Students deepen their understanding of multiplication by exploring factors and multiples, multiplicative comparison, as well as multi-digit multiplication.
In Grade 4 Unit 2, students multiply up to four-digit numbers by one-digit 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 multi-year 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 skip-counted 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 two-step 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 skip-counting 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 two-digit by one-digit, three-digit by one-digit, four-digit by one-digit, and two-digit by two-digit 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 multi-step 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 base-ten 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 multi-step 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)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 4th Grade Scope and Sequence Recommended Adjustments.
This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
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Models for up to 4-digit by 1-digit 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 |
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Standard algorithm |
Models for up to 2-digit by 2-digit 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 |
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Standard algorithm |
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prime number
composite number
partial product
square number
multiple
factor pair
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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.
View Preview4.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 two-digit numbers.
4.NBT.B.5
Multiply multiples of 10, 100, and 1,000 by one-digit numbers. Estimate multi-digit products by rounding numbers to their largest place value.
4.NBT.B.5
Multiply two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.
4.NBT.B.5
Multiply two-digit numbers by one-digit numbers.
4.NBT.B.5
Multiply three-digit numbers by one-digit numbers.
4.NBT.B.5
Multiply four-digit numbers by one-digit numbers.
4.NBT.B.5
Multiply four-digit, three-digit, and two-digit numbers by one-digit numbers and assess the reasonableness of the product.
4.NBT.B.5
Multiply two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.
4.NBT.B.5
Multiply two-digit multiples of 10 by two-digit numbers.
4.NBT.B.5
Multiply two-digit numbers by two-digit numbers using a variety of mental strategies.
4.NBT.B.5
Multiply two-digit by two-digit numbers using four partial products.
4.NBT.B.5
Multiply two-digit by two-digit 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 real-world and mathematical problems involving multiplication, addition, and subtraction.
4.OA.A.2
4.OA.A.3
Solve two-step word problems involving multiplication, addition, and subtraction and assess the reasonableness of answers.
4.OA.A.3
Solve multi-step word problems involving multiplication, addition, and subtraction and assess the reasonableness of answers.
Key: Major Cluster Supporting Cluster Additional Cluster
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