7.NS.2 - About the Math, Learning Targets, and Rigor

Grade 5 GT The Number System

7.NS.2

About the Math

Full Standard

7.NS.A.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.

2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1)=1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

2b. Understand 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, then $-\left(\frac{p}{q}\right)=\frac{\left(-p\right)}{q}=\frac{p}{\left(-q\right)}$ $-\left(\frac{p}{q}\right)=\frac{\left(-p\right)}{q}=\frac{p}{\left(-q\right)}$ . Interpret quotients of rational numbers by describing real-world contexts.

2c. Apply properties of operations as strategies to multiply and divide rational numbers.

2d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**5th Grade Students Learning 5 G/T Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of multiplication and division of different number types.	Report Card Measurement Topic: Demonstrates understanding of multiplication and division of different number types.

Learning Targets (I can)

Explain multiplication and division of integers and other rational numbers with representations.
Connect representations of multiplication and division of integers to equations.
Estimate the product or quotient of two integers or rational numbers.
Convert a rational number to a decimal.
Estimate the result of a converting a rational number to a decimal (e.g. 13/4 is a little more than 3 but less than 3.5).
Explain why a decimal terminates or repeats.
Solve real-world problems by multiplying and dividing integers and rational numbers.

About the Math

Students will add, subtract, multiply, and divide within the system of rational numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in Grade 5 GT depends on rational number arithmetic, fluency with rational number arithmetic should be the goal.

Progression of Standard within Grade 5 G/T

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Explain multiplication and division of integers and other rational numbers with representations. Connect representations of multiplication and division of integers to equations. Estimate the product or quotient of two integers or rational numbers. Convert a rational number to a decimal. Estimate the result of a converting a rational number to a decimal (e.g. 13/4 is a little more than 3 but less than 3.5). Explain why a decimal terminates or repeats. Solve real-world problems by multiplying and dividing integers and rational numbers	Explain multiplication and division of integers and other rational numbers with representations. Connect representations of multiplication and division of integers to equations. Estimate the product or quotient of two integers or rational numbers. Convert a rational number to a decimal. Estimate the result of a converting a rational number to a decimal (e.g. 13/4 is a little more than 3 but less than 3.5). Explain why a decimal terminates or repeats. Solve real-world problems by multiplying and dividing integers and rational numbers

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 6	Grade 8
Interpret and compute quotients of fractions and solve word problems (6.NS.1)	Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion (8.NS.1)

Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

One number is 4 times another. If the sum of their reciprocals is 5/12, ﬁnd the two numbers. (answer: 3, 12)
One number is 5 times another number. If the sum of their reciprocals is 6/35 , what are the two numbers? (answer: 7, 35)
If the reciprocal of 5 times a number is subtracted from the reciprocal of that number, the result is 4/25. What is the number? (answer: 5)

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 5 • Fractions and Decimals

Multiply and Divide Fractions and Decimals:

Module 8 • Four Operations Rational Numbers

Multiply and Divide Rational Numbers:

Additional Tasks

These links provide instructional ideas connected to this standard.

Repeating or Terminating Links to an external site.(Illustrative Math)
Decimal Expansion of Fractions Links to an external site.(Illustrative Math)
Repeating Decimal as Approximation Links to an external site. (Illustrative Math)
Equivalent Fractions Approach to Non-Repeating Decimals Links to an external site. (Illustrative Math)
Lesson 5.8 -Position, Speed, and Direction Links to an external site. (Open-Up Resources - Illustrative Math)
Lesson 5.9 - Multiplying Rational Numbers Links to an external site. (Open-Up Resources - Illustrative Math)
Lesson 5.10 - Multiply! Links to an external site. (Open-Up Resources - Illustrative Math )
Lesson 5.11 -Dividing Rational Numbers Links to an external site. (Open-Up Resources - Illustrative Math) Links to an external site.
Why is a Negative Times a Negative Always Positive Links to an external site.(Illustrative Math)
Distributive Property of Multiplication Links to an external site.(Illustrative Math)
Temperature Change Links to an external site.(Illustrative Math)
Cat Food Links to an external site. (Inside Mathematics)
Understanding Multiplication of Integers Links to an external site. (Engage NY)
Develop Rules for Multiplying Signed Numbers Links to an external site. (Engage NY)
Division of Integers Links to an external site. (Engage NY)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Hands on Standards Common Core Edition	7	p.42- 45 p.46- 49 p.50- 53 p.54- 57
Groundworks Reasoning with Numbers	7	p.24- 31
Teaching Common Core Math Standards with Hands on Activities	6-8	p.93- 95 p.96-97

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Assessment

Learning Targets

rubric

Explain multiplication and division of integers and other rational numbers with representations.
Connect representations of multiplication and division of integers to equations.
Estimate the product or quotient of two integers or rational numbers.
Convert a rational number to a decimal.
Estimate the result of a converting a rational number to a decimal (e.g. 13/4 is a little more than 3 but less than 3.5).
Explain why a decimal terminates or repeats.
Solve real-world problems by multiplying and dividing integers and rational numbers.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.