Targets & Standards
In 7th grade, students learn to construct, solve and interpret proportions and two step equations using rational numbers in order to apply and represent these skills in real world situations including statistics, percent, geometry and probability.
Essential Standards
7.NS.A Target B - Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (DOK 1, 2)
7.EE.B Target D - Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (DOK Levels 1, 2)
7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. 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.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with a non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. 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.
Embed 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
This standard should be emedded as application of 7.NS1 & 7.NS.2.
7.EE.3 Solve multi-step, real-life, and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
There are no substandards for this standard. This standard should be emedded as application of 7.NS1 & 7.NS.2.
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Supporting Standards
7.NS.A Target B - Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (DOK 1, 2)
7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
This standard should be emedded as application of 7.NS1 & 7.NS.2.