Quarter 2
Accentuate the Negative
7.NS.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.
NS.1a Describe situations in which opposite quantities combine to make 0.
NS.1b 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).
NS.1c 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.
NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
NS.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.
NS.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 –(p/q) = (-p)/q = p/)-q).
NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
NS.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.
7.NS.3 Solve real-world and mathematical problems involving four operations with rational numbers.
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.
7.EE.4b Solve word problems leading to inequalities of the form px+ q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
NS.1a Describe situations in which opposite quantities combine to make 0.
NS.1b 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).
NS.1c 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.
NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
NS.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.
NS.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 –(p/q) = (-p)/q = p/)-q).
NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
NS.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.
7.NS.3 Solve real-world and mathematical problems involving four operations with rational numbers.
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.
7.EE.4b Solve word problems leading to inequalities of the form px+ q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
7.RP.2 Recognize and represent proportional relationships between quantities.
RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.
7.EE.4 Use variables to represent quantities in a real world or mathematical problem, andconstruct simple equations and inequalities to solve problems by reasoning about thequantities.
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometricshapes with given conditions. Focus on constructing triangles from three measuresof angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals,polygons, cubes, and right prisms.
RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.
7.EE.4 Use variables to represent quantities in a real world or mathematical problem, andconstruct simple equations and inequalities to solve problems by reasoning about thequantities.
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometricshapes with given conditions. Focus on constructing triangles from three measuresof angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals,polygons, cubes, and right prisms.
7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or unlike units.
7.RP.2 Recognize and represent proportional relationships between quantities.
RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
RP.2c Represent proportional relationships by equations.
7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.
7.EE.4 Use variables to represent quantities in a real world or mathematical problem, andconstruct simple equations and inequalities to solve problems by reasoning about thequantities.
7.RP.2 Recognize and represent proportional relationships between quantities.
RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
RP.2c Represent proportional relationships by equations.
7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.
7.EE.4 Use variables to represent quantities in a real world or mathematical problem, andconstruct simple equations and inequalities to solve problems by reasoning about thequantities.