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Input/Output Machines
Number Patterns
Patterns in Divisibility
Solving Equations
Integers
100

What is an input/output machine?

Input and output machines perform operations on a number (the input) to produce another number (the output)

100

List the first six multiple of the number 4

4, 8, 12, 16, 20, 24

100

What is the divisibility rule for the number 3? 

The sum of the digits is divisible by 3. 

100

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. 

100

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

200

If the operation in the machine is (x6) determine the output for numbers 1-4

6, 12, 18, 24 

200

Write the first 4 terms for this pattern rule: Start at 7. Add 4 each time: ______, ______, ______, ______,...

7, 11, 15, 19, 

200

Explain why a number with a 0 in the ones place, is divisible by 10. 

It has 10 as a factor. 

200

Find the missing number:

____ - 91 = 33

58 

200

What are the two types of integers? 

Provide an example

Positive and negative 

+35, -81

300

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.

300

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

300

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

300

Find the missing number:

96 + _____= 147

147-96= 51

300

List the opposite of the following:

a) 6

b) -52

c) 0

a) - 6

b) 52

c) 0

400

What is the pattern rule for the output column?

input column:       output column

1                               1      

2                               4

3                               7

4                              10

5                              13


Start at 1. Add 3 each time

400

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.

400

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. 

400

Balance the following equation:

32 x 2 = ______ x 16

32 x 2 = ___4___ x 16

32x3= 64

64/16 = 4

400

What integers are included in the situation? 

  • At the beginning of the month, Lisa had $450 in her bank account.
  • At the end of the month, she realized she overspent and had -$50 in her account.

+450 and -50 

500

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

500

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.

500

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.

500

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

500

What are two different real-life scenarios that can be used for the following integer? 

 +155

Example: Sally raised $155 for the fundraiser