Mathematics
Grade 11
15 min
Multiply one-digit numbers by three-digit numbers
Multiply one-digit numbers by three-digit numbers
What you'll learn
- Solve multiplication problems involving a one-digit number and a three-digit number using the standard algorithm with at least 80% accuracy on a worksheet.
- Explain the steps involved in multiplying a one-digit number by a three-digit number using the standard algorithm in their own words to a partner.
- Apply the distributive property to break down a three-digit number into hundreds, tens, and ones to multiply it by a one-digit number.
- Identify at least three real-world scenarios where multiplying a one-digit number by a three-digit number would be useful.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the measure of a coterminal angle by multiplying 360° by a one-digit integer representing the number of rotations.
Determine the arc length of a circle by multiplying a three-digit radius by a one-digit central angle in radians.
Compute the area of a circular sector where the calculation involves multiplying a three-digit number (derived from the radius squared) by a one-digit central angle.
Apply the Law of Sines to find a missing side length when it requires multiplying a three-digit side length by a one-digit scalar.
Solve for total angular displacement by multiplying a three-digit angular velocity by a one-digit time interval.
Accurately perform the multiplication of a one-digit number by a three-digit number as a critical step within complex...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coterminal AnglesAngles in standard position (vertex at the origin, initial side on the positive x-axis) that have the same terminal side. They are found by adding or subtracting integer multiples of 360° or 2π radians.An angle of 450° is coterminal with 90° because 450° = 90° + 360° × 1. The multiplication step is 360 × 1.
Arc Length (s)The physical distance along the curved line making up an arc. The calculation requires the central angle to be in radians.For a circle with a radius of 150 meters and a central angle of 3 radians, the arc length is s = 150 × 3 = 450 meters.
Sector Area (A)The area of the portion of a circle enclosed by two radii and their intercepted arc. The calculation requires the central angle to be in radians.For a circle with a radius of 20 ft...
3
Core Formulas
Coterminal Angle Formula (Degrees)
\theta_{coterminal} = \theta + 360^\circ \times n
Use this formula to find a coterminal angle, where 'θ' is the given angle and 'n' is an integer representing the number of full rotations. The core multiplication is 360 × n.
Arc Length Formula
s = r \times \theta
Calculates the arc length 's' of a circle with radius 'r' and a central angle 'θ' measured in radians. The core multiplication is r × θ.
Sector Area Formula
A = \frac{1}{2} r^2 \theta
Calculates the area 'A' of a circular sector with radius 'r' and a central angle 'θ' measured in radians. The multiplication often involves a three-digit number (from r²) and a one-digit number (θ).
5 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 satellite in a circular orbit has an angular velocity of 125 milliradians per second. After 8 seconds, it has traveled an arc length of 800 km. What is the radius of its orbit in kilometers?
A.100 km
B.800 km
C.1000 km
D.6400 km
Challenging
An angle θ is coterminal with 40° and is found by making 5 full counter-clockwise rotations. This angle θ (in radians) is then used to find the arc length on a circle with a 100-unit radius. What is that arc length? (Use π ≈ 3.14)
A.1840 units
B.3211 units
C.1800 units
D.70 units
Easy
Which formula is used to calculate the arc length 's' of a circle with radius 'r' and a central angle 'θ' in radians?
A.= (1/2)r²θ
B.θ_coterminal = θ + 360° × n
C.s = r + θ
D.s = r × θ
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 "Multiply one-digit numbers by three-digit numbers"?
Multiply one-digit numbers by three-digit numbers is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Multiply one-digit numbers by three-digit numbers?
You'll be able to: Solve multiplication problems involving a one-digit number and a three-digit number using the standard algorithm with at least 80% accuracy on a worksheet; Explain the steps involved in multiplying a one-digit number by a….
Is "Multiply one-digit numbers by three-digit numbers" 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 Multiply one-digit numbers by three-digit numbers?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.