Topic A begins by revisiting the commutative property. Students study familiar facts from Module 1 to identify known facts using units of 6, 7, 8, and 9. They realize that they already know more than half of their facts by recognizing, for example, that if they know 2 × 8, they also know 8 × 2 through commutativity. This begins a study of arithmetic patterns that becomes an increasingly prominent theme in the module. The subsequent lesson carries this study a step further; students apply the commutative property to relate 5 × 8 and 8 × 5, and then add one more group of 8 to solve 6 × 8 and, by extension, 8 × 6. The final lesson in this topic builds fluency with familiar multiplication and division facts, preparing students for the work ahead by introducing the use of a letter to represent the unknown in various positions

Content Standard(s):

Mathematics MA2019 (2019) Grade: 3

5. Develop and apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for the properties)

Unpacked Content

Evidence Of Student Attainment:

Students:

Use their understanding of multiplication and division to develop and apply a variety of properties to various situations.

Examples: given 4 x 9 = 36 is known, then 9 x 4 = 36 is also known. (commutative property).
If 3 x 5 x 2 can be found by 3 x 5 =15, then 15 x 2 = 30 or 5 x 2 = 10, then 3 x 10 = 30. (associative property). If 8 x 5 = 40 and 8 x 2 = 16 are known, then 8 x 7 can be found by 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (distributive property.)

Identify an equivalent expression where the properties of operations has been applied.

Describe the properties of multiplication related to visual models.

Write multiplication equations to represent visual models.

Apply properties of operations as strategies to multiply and divide.

Note: Students need not use formal terms for the properties of operations.

Teacher Vocabulary:

Product

Sum

Property of operations

Multiplication expression

Decompose

Array

Area model

Knowledge:

Students know:

When any factor, x, is multiplied by a factor of 1, the product is the value of x.

If one factor is zero, then there are zero groups or zero items in a group and the product is zero.

The commutative property of multiplication shows a x b = c and b x a = c.

The associative property of multiplication shows that when multiplying three or more numbers, the product is always the same regardless of the grouping.

The distributive property will help in finding products of more difficult multiplication facts.

Skills:

Students are able to:

Develop properties as strategies for multiplication and division.

Apply properties of operations as strategies to multiply and divide.

Understanding:

Students understand that:

applying properties of operations can help develop strategies to find solutions to multiplication and division problems.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.3.5.1: Define properties of operations.
M.3.5.2: Apply basic multiplication facts.
M.3.5.3: Apply properties of operations as strategies to add and subtract.
M.3.5.4: Count to answer "how many?" questions about as many as 30 things arranged in a rectangular array.

Prior Knowledge Skills:

Match the numeral in the ones and tens position to a pictorial representation or manipulative of the value.

Count forward in multiples from a given number.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Represent numbers with objects or drawings.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.

Mathematics MA2019 (2019) Grade: 3

6. Use the relationship between multiplication and division to represent division as an equation with an unknown factor.

Unpacked Content

Evidence Of Student Attainment:

Students: When given a division problem with an unknown quotient,

Use a variety of strategies to solve the division problem and justify the solution.

Use the relationship between multiplication and division to write an equation with an unknown factor to represent a division problem.

Use symbols to represent the unknown quantities in equations.

Use the inverse relationship between multiplication and division to find quotients.

Teacher Vocabulary:

Product

Quotient

Equation

Unknown factor

Dividend

Divisor

Knowledge:

Students know:

Multiplication and division are related operations.

Using known multiplication facts and the relationship between multiplication and division, will help build fluency with division facts.

Skills:

Students are able to:

Use the relationship between multiplication and division to find quotients.

Write a multiplication equation with a missing factor to represent a division situation.

Use symbols to represent an unknown quantity in equations.

Understanding:

Students understand that:

Multiplication and division are related operations.

The dividend in a division equation is the same as the product in a related multiplication equation.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.3.6.1: Apply divisibility rules for 2, 5, and 10.
M.3.6.2: Apply basic multiplication facts.
M.3.6.3: Understand subtraction as an unknown-addend problem.
M.3.6.4: Recognize division as repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.

Prior Knowledge Skills:

Add and subtract within 5.

Match the numeral in the ones and tens position to a pictorial representation or manipulative of the value.

Count forward in multiples from a given number.

Skip count by 2s.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.