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 −(pq)=(−p)q=p(−q). 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
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.
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 Thumbnail
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
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.