37
Write the next 3 terms in this pattern: 4, 5, 7, 11, 19
Then state the pattern rule.
35, 67, 131
Rule: Start at 4. Multiply by 2, then subtract 3 each time.
Which of these numbers is divisible by 4? by 9? How do you know?
140. 150. 612. 1089.
Divisible by 4; 140 and 612 because the number formed by the last 2 digits is divisible by 4.
Divisible by 9: 612, 1089 because the sum of the digits is divisible by 9.
Solve the following equations:
a) 8-6 = ____ - ____
b) 16 x 3 = ____ x ____
c) 5 + 3= ____ + _____
a) any pair of numbers with a difference of 2 (6-4, 10-8, 7-5, etc)
b) 1 x 48, 2 x 24, 4 x 12, 6 x 8, etc
c) any pair of numbers that have a sum of 8
What are two different real-life scenarios that can be used for the following integer?
+155
Example: Sally raised $155 for the fundraiser