Mathematics
Grade 10
15 min
Multiply 2-digit numbers by larger numbers
Multiply 2-digit numbers by larger numbers
What you'll learn
- Solve multiplication problems involving a 2-digit number and a 3-digit number with at least 80% accuracy using the standard algorithm.
- Explain the steps of the standard algorithm for multiplying a 2-digit number by a larger number in their own words, demonstrating understanding of place value.
- Apply multiplication skills to solve real-world word problems involving 2-digit numbers multiplied by larger numbers, showing their work and correct units.
- Identify and correct errors in multiplication problems involving 2-digit numbers and larger numbers, explaining the mistake and providing the correct solution.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Apply the standard algorithm to multiply any 2-digit number by a 3- or 4-digit number within a geometric context.
Calculate the circumference of a circle with a large radius over multiple rotations.
Determine the area of a circle whose large radius is the result of a calculation.
Calculate the new radius and area of a circle after its dimensions are scaled by a 2-digit factor.
Use estimation to verify the reasonableness of products in circle-related word problems.
Accurately perform multi-step calculations involving circle formulas and large-number multiplication.
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Key Concepts & Vocabulary
TermDefinitionExample
Standard Multiplication AlgorithmThe traditional, step-by-step method for multiplication where numbers are stacked vertically. You multiply the bottom number's digits, one at a time from right to left, with the top number, creating partial products that are then added together.To calculate 415 x 23, you first multiply 415 by 3, then multiply 415 by 20 (by adding a placeholder zero), and finally add the two results (1245 + 8300) to get 9545.
Partial ProductThe result of multiplying one number by a single digit of the other number. In the standard algorithm, each row of calculation before the final sum is a partial product.In 1250 x 45, the first partial product is 1250 x 5 = 6250. The second partial product is 1250 x 40 = 50000.
Scalar FactorA number by which a g...
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Core Formulas
Equation of a Circle
(x - h)^2 + (y - k)^2 = r^2
The standard form for the equation of a circle with center (h, k) and radius r. Calculating r^2 when r is a 2-digit number is a direct application of multiplication.
Circumference Formula
C = 2 * π * r
Used to find the distance around a circle. When r is a large number, calculating the total distance over multiple rotations (e.g., C * 25) requires multiplying a large number by a 2-digit number.
Area Formula
A = π * r^2
Used to find the space inside a circle. This often involves squaring a number (e.g., 85 * 85) and then multiplying the result by π (approximated as 3.14), which can involve multiplying a 2-digit number by a larger number.
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Challenging
A student is asked to find the total distance a wheel with a circumference of 1150 cm travels in 45 rotations. Their work is shown: 1150 × 45 = 5750 + 4600 = 10350 cm. Identify the error.
A.The first partial product (1150 × 5) is incorrect.
B.The final sum of the partial products is incorrect.
C.The second partial product (1150 × 40) was calculated without a placeholder zero and misaligned.
D.The circumference was calculated incorrectly.
Challenging
A city park is a circle with the equation x² + y² = 250,000 (in meters). The council approves a plan to increase the park's AREA by a factor of 1,296. This is equivalent to scaling the RADIUS by what 2-digit integer factor, and what is the new circumference? Use π ≈ 3.14.
A.Factor of 12; New C = 37,680 m
B.Factor of 36; New C = 113,040 m
C.Factor of 36; New C = 18,000 m
D.Factor of 46; New C = 144,440 m
Challenging
A large gear with a radius of 875 mm interlocks with a smaller gear. The large gear completes 24 rotations. To travel the same total circumferential distance, how many full rotations must the smaller gear with a 420 mm radius make?
A.50 rotations
B.24 rotations
C.12 rotations
D.40 rotations
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What grade level is "Multiply 2-digit numbers by larger numbers"?
Multiply 2-digit numbers by larger numbers is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiply 2-digit numbers by larger numbers?
You'll be able to: Solve multiplication problems involving a 2-digit number and a 3-digit number with at least 80% accuracy using the standard algorithm; Explain the steps of the standard algorithm for multiplying a 2-digit number by a larger….
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This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.