Mathematics
Grade 10
15 min
Multiply by 2-digit numbers: complete the missing steps
Multiply by 2-digit numbers: complete the missing steps
What you'll learn
- Identify the missing digits in a multi-digit multiplication problem with 2-digit multipliers with 80% accuracy.
- Solve multiplication problems with 2-digit multipliers, showing all steps clearly, and correctly complete at least 3 out of 4 problems.
- Explain the process of multiplying by a 2-digit number, including the importance of place value, in their own words to a partner.
- Apply the concept of partial products to complete incomplete multiplication problems with 2-digit multipliers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Accurately calculate the square of a 2-digit radius (r²) to write the standard equation of a circle.
Identify and fill in missing partial products in the standard algorithm for 2-digit multiplication.
Apply the distance formula by correctly squaring 2-digit differences in x and y coordinates.
Use 2-digit multiplication to find the constant term needed when completing the square for a circle's general equation.
Verify the components of a circle's equation by deconstructing and completing multiplication steps.
Distinguish between the radius (r) and the radius squared (r²) in circle equations, avoiding common calculation errors.
Ever wondered how GPS pinpoints your location within a circular range? It all comes down to precise calculations! 🗺️
In...
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Key Concepts & Vocabulary
TermDefinitionExample
Standard Equation of a CircleThe formula (x - h)² + (y - k)² = r², which defines a circle with a center at point (h, k) and a radius of length r.The equation (x - 3)² + (y + 1)² = 25 represents a circle with its center at (3, -1) and a radius of 5.
Radius Squared (r²)The value that completes the circle equation, found by multiplying the radius (r) by itself. This value represents the square of the distance from the center to any point on the circle.If a circle has a radius r = 12, then the radius squared is r² = 12 x 12 = 144.
Distance FormulaA formula derived from the Pythagorean theorem used to find the distance between two points (x₁, y₁) and (x₂, y₂) in the coordinate plane.The distance between (1, 2) and (4, 6) is √((4-1)² + (6-2)²) = √(3² + 4²) = √25 = 5.
Stand...
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Core Formulas
Standard Equation of a Circle
(x - h)² + (y - k)² = r²
This formula defines a circle with center (h, k) and radius r. Calculating r² when r is a 2-digit number is a key application of the skill in this lesson.
Distance Formula (Squared Form)
d² = (x₂ - x₁)² + (y₂ - y₁)²
Used to find the square of the distance between two points. This is useful for finding the radius squared (r²) if you know the center and a point on the circle. The terms (x₂ - x₁)² and (y₂ - y₁)² may involve squaring 2-digit numbers.
Completing the Square Term
For x² + bx, add (b/2)²
To complete the square for an expression like x² + bx, you must add the term (b/2)². If b is a large even number, b/2 can be a 2-digit number that you need to square.
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
In the calculation of 24 x 24 to find r², what is the first partial product, which represents 4 x 24?
A.96
B.86
C.48
D.480
Easy
When calculating 45 x 45, the first partial product is 225. What is the correct second partial product that should be added to 225?
A.180
B.225
C.1800
D.2250
Easy
In the distance formula, a student calculates the difference in y-coordinates to be -13. What is the value of (Δy)² that should be used to find r²?
A.-169
B.169
C.26
D.-26
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Frequently asked questions
What grade level is "Multiply by 2-digit numbers: complete the missing steps"?
Multiply by 2-digit numbers: complete the missing steps is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiply by 2-digit numbers: complete the missing steps?
You'll be able to: Identify the missing digits in a multi-digit multiplication problem with 2-digit multipliers with 80% accuracy; Solve multiplication problems with 2-digit multipliers, showing all steps clearly, and correctly complete at least 3….
Is "Multiply by 2-digit numbers: complete the missing steps" free to practice?
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How many practice questions are included with Multiply by 2-digit numbers: complete the missing steps?
This lesson includes 20 practice questions across multiple difficulty levels, each with instant feedback and explanations.