Curriculum / Math / 5th Grade / Unit 2: Multiplication and Division of Whole Numbers / Lesson 9
Math
Unit 2
5th Grade
Lesson 9 of 20
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Multiply three- and four-digit numbers by three-digit numbers.
The core standards covered in this lesson
5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.
The foundational standards covered in this lesson
4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson includes a mix of three- and four-digit by three-digit computations. There are some differing opinions on the extent to which both cases should be explicitly taught. As Bill McCallum notes, “multi-digit for all these standards means ‘enough digits to reveal the algorithm in all its generality, but not so many as to constitute pointless torture of children.’ Exactly where that point is depends a lot on the classroom context, and is a matter of opinion anyway. I would guess that $$3\times3$$ and $$2\times4$$ are enough for 5.NBT.5" (Mathematical Musings, Division and Multiplication Algorithms in the Progressions). However, there are examples of the expectation going beyond these computational cases, such as the PARCC evidence statements including four-digit by three-digit multiplication. Thus, it is at the teacher’s discretion to modify this lesson based on whether to include or exclude four-digit by three-digit multiplication.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Find the products using the method you think is most efficient. Then assess the reasonableness of your answer.
a. $$714\times235$$
b. $$509\times360$$
c. $$809\times6,791$$
On Friday, April 13, 2018, there were 749 outbound flights each carrying approximately 101 passengers. If there are usually 58,112 daily outbound passengers from Logan, how many more passengers flew out of Logan that Friday than usual?
Problem Set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Solve.
652 × 409
Last year, the middle school ordered 118 laptops for students that each cost $854. If shipping and handling for the order cost an additional $295, how much money did the middle school spend on the whole laptop order?
An example response to the Target Task at the level of detail expected of the students.
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
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Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Lesson 8
Lesson 10
Topic A: Writing and Interpreting Numerical Expressions
Evaluate numerical expressions involving addition, subtraction, multiplication, division, and grouping symbols.
5.OA.A.1
Write expressions that record calculations with numbers, and interpret expressions without evaluating them.
5.OA.A.1 5.OA.A.2
Write expressions that represent real-world situations and evaluate them.
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Topic B: Multi-Digit Whole Number Multiplication
Multiply multiples of powers of ten. Estimate multi-digit products by rounding numbers to their largest place value.
5.NBT.B.5
Multiply two-digit, three-digit, and four-digit numbers by one-digit numbers.
Multiply two-digit numbers by two-digit numbers.
Multiply three-digit numbers by two-digit numbers.
Multiply four-digit numbers by two-digit numbers.
Multiply multi-digit numbers and assess the reasonableness of the product.
Topic C: Multi-Digit Whole Number Division
Divide multiples of powers of ten by multiples of ten without remainders. Estimate multi-digit quotients by rounding numbers to their largest place value.
5.NBT.B.6
Estimate multi-digit quotients using compatible numbers.
Divide two-digit, three-digit, and four-digit dividends by one-digit divisors.
Divide two- and three-digit dividends by multiples of 10 with one-digit quotients and remainders in the ones place.
Divide two-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.
Divide three-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.
Divide three-digit dividends by two-digit divisors with two-digit quotients, reasoning about the decomposition of a remainder in any place.
Divide four-digit dividends by two-digit divisors with two- and three-digit quotients, reasoning about the decomposition of a remainder in any place.
Divide multi-digit numbers by one- and two-digit divisors and assess the reasonableness of the quotient.
Solve word problems involving multi-digit multiplication and division.
5.NBT.B.5 5.NBT.B.6 5.OA.A.1 5.OA.A.2
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