Standard 4 : Extend understanding of operations with integers.



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General Information

Number: MA.6.NSO.4
Title: Extend understanding of operations with integers.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 6
Strand: Number Sense and Operations

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.6.NSO.4.1: Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency.
Clarifications:
Clarification 1: Instruction begins with the use of manipulatives, models and number lines working towards becoming procedurally fluent by the end of grade 6.
Clarification 2: Instruction focuses on the inverse relationship between the operations of addition and subtraction. If p and q are integers, then p-q=p+(-q) and p+q=p-(-q).
MA.6.NSO.4.2: Apply and extend previous understandings of operations with whole numbers to multiply and divide integers with procedural fluency.
Clarifications:
Clarification 1: Instruction includes the use of models and number lines and the inverse relationship between multiplication and division, working towards becoming procedurally fluent by the end of grade 6.

Clarification 2: Instruction focuses on the understanding that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers where q≠0, then begin mathsize 12px style negative open parentheses p over q close parentheses equals fraction numerator negative p over denominator q end fraction end style , begin mathsize 12px style negative open parentheses p over q close parentheses equals fraction numerator p over denominator negative q end fraction end styleand begin mathsize 12px style p over q equals fraction numerator negative p over denominator negative q end fraction end style.



Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.6.NSO.4.AP.1: Use tools to add and subtract integers between 50 and −50.
MA.6.NSO.4.AP.2: Use tools to multiply and divide integers between 20 and −20.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorials

Name Description
Amazing Adventures:

Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial.

Why Does a Negative Times a Negative Equal a Positive?:

Use mathematical properties to explain why a negative factor times a negative factor equals a positive product instead of just quoting a rule with this interactive tutorial.

Educational Software / Tool

Name Description
Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Formative Assessments

Name Description
Adding Integers:

Students are asked to add integers using a number line.

Negative Times:

Students are shown a problem that illustrates why the product of two negatives is a positive and are asked to provide a rationale.

Integer Division:

Students are asked to describe a real-world context for a given expression involving the quotient of two rational integers.

Finding the Difference:

Students are asked to find the difference between two integers using a number line.

Rational Addition and Subtraction:

Students are asked to rewrite a subtraction problem as an equivalent addition problem and explain the equivalence using a number line.

Exploring Additive Inverse:

Students are asked to describe an example of additive inverse and demonstrate the concept on a number line.

Lesson Plans

Name Description
Party Planners:

The client is going to have a party and is in need of tables for a certain number of guests. The team needs to use a variety of tables that will fit the number of guests that are attending the party. The students will understand area and perimeter through this activity.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

When Pigs Fly:

In this lesson students will explore probability and likelihood that an event will occur. They will place both serious and silly events on a number line, once they have assigned a value to that event. They will work with a group and then justify their classifications to their peers.

Have You Met Your Match?-Understanding Equivalent Expressions :

In this lesson, students will use the properties of operations to generate and identify equivalent algebraic expressions. Students will apply their prior knowledge of the distributive property and combining like terms to create equivalent algebraic expressions. The hands-on memory "match" game will engage students and support student understanding of algebraic thinking.

Practically Probable:

In this lesson, students will differentiate between likely and unlikely event, as well as learn the difference between dependent and independent events. Finally, they learn how to compute theoretical probabilities in simple experiments.

Absolutely Integers:

Students will review how to graph positive numbers and then negative numbers on a number line. The students will review absolute value and apply this to different integers. They will then play a fun game to check their understanding.

Order Matters:

Students will analyze a Scratch program and compare its computerized algorithm to the mathematical order of operations, in this lesson plan.

Really! I'm Rational!:

In this lesson students will gain an understanding of how repeating decimals are converted into a ratio in the form of a over b by completing an exploration worksheet. They will conclude that any number which can be written in this form is called a rational number.

What are binary numbers?:

Students will decode equations to explain how base ten numbers are represented using binary numbers.

Perspectives Video: Experts

Name Description
Fluency vs. Automaticity:

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

What is Fluency?:

What is fluency? What are the ingredients required to become procedurally fluent in mathematics? Dr. Lawrence Gray explores what it means for students to be fluent in mathematics in this Expert Perspectives video.

Why Isn't Getting the "Right" Answer Good Enough?:

Why is it important to look beyond whether a student gets the right answer? Dr. Lawrence Gray explores the importance of understanding why we perform certain steps or what those steps mean, and the impact this understanding can have on our ability to solve more complex problems and address them in the context of real life in this Expert Perspectives video.

Perspectives Video: Teaching Ideas

Name Description
Adding Integers:

Unlock an effective teaching strategy for using patterns to help students make generalizations when adding integers in this Teacher Perspectives video for educators.

Zero Pairs and Integer Operations:

Unlock an effective teaching strategy for using manipulatives to help students understand zero pairs when adding integers in this Teacher Perspectives video for educators.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Title Description
Amazing Adventures:

Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial.

Why Does a Negative Times a Negative Equal a Positive?:

Use mathematical properties to explain why a negative factor times a negative factor equals a positive product instead of just quoting a rule with this interactive tutorial.

Educational Software / Tool

Title Description
Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.