الأسبوع 9 · المتغيران التابع والمستقل: العلاقات والقواعد · 3 دروس
3
Input and output rules in everyday stories
Discover Mathematics P6: Term 1, Unit 5, Lessons 1–2
GoalUse an input-output rule to find outputs, find a missing input, and describe how the output changes.
New words
input · the number we put into the ruleoutput · the number that comes out of the ruleundo · use the opposite operation to go from output back to input
Explanation
An input-output rule works like a machine in a bakery: put in a number, the machine does the same thing every time, and a number comes out. To find an output, apply the rule to the input. To find a missing input, undo the rule: if the rule is ×4 and the output is 28, divide: 28 ÷ 4 = 7. A table helps us to see the pattern. For the rule “double and add 1” the outputs for 1, 2, 3 and 4 are 3, 5, 7 and 9. Each time the input goes up by 1, the output goes up by 2. That is the change in the dependent variable.
★Remember
Find an output: apply the rule. Find an input: undo the rule.
Worked examples
Trays t
2
5
7
Rolls r = 12t
24
60
84
A baker puts 12 rolls on each tray: r = 12t. For 2, 5 and 7 trays the rolls are 24, 60 and 84.
Input
?
5
9
Output (× 4)
28
20
36
Missing input. A machine multiplies by 4 and the output is 28. Undo it: 28 ÷ 4 = 7, so the input is 7. Check: 7 × 4 = 28.
Input x
1
2
3
4
Output 2x + 1
3
5
7
9
A two-step rule: double, then add 1. The outputs are 3, 5, 7, 9. When the input goes up by 1, the output goes up by 2.
Class activity
Be the machine. Cut a cardboard box into a “machine” with a slot. A grown-up chooses a rule and secretly writes it down. Slip in cards with inputs, write the outputs on the other side and let the other player guess the rule. Try a rule with two steps.
Practice
1
The rule is × 6. What is the output for the input 9?
9 × 6 = 54.
2
A machine multiplies by 4 and gives 36. What number went in?
36 ÷ 4 = 9.
3
The rule is + 7. Find the outputs for 3, 8 and 20.
10, 15 and 27.
4
The rule is “double and add 1”. What is the output for the input 10?
2 × 10 + 1 = 21.
5
Karim pays 5 LE for each ride and pays 45 LE in all. How many rides did he take?
