Illustrative Math Alignment: Grade 6 Unit 1

Topic

Multiplication and Division

Description

The Zero Property of Multiplication states that the product of zero and any number is zero. Examples include 1 * 0 = 0, 2 * 0 = 0, and 3 * 0 = 0. This is a fundamental property of multiplication. This property builds foundational knowledge of multiplication rules, which are critical for more advanced mathematical reasoning.

Topic

Multiplication and Division

Description

The Identity Property of Multiplication states that the product of 1 and any number is the number itself. For example, 1 x 1 = 1, 2 x 1 = 2, and 3 x 1 = 3. This property simplifies multiplication with 1. This term highlights a basic rule of multiplication, building foundational understanding.

Topic

Multiplication and Division

Description

The Identity Property of Division states that any number divided by 1 is the number itself. For example, 15 ÷ 1 = 15 and 25 ÷ 1 = 25. This property is fundamental in understanding division operations. This term reinforces the foundational properties of arithmetic operations.

Topic

Multiplication and Division

Topic

Multiplication and Division

Description

A False Equation is an equation that shows an inaccurate product or quotient. For example, 6 x 2 = 10 or 12 ÷ 3 = 5. This concept highlights the importance of verifying calculations for correctness. This term teaches students to identify and avoid common errors in mathematical equations.

Topic

Multiplication and Division

Description

A Factor is a number that divides another number without leaving a remainder. Examples include factors of 6 (1, 2, 3, 6) and factors of 8 (1, 2, 4, 8). Understanding factors supports number decomposition and multiplication. This term relates to division and multiplication, laying a foundation for understanding divisibility and multiples.

Topic

Multiplication and Division

Description

A Fact Family consists of four related multiplication and division equations using the same three numbers. For example, 5 x 3 = 15, 3 x 5 = 15, 15 ÷ 3 = 5, and 15 ÷ 5 = 3. This demonstrates the relationship between multiplication and division. This term illustrates the inverse relationship between multiplication and division, deepening understanding of fact relationships.

Topic

Multiplication and Division

Description

An Even Number is a number that has no remainder when divided by 2. Examples include 20, 32, and 44, as shown by 32 ÷ 2 = 16, demonstrating that 32 is even. Understanding even numbers supports number classification and arithmetic operations. This term introduces number properties, linking to divisibility and multiplication concepts.

Topic

Multiplication and Division

Description

Equal Groups involve creating groupings of objects with the same number of items in each group. For example, 12 ÷ 4 = 3 is shown as dividing 12 items into 4 equal groups of 3. This concept applies to both multiplication and division. This term connects multiplication and division by emphasizing equal distribution.

Topic

Multiplication and Division

Description

The Divisor is the number by which another number is divided. For example, in 12 ÷ 3 = 4, 3 is the divisor. Identifying the divisor is key to understanding division problems. This term clarifies the role of the divisor, which is essential for setting up and solving division problems.

Topic

Multiplication and Division

Description

A Division Strategy involves deciding how to divide two numbers, often using visual aids. For example, 18 ÷ 3 = 6 is illustrated using arrays or equal groups to find the quotient. Strategies help break down division problems into steps. This term focuses on methods to solve division, aiding problem-solving and conceptual understanding.

Topic

Multiplication and Division

Description

A Division Sentence is a complete equation that includes the dividend, divisor, and quotient. For example, 36 ÷ 9 = 4 is described as 'Thirty-six divided by nine equals four.' This representation integrates both numerical and verbal descriptions of division. This term strengthens understanding by combining numerical and language-based representations of division.

Topic

Multiplication and Division

Description

A Division Expression includes numbers involved in division but does not include an equality. For example, 12 ÷ 3 or (36 ÷ 3) ÷ 4. This prepares students to transition from basic division to equations. This term connects to equations, bridging basic division operations with algebraic thinking.

Topic

Multiplication and Division

Description

A Division Array visually represents division using an arrangement of items in rows and columns. For example, 20 ÷ 5 = 4 is shown as an array with 5 rows and 4 columns. This representation connects division to repeated subtraction and helps visualize equal grouping. This term provides a spatial understanding of division, linking it to array models used in multiplication.

Topic

Multiplication and Division

Description

Division is the process of separating a group of items into an equal number of smaller groups. For example, 6 ÷ 3 = 2 is shown as dividing 6 items into 3 equal groups of 2. This concept is fundamental for understanding how to distribute or share quantities equally. This term introduces the core idea of division, which is crucial for progressing to more complex operations.

Topic

Multiplication and Division

Description

Divisibility tests whether a number can be evenly divided by another without a remainder. Examples include numbers divisible by 3 (9, 27, 48) and by 4 (8, 24, 36). These tests simplify identifying factors and multiples. This term supports multiplication and division by introducing rules that streamline calculations involving factors.

Topic

Multiplication and Division

Description

Dividing is the process of determining how many times one number is contained within another. For example, 8 / 4 = 2 is shown using visual aids like objects grouped into equal parts. This process relates to sharing and grouping. This term provides a foundational understanding of division, connecting it to real-life scenarios like sharing equally.

Topic

Multiplication and Division

Description

The Dividend is the number being divided in a division expression. For example, in 12 / 3 = 4, 12 is the dividend. This term identifies the starting point for division calculations. This term clarifies the roles of numbers in division, aiding in understanding the structure of division problems.

Topic

Multiplication and Division

Description

The Distributive Property allows breaking a multiplication expression into smaller parts. For example, 2(3 + 5) = 2 x 3 + 2 x 5 = 6 + 10 = 16. This property is useful for simplifying expressions and solving equations. This term bridges multiplication and addition, helping students solve complex problems by breaking them into simpler steps.

Topic

Multiplication and Division

Description

A Composite Number is a whole number with factors other than 1 and itself. Examples include 4 (factors: 1, 2, 4) and 15 (factors: 1, 3, 5, 15). These are contrasted with prime numbers, which have only two factors, 1 and the number itself. This term supports the topic by introducing factorization, a key concept for understanding multiplication and division relationships.

Topic

Multiplication and Division

Description

The Commutative Property of Multiplication states that the order of numbers in multiplication does not affect the product. For example, 2 x 3 = 6 and 3 x 2 = 6. This property ensures flexibility in solving multiplication problems. This term reinforces the consistency of multiplication outcomes, fostering confidence in solving problems in varied formats.

Topic

Multiplication and Division

Description

Column Multiplication is a technique for multiplying large numbers by breaking them into smaller components. For example, 48 x 25 is solved step-by-step: 240, 96, then added to get 1200. This method organizes calculations systematically. This term is essential for understanding long multiplication, bridging basic skills to more advanced arithmetic operations.

Topic

Multiplication and Division

Topic

Multiplication and Division

Description

An Array arranges objects in rows and columns to model multiplication. For example, 6 x 2 = 12 is depicted as an array with 6 rows and 2 columns. Arrays illustrate multiplication as repeated addition, making it easier to visualize groupings of numbers. This term supports the topic by showing how multiplication can be understood as a spatial arrangement, aiding early math skills development.

Topic

Multiplication and Division

Topic

Multiplication and Division

Description

Inverse Operations are operations that undo each other. For example, multiplication and division are inverses: 5 x 5 = 25 and 25 ÷ 5 = 5. This concept is crucial for solving equations and understanding relationships between operations. This term bridges multiplication and division, promoting algebraic thinking.

Topic

Multiplication and Division

Description

The Least Common Multiple (LCM) of two integers is the smallest positive integer that is a multiple of both numbers. For example, the LCM of 2 and 5 is 10. This concept is used in adding fractions and solving problems involving multiples. This term builds on understanding multiples, aiding in fraction operations and problem-solving.

Topic

Multiplication and Division

Description

A Multiple is a product of a number and any whole number. For example, multiples of 2 are 2, 4, 6, 8, and multiples of 3 are 3, 6, 9, 12. Multiples are essential for understanding patterns in arithmetic. This term connects to multiplication concepts, forming a basis for advanced topics like LCM and divisibility.

Topic

Multiplication and Division

Description

Long Division is a technique for dividing large numbers into smaller parts systematically. For example, 98 ÷ 7 is solved step-by-step using division, multiplication, and subtraction. This method simplifies complex division problems. This term teaches systematic approaches to dividing large numbers, improving arithmetic skills.

Topic

Multiplication and Division

Description

Multiplication is the process of adding equal groups of items to find a total. For example, 2 x 3 = 6 is shown as 2 groups of 3 items. This operation is fundamental in arithmetic and algebra. This term introduces the basic operation of multiplication, foundational to all arithmetic.

Topic

Multiplication and Division

Description

A multiplication array is a rectangular arrangement of rows and columns used to model multiplication. For example, 5 • 7 = 35 using a grid. The array model provides a visual way to understand and compute multiplication.

Topic

Multiplication and Division

Description

A multiplication expression consists of a set of numbers that are multiplied, forming part of a multiplication equation. For example, 3 • 7 = 21. This builds understanding of multiplication as part of algebraic thinking and numerical concepts.

Topic

Multiplication and Division

Description

A multiplication sentence is a multiplication equation including a multiplicand, multiplier, and product. Example: "24 times 3 equals 72." This contextualizes multiplication in spoken and written formats, aiding comprehension.

Topic

Multiplication and Division

Description

A multiplication strategy involves deciding how to multiply two numbers. For example, 4 • 5 = 20 can use an array for support. This connects multiplication reasoning with tools like arrays and mental strategies.

Topic

Multiplication and Division

Description

A multiplication table is a series of multiplication statements for a particular multiplicand. Example: 2 • 1 = 2, 2 • 2 = 4, etc. This reinforces repetitive practice and memorization for multiplication fluency.

Topic

Multiplication and Division

Description

The multiplier is the number by which another number (multiplicand) is multiplied. Examples: 13 • 3 = 39, 18 • 5 = 90. Highlights the role of the multiplier in the context of multiplication problems.

Topic

Multiplication and Division

Description

Multiplying refers to the process of multiplication. Example: 3 • 2 = 6. Emphasizes the active process of combining equal groups in multiplication.

Topic

Multiplication and Division

Description

A numerical expression consists of numbers, operations, and grouping symbols. Examples include 2 • 4 + 9 ÷ 3. Lays the foundation for solving complex problems and understanding order of operations.

Topic

Multiplication and Division

Description

An odd number has a remainder of 1 when divided by 2. Example: 33 ÷ 2 = 16 R 1; 33 is an odd number. Identifies key properties of numbers in arithmetic and division patterns.

Topic

Multiplication and Division

Description

The order of operations specifies the sequence for simplifying numerical expressions: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Example: (2 + 3)^2 • 3 + 4 - 2 = 77. Organizes complex computations by establishing a consistent problem-solving framework.

Topic

Multiplication and Division

Topic

Multiplication and Division

Topic

Multiplication and Division

Description

The Multiplicand is the number being multiplied by another number (the multiplier). For example, in 12 x 3 = 36, 12 is the multiplicand. Identifying the multiplicand helps understand multiplication equations. This term reinforces the structure of multiplication problems, aiding comprehension.

Topic

Multiplication and Division

Description

A True Equation is an equation that shows an accurate product or quotient. Examples include 5 * 2 = 10 and 8 / 2 = 4. It validates the correctness of mathematical operations. This concept reinforces understanding and application of multiplication and division, focusing on the accuracy of operations.

Topic

Multiplication and Division

Topic

Multiplication and Division

Description

Skip Counting involves counting by values greater than 1, such as by 2s, 5s, or 10s. For example, counting by 2s from 0 to 10 results in 0, 2, 4, 6, 8, 10. This skill is foundational for understanding multiplication as repeated addition. This emphasizes patterns in numbers and prepares students for multiplication by establishing connections between counting and grouping.

Topic

Multiplication and Division

Description

Repeated Addition is a way to multiply by adding a number to itself multiple times. For example, 15 * 5 is expressed as 15 + 15 + 15 + 15 + 15 = 75. This demonstrates multiplication as a form of addition. This introduces multiplication conceptually, showing how it builds on addition and prepares for understanding scaling.

Topic

Multiplication and Division

Description

Quotient is the result of dividing one number by another. For example, 12 / 3 = 4, 15 / 5 = 3, and 20 / 10 = 2. The quotient represents how many times a divisor fits into a dividend. This connects to division, showing the outcome of dividing numbers and tying back to multiplication as the inverse operation.

Topic

Multiplication and Division

Topic

Multiplication and Division