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Mathematics /
5th Grade /
Unit 2: Multiplication and Division of Whole Numbers
Multiplication and Division of Whole Numbers
Students continue their work with multi-digit multiplication and division and the base-ten system in order to finalize fluency with multi-digit multiplication and extend division to two-digit divisors.
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Unit Prep
Unit Practice
Lesson Map
In Unit 2, students will build on their work on multi-digit multiplication and division from Grade 4 as well as their understanding of the structure of the base-ten system in Unit 1 to finalize fluency with multi-digit multiplication and extend multi-digit division to include two-digit divisors.
In Grade 4, students attained fluency with multi-digit addition and subtraction (4.NBT.4), a necessary skill for computing sums and differences in the standard algorithm for multiplication and division, respectively. Students also multiplied a whole number of up to four digits by a one-digit whole number, as well as two two-digit numbers (4.NBT.5). By the end of Grade 4, students can compute those products using the standard algorithm, but "reason repeatedly about the connection between math drawings and written numerical work, help[ing] them come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities" (Progressions for the CCSSM, "Number and Operation in Base Ten, K-5", p. 14). Students also find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors (4.NBT.6). Similar to multiplication, by the end of Grade 4, students can compute these quotients using the standard algorithm alongside other strategies and representations so that the algorithms are meaningful rather than rote.
Unit 2 of Grade 5 begins with writing, evaluating, and interpreting simple numerical expressions (5.OA.1, 5.OA.2). This serves both to review basic multiplication and division facts, which supports major content later on in the unit, and as a way to record calculations that will grow increasingly complex as the unit progresses. Then, students solidify the standard algorithm for multiplication with the computational cases from Grade 4 before extending its use to larger and larger factors (5.NBT.5). Next, students follow a similar progression with division, first computing quotients involving cases from Grade 4 using a variety of strategies and then extending those methods to computations involving two-digit divisors. Note, however, that unlike multiplication, fluency with the standard division algorithm is not expected until Grade 6 (6.NS.2). Throughout the unit, students "learn to use [the] structure [of base-ten numbers] and the properties of operations to reduce computing a multi-digit…product or quotient to a collection of single-digit computations in different base-ten units" (MP.7) (Progressions for the CCSSM, "Number and Operation in Base Ten, K-5", p. 4). Further, "repeated reasoning (MP.8) that draws on the uniformity of the base-ten system is a part of this process" (Progressions for the CCSSM, "Number and Operation in Base Ten, K-5", p. 4).
Later this year, students will rely on their knowledge of whole-number computations to perform them with decimals (5.NBT.7). They will also write, evaluate, and interpret expressions with fractions and decimals in Units 5 and 6 (5.OA.1, 5.OA.2). This work "in Grade 5 prefigure[s] their later work with variable expressions" (6—8.EE) (OA Progression, p. 32). Further, students solidify fluency with the division algorithm and extend fluency with all four operations to decimals (6.EE.2—3). They also extend these computations to yet unknown parts of our number system, such as negative numbers (7.NS). Thus, by the end of this unit, students will be just shy of fluency with all four operations with whole numbers and ready to tackle them with other types of numbers while simultaneously starting to think beyond calculation of numerical expressions to the understanding and interpretation of them, hinting at a new world of mathematics—algebra.
Pacing: 23 instructional days (20 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 5th Grade Scope and Sequence Recommended Adjustments.
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This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
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Intellectual Prep
Intellectual Prep for All Units
Read and annotate "Unit Summary" and "Essential Understandings" portion of the unit plan.
Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind.
Take the unit assessment.
Unit-Specific Intellectual Prep
Read the article "Modeling with Mathematics", and watch the second video about Three-Act Tasks.
Read the following table that includes models used throughout the unit.
Area model
Example: Solve $$21 \times 11$$ using an area model.
Partial products algorithm
Standard algorithm for multiplication
Partial quotients algorithm
Standard algorithm for division
Essential Understandings
When multiplying, it is more efficient to decompose the value with fewer non-zero digits. In the standard algorithm, this means writing the number with fewer non-zero digits on the bottom.
When estimating with division, it is more effective to use numbers that are easy to compute mentally rather than rounded numbers (e.g., $${413 \div 64 \rightarrow 420 \div 60}$$).
Some computational estimates can be better than others, depending on what numbers are chosen to use in place of the actual values. Computational estimates can be too high or too low, depending on how the numbers were originally estimated, the computation being performed, and where in the number sentence it's located.
General base-ten methods for multiplication and division (including the standard algorithm) are dependent on (1) an understanding how to compute products and quotients of multiples of 10, 100, 1,000, etc., and one-digit numbers, and (2) the distributive property.
grouping symbols (parenthesis, brackets, braces)
Related Teacher Tools:
5th Grade Vocabulary Glossary
Unit Materials, Representations and Tools
area models
standard algorithm for division/long division
Additional Unit Practice
With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.
Topic A: Writing and Interpreting Numerical Expressions
5.OA.A.1
Evaluate numerical expressions involving addition, subtraction, multiplication, division, and grouping symbols.
Write expressions that record calculations with numbers, and interpret expressions without evaluating them.
Write expressions that represent real-world situations and evaluate them.
Topic B: Multi-Digit Whole Number Multiplication
5.NBT.B.5
Multiply multiples of powers of ten. Estimate multi-digit products by rounding numbers to their largest place value.
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 three- and four-digit numbers by three-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.
Estimate multi-digit quotients by rounding numbers to 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.
Key: Major Cluster Supporting Cluster Additional Cluster
5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.OA.A.1 — Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
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.
4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. 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.
3.OA.D.8
3.OA.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Future Standards
Expressions and Equations
6.EE.A.2
6.EE.A.2 — Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
The Number System
6.NS.B.2
6.NS.B.2 — Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.3 — Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.B.4 — Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Place Value with Decimals
Shapes and Volume
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