### 7th/8th Math ELTs

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 real-world 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 real-world 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 multi-step real-life 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 multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.B.5)
• 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.G.B.6).

Unit 7: Rigid Transformations and Congruence

Geometry
• Understand that a two-dimensional 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 angle-angle criterion for similarity of triangles. (8.G.A.5).

Unit 8: Dilations, Similarity and Introducing Slope

Geometry
• Understand that a two-dimensional 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 two-dimensional 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 non-vertical 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 long-run 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 real-world 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 real-world 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 multi-step real-life 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 non-vertical 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 multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.B.5)
• 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.G.B.6).
• Understand that a two-dimensional 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 two-dimensional 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 two-dimensional 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 angle-angle criterion for similarity of triangles. (8.G.A.5)
• Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world 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 real-world 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 real-world 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 real-world 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 long-run 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)