Seventh Grade Mathematics

Unit

0 Review Unit

1 Scale Drawings

2 Introducing Proportional

Relationships

3 Measuring Circles

4 Proportional

Relationships & Percentages

5 Rational Number

Arithmetic

6 Expressions,

Equations, and Inequalities

7 Angles, Triangles, and

Prisms

8 Probability and

Sampling

Days 5 days 11-12 days 20 days 8-10 days 24 days 19 days 32 days 16 days 35 days

Test Specs

16-20% (G) 24-28% (RP) Calc. Inactive (RP1, RP2b,c)

16-20% (G) 24-28% (RP) Calc. Inactive (RP1, RP2)

8-12% (NS) Calc. Inactive (NS3)

20-24% (EE) Calc. Inactive (EE1, EE4a)

16-20% (G) Calc. Inactive (G5)

22-26% (SP) Calc. Inactive (SP4, SP7)

Spiral Topics

One step equations Add/Subtract integers

Ratios Unit ratios Solve one-step equations Integer Rules Additive Inverse/zero pairs

Substitution Writing/Solving Equations

Inequalities

Nets Surface area

Measures of center Histograms Dot Plots

NS9 Apply and extend previous understandings of addition and subtraction. EE7 Solve real-world and mathematical problems by writing and solving equations.

G1 Solve problems involving scale drawings of geometric figures by: ● Building an

understanding that angle measures remain the same and side lengths are proportional.

● Using a scale factor to compute actual lengths and areas from a scale drawing.

● Creating a scale drawing.

G6 Solve real-world and mathematical problems involving:

● Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.

● Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

RP1 Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.

RP2 Recognize and represent proportional

relationships between

quantities.

G1 Solve problems involving scale drawings of geometric figures by: ● Building an

understanding that angle measures remain the same and side lengths are proportional.

● Using a scale factor to compute actual lengths and areas from a scale drawing.

● Creating a scale drawing.

G4 Understand area and circumference of a circle. ● Understand the

relationships between the radius, diameter, circumference, & area.

● Apply the formulas for

area and

circumference of a

circle to solve

problems.

RP1 Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.

RP2 Recognize and represent proportional

relationships between

quantities.

RP3 Use scale factors and unit rates in proportional

relationships to solve ratio

and percent problems.

NS1 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.

NS2 Apply and extend previous understandings of multiplication and division.

NS3 Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.

EE1 Apply properties of operations as strategies to: ● Add, subtract, and

expand linear expressions with rational coefficients.

● Factor linear expression with an integer GCF.

EE2 Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression in context.

EE3 Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions.

EE4 Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

G2 Understand the

characteristics of angles

and side lengths that

create a unique triangle,

more than one triangle or

no triangle. Build triangles

from three measures of

angles and/or sides.

G5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure. G6 Solve real-world and mathematical problems involving:

● Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.

● Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

SP1 Use random sampling to draw inferences about a population. SP2 Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions and use to draw inferences. SP3 Make informal inferences to compare two populations. SP4 Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences about two populations. SP5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. SP6 Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.

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Mathematical Practices 1, 5, 7 3, 6, 7 1, 3, 6 1, 3,4, 7 2, 5, 8 2, 7 2, 4, 6 2, 3, 5, 8

1- Make sense of problems & persevere in solving them. 2- Reason abstractly and quantitatively.

3- Construct viable arguments & critique the reasoning of others. 4- Model with mathematics.

5- Use appropriate tools strategically. 6- Attend to precision.

7- Look for & make use of structure. 8- Look for & express regularity in repeated reasoning.

7th Grade Math Standards: G - Geometry EE - Equations & Expressions NS - The Number System RP - Ratios & Proportions SP - Statistics and Probability

NC Alignment Document

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

 Unit 0: Review

Unit 0: Review 5 days

7.NS1 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. 7.EE4 Use variables to represent quantities to solve real-world or mathematical problems. a. Construct equations to solve problems by reasoning about the quantities. o Fluently solve multistep equations with the variable on one side, including those generated by word problems. o Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. o Interpret the solution in context.

66NS9 Students add and subtract integers between -20 and 20, using models. Rules are not expected at this grade level. When derived from a real-world problem, students describe the sum or difference in context. These problems may require multiple steps. -Making Zero Pairs: Students are expected to create examples in which a number and the opposite of that number combine to make zero. Students describe these numbers as an additive inverse of each other and recognize that together they make a zero pair. Students are expected to interpret integers as having both a distance and a direction. Students demonstrate this understanding using a number line to: -Add integers o Students interpret the sum as the combination of distances with their corresponding direction. o Students explain how additive inverses create a zero pair. -Subtract integers o Students interpret the absolute value of the difference as the distance between numbers. o Students explain why they can rewrite subtraction as addition and use this property as needed.

While students are required to understand addition and subtraction of integers using number lines, students may use and interpret other models to find sums & differences or to demonstrate an understanding of the concepts of this standard. Students may start using physical models, such as algebra tiles and integer chips. Students should move to visual models.

6EE7 Students write and solve one-step equations. The expectation of the standard is that students will learn to write an equation to represent this problem, 12 · 𝑣 = 36. This means starting at beginning and working forward through the problem to the known value of the expression, using variables to represent unknown quantities. Students see the relationship between the equation and the arithmetic process. This leads students to seeing the relationship of inverse operations and the beginning of an algebraic approach to solving equations. As problems become more complex, the algebraic approach becomes the more efficient method to find solutions. While subtraction and division can be used when selecting problems for this standard, problems involving negative numbers, negative variables, a variable in the denominator, and complex fractions are beyond the expectation of this standard.

NS9 Answer the following questions. A student laid out these squares to represent a positive and a negative number. Each yellow square represents a positive one while each red square represents a negative one.

a) What number is represented by the yellow squares? b) What number is represented by the red squares? c) How many zero pairs are represented by the yellow and red squares? How do you know? d) If the squares represented an addition problem, write an expression to represent the problem, and what would be the sum? NS9 The number line shows the record low temperatures for these North Carolina cities in the month of February.

a) How much warmer was the record low in Cape Hatteras than the record low in Boone? b) How much cooler was the record low in Boone than the record low in Greensboro? c) How much warmer was the record low in Winston-Salem than in Greensboro? d) How much cooler was the record low in Greensboro than Winston-Salem? e) A student got the same answer for questions c) and d). The students shared in a discussion, “I thought that when I was counting down the number line, I would get a negative answer, but I got a positive answer no matter which way I counted.” Explain to the student why all of these answers were

positive. NS9 Rewrite the following into equivalent expressions and then evaluate each expression. a) 5 +(−3) b) 8 −17 c) −7 + (−15) d) −4 − 12

Activities: ● Subtract Integers with Same Sign ● Add Integers with Same Signs (-10

to 10) ● Add & Subtract Integers with

Different Signs ● Integer Chips Digital

Manipulatives ● One Step Equations

Khan Academy Videos - Illustrative Mathematics

● Testing solutions to equations ● Why aren't we using the

multiplication sign? ● Same thing to both sides of

equations ● Representing a relationship with

an equation ● Dividing both sides of an equation ● One-step equations intuition ● One-step subtraction equations ● One-step addition & subtraction

equations: fractions & decimals ● One-step multiplication equations ● One-step multiplication & division

equations: fractions & decimals ● Modeling with one-step

equations ● What is a variable? ● Evaluating an expression with one

variable ● Writing basic expressions word

problems

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 0: Review

EE7 Jim and Ed are debating the answer to the equation m .3

2 = 41

● Jim states that m is equal to 2 .32

● Ed states that m is equal to .8

3 Which statement is true?

A. im’s answer of is correct because he divided by to get his answer.2 32

32

41

B. Jim’s answer of is correct because he divided by to get his answer.2 32

41

32

C. Ed’s answer of is correct because he multiplied by to get his answer.83

41

32

D. Ed’s answer of is correct because he divided by to get his answer.83

41

32

EE7 Meagan spent $56.58 on three pairs of jeans. If each pair of jeans costs the same amount, write an algebraic equation that represents this situation and solve to determine how much one pair of jeans cost. EE7 Select all equations that have as a solution.n = 6

A. 2 + n = 6

B. 2n + 6 = 1

C. 44 · n = 2

D. n · 3 = 2

EE7 A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad? EE7 Robert has x books. Marie has twice as many books Robert has. Together they have 18 books. Which of the following equations can be used to find the number of books that Robert has?

A. 8x + 2 = 1

B. 8x + x + 2 = 1

C. x 8x + 2 = 1

D. x 82 = 1

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 0: Review

E. x x 82 + 2 = 1

EE7 Solve the following equations:

A. 2 1 = 8 + y B. f − 3

2 = 41

C. .3 .1 2 + r = 7 D. 1 5

2 = k · 61

E. .3 4w = 3

F. .5 .8 0.2 9 − 2 + a = 2

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

  Unit 1: Scale Drawings

Unit 1: Scale Drawings

11-12 days

G1 G6

6.NS1 Use visual models and common denominators to:

● Interpret and compute

quotients of fractions.

● Solve real-world and

mathematical problems involving division of fractions.

6.RP3 Use ratio reasoning with equivalent whole-number ratios to solve real-world and mathematical problems by:

● Creating and using a table to

compare ratios.

● Finding missing values in the

tables.

● Using a unit ratio.

● Converting and manipulating

measurements using given ratios.

● Plotting the pairs of values on

the coordinate plane.

8.G3 Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the 𝑥- axis and 𝑦-axis on two-dimensional figures using coordinates.

8.G4 Use transformations to define similarity.

Guidance for Unit 1 Teacher Notes: Be sure to include questions that involve finding the area of compound shapes when given a scale. G1 Students notice that the scale factor impacts the length of line segments and the area between the scale drawing and the original drawing, while noting that the scale factor does not change the angle measurements. They also recognize how the scale factor changes in relation to the type of measurement.

Students can identify the scale factor, reproduce drawings at a different scale from a given scale and flexibly move between the actual dimensions and scaled dimensions of a drawing.

G1 This diagram is a scale drawing of a store.

To the nearest 50 square foot, what is the area of the actual store?

a) 2,350 square feet b) 2,400 square feet c) 2,450 square feet d) 2,500 square feet

G1 A triangle has an area of 6 square feet. The height is four feet. What is the length of the base? G1 Julie shows the scale drawing of her room below.

● If each 2 cm on the scale drawing equals 5 ft, what are the actual dimensions of Julie’s room?

● Reproduce the drawing at 3 times its current size.

Activities: ● 7th Grade Digital Notebook ● Desmos Scale Card Sort

Mr. Morgan Videos

● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12

Khan Academy Videos - Illustrative Mathematics

● Exploring scale copies ● Identifying corresponding parts

of scaled copies ● Identifying scale copies ● Identifying scale factor in

drawings ● Scale factors and area ● Scale Drawings ● Creating scale drawings ● Interpreting a scale drawing ● Solving a scale drawing word

problem

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 1 Vocabulary

scaled copy: a copy of an figure where every length in the

original figure is multiplied by the same number

polygon: a plane shape (two-dimensional) with straight sides

scale factor: the number multiplied by all the lengths in the

original figure, used to create a scaled copy

area: the number of unit squares equal in measure to the

surface

quadrilateral: a polygon of four sides

distance: an extent of area or an advance along a route

measured in a straight line

scale drawing: represents an actual place or object. all the

measurements in the drawing correspond to the

measurements of the actual object by the same scale

scale: tells how the measurements in a scale drawing represent

the actual measurements of the object

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

  Unit 2: Introducing Proportional Relationships

Unit 2: Introducing

Proportional Relationships

20 days

G1 G6

RP2a RP2b RP2c RP2d RP1

6RP2 Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. 6RP3 Use ratio reasoning with equivalent whole-number ratios to solve real-world and mathematical problems by:

● Creating and using a table to

compare ratios.

● Finding missing values in the

tables.

● Using a unit ratio.

● Converting and manipulating

measurements using given ratios.

● Plotting the pairs of values on

the coordinate plane.

6.EE2 Write, read, and evaluate algebraic expressions.

6.NS8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Guidance for Unit 2 RP1 This standard asks students to understand the concepts of a unit rate in proportional relationships. This concept will allow students to write equations, graph and compare proportional relationships.

In 7th grade, students build on this understanding to:

● Find the appropriate rate based on context. ● Rewrite any rate as a unit rate. ● Know that a rate can be used to express all of its associated

equivalent ratios. Ratios in 7th grade can include fractions and decimals, which may lead to students to interpret a complex fraction as the division of two fractions.

Students working with complex fractions, a fraction in the form

.

RP2 Understand that a proportion is a relationship of equality between ratios. Students represent given proportional relationships with tables and graphs. Students determine the characteristics that remain consistent in proportional relationships, such as the unit rate and inclusion of the origin. Students determine a proportional relationship by:

● Creating tables to analyze the multiplicative relationships between the quantities (the rate) and determine their consistency.

● Creating graphs to visually verify a constant rate as a straight line through the corresponding coordinates and the origin.

Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.This unit rate is sometimes referred to as the constant of proportionality. This is because in a proportional relationship, the rate is unchanging, or constant even as the quantities increase or decrease by the scale factor. This is the most important characteristic to be identified in a proportional relationship.

RP1

Julia walks mile in each hour. She continues to walk at the same pace.21

21

a) What unit rate would be needed to find how many miles Julia walked if we know the number of hours? b) What unit rate would be needed to find how many hours Julia walked if we know how far she walked?

c) If Julia walked for 1 hours, how far did Julia walk?31

d) If Julia walked for 5.2 miles, how long did Julia’s walk take?

RP1

If a gallon of paint covers of a wall, continuing at this rate how much paint is needed21

61

for the entire wall? RP1 Emily leaves her house at exactly 8:25 am to bike to her school, which is 3.42 miles away. When she passes the post office, which is 3⁄4 miles away from her home, she looks at her watch and sees that it is 30 seconds past 8:29 am.

If Emily’s school starts at 8:50 am, can Emily make it to school on time without increasing her rate of speed? Show and/or explain the work necessary to support your answer.

Activities: ● Unit Rate ● Coordinate Plane Digital

Manipulative ● Desmos Activity - Matching

Tables and Graphs ● Desmos Activity - Space Rocks

and Rope Lengths ● Proportional Relationships with

Tables ● Hot Dog Eating 13.3

Mr. Morgan Videos

● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12 ● Lesson 13 ● Lesson 14

Khan Academy Videos - Illustrative Mathematics

● Constant of proportionality from tables

● Identifying the constant of proportionality from equation

● Constant of proportionality from table (with equations)

● Equations for proportional relationships

● Writing proportional equations

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 2: Introducing

Proportional Relationships

Create equations and graphs to represent proportional relationships. Students graph proportional relationships on the coordinate plane using the unit rate. Students will determine the appropriateness between plotting points and drawing a line based on the characteristics of the quantities involved. Students solve problems using generated equations. In 7th grade, the term slope and the slope formula are inappropriate, as the focus should remain on the multiplicative relationships.

Use a graphical representation of a proportional relationship

Students interpret the meaning of coordinates, including the origin, plotted as part of a proportional relationships.

Students use the context of the situation to determine if the quantities are discrete or continuous and will only draw a line connecting the coordinates if both quantities are continuous.

Tables, equations and graphs of proportional relationships

Students also explain how the coordinate (1,r) relates to the proportional relationship and its corresponding equation and table.

Students recognize that the r is the multiplicative relationship between the x and y coordinates of the ordered pair

RP2a The equation y=6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. This table shows the cost to buy different weights of steak at grocery store 2.

Which statement is true?

a) The cost of steak in grocery store 1 is $0.75 less per pound than at grocery store 2. b) The cost of steak in grocery store 1 is $0.75 more per pound than at grocery store

2. c) The cost of steak in grocery store 1 is $0.50 less per pound than at grocery store 2. d) The cost of steak in grocery store 1 is $0.50 more per pound than at grocery store

2. RP2b A 5-lb bag of apples costs $4.50, and an 8-lb bag of the same type of apples costs $7.52. Greg found the unit price, which is the constant of proportionality between cost and weight, for each bag of apples. What is the difference in the unit prices?

a) $0.04 per pound b) $0.12 per pound c) $0.16 per pound d) $0.21 per pound

RP2c This table shows the relationship between x and y.

Which equation models this relationship?

A. 3xy = 5

B. 3.5xy = 5

C. 4xy = 5

D. 4.5xy = 5

from tables ● Interpret proportionality

constants ● Writing proportional equations ● Proportional relationships:

movie tickets ● Proportional relationships:

bananas ● Proportional relationships:

spaghetti ● Is side length & area

proportional? ● Is side length & perimeter

proportional? ● Comparing proportionality

constants ● Identifying proportional

relationships from graphs ● Constant of proportionality from

graph ● Interpreting graphs of

proportional relationships ● Comparing constants of

proportionality

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 2: Introducing

Proportional Relationships

RP2 Determine which of the following tables represent a proportional relationship? Explain your reasoning.

Find the unit rate, when 𝑥 = 1, of each proportional relationship identified above and describe how you see the unit rate in the table.

RP2 The graph shows a proportional relationship between the number of gallons of gasoline used (g) and the total cost of gasoline (c). Find the unit rate (r). Using the value of r, write an equation in the form of 𝑐 = 𝑟𝑔 that represents the relationship between the number of gallons of gasoline used (g) and the total cost (c).

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 2: Introducing

Proportional Relationships

RP2 The school bus driver follows the same route to pick students up in the morning and to drop them off in the afternoon. Because of traffic, the afternoon drive takes 1.5 times as long as the morning drive.

a) Write an equation that represents the relationship between the number of minutes m, of the morning drive, to the total number of minutes, t, that the bus driver spends picking up and dropping off students each day. b) Using the unit rate, graph the equation on a coordinate plane. On your graph, should the points be connected to make a line? Explain.

RP2 Select the phrase from the box to make true statements. Be prepared to justify your answer.

Greater than Equal to Less than

● In a proportional relationship, if the unit rate is _______ 1,

the value of the output will be _______ the value of the input.

● When comparing proportional relationships, if the unit rate of first relationship is _______ the unit rate of the second, the value of the output of the first relationship will be _______ the value of the output of the second relationship for the same input value.

RP2 A landscaper is hired to take care of the lawn and shrubs around the house. The landscaper claims that the relationship between the number of hours worked and the total work fee is proportional. The fee for 4 hours of work is $140. a) Which of the following combinations of values for the landscaper’s work hours and total work fee support the claim that the relationship between the two values is proportional? b) Write an equation that describes the proportional relationship.

c) What is the relationship between your answers for part a and the equation you wrote for part b? d) What is the relationship between your non-answers for part a and the equation you wrote for part b?

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 2: Introducing

Proportional Relationships

RP2 Kell works at an after-school program at an elementary school. The table below shows how much money he earned every day last week.

Mariko has a job mowing lawns that pays $7 per hour. a) Who would make more money for working 10 hours? Explain or show work. b) Draw a graph that represents y, the amount of money Kell would make for working x hours, assuming he made the same hourly rate he was making last week. c) Using the same coordinate plane, draw a graph that represents y, the amount of money Mariko would make for working x hours. d) How can you see who makes more per hour just by looking at the graphs? Explain.

Unit 2 Vocabulary

equivalent ratios: two ratios are equivalent if you can multiply each of the numbers in the first ratio by the same factor to get the numbers in the second ratio constant of proportionality: in a proportional relationship, the

values for one quantity are each multiplied by the same

number to get the values for the other quantity

proportional relationship: the values for one quantity are each

multiplied by the same number to get the values for the other

quantity

equation: a statement that the values of two mathematical

expressions are equal (indicated by the sign =)

quotient: a result obtained by dividing one quantity by another

origin: a fixed point from which coordinates are measured, as

where axes intersect

plot: a graph showing the relation between two variables

coordinate plane: the plane containing the "x" axis and "y" axis

quantity: a value or component that may be expressed in

numbers

axes: the "x" and "y" lines that cross at right angles to make a

graph

coordinates: a set of values that show an exact position

x-coordinate: the horizontal value in a pair of coordinates: how

far along the point is

y-coordinate: the line on a graph that runs vertically (up-down)

through zero

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

 Unit 3: Measuring Circles

Unit 3: Measuring

Circles 8-10 days

G1 G6

RP2a RP2c G2 G4

RP3 EE3

.

8.G9 Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems

G4 Beginning with the understanding that a circle is defined as a 2-dimensional figure whose boundary (circumference) consists of points equidistant from a fixed point (the center), students can decompose the figure into triangular shapes and then compose the shape into a rectangular shape.

Students also use their understanding of ratios and rate to recognize that the ratio between the circumference and diameter of the circle is equivalent to the irrational number 𝜋.

Students DO NOT need to know the definition of irrational number in 7th grade.

G4 Circle M has a radius of 7.0 cm. The shortest distance between P and Q on the circle is 7.3 cm.

What is the approximate area of the shaded portion of circle M?

A. 153.9 m c 2

B. 44.0 m c 2

C. 25.6 m c 2

D. 21.0 m c 2

G4 The seventh-grade class is building a mini-golf game for the school carnival. The end of the putting green will be a circle. If the circle is 10 feet in diameter, how many square feet of grass carpet will they need to buy to cover the circle? How might someone communicate this information to the salesperson to make sure he receives a piece of carpet that is the correct size? Use 3.14 for pi. G4 The center of the circle is at (2, -3). What is the area of the circle?

Activities: ● Measuring Circles ● How Well Can You Measure ● Polygraph-circles ● Card sort-digital ● Rolling Tires ● Exploring Circumference ● Applying Circumference ● How far is it around? ● Area Review ● Exploring Area ● Relating Area ● Applying Area ● 7.3.10 Card Sort

Mr. Morgan Videos

● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11

Khan Academy Videos - Illustrative Mathematics

● Labeling parts of a circle ● Radius, diameter, circumference

& π ● Area of a circle ● Area of a shaded region ● Partial circle area and arc length ● Radius & diameter from

circumference

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 3: Measuring

Circles

G4 If a circle is cut from a square piece of plywood, how much plywood would be left over?

G4 What is the perimeter of the inside track?

Unit 3 Vocabulary

perimeter: the distance around a two-dimensional shape

radius: a line segment that goes from the center to the edge of

a circle diameter: a line segment that goes from one edge of a circle to

the other and passes through the center circumference: the distance around the circle

pi: the ratio of a circle's circumference to its diameter

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

 Unit 4: Proportional Relationships and Percentages

Unit 4: Proportional Relationships

and Percentages

24 days

RP1 RP3

NS2c

6.RP1 Understand the concept of a ratio and use ratio language to:

● Describe a ratio as a

multiplicative relationship between two quantities.

● Model a ratio relationship using

a variety of representation

6.RP2 Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context.

6.RP4 Use ratio reasoning to solve real-world and mathematical problems with percents by:

● Understanding and finding a

percent of a quantity as a ratio per 100.

● Using equivalent ratios, such as

benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity.

● Finding the whole, given a part

and the percent.

RP3 Students are expected to use scale factors and unit rates to make the conversions. Uncommon conversion ratios should be provided. Students are expected to use scale factors and unit rates to solve percent problems. While students should avoid “rules” or formulaic approaches, students should see the pattern and know that at percent increase or decrease is the proportional relationship between the initial value and the new value. Students know what terms may suggest a percent increase or decrease. Some of these terms include: tax, tip, commission, fee, discount, sale, mark up, and mark down. Students may be asked to answer questions that require multiple percent increases and decreases.

Given the appropriate information, students may be asked to find the original amount, a new amount, or the percent of change.

Students interpret a degree as being an equivalent ratio to a percent. The relationship between percents and degrees allows categorical data that form part-to-total relationships to be represented as sectors of a circle. Given appropriate information, students:

● find missing values (data, percents, or degrees) ● create a circle graph ● interpret a circle graph and use that information to solve

problems

RP3 Erica saw a skateboard on sale for $59.95. The original price of the skateboard was $79.95. What is the approximate percent discount on the skateboard?

A. 20% B. 25% C. 75% D. 80%

RP3 Zoomy is a racing garden snail. In a snail race, the snails are given one minute to travel as far as they can. The distance traveled is then measured in feet to determine the winner. According to internet resources, a garden snail’s top speed is 0.029 mph. If Zoomy traveled at top speed, how many feet could Zoomy travel during the race? (1 𝑚𝑖 = 5280 𝑓𝑡) RP3 There were 70 employees working at a rental company. This year the number of employees increased by 10 percent. How many employees work for the rental company his year? RP3 In 1980, the populations of Town A and Town B were 5,000 and 6,000, respectively. The 1990 populations of Town A and Town B were 8,000 and 9,000, respectively.

a) Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim.

b) Darlene claims that from 1980 to 1990 the population of Town A grew more. Use mathematics to explain how Darlene might have justified her claim.

Activities: ● Simple Interest ● Percent of Change ● On Your Mark ● Representations of Proportional

Relationships ● Proportional Relationships with

Repeating Decimals Card Sort ● Percentage Situations - Card

Sort

Mr. Morgan Videos

● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12 ● Lesson 13 ● Lesson 14 ● Lesson 15

Khan Academy Videos - Illustrative Mathematics

● Fraction to decimal: 11/25 ● Worked example: Converting a

fraction (7/8) to a decimal ● Rational number word problem:

ice ● Interpreting linear expressions:

diamonds ● Percent word problem: guavas ● Percent word problems: tax and

discount

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 4: Proportional Relationships

and Percentages

RP3 A car dealer is calculating the list price for a used car. The dealer takes the initial price of the car and adds $259 dollars for cleaning and shipping the car to the dealer. The dealer then increases that price by 25% for the dealer’s profit. That Price is then increased again by 10% for the salesperson’s commission.

a) If a used car is initially priced $10,000, what will be the list price for this car? b) Write an equation that shows the relationship between the initial price and the list price.

a) Using the circle graph, approximately how many cell phones were sold with an unlimited data plan? b) What percent of the cell phone cells are sold without an unlimited data plan? RP3 A shirt is on sale for 40% off. The sale price is $12.

a) How much was the discount? b) Write an equation that shows the relationship between the original price and the amount paid taking into an account an 8.5% sales tax.

RP3 The circle graph shows the number of cell phones sold at a local store. The darker shaded portion shows the number of cell phones that were sold with an unlimited data plan. A total of 2,712 cell phones were sold.

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 4: Proportional Relationships

and Percentages

RP3 Students collected the following data about the students’ haircolor in their school. Create a circle graph that illustrates the data in the table. Label each part of the circle graph with the correct hair color and the percent of the whole each part represents.

Unit 4 Vocabulary

repeating decimal: has digits that keep going in the same

pattern over and over; has a line over the digits that repeat

percentage increase: tell how much a quantity went up,

expressed as a percentage of the starting amount

percentage decrease: tells how much a quantity went down,

expressed as a percentage of the starting amount

discount: a deduction from the usual cost of something, typically given for prompt or advance payment or to a special category of buyers sales tax: a tax from the government; a percentage of the price

of an item

tip: a sum of money given to someone as a reward for their

services

interest: money paid regularly at a particular rate for the use of

money lent, or for delaying the repayment of a debt

commission: a fee paid for services, usually a percentage of the

total cost

markup: how much a retailer increases the price over what

they paid for it

percent error: a way to describe error, expressed as a

percentage of the actual amount

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  Unit 5: Rational Number Arithmetic

Unit 5: Rational Number

Arithmetic 19 days

NS1 NS2 NS3 EE3 EE4

6.NS9 Apply and extend previous understandings of addition and subtraction.

• Describe situations in which opposite quantities combine to make 0.

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.

● 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.

● Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences.

6.EE7 Solve real-world and mathematical problems by writing and solving equations of the form:

● 𝑥 + 𝑝 = 𝑞 in which 𝑝 , 𝑞 and 𝑥 are all nonnegative rational numbers; and,

● 𝑝 · 𝑥 = 𝑞 for cases in which 𝑝 , 𝑞 and 𝑥 are all nonnegative rational numbers.

NS1 Students understand that the properties of operations learned with whole numbers in elementary apply to rational numbers. Those properties include the identity, commutative and associative properties. Students rewrite subtraction as addition to apply properties as needed. Students apply their knowledge of addition and subtraction of rational numbers to describe real-world contexts and develop a process, their own rules, to add and subtract rational numbers.

NS2 Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.

Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.

Using division and previous understandings of fractions and decimals.

NS3 Students solve multi-step problems using numerical expressions that involve addition, subtraction, multiplication, or division of rational numbers. This includes problems that involve complex fractions. It is important for students to know common expressions that have understood grouping symbols, such as the numerator or denominator of a fraction. EE3 Students solve real-world and mathematical problems using a sequence of algebraic expressions. In these problems, students must express each step in the sequence using appropriate and corresponding variables. The student can then find the answer by evaluating each step in the sequence.

Students should be able to work with all rational numbers and expressions, converting to different forms, as needed, to find the answer.

EE4 Students write and solve multi-step one-variable equations and inequalities. Variables will only be on one side of the equation/inequality. Students move from arithmetic approach to algebraic approach. Students are expected to create multi-step one variable equations and inequalities with variables only on one side.

NS1 Evaluate the following expressions:

a) − .25)5 21 + ( 3

b) 4.17 .89− 5 − 3

c) 83 − 5)− 2 + ( 3

d) − )− 4 41 − ( 6 3

1

NS1 Justin is trying to determine if he has enough money to buy a new video game. The game cost $54.79. He started the day with $210 in his bank account. Looking at his receipts, he has spent $87.35 at a clothing store, $42.79 at a party store, and $25.68 at a gas station. Does he have enough money to buy the video game? Beyond estimating, explain your answer mathematically. NS2 Evaluate the following expressions:

a) (− )5 3

b) (10)(− )− 2 3

c) (− 6)65 6

d) .3( )(− )− 6 21−10 7

NS2 Two students are debating in your group. One student says that any number that can be written as a fraction is a rational number. The other student disagrees. Who is correct? If you disagree, provide a counterexample. NS2 Which of the following fractions are equivalent to ? Explain.

− 45

, , 4−5 5

−4 − 1 41

NS2 Evaluate the following expressions:

a) − 43 ÷ 2

1 b) 5 − ) 1 ÷ ( 3 c) .25 − ) − 5 ÷ ( 5

Activities: ● Multiply Integers:TV Show Skip

Back ● Divide Integers: Dropping

Anchor ● Additive Inverse and Absolute

Value ● Integer Chips Digital

Manipulatives ● Multiplying Rational Numbers -

Desmos Activity ● Matching Expressions Card Sort

Mr. Morgan’s Videos

● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12 ● Lesson 13 ● Lesson 14 ● Lesson 15 ● Lesson 16 ● Lesson 17

Khan Academy Videos - Illustrative Mathematics

● Missing numbers on the number line examples

● Comparing rational numbers ● Adding negative numbers

example ● Adding numbers with different

signs

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Unit 5: Rational Number

Arithmetic

d)3

−42 3

2

NS2 Five partners are investing in a business. The investment will cost $21,438. One of the

partners wrote this expression on a notepad, . What is the quotient and what5−21,438

would it represent in this situation? NS2 A water well drilling rig has dug to a height of –60 meters after one full day of continuous use.

a) Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours? b) If the rig has been running constantly and is currently at a height of –143.6 meters, for how long has the rig been running?

NS3 Which choice has a value that is closest to the value of the following expression?

1217 − 40

49

a) 41

b) 51

c) 61

d) 71

NS3 The three seventh grade classes at Sunview Middle School collected the most box tops for a school fundraiser, and so they won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected? EE3 Katie and Margarita have $20.00 each to spend at Students' Choice book store, where all students receive a 20% discount. Katie wants to purchase a book which normally sells for $22.50 and Margarita wants to purchase a book which normally sells for $22.75. With a sales tax of 10%, can Katie and

● Adding negative numbers on the number line

● Number equations & number lines

● Adding fractions with different signs

● Rational number word problem: checking account

● Adding & subtracting negative numbers

● Interpreting numeric expressions example

● Absolute value as distance between numbers

● Interpreting negative number statements

● Negative number word problem: Alaska

● Why a negative times a negative makes sense

● Why a negative times a negative is a positive

● Multiplying positive and negative fractions

● Dividing positive and negative numbers

● Dividing negative fractions ● Interpreting multiplication &

division of negative numbers ● Substitution with negative

numbers ● Ordering expressions ● Negative signs in fractions ● Expressions with rational

numbers ● Intro to order of operations ● Rational number word problem:

cab

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 5: Rational Number

Arithmetic

Margarita buy their books? Use algebraic expressions to describe your steps to find the answer. EE3 A teacher divided the class into two groups of equal size.

● of the first group are right-handed53

● 8% of the second group are right-handed. What fraction of the class is right-handed?

A. 98

B. 54

C. 710

D. 75

EE3 Trina is creating a small concrete sidewalk to and from her driveway to her front door as seen below. Trina needs to figure out how much to budget for the concrete.

● She is buying 80 lb. bags of concrete mix that cost $4.50 at the local home improvement store.

● Each 80 lb. bag will produce 1156 cubic inches of concrete. ● Each block measures 2 ft. by 2 ft. She wants the sidewalk to

be 4 in. deep.

How much should Trina budget for concrete? Use algebraic expressions to describe your steps to find the answer. EE4a

What is the value of when ?y − 5 = 9y−7

A. -7 B. -11

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 5: Rational Number

Arithmetic

C. -38 D. -52

EE4 The youth group is going on a two-day trip to the state fair that includes a concert after the 2nd day. The trip costs $52 for each person. Included in that price is $11 for a concert ticket and the cost of a pass for each day.

a) Write an equation representing the cost of the trip. b) How much did a pass for one day cost?

EE4 Solve the following:

a) c − 632 − 4 = 1

b) −−2t+3 = 5

c) 0 25(4z ) 1 = 2 − . − 3

d) (6 a) (6 a) 8 2 − 2 − 4 − 2 = 2 EE4 Amy had $26 dollars to spend on school supplies. After buying 10 pens at the same price, she had $14.30 left. Write and solve an equation to determine how much each pen cost.

Unit 5 Vocabulary

deposit: a sum of money placed or kept in a bank account,

usually to gain interest 

withdrawal: remove or take away (something) from a

particular place or position 

debt: something owed, usually money

difference: the result of subtracting one number from another; how much one number differs from another factor: numbers we can multiply together to get another number

rational number: a number that can be expressed as an integer or the quotient of an integer divided by a nonzero integer variable: a symbol for a number we don't know yet

additive inverse: a number that when added to a given number gives zero multiplicative inverse: what you multiply by a number to get 1; another name for reciprocal

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Unit 6: Expressions, Equations, and Inequalities

Unit 6: Expressions, Equations,

and Inequalities

32 days

NS1 EE1 EE2 EE3 EE4

6.EE5 Use substitution to determine whether a given number in a specified set makes an equation true. 6.EE6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 6.EE7 Solve real-world and mathematical problems by writing and solving equations of the form:

● 𝑥 + 𝑝 = 𝑞 in which 𝑝 , 𝑞 and 𝑥 are all nonnegative rational numbers; and,

● 𝑝 · 𝑥 = 𝑞 for cases in which 𝑝 , 𝑞 and 𝑥 are all nonnegative rational numbers.

6.EE8 Reason about inequalities by: ● Using substitution to determine

whether a given number in a specified set makes an inequality true.

● Writing an inequality of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 to represent a constraint or condition in a real-world or mathematical problem.

● Recognizing that inequalities of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 have infinitely many solutions.

● Representing solutions of inequalities on number line diagrams.

8.EE7 Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable.

● Recognize linear equations in one variable as having one solution, infinitely many solutions, or no solutions.

EE1 Students are expected to rewrite expressions into equivalent forms by combining like terms, using the distributive property, and factoring. Students can show the created expression is equivalent to the original expression. In 7th grade, this is limited to:

● adding and subtracting linear terms ● distribution with the product of a rational number and a linear

expression ● factoring a linear expression with an integer as the greatest

common factor

EE2 Students understand that rewriting an expression into an equivalent form can provide additional information and insight into real-world and mathematical problems. Students are expected to interpret the parts of an expression, such as the coefficient, constant, term, and variable, based on the context of the problem. EE3 Students solve real-world and mathematical problems using a sequence of algebraic expressions. In these problems, students must express each step in the sequence using appropriate and corresponding variables. The student can then find the answer by evaluating each step in the sequence. While these problems can be answered using a purely arithmetic approach, to meet the expectation of this standard, students should write each step as an algebraic expression.

Students should be able to work with all rational numbers and expressions, converting to different forms, as needed, to find the answer.

EE4 Students write and solve multi step one-variable equations and inequalities with the variables only on one side. Students move from an arithmetic approach to develop an algebraic approach to solve equations and inequalities. Students describe the relationship between both approaches, paying particular attention to the sequence of steps in both approaches.

7EE1

Which expression is equivalent to ?( x )2−1

41 − 8

2

A. x8−1 + 3

16

B. x8−1 + 8

3

C. x81 − 3

16

D. x81 − 8

3 7EE1 Select all expressions that are equivalent to ..75 (− x .1) .25x− 3 + 2 4 + 6 − 3

A. x x .17 − 2 + 8

B. .45 x .25x8 − 8 − 3

C. .75 .25x .1− 1 − 7 + 6

D. 1.25x 2.2 .75− 1 + 1 − 3

7EE1 Find the value for k that will make the following two expressions equivalent.

and 0.5x− 1 + k .1(5x .7) .1− 2 − 3 + 4

7EE1 Select all expressions that are equivalent to .2 x1 − 4

A. (3 )4 − x

B. (x )− 4 − 3

C. (− )− 4 3 + x

D. (6 x)2 − 2

7EE4 Amy had $26 dollars to spend on school supplies. After buying 10 pens at the same price, she had $14.30 left. Write and solve an equation to determine how much each pen cost. 7EE4 The youth group is going on a two-day trip to the state fair that includes a concert after the 2nd day. The trip costs $52 for each person. Included in that price is $11 for a concert ticket and the cost of a pass for each day.

Activities: ● Simplify Variable Expressions

Involving Multiplication and Division

● Desmos - Unit 6 Activities ● Equations Hyperdoc

Mr. Morgan’s Videos ● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12 ● Lesson 13 ● Lesson 14 ● Lesson 15 ● Lesson 16 ● Lesson 17 ● Lesson 18 ● Lesson 19 ● Lesson 20 ● Lesson 21 ● Lesson 22

Khan Academy Videos - Illustrative Mathematics

● Writing expressions word problems

● Equation word problem: super yoga (1 of 2)

● Equation word problem: super yoga (2 of 2)

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 6: Expressions, Equations,

and Inequalities

● Solve linear equations and

inequalities including multi-step equations and inequalities with the same variable on both sides.

a) Write an equation representing the cost of the trip. b) How much did a pass for one day cost?

7EE4b Which choice describes the value of m when ?(m ) 3− 5 + 1 ≤ 2

A. m ≥ 5−28

B. m ≤ 5−28

C. m ≥ 5−18

D. m ≤ 5−18

EE4 Solve the following:

a) c − 632 − 4 = 1

b) −−2t+3 = 5

c) 0 25(4z ) 1 = 2 − . − 3 d) (6 a) (6 a) 8 2 − 2 − 4 − 2 = 2

7EE4 Florencia cannot spend more than $60 on clothes. She wants to buy jeans for $22 dollars and spend the rest on shirts. Each shirt costs $8.

a) Write an inequality to describe this situation. b) How many shirts can she buy?

7EE4 Explain why 𝑑 < −5 and −𝑑 > 5 have the same solutions. 7EE4 Solve the following and graph your solution on the number line:

a) .47 − x > 5

b) −2t−1 ≤ − 4

5

c) .5f 5 − 1 > − 0 −

d) (4 w)32 ≤ 5 − 2

1 − 3

7EE4 Marcus has a pool that can hold a maximum of 4500 gallons of water. The pool already contains 1500 gallons of water. Marcus begins to add more water at a rate of 30 gallons per minute.

● Interpreting linear expressions: flowers

● Intro to two-step equations ● Two-step equations intuition ● Worked example: two-step

equations ● Two-step equations with

decimals and fractions ● Find the mistake: two-step

equations ● Two-step equation word

problem: computers ● Two-step equation word

problem: oranges ● Testing solutions to inequalities ● Two-step inequality word

problem: R&B ● Adding & subtracting fractions ● Distributive property with

variables ● Factoring with the distributive

property ● Combining like terms with

negative coefficients & distribution

● Equivalent expressions: negative numbers & distribution

● Combining like terms with rational coefficients

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Write an inequality that shows the number of minutes, m, Marcus can continue to add water to the pool without exceeding the maximum number of gallons.

Unit 6 Vocabulary

commutative (property): the order of numbers can be changed

when adding and multiplying values and will still result in the

same answer

equivalent expression: two expressions that are equal when

simplified

distribute: being an operation (such as multiplication in a(b + c)

= ab + ac) that produces the same result when operating on the

whole mathematical expression as when operating on each

part and collecting the results

substitute: putting values where the letters are

inequality: compares two values, showing if one is less than,

greater than, or simply not equal to another value.

term: either a single number or variable, or numbers and variables multiplied together

like terms: terms whose variables (such as x or y) with any

exponents (such as the 2 in x2) are the same

associative property: when adding and also when multiplying,

numbers can be grouped in any way and still yield the same

result

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Unit 7: Angles, Triangles, and Prisms

Unit 7: Angles,

Triangles, and Prisms

16 days

G6 G2 G5

NS1 EE4

6.G4 Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 8.G5 Use informal arguments to analyze angle relationships.

● Recognize relationships

between interior and exterior angles of a triangle.

● Recognize the relationships

between the angles created when parallel lines are cut by a transversal.

● Recognize the angle-angle

criterion for similarity of triangles.

● Solve real-world and mathematical problems involving angles.

8.G9 Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.

G6 Volume of Right Prisms. Students have found the volume of right rectangular prisms with rectangular sides and bases in the elementary grades. They will extend this understanding to right prisms with polygonal bases composed of triangles, quadrilaterals and polygons. Students understand the height to be a multiple of the bases thus understanding the volume to be the product of the area of the base and the height.

Volume of Pyramids

Students recognize the volume relationship between pyramids and prisms with the same base area and height. Since it takes 3 pyramids to fill 1 prism, the volume of a pyramid is 1⁄3the volume of a prism.

To find the volume of a pyramid, find the area of the base (B), multiply by the height (h) and then divide by three. Therefore,

OR

Surface Area of Right Prisms. Students will build on their understanding of nets in 6th grade to develop understanding of surface area of prisms and pyramids. Students recognize that the lateral edges of a prism are rectangles and that the lateral edges of a pyramid are triangles. Students can then use what they know about area of triangles and rectangles from earlier grades to determine the area of the lateral edges and bases combined to find the surface area of the figure. Memorization of the formulas for surface area is not expected. Students should be using visualization to conceptualize surface area.

G2 Side Lengths. When determining side length characteristics for triangles, students begin to closely examine the two situations (no triangle or a unique triangle) that may arise in the formation of a triangle from 3 distinct line segments and the characteristics that determine when a triangle does or does not exist.

Angle measures. When determining angle characteristics for triangles, students use a variety of tools to explore the cases where triangles may be formed noting cases where a triangle cannot be formed, and multiple triangles can be formed. This is where

G1 Jennie purchased a box of crackers from the deli. The box is in the shape of a triangular prism.

a. If the volume of the box is 3,240 cubic centimeters, what is the height of the triangular face of the box?

b. How much packaging material was used to construct the cracker box? c. Explain how you got your answer.

G1 The surface area of a cube is 96 . What is the volume of the cube?in2

G6 The two ends of this triangular right prism are equilateral triangles. The measurements are given to the nearest tenth of a cm.

What is the surface area of the prism?

A. 70 cm2

B. 74 cm2

Activities: ● Volume of Pyramids ● Complementary Angles ● Supplementary Angles ● Missing Measures of

Complementary and Supplementary Angles

● Vertical Angles ● Angles Hyperdoc ● Volume Hyperdoc ● Surface Area Hyperdoc ● Volume or Surface Area Card Sort

- Desmos Activity

Mr. Morgan Videos

● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12 ● Lesson 13 ● Lesson 14 ● Lesson 15 ● Lesson 16

Khan Academy Videos - Illustrative Mathematics

● Angles: introduction ● Complementary & supplementary

angles

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Unit 7: Angles,

Triangles, and Prisms

students “discover” that the angle measures have to sum to 180 to form a triangle. Sides lengths and angle measures. In preparation for future study of congruence, students explore situations where they are given two sides and an angle of triangle, or two angles and a side of a triangle to determine whether a unique triangle can be formed.

G5 This standard focuses on angles formed by intersecting lines, vertical angles and adjacent angles, and their relationships.

● Vertical angles are opposite angles formed by intersecting lines that share a vertex. Vertical angles are congruent (same measure).

● Adjacent angles are two angles that have a common vertex and side.

● Linear pairs are adjacent angles formed by intersecting lines. Linear pairs are supplementary (sum to 180).

C. 140 cm2

D. 280 cm2

G6 A triangle has an area of 6 square feet. The height is four feet. What is the length of the base? G6 Huong covered the box to the right with sticky-backed decorating paper. The paper costs 3¢ per square inch. How much money will Huong need to spend on paper?

● Vertical angles ● Equation practice with

complementary angles ● Equation practice with

supplementary angles ● Construct a triangle with

constraints ● Triangle inequality theorem ● Construct a right isosceles

triangle ● Volume of triangular prism &

cube

Unit 7 Vocabulary

straight angle: an angle that forms a straight line; it measures

180 degrees

adjacent angles: share a side and a vertex

degree: a measure for angles

right angle: is half of a straight angle; measures 90 degrees

supplementary: angle measures that add up to 180 degrees

complementary: angle measures that add up to 90 degrees

vertical angles: opposite angles that share the same vertex,

that are formed by a pair of intersecting lines and their angle

measures are equal

intersect: to cross over (have some common point)

vertex (of an angle): a point where two or more line segments

meet; a corner

perpendicular: a line at right angles to a line or plane (as of the horizon)

parallel: always the same distance apart and never touching

face: any of the individual flat surfaces of a solid object

volume: the amount of 3-dimensional space something takes up surface area: the total area of the surface of a three-dimensional object

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Unit 8: Probability and Sampling

Unit 8: Probability

and Sampling 35 days

SP1 SP2 SP3 SP4 SP5 SP6 SP7 SP8

6.SP3 Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. a. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. o Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. o Understand the median as a measure of center that is the numerical middle of an ordered data set.

b. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads.

6.SP5 Summarize numerical data sets in relation to their context. a. Describe the collected data by: o Reporting the number of observations in dot plots and histograms. o Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. b. Analyze center and variability by:

o Giving quantitative measures of center, describing variability, and any overall pattern, and noting any

SP1 Students know the difference between a population and a sample. They should understand that a sample is a subset of the population. Therefore, inferences can only be drawn if the sample is a subset AND representative of the population. Students should know that statistics are the summaries that we gather from samples and parameters reference the population.

Students understand that randomization is a condition for drawing a valid sample. Randomization reduces bias in samples. Bias in sampling interferes with the validity of inferences made based on those samples. While students are NOT expected to name the different types of bias, they should be able to articulate how an invalid sampling technique violates randomization.

SP2 This standard requires students to collect and use multiple samples of data to make generalizations about a population. This can be done through actual experimentation (i.e. gathering data from samples of the population) or simulation methods (i.e. flipping a fair coin to represent 1 of 2 equally likely outcomes). Students continue to focus on statistics as a tool for explaining variability.

Students should understand there is variation in a measure from sample to sample collected from the same population and that a sample statistic estimates a population parameter. They should also understand that a distribution of sample statistics (i.e. means, proportions, or medians) of the same size created by re-sampling can be used to estimate a population parameter by using the center and variation of the distribution to estimate an interval that the population parameter is likely within.

SP3 This standard extends the understanding of comparing different data displays of one set of data (NC.6.SP.4) to making comparisons of data sets of two distinct populations.

Students will compute measures of variability (range, interquartile range, and mean absolute deviation) and compare the values for the two groups noting how larger values indicate more variability meaning the values are more spread out from the center of the distribution. Students understand that measures of variability are necessary to measure how far apart the centers of two different groups are to assess if they are significantly different or not.

SP 1 Nicole wants to conduct a survey of the opinions of students at her middle school. Which survey sample would give her the most accurate results?

A. Random students as they enter the school B. Students during math class C. Random seventh-grade students during lunch D. Teachers in the seventh-grade hallway

SP1 The school food service wants to increase the number of students who eat hot lunch in the cafeteria. The student council has been asked to conduct a survey of the student body to determine the students preferences for hot lunch. They have determined three ways to select students to complete the survey. The three methods are listed below.Determine if each survey option would produce a random sample. If so, how do you know? If not, what condition(s) have been violated? Explain.

1. Write all of the students’ names on cards and pull them out in a draw to determine who will complete the survey.

2. Survey the first 20 students that enter the lunchroom. 3. Survey every 3rd student who gets off a bus.

SP2 Each student in a class selected a random sample of 25 marbles from a large jar of red and white marbles and then determined the proportion of red marbles in his or her sample. The proportion in one student’s sample was 0.28. The two- people sitting beside that student got sample proportions of 0.36 and 0.24. Of the following, which gives the best explanation for the differences in the sample proportions?

● Sample proportions will generally differ from one random sample to another. ● Only one of the students knew the true proportion of red marbles. ● Two of the three students obtained bad samples. ● Two of the three students miscalculated the percentages.

Activities: ● Definition of Probability,

Probability of Dependent Events ● Measurement of Probability ● Sample Spaces and Events ● Simple Random Sampling ● Digital Dice Manipulative ● Area Models - Desmos Activity ● Tree Diagrams ● Tree Diagrams with dependent

events ● Probability Hyperdoc

Mr. Morgan’s Videos ● Lesson 1 ● Lesson 2 ● Lesson 3 ● Lesson 4 ● Lesson 5 ● Lesson 6 ● Lesson 7 ● Lesson 8 ● Lesson 9 ● Lesson 10 ● Lesson 11 ● Lesson 12 ● Lesson 13 ● Lesson 14 ● Lesson 15 ● Lesson 16 ● Lesson 17 ● Lesson 18 ● Lesson 19

Khan Academy Videos - Illustrative

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Unit 8: Probability

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striking deviations. o Justifying the appropriate choice of measures of center using the shape of the data distribution. 8.SP1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

● Construct and interpret a

two-way table summarizing data on two categorical variables collected from the same subjects.

● Use relative frequencies

calculated for rows or columns to describe possible association between the two variables.

Students will compare two data sets visually by examining the degree of overlap and separation in the graphs of data distributions noting similarities and differences in the context of the data. SP4 Students are expected to compare two sets of data using measures of center and variability, noting which measure of center and variability are appropriate according to the shape of the distribution (i.e. mean and MAD for symmetric distributions and median and IQR for heavily skewed distributions).

Students compare data from random samples in two populations and incorporates using measures of variability to measure the differences in the measures of center of two distributions. Students should know that both distributions must be symmetrical to use the mean and mean absolute deviation (MAD) to summarize the data; otherwise, they should use the median and interquartile range.

SP5 Students recognize that the probability of any single event can be expressed using terminology like impossible, unlikely, likely, or certain or as a number between 0 and 1, inclusive, with numbers closer to 1 indicating greater likelihood.

Students understand that probabilities are expressed as ratios of the number of times that an event occurs to the total number of trials that are conducted. Students know that probabilities can be represented by a fraction, decimal, or a percent. Students should be able to describe the likelihood based on the proportion of successes for the event. Students also understand the relationship between an event and the compliment of the same event.

Students understand the likelihood of simple events and the connection to the tool being used.

Students can use a variety of random experiments to perform simple probability experiments by hand to quantify and interpret likeliness of an event occurring.

SP6 This standard is focused on relative frequency, which is the observed proportion of successful outcomes compared to the total number of trials for chance events.

Students recognize that individual experimental results may vary for each separate trial, which may also differ from the long run

SP2 A state representative took several random surveys of adults to find which place they visited most frequently. The average of all of the surveys is shown in this table.

Based on the table, which conclusion can be made?

A. On average, 50% of the adults visited the zoo most frequently. B. On average, 17% of the adults visited the park most frequently. C. On average, 2 out of 25 adults visited the aquarium most frequently. D. On average, 2 out of 10 adults visited the museum most frequently.

SP2 Below is a graph of a sampling distribution of 100 sample means of samples of size 25 from a sample of 199 NC high school student’s responses to the question, “About how many text messages did you send yesterday?” . The blue line represents the mean of the sampling distribution which is 111.4.

● What does the highlighted dot in the sampling distribution represent? ● Describe the shape, center, and spread of the sampling distribution based on its graph. ● Consider the center and spread of the distribution of sample means to

estimate what the population mean is for NC high school students number of texts sent in a day.

Mathematics ● Intuitive sense of probabilities ● Intro to theoretical probability ● Experimental probability ● Theoretical and experimental

probabilities ● Making predictions with

probability ● Probability models example:

frozen yogurt ● Simple probability: yellow

marble ● Simple probability: non-blue

marble ● Sample spaces for compound

events ● Counting outcomes: flower pots ● Die rolling probability ● Probability of a compound

event ● Count outcomes using tree

diagram ● Comparing distributions with

dot plots (example problem) ● Reasonable samples

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Unit 8: Probability

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probability.

This standard is intended to use experimentation to show that over a large number of trials that relative frequencies for experimental probabilities become closer to the theoretical probabilities. Students should make predictions before conducting the experiment, run trials of the experiment and refine their conjectures as they run additional trials. It is appropriate to use graphing calculators or computer simulation programs to collect large amounts of data on chance events.

SP7 Students understand that the sample space and related probabilities define the probability model for a random circumstance. Students also understand the difference between uniform probability models (all outcomes have the same probability) and non-uniform probability models (outcomes with different probabilities).

Using theoretical probability, students predict frequencies of outcomes, then compare the theoretical and experimental probabilities from a model and explain possible sources of noted variation between the probabilities. Students recognize an appropriate design to conduct an experiment with simple probability events, understanding that the experimental data give realistic estimates of the probability of an event but are affected by sample size. Students should be provided with multiple opportunities to perform probability experiments and to compare the results to theoretical probabilities. Critical components of each experimental process:

● Making predictions about the outcomes by applying the principles of theoretical probability;

● Comparing the predictions to the outcomes of the experiments;

● Replicating the experiment and continuing to compare results.

SP8 Students are expected to extend their understanding of simple events to that of compound events. They should compare and contrast simple and compound events both orally and in writing and draw on context to demonstrate their understanding. Students are also expected to know and understand how to

SP3 The test scores for the students in Mr. Miller’s math class are shown here.

52, 61, 69, 76, 82, 84,85, 90, 94

What is the range of the test scores?

A. 82.0 B. 77.0 C. 42.0 D. 22.5

SP3 The following data sets and boxplots represent the heights of players of a team from the WNBA and a team from the NBA, respectively.

● Describe the heights of the WNBA players. How much do they vary from each other?

● Describe the heights of the NBA players. How much do they vary from each other? ● Box plots were used to visually compare the teams. What do the graphical

displays tell us about the heights of WNBA players in comparison to the NBA players? What heights are similar? What are the differences?

● Why is it appropriate to use box plots to compare the groups instead of dot plots or histograms?

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Unit 8: Probability

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determine the sample space of compound events and explain how the sample space is used to find the probability of compound events (with or without replacement). Additionally, students can design simulations to collect data for compound events to generate frequencies of compound events for the purpose of approximating probabilities of compound events.

SP4 This table shows the number of points two teams scored in five games.

What is the difference in the mean absolute deviation of the two teams? A. 2.16 B. 6.2 C. 7.0 D. 8.96

SP4

Box plots are a good tool to use to visually compare range and IQR when comparing data

sets. In general, no overlap in the IQR of data sets indicates that there is likely a significant

difference in the centers. This means that the heights there is a significant difference in the

heights of male and female professional basketball players. Explain how the graphical

displays below confirm that NBA player heights are generally higher than WNBA heights.

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Units Vertical Alignment Clarification Sample EOG Questions Digital Resources

Unit 8: Probability

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SP5

The container below contains 2 gray, 1 white, and 4 black marbles.

Without looking, if Eric chooses a marble from the container, will the probability be closer to

0 or to 1 that Eric will select a white marble? A gray marble? A black marble? Justify each of

your predictions.

SP5

There are three choices of jellybeans – grape, cherry and orange. If the probability of getting

a grape is and the probability of getting cherry is310

, what is the probability of getting orange?51

SP6

Paul has a spinner with 4 colors: green, yellow, blue, and orange. He spins the spinner 60

times and records each color it stops on. The results are shown in this table.

Paul will spin the spinner an additional 450 times. How many times should he expect the

spinner to stop on blue?

A. 140

B. 124

C. 113

D. 105

SP6

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Unit 8: Probability

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A bag contains 100 marbles, some red and some purple. Suppose a student, without

looking, chooses a marble out of the bag, records the color, and then places that marble

back in the bag. The student has recorded 9 red marbles and 11 purple marbles. Using these

results, predict the number of red marbles in the bag.

SP6

Design a Probability Experiment: For example, give each pair of students a bag that contains 4 green marbles, 6 red marbles, and 10 blue marbles.

1. Each group performs 50 pulls, recording the color of marble drawn and replacing the marble into the bag before the next draw.

2. Students summarize their data as experimental probabilities and make conjectures about theoretical probabilities. How many green draws would be expected if 1000 pulls are conducted? 10,000 pulls?

3. Students record their data in a relative frequency table as they compile their results with the class. How did the relative frequencies change?

4. Optional: Students can create another scenario with a different ratio of marbles in the bag and make a conjecture about the outcome of 50 marble pulls with replacement.

SP7

The cafeteria staff made sandwiches. Each sandwich had either rye or white bread, either

ham or turkey, and either cheese or no cheese. The staff made an equal number of each

type of sandwich. The sandwiches were placed on a tray. Without looking, Mary will choose

a sandwich. What are the chances that Mary will get a sandwich with cheese?

A. 81

B. 61

C. 31

D. 21

SP7

Robert’s mother lets him pick one candy from a bag. He can’t see the candies. The number of candies of each color in the bag is shown in the following graph.

What is the probability that Robert will pick a red candy? Explain. A. 10% B. 20% C. 25% D. 50%

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Unit 8: Probability

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SP7

Look at the shirt you are wearing today and determine how many buttons it has. Then complete the following table for all the members of your class.

Suppose each student writes his or her name on an index card, and one card is selected randomly.

● What is the probability that the student whose card is selected is wearing a shirt with no buttons?

● What is the probability that the student whose card is selected is female and is wearing a shirt with two or fewer buttons?

SP8

Jane wants to pick out an outfit for the school dance. She can choose from 3 pairs of pants,

5 shirts, and 2 pairs of shoes. How many different outfits does Jane have to choose from?

A. 10

B. 15

C. 30

D. 60

SP8

A fair coin will be tossed three times. What is the probability of getting two heads and one

tail for the three tosses in any order?

SP8

● Show all possible arrangements of the letters in the word FRED using a tree

diagram.

● If each of the letters is on a tile and drawn at random, what is the probability of

drawing the letters F-R-E-D in that order?

● What is the probability that a “word” will have an F as the first letter?

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Unit 8 Vocabulary

event: a set of one or more outcomes in a chance experiment chance experiment: something you can do over and over again, and you don’t know what will happen each time outcome: one of the things that can happen when you do the experiment likely: having a high probability of occurring or being true unlikely: not likely

impossible: incapable of being or of occurring certain: something with a probability of 1; it is sure to happen probability: a number that tells how likely it is to happen random: outcomes that are equally likely to happen sample space: the list of every possible outcome for a chance experiment

bias: a systematic (built-in) error which makes all values wrong by a certain amount mean absolute deviation: one way to measure how spread out a data set is range: the distance between the smallest and largest values in a data set mean: a calculated "central" value of a set of numbers (average)

median: the middle number when the data set is listed in order interquartile range: the range from quartile 1 to quartile 3: q3 − q1 experimental probability: the ratio of the number of times an event occurs to the total number of trials or times the activity is performed theoretical probability: probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes

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