Students deepen their understanding of multiplication by exploring factors and multiples, multiplicative comparison, as well as multidigit multiplication.
In Grade 4 Unit 2, students multiply up to fourdigit numbers by onedigit numbers, relying on their understanding of place value and properties of operations, as well as visual models like an area model, to solve.
As a foundation for their multiyear work with multiplication and division, students in Grade 2 learned to partition a rectangle into rows and columns and write a repeated addition sentence to determine the total. They also skipcounted by 5s, 10s, and 100s. Then, in Grade 3, students developed a conceptual understanding of multiplication and division in relation to equal groups, arrays, and area. They developed a variety of strategies to build toward fluency with multiplication and division within 100 and applied that knowledge to the context of one and twostep problems using the four operations.
To begin the unit, students extend their understanding of multiplication situations that they learned in Grade 3 to include multiplicative comparison using the words “times as many.” Next, to continue to refresh students’ work in Grades 2 and 3 on skipcounting and basic multiplication facts and extend it further to values they have not yet worked with, students investigate factors and multiples within 100, as well as prime and composite numbers (4.OA.4). Thus, this supporting cluster content serves as a foundation for the major work with multiplication and division with larger quantities. Tangentially, it will also support the major work in Unit 5 to recognize and generate equivalent fractions. Then, students move into twodigit by onedigit, threedigit by onedigit, fourdigit by onedigit, and twodigit by twodigit multiplication, using the area model, partial products, and finally the standard algorithm, making connections between all representations as they go. The use of the area model serves to help students conceptually understand multiplication and as a connection to their work with area and perimeter (4.MD.3), a supporting cluster standard. Finally, with a full understanding of all multiplication cases, they then apply their new multiplication skills to solve multistep word problems using multiplication, addition, and subtraction, including cases involving multiplicative comparison (4.NBT.5, 4.OA.3, 4.MD.3), allowing for many opportunities to connect content across multiple domains.
This unit affords lots of opportunities to deepen students’ mathematical practices. For example, “when students decompose numbers into sums of multiples of baseten units to multiply them, they are seeing and making use of structure (MP.7). Students “reason repeatedly (MP.8) about the connection between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities” (NBT Progression, p. 14). Lastly, as students solve multistep word problems involving addition, subtraction, and multiplication, they are modeling with mathematics (MP.4).
Students’ work in this unit will prepare them for fluency with the multiplication algorithm in Grade 5 (5.NBT.5). Students also learn about new applications of multiplication in future grades, including scaling quantities up and down in Grade 5 (5.NF.5), all the way up to rates and slopes in the middle grades (6.RP, 7.RP). Every subsequent grade level depends on the understanding of multiplication and its algorithm, making this unit an important one for students in Grade 4.
Pacing: 26 instructional days (23 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
Additional assessment tools to help you monitor student learning
and identify any skill or knowledge gaps.
Learn how to use these tools with our
Guide to Assessments
?
?
composite number  partial product 
factor pair  prime number 
multiple  square number 
?
?
Models for up to 4digit by 1digit Multiplication 
Written Numerical Work 
Base ten block array (remedial  can be concrete or pictorial) 
Horizontally written partial products 
Graph paper array (remedial) 
Vertically written partial products 
Area model 
Vertically written partial products 

Standard algorithm 
Models for up to 2digit by 2digit Multiplication 
Written Numerical Work 
Base ten block array (remedial  can be concrete or pictorial) 
Horizontally written partial products 
Graph paper array (remedial) 
Vertically written partial products 
Area model 
Vertically written partial products 

Standard algorithm 
4.OA.A.1
4.OA.A.2
Solve multiplicative comparison problems. Distinguish multiplicative comparison from additive comparison.
4.OA.A.1
4.OA.A.2
Solve multiplicative comparison problems with a smaller unknown, including cases that involve difficult language.
4.OA.A.1
4.OA.A.2
Solve multiplicative comparison problems with an unknown multiplier. Interpret a multiplication equation as a comparison.
4.OA.B.4
Identify multiples and determine if a whole number is a multiple of another number.
4.OA.A.3
4.OA.B.4
Explore patterns in multiples of various whole numbers.
4.OA.A.3
4.OA.B.4
Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.
4.OA.B.4
Determine whether a given number is prime or composite.
4.OA.B.4
Solve contextual problems that involve factors, multiples, prime, composite, and/or square numbers.
4.NBT.B.5
Multiply 10, 100, and 1,000 by one and twodigit numbers.
4.NBT.B.5
Multiply multiples of 10, 100, and 1,000 by onedigit numbers. Estimate multidigit products by rounding numbers to their largest place value.
4.NBT.B.5
Multiply two, three, and fourdigit numbers by onedigit numbers using a variety of simplifying strategies.
4.NBT.B.5
Multiply twodigit numbers by onedigit numbers.
4.NBT.B.5
Multiply threedigit numbers by onedigit numbers.
4.NBT.B.5
Multiply fourdigit numbers by onedigit numbers.
4.NBT.B.5
Multiply fourdigit, threedigit, and twodigit numbers by onedigit numbers and assess the reasonableness of the product.
4.NBT.B.5
Multiply twodigit multiples of 10 by twodigit multiples of 10. Estimate multidigit products by rounding numbers to their largest place value.
4.NBT.B.5
Multiply twodigit multiples of 10 by twodigit numbers.
4.NBT.B.5
Multiply twodigit numbers by twodigit numbers using a variety of simplifying strategies.
4.NBT.B.5
Multiply twodigit by twodigit numbers using four partial products.
4.NBT.B.5
Multiply twodigit by twodigit numbers using two partial products and assess the reasonableness of the product.
4.OA.A.3
4.MD.A.3
Abstract the formulas for the area and perimeter of a rectangle and apply those formulas in realworld and mathematical problems involving multiplication, addition, and subtraction.
4.OA.A.2
4.OA.A.3
Solve twostep word problems involving multiplication, addition, and subtraction and assess the reasonbleness of answers.
4.OA.A.3
Solve multistep word problems involving multiplication, addition, and subtraction and assess the reasonableness of answers.
Key: Major Cluster Supporting Cluster Additional Cluster
?
?
?