Mathematics
Grade 11
15 min
Multiply one-digit numbers by three-digit numbers: word problems
Multiply one-digit numbers by three-digit numbers: word problems
What you'll learn
- Identify the multiplication problem hidden in a word problem with one-digit and three-digit numbers with 80% accuracy.
- Solve multiplication word problems involving one-digit and three-digit numbers using the standard algorithm, showing all steps clearly, and arriving at the correct answer in 4 out of 5 problems.
- Explain the steps used to solve a multiplication word problem with one-digit and three-digit numbers to a partner, demonstrating understanding of place value and carrying in at least 3 out of 4 opportunities.
- Apply multiplication of one-digit and three-digit numbers to solve real-world word problems with different contexts (e.g., money, distance, quantity) with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate complex rotational word problems into mathematical expressions involving the multiplication of a one-digit scalar and a three-digit angle.
Calculate the total angular displacement and determine the final position of a rotating object after multiple iterations.
Apply De Moivre's Theorem to find integer powers of complex numbers, where the resulting argument is a product of a one-digit and a three-digit number.
Determine the principal angle and reference angle for a total angle calculated from a word problem.
Solve for unknown variables in geometric and trigonometric contexts that require multiplying a one-digit integer by a three-digit angle.
Analyze the terminal quadrant of an angle resulting from scalar multiplication and correctly apply tri...
2
Key Concepts & Vocabulary
TermDefinitionExample
Angular Displacement (Δθ)The total angle through which a point or line has been rotated in a specified direction about a specified axis. It is the product of the number of rotations and the angle per rotation.A wheel spins 4 times. Since one full rotation is 360°, the total angular displacement is Δθ = 4 * 360° = 1440°.
Coterminal AnglesAngles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. To find a coterminal angle, add or subtract multiples of 360°.An angle of 480° is coterminal with 120° because 480° - 360° = 120°. They end at the same position.
Principal AngleThe smallest positive coterminal angle of a given angle. It is always between 0° and 360° (or 0 and 2π radians).For an angle of 800°, the princip...
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Core Formulas
Total Angular Displacement Formula
\Delta\theta_{total} = n \times \theta_{rotation}
Used to find the total angle of rotation. Here, 'n' is a one-digit integer representing the number of identical rotations, and 'θ_rotation' is the three-digit angle of a single rotation.
Coterminal Angle General Form
\theta_{coterminal} = \theta + k \cdot 360^{\circ}
Used to find an angle that is in the same position as θ. 'k' is any integer. In our problems, we often use this to find the principal angle after calculating a large total displacement.
De Moivre's Theorem (for integer powers)
[r(\cos \theta + i \sin \theta)]^n = r^n(\cos(n\theta) + i \sin(n\theta))
This is crucial for finding powers of complex numbers. The multiplication of the one-dig...
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Challenging
A motor rotates by an angle of 150°. After 'n' identical rotations, where n is a single-digit integer, its final orientation is 330°. What is the value of n?
A.5
B.9
C.6
D.7
Challenging
A ship's rudder is moved 3 times by 150° counter-clockwise, then moved 2 times by 110° clockwise. Starting from 0°, what is its final orientation as a principal angle?
A.230°
B.40°
C.670°
D.290°
Challenging
The position of a particle on a complex plane after n seconds is given by z^n, where z = cos(110°) + i sin(110°). After 9 seconds, is the particle at the same angular position as a second particle located at w = cos(270°) + i sin(270°)?
A.Yes, because the final principal angle is 270°.
B.No, because the final principal angle is 990°.
C.No, because the final principal angle is 90°.
D.Yes, because the modulus is the same.
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What grade level is "Multiply one-digit numbers by three-digit numbers: word problems"?
Multiply one-digit numbers by three-digit numbers: word problems is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Multiply one-digit numbers by three-digit numbers: word problems?
You'll be able to: Identify the multiplication problem hidden in a word problem with one-digit and three-digit numbers with 80% accuracy; Solve multiplication word problems involving one-digit and three-digit numbers using the standard algorithm….
Is "Multiply one-digit numbers by three-digit numbers: word problems" free to practice?
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How many practice questions are included with Multiply one-digit numbers by three-digit numbers: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.