ELTs BY UNIT
Unit 1: Scale Drawings and Proportional Relationships
Geometry / Ratios & Proportional Relationships
 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.A.1)
 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (7.RP.A.1)
 Recognize and represent proportional relationships between quantities using tables, graphs, and equations. (7.RP.A.2).
Unit 2: Measuring Circles
Geometry
 Know the formulas for the area and circumference of a circle and use them to solve problems. (7.G.B.4)
.
Unit 3: Proportional Relationships and Percentages
Ratios & Proportional Relationships
 Use proportional relationships to solve multistep ratio and percent problems, such as simple interest, tax, markups and markdowns, gratuities and commissions, fees, and percent increase and decrease. (7.RP.A.3)
. Unit 4: Rational Number Arithmetic
The Number System
 Apply properties of operations as strategies to add and subtract rational numbers to solve realworld and mathematical problems. (7.NS.A.1)
 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers to solve realworld and mathematical problems. (7.NS.A.2)
Unit 5: Expressions, Equations and Inequalities
Expressions & Equations
 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (7.EE.A.1)
 Use tools strategically to solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form. (7.EE.B.3)
.Unit 6: Angles, Triangles and Prisms
Geometry
 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. (7.G.B.5)
 Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (7.G.B.6).
Unit 7: Rigid Transformations and Congruence
Geometry
 Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (8.G.A.2)
 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. (8.G.A.5).
Unit 8: Dilations, Similarity and Introducing Slope
Geometry
 Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. (8.G.A.4).
Unit 9: Linear Relationships
Expressions & Equations
 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented by a graph and an equation. (8.EE.B.5)
 Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (8.EE.B.6).
Unit 10: Exponents and Scientific Notation
Expressions & Equations
 Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.A.1).
Unit 11: Probability and Sampling
Statistics & Probability
 Approximate the experimental probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. (7.SP.C.6)
 Develop a probability model and use it to find theoretical probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (7.SP.C.7)
 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (7.SP.C.8)
Unit 12: Pythagorean Theorem and Irrational Numbers
Geometry
 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. (8.G.B.7)
 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.B.8).
Unit 13: Linear Equations and Linear Systems
Expressions & Equations
 Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (B.EE.C.7.b)
 Analyze and solve pairs of simultaneous linear equations using points of intersection on their graphs and algebraically. (8.EE.C.8).
Unit 15: Functions and Volume
Functions / Geometry
 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values (8.F.B.4)
 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. (8.G.C.9)
ELTs BY STANDARD
Expressions & Equations:
 Apply
properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients. (7.EE.A.1)
 Use
tools strategically to solve multistep reallife and mathematical
problems posed with positive and negative rational numbers in any form.
(7.EE.B.3)
 Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.A.1).
 Graph
proportional relationships, interpreting the unit rate as the slope of
the graph. Compare two different proportional relationships represented
by a graph and an equation. (8.EE.B.5)
 Use
similar triangles to explain why the slope m is the same between any
two distinct points on a nonvertical line in the coordinate plane;
derive the equation y = mx for a line through the origin and the
equation y = mx + b for a line intercepting the vertical axis at b.
(8.EE.B.6).
 Solve
linear equations with rational number coefficients, including equations
whose solutions require expanding expressions using the distributive
property and collecting like terms. (8.EE.C.7.b)
 Analyze
and solve pairs of simultaneous linear equations using points of
intersection on their graphs and algebraically. (8.EE.C.8).
Functions
 Construct
a function to model a linear relationship between two quantities.
Determine the rate of change and initial value of the function from a
description of a relationship or from two (x, y) values (8.F.B.4)
Geometry: 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.A.1)
 Know the formulas for the area and circumference of a circle and use them to solve problems. (7.G.B.4)
 Use
facts about supplementary, complementary, vertical, and adjacent angles
in a multistep problem to write and solve simple equations for an
unknown angle in a figure. (7.G.B.5)
 Solve
realworld and mathematical problems involving area, volume and surface
area of two and threedimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms. (7.G.B.6).
 Understand
that a twodimensional figure is congruent to another if the second can
be obtained from the first by a sequence of rotations, reflections, and
translations; given two congruent figures, describe a sequence that
exhibits the congruence between them. (8.G.A.2)
 Understand
that a twodimensional figure is similar to another if the second can
be obtained from the first by a sequence of rotations, reflections,
translations, and dilations; given two similar twodimensional figures,
describe a sequence that exhibits the similarity between them.
(8.G.A.4).
 Use
informal arguments to establish facts about the angle sum and exterior
angle of triangles, about the angles created when parallel lines are cut
by a transversal, and the angleangle criterion for similarity of
triangles. (8.G.A.5)
 Apply the Pythagorean Theorem to determine unknown
side lengths in right triangles in realworld and mathematical problems
in two and three dimensions. (8.G.B.7)
 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.B.8).
 Know
the formulas for the volumes of cones, cylinders, and spheres and use
them to solve realworld and mathematical problems. (8.G.C.9)
Ratios & Proportional Relationships:
 Compute
unit rates associated with ratios of fractions, including ratios of
lengths, areas and other quantities measured in like or different units.
(7.RP.A.1)
 Recognize and represent proportional relationships between quantities using tables, graphs, and equations. (7.RP.A.2).
 Use
proportional relationships to solve multistep ratio and percent
problems, such as simple interest, tax, markups and markdowns,
gratuities and commissions, fees, and percent increase and decrease.
(7.RP.A.3)
. The Number System:
 Apply
properties of operations as strategies to add and subtract rational
numbers to solve realworld and mathematical problems. (7.NS.A.1)
 Apply
and extend previous understandings of multiplication and division and
of fractions to multiply and divide rational numbers to solve realworld
and mathematical problems. (7.NS.A.2)
Statistics & Probability:
 Approximate
the experimental probability of a chance event by collecting data on
the chance process that produces it and observing its longrun relative
frequency, and predict the approximate relative frequency given the
probability. (7.SP.C.6)
 Develop a
probability model and use it to find theoretical probabilities of
events. Compare probabilities from a model to observed frequencies; if
the agreement is not good, explain possible sources of the discrepancy.
(7.SP.C.7)
 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (7.SP.C.8)
