Standards in Unit:
NC.6.NS.1- Use visual models and common denominators to:
o Interpret and compute quotients of fractions.
o Solve real-world and mathematical problems involving division of fractions.
NC.6.NS.9- Apply and extend previous understandings of addition and subtraction.
o Describe situations in which opposite quantities combine to make 0. o Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair.
o Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference.
o Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences
NC.7.NS.1- Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.
NC.7.NS.2- Apply and extend previous understandings of multiplication and division.
NC.7.NS.3- Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.
Summary of Unpacking for Each Standard:
NC.6.NS.1: PREREQUISITE: Students will understand division of fractions using models and common denominators to understand the concept of breaking a fraction into equal fractional parts. The equal units are the key to ensuring this conceptual understanding, rather than jumping straight to the common algorithm. Students will need to interpret and solve problems involving division of fractions in a mathematical and real-world context.
NC.6.NS.9: PREREQUISITE: This new standard for 2018-19 introduces students to adding and subtracting positive and negative integers from -20 to 20 using models. They will explore opposite quantities, zero pairs, and subtraction as adding the opposite as an introduction to the actual operations of addition and subtraction of negatives, and number lines, algebra tiles, and other representations are appropriate for learning the concept. This will build into discovering algorithms for operations with negatives in the 7th grade standards.
NC.7.NS.1: Students will build on their understanding of operations with fractions and decimals to add and subtract all rational numbers, including positive and negative fractions and decimals. They will understand that the commutative, associative, distributive, and other properties of operations apply the same to all rational numbers as positive numbers, and they will discover algorithms and processes to help in their calculations. Calculations will be performed in real-world and mathematical contexts, and multi-step problems can be expected.
NC.7.NS.2: Students will continue to build on their understanding of negative numbers to discover and understand rules for multiplying and dividing all rational numbers, including positive and negative fractions and decimals. They will extend their understanding of dividing fractions to conceptually build the algorithm of multiplying times the reciprocal, and they will use long division to show convert rational numbers to decimals that ultimately terminate or repeat. Calculations will be performed in real-world and mathematical contexts, and multi-step problems can be expected.
NC.7.NS.3: Students will solve problems, in real-world and mathematical contexts, using all four operations on all rational numbers, multiple steps, and interpretation of word problems. These problems can include complex fractions and problems that involve more than one representation of rational numbers (computing with fractions and decimals in the same problem).
Prerequisite Skills:
Future Skills
• Understand that every number has a decimal expansion, and irrational numbers have non-repeating, non-terminating decimal expansions.
• Estimating non-perfect square and non-perfect cube roots
• Exponent Rules
• Solving equations using roots
• Solving equations with rational coefficients
Key Vocabulary:
Rational Numbers Integers Additive Inverse
Opposite Quantities Equivalent
Absolute Value Divisor Terminating/Repeating
Unit Test/Cornerstone Tasks
Unit Test: Schoolnet #2502838
Open-Ended Questions for Test: Unit 1 Open-Ended Test (Links to an external site.)Links to an external site.
Tasks: Patterns of Fractions and Decimals (Links to an external site.)Links to an external site.
Cat Food Task (Links to an external site.)Links to an external site.
MTSS/Remediation Resources
Math Topic/DPI Bucket: Adding, Subtracting, Multiplying, and Dividing Rationals/Rational Numbers
Engage NY F2F Intervention: Grade 7, Module 2 (Links to an external site.)Links to an external site., Topics A and B
Edgenuity Online Intervention: Grade 7, Operations with Integers and Operations with Rational Numbers Units