This visual tool illustrates how to decompose numbers and find four different products. As students' skills improve, they will move from this pictorial model into a concrete method called partial products.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 4

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Unpacked Content

Evidence Of Student Attainment:

Students:

Use strategies based on place value, properties of operations, rectangular arrays, area models, and equations to illustrate and explain the product of two factors (up to four digits by a one-digit number and two two-digit numbers).

Note: Standard algorithm is not an expectation for grade 4.

Teacher Vocabulary:

Product

Factor

Compose

Decompose

Digit

Strategy

Place value

Properties of operations

Equation

Rectangular array

Area model

Partial product

Multiple of 10

Knowledge:

Students know:

How to compose and decompose numbers in a variety of ways using place value and the properties of operations.

How to represent the product of two factors using an area model.

Use strategies based on place value (partial products), the properties of operations, arrays and area models to represent a two digit factor times a two digit factor.

Skills:

Students are able to:

Use strategies based on place value and the properties of operations to find products.

Illustrate the product of two factors using rectangular arrays and area models.

Explain the product of two factors using equations.

Make connections between models and equations.

Understanding:

Students understand that:

arrays, area models, place value strategies, and the properties of operations can be used to find products of a single digit factor by a multi-digit factor and products of two two-digit factors.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.11.1: Divide within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
M.4.11.2: Divide within 100, using strategies such as properties of operations.
M.4.11.3: Multiply within 100, using strategies such as properties of operations.
M.4.11.4: Multiply within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
M.4.11.5: Recall products of two one-digit numbers.
M.4.11.6: Name the first 10 multiples of each one-digit natural number. Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
M.4.11.7: Recall basic addition, subtraction, and multiplication facts.

Prior Knowledge Skills:

Apply divisibility rules for 2, 5, and 10.
Example: Recognizing that 32 is divisible by 2 because the digit in the ones place is even.

Apply basic multiplication facts.

Understand subtraction as an unknown

addend problem.

Recognize division as repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.

Name the first 10 multiples of each one-digit natural number.
Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

Recognize multiplication as repeated addition, and division as repeated subtraction.

Apply properties of operations as strategies to add and subtract.

Recall basic addition and subtraction facts.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number.
Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.11 Add and subtract one and two-digit numbers up to 49 with regrouping using concrete manipulatives and visual models.

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations. a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Note: Standard algorithm is not an expectation for grade 4.