Mathematics
Grade 11
15 min
Multiplication input/output tables: find the rule
Multiplication input/output tables: find the rule
What you'll learn
- Identify the multiplication rule (e.g., x2, x5) in at least 3 out of 4 given input/output tables.
- Solve for the missing output number in a multiplication input/output table, using the identified rule, with 80% accuracy.
- Explain, using words or pictures, how to find the missing number in an input/output table by identifying the multiplication rule.
- Apply the identified multiplication rule to complete at least 2 out of 3 partially filled input/output tables.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the constant of proportionality in tables relating different units of angle measure, such as degrees and radians.
Formulate a multiplicative rule of the form y = kx to model the relationship between inputs and outputs in a table.
Determine the rule for angular displacement given a table of time and angle data, identifying the constant as the angular velocity.
Apply the derived rule to predict unknown output values (e.g., angular displacement) for given input values (e.g., time).
Verify that a rule is consistently multiplicative by testing the ratio y/x for multiple data pairs.
Connect the multiplicative constant 'k' to its physical or geometric meaning, such as a conversion factor or a rate of rotation.
How does a satellite orbiting Ear...
2
Key Concepts & Vocabulary
TermDefinitionExample
Input/Output TableA table that organizes pairs of related numbers. For each input value (x), there is a corresponding output value (y) determined by a specific rule.A table with inputs (Time in s) of 1, 2, 3 and outputs (Angle in rad) of π/2, π, 3π/2.
Multiplicative RuleA rule that describes a direct proportion between two variables, expressed as y = kx. The output (y) is obtained by multiplying the input (x) by a fixed, non-zero number (k).If the rule is y = 4x, an input of 3 gives an output of 12.
Constant of Proportionality (k)The constant multiplier in a multiplicative rule. It is the ratio of the output to the input (k = y/x) and remains the same for every pair in the relationship.In the relationship between degrees (x) and radians (y), the constant is k = π/180...
3
Core Formulas
The Rule-Finding Formula
k = \frac{y}{x}
To find the constant of proportionality (k) in a multiplicative relationship, choose any corresponding input (x) and output (y) pair from the table and calculate their ratio. This constant is the 'rule'.
General Multiplicative Rule
y = kx
Once the constant (k) is found, this formula represents the rule for the entire table. You can use it to find any output (y) for a given input (x), or vice-versa.
Angular Displacement with Constant Velocity
\theta(t) = \omega t
A specific application of y = kx in physics. The angular displacement (θ) is the output, time (t) is the input, and the constant angular velocity (ω) is the multiplicative rule (k).
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A lighthouse beacon completes 5 full rotations every minute. What is its total angular displacement in radians after 12 seconds?
A.π radians
B.2π radians
C.60π radians
D.π/2 radians
Challenging
The table relates the central angle θ in radians (input) to the arc length s in centimeters (output) for a given circle. What does the constant of proportionality 'k' in the rule s = kθ represent?
| Angle θ (rad) | π/2 | π |
| Arc Length s (cm) | 5π | 10π |
A.The circle's circumference
B.The circle's area
C.The circle's radius
D.The value of π
Challenging
An unconventional clock's hand has an angular displacement θ that is proportional to the logarithm of time, t. The table shows this relationship. What is the rule relating θ and t?
| Input x = log₃(t) | 1 | 2 | 3 |
| Output y = θ (rad)| π | 2π | 3π |
A.θ = π * log₃(t)
B.θ = log₃(πt)
C.θ = πᵗ
D.θ = 3^(πt)
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Angle measures
Mathematics for other grades
Frequently asked questions
What grade level is "Multiplication input/output tables: find the rule"?
Multiplication input/output tables: find the rule is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Multiplication input/output tables: find the rule?
You'll be able to: Identify the multiplication rule (e.g., x2, x5) in at least 3 out of 4 given input/output tables; Solve for the missing output number in a multiplication input/output table, using the identified rule, with 80% accuracy; Explain….
Is "Multiplication input/output tables: find the rule" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Multiplication input/output tables: find the rule?
This lesson includes 32 practice questions across multiple difficulty levels, each with instant feedback and explanations.