Supporting STAAR™ Achievement: Targeting the TEKS and ... · Supporting STAAR™ Achievement: Targeting the TEKS and Readiness Standards Grade 8 Mathematics Teacher Edition Product

Supporting STAAR™ Achievement:

Targeting the TEKS and Readiness

Standards

Grade 8 Mathematics

Teacher Edition

Product ID: 407-1673

SAMPLE

Supporting STAARTM Achievement: Grade 8 © Region 4 Education Service Center ii All rights reserved.

Table of Contents Introduction ......................................................................................... iv–xi

What Is Supporting STAAR™ Achievement: Targeting the TEKS and Readiness Standards? ......................................................................... iv What Is in a Lesson Found in Supporting STAAR™ Achievement: Targeting the TEKS and Readiness Standards?....................................................... v References and Bibliography ................................................................. x

Compare and Order Fractions and Decimals ........................................ 2–15

Lesson Notes ...................................................................................... 2 Answer Keys ....................................................................................... 9 Activity Masters and Student Pages ................................................. on CD

Problem Solving With Rational Numbers ........................................... 16–27

Lesson Notes .................................................................................... 16 Answer Keys ..................................................................................... 22 Activity Masters and Student Pages ................................................. on CD

Proportions ....................................................................................... 28–41


Percents ............................................................................................ 42–53


Writing Equations .............................................................................. 54–65


Tables, Graphs, and Equations .......................................................... 66–79


Dilations ............................................................................................ 80–97


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© Region 4 Education Service Center Supporting STAARTM Achievement: Grade 8 All rights reserved. iii

Pythagorean Theorem ..................................................................... 98–111 Lesson Notes .................................................................................... 98 Answer Keys ................................................................................... 105 Activity Masters and Student Pages ................................................. on CD

Volume .......................................................................................... 112–123

Lesson Notes .................................................................................. 112 Answer Keys ................................................................................... 118 Activity Masters and Student Pages ................................................. on CD

Similar Figures .............................................................................. 124–135


Probability ..................................................................................... 136–151


Data Analysis ................................................................................ 152–164


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Supporting STAARTM Achievement: Grade 8 © Region 4 Education Service Center All rights reserved.

What Is Supporting STAARTM Achievement: Targeting the TEKS and Readiness Standards?

A resource that focuses on the TEKS identified as readiness standards while integrating appropriate supporting standards and mathematical processes and skills

A resource that provides opportunities for rigorous mathematical conversations while providing supports for students at varying levels of readiness

A resource that provides support for English language learners and students struggling to learn mathematics through Tier I differentiated activities, preteaching experiences, scaffolds for activities such as hint cards and graphic organizers, and facilitation questions

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4 A resource that supports beginning as well as experienced teachers through clear instructions and facilitation questions that focus on potential stumbling blocks for students in the effort to bridge to formal understanding of mathematics

5 A resource of classroom-ready 5E lessons. The Engage phase of each lesson consists of a student-centered activity that either bridges from students’ prior knowledge or encourages interest in deeper exploration of the concepts in the lesson. The Explore phase of each lesson provides students with an opportunity to “do mathematics” and begin to formulate ideas and conjectures. In the Explain phase of each lesson, students formalize the mathematical ideas from the Explore phase with a focus on academic vocabulary, as well as procedures related to the concepts. The Elaborate phase of each lesson allows students to apply or extend their understanding of the concepts in the lesson. The Evaluate phase consists of four selected-response or griddable items that can be used to assess student understanding.

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Each readiness standard has been rewritten in student-friendly language so that students may gauge their learning.

Each lesson includes an English Language Proficiency Standard rewritten in student-friendly language.

Each lesson includes prerequisite knowledge that may impact student success within the lesson as well as vocabulary that will be used during the lesson.

© Region 4 Education Service Center Supporting STAARTM Achievement: Grade 8 All rights reserved.

Additional TEKS that support the conceptual and procedural development of the readiness standard within this lesson are identified.

What Is in a Lesson Found in Supporting STAARTM Achievement: Targeting the TEKS and Readiness Standards?

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Materials for each phase are summarized on one page for ease in preparation.

Grouping strategies for each phase are summarized to assist in the arrangement of the classroom.

The Elaborate phase has two concurrent components: a student-facilitated activity and a teacher-facilitated activity that focuses on the needs of students struggling with the content.

Materials that are provided as supports for students in need of additional help are labeled with an asterisk.

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Each lesson includes a preteach activity that teachers may use with students who might benefit from exposure to related concepts prior to the lesson.

Each phase includes directions to implement the activity and the identification of additional student supports for the activity.

Each phase includes facilitation questions to help students who may be struggling to interpret or process components of the activity.

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Titles of activity masters and student pages are printed in bold for ease of reference.

The Tier I intervention provides instructions on how to make the mathematics content more explicit for students struggling with the concepts within the lesson. The activity is at the same rigor as the activity being completed by the students in a self-directed environment.

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Each selected-response item is labeled with the STAARTM reporting category, a content student expectation, and an underlying processes and tools student expectation as appropriate. Incorrect answer choices are classified according to type.

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Tables, Graphs, and Equations

Supporting STAAR™ Achievement: Grade 8 © Region 4 Education Service Center All rights reserved.

Tables, Graphs, and Equations Readiness Standard 8.5A The student is expected to predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations.

Content Objective I can solve an application problem using a table, graph and/or equation.

Additional TEKS

8.2A The student is expected to select appropriate operations to solve problems involving rational numbers and justify the selections. 8.3A The student is expected to compare and contrast proportional and non-proportional linear relationships. 8.4A The student is expected to generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). 8.14A The student is expected to identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

ELPS c1C The student is expected to use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary.

Language Objective I can use correct vocabulary to complete a concept organizer.

Additional ELPS

c3D The student is expected to speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency.

Prerequisite Knowledge

• Locate and name points on a coordinate plane using ordered pairs • Write an equation from a table of values

Vocabulary Focus

Equation Graph Table Variable

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© Region 4 Education Service Center Supporting STAAR™ Achievement: Grade 8 All rights reserved.

Notes

Read and select facilitation questions as appropriate to meet your students’ needs.

Preteach

Materials Instructional Grouping

♦ V is for Variable ♦ Highlighters (yellow and blue)

Small group with teacher facilitation

Phase Materials one per student unless otherwise noted

Instructional Grouping

Engage ♦ Who’s Correct? ♦ Calculator*

Pairs of students

Explore

♦ Four Square Equations ♦ Four Square Equations Hint Cards* ♦ Ruler or straightedge ♦ Highlighters* (yellow and blue)

Pairs of students

Explain ♦ Solving Application Problems Organizer

(copied two-sided) ♦ Scissors

Whole-group discussion

Elaborate

♦ Female Elephants Independent

Intervention ♦ Female Elephants*

Small group with teacher facilitation

Evaluate ♦ Evaluate: Multiple Representations Individual

* for targeted students only

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1. Distribute V is for Variable and highlighters to each student. 2. Prompt students to silently read Problem 1 to themselves. 3. Once students have preread the problem, read the problem out loud. 4. Prompt students to restate the problem in their own words. Listen for an understanding of

what the problem is asking them to find. • What information are you given about the sales tax? • What does the variable t represent? The variable p?

5. Prompt student to use a yellow highlighter to highlight where the variable t is defined in the problem.

6. Ask, “Are you given a value for the variable t? How do you know?” 7. Prompt student to use a blue highlighter to highlight where the variable p is defined in the

problem. 8. Ask, “Are you given a value for the variable p? How do you know?” 9. Prompt students to write the equation in their own words and then solve the problem. 10. If students demonstrate continued need for support, provide guidance through Problem 2. 11. Upon completion, debrief with the following questions:

• How did you find the amount of the sales tax on the customer’s purchase? • How did you find the amount Carlos will earn in 4 hours and 45 minutes?

1. Distribute Who’s Correct? to each

student. 2. Prompt students to work with their

partners to complete Who’s Correct?

Facilitation Questions • How could you use order of

operations to help you find the value?

Listen for . . .

• Correct use of the order of operations

Supports Provide students with calculators.

1. Distribute Four Square Equations and

a ruler or straightedge to each pair of students.

2. Prompt students to work with their partners to complete the activity.

3. Upon completion, debrief with the following questions: Problem 1 • How did you determine the cost per

half hour? • What is the rate of change? How is

the rate of change seen in the table? The graph? The equation?

• What would be the cost for zero hours in the table?

Facilitation Questions • In the equation, 15 is multiplied

by h, the number of hours. How could you use the 15 to determine the charge per half hour?

• How could you determine the number of miles Ms. Jones’ van will travel on one gallon of gasoline?

• Which values are represented on the x-axis? How do you know?

• Which values are represented on the y-axis? How do you know?

Explore

Engage

Preteach

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• How does this value connect to the equation?

Problem 2 • How did you determine the number

of miles Ms. Jones’ van will travel on one gallon of gasoline?

• What is the rate of change? How do you know?

• How is the rate of change seen in the table? The graph? The equation?

• What would be the number of miles at zero gallons in the table?

• How does this value connect to the equation?

• How did you determine the equation?

Listen for . . . • Students verbalization of the

processes that could be used to solve the problem, such as, I could divide 15 by two to determine the half hourly fee

• Connections between what the student is verbalizing as a process(es) and the numerial expression

Supports Provide students with a calculator and Four Square Equations Hint Card*. During the debriefing activity the teacher may prompt students to highlight the relationships found between the variable, written explanation, table, and graph of each problem situation. 1. Prompt students to use a yellow

highlighter to mark the following: • Variable c in the equation • The defining of c as the total cost in

the problem situation • The column in the table that

represents the total cost • The axis on the coordinate plane that

represents the total cost 2. Prompt students to use a blue

highlighter to mark the different representations for hours.

3. Repeat this process for Problem 2.

1. Prompt students to compare and contrast the two problems. Listen for a distinction between

an equation without a constant that includes the origin (proportional), an equation with a constant that does not include the origin (nonproportional), and a rate of change. • How are the two problems alike? • How are the two problems different?

2. Distribute Solving Application Problems Organizer and scissors to each student.

3. Prompt students to cut along the dotted lines and then fold as shown.

4. Once students have created their organizers, prompt student to complete the problems.

Explain

Solving Application Problems Using: Tables Graphs Equation Notes: Notes: Notes:

Fold Line

Cut Lines

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5. Upon completion, prompt students to share their strategies for using a table, graph, or equation to find the solution to application problems such as this.

6. Prompt students to record the strategies discussed on the Notes section of their organizers. • How could you use a table to help you solve an application problem similar to this one? • How could you use a graph to help you solve an application problem similar to this one? • How could you use an equation to help you solve an application problem similar to this

one?

1. Distribute Female Elephants to each

student. 2. Prompt students to complete Female

Elephants. 3. If a student appears to be struggling

with Female Elephants, the student may use the guide questions from Female Elephants* to complete independently or join the teacher-led intervention group.

Intervention 1. Distribute Female Elephants* to each

student. 2. Prompt students to silently read the

problem to themselves. 3. Once students have preread the

problem, read the problem out loud. 4. Prompt students to restate the problem

in their own words. Listen for an understanding of what the problem is asking them to find.

5. Ask, “What information are you given about the female elephants?”

6. Work with this group of students to complete the table.

7. Pose the following questions: • How could you find the rate of

change for this situation? • How could you find the constant?

8. Prompt students to complete Female Elephants*.

9. If students demonstrate continued need for support, guide them through problems 2–6. If students appear ready to work with a partner or independently, allow the students to do so.

Question Number

Correct Answer

Reporting Category

TEKS TEKS Conceptual

Error Procedural

Error Guess

1 C 2 8.5A B D A

2 B 2 8.5A A D C

3 30.75 2 8.5A

4 C 2 8.5A B D A

Evaluate

Elaborate

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Four Square Equations (Answer Key) Use the provided information in the four sections of the board to complete any missing information. Then answer the questions that follow the board.

Problem 1 Equation Hal’s Plumbing charges $7.50 per half

hour for labor in addition to a service fee of

$25.00. Write an equation that could be

used to determine c, the total cost for

plumbing repairs by Hal’s Plumbing for

h hours.

Define each variable:

c = the total cost

h = number of hours

= +25 15c h

Table Graph Complete the table to determine c, the total cost for plumbing repairs by Hal’s Plumbing for h hours.

Hours Process Total Cost (dollars)

0.5 25 + 15(0.5) 32.50

1 25 + 15(1) 40.00

1.5 25 + 15(1.5) 47.50

2 25 + 15(2) 55.00

2.5 25 + 15(2.5) 62.50

h

25 + 15h

Complete the graph to represent c, the total cost for plumbing repairs by Hal’s Plumbing for h hours. Label the graph.

a. Use your equation to determine the total cost for a plumbing job that takes 4.5 hours to complete. $92.50

b. How could you use your graph to determine the reasonableness of the cost for a 4.5 hours plumbing job? I could find 4.5 hours on the x-axis and then move across to the y-axis to verify a cost of $92.50.

c. Use your equation to determine the number of hours if the final cost was $90.

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hours

d. Use your graph to determine the reasonableness of the number of hours it took for a plumbing job that cost $90.

Hal’s Plumbing Cost

Hours

To

tal C

ost

(d

ollars

)

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a. Use your equation to determine how many miles Ms. Jones’ van can travel on 40 gallons of gas. 920 miles

b. How could you use your graph to determine the reasonableness of the number of miles Ms. Jones’ van can travel on 40 gallons of gas?

I could find 40 gallons on the x-axis and then move across to the y-axis to verify that it would take 920 miles.

c. Use your equation to determine how many gallons of gas Ms. Jones’ van needs for a trip that is 701.5 miles. 30.5 gallons

d. Use your graph to determine the reasonableness of the number of gallons of gas Ms. Jones’ van would need for a 701.5 mile trip.

Problem 2 Equation Ms. Jones’ new van travels 345 miles on 15 gallons of gas. Write an equation that could be used to determine, m, the total number of miles Ms. Jones’ van can travel on g gallons of gas.

Define each variable:

m = total number of miles

g = gallons of gas

Write the equation:

m = 23g Table Graph

Complete the table to determine m, the total number of miles Ms. Jones’ van can travel on g gallons of gas.

Gas (gallons)

Process Miles

5 23(5) 115

10 23(10) 230

15 23(15) 345

20 23(20) 460

25 23(25) 575

g

23g

Complete the graph to represent m, the total number of miles Ms. Jones’ van can travel on g gallons of gas.

1000 900 800 700 600 500 400 300 200 100

Ms. Jones’ Van

Gasoline (gallons)

Miles

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Four Square Equations Hint Cards* Cut along the dotted lines. Two hint cards are provided.

Hint Card

Problem 1 Where is the cost per hour seen in the equation? How could you use the cost per hour to find the cost per half hour? If the constant in the equation represents the service fee, how much is the service fee? Problem 2 How many miles can Ms. Jones travel on 1 gallon of gas?

Hint Card

Problem 1 Where is the cost per hour seen in the equation? How could you use the cost per hour to find the cost per half hour? If the constant in the equation represents the service fee, how much is the service fee? Problem 2 How many miles can Ms. Jones travel on 1 gallon of gas?

Total Cost

Service Fee Labor Fee

Per Hour

Total Cost

Service Fee Labor Fee

Per Hour SAMPLE

Name: _________________________________ Tables, Graphs, and Equations


Female Elephants The table below shows the relationship between the weight of a female elephant and the amount of vegetation she eats daily.

Daily Feeding Weight

Of Elephant (w)

Weight of Vegetation

(v)

550 330

600 360

650 390

700 420

Determine if each statement is True (T) or False (F). 1. An elephant that weighs 625 pounds would eat 375 pounds of vegetation.

2. The equation is 0 6=w v. .

3. An elephant that eats 700 pounds of vegetation daily would weigh about 1,200 pounds.

4. The equation is 0 6=v w. .

5. Female elephants eat approximately 60% of their weight in vegetation daily.

6. If an 80-pound girl ate at this rate, she would eat 52 pounds of food daily. SAMPLE

Name: _________________________________ Tables, Graphs, and Equations


Female Elephants* Some female elephants can eat as much as 330 pounds of vegetation daily, which is approximately 60% of their weight. The table below shows the relationship between the weight of a female elephant and the amount of vegetation she eats daily.

Daily Feeding

Weight Of Elephant

(w) Process

Weight of Vegetation

(v)

550 330

600 360

650 390

700 420

w

1. Complete the process column of the table above. 2. Write an equation that could be used to find v, the amount of vegetation of w, the weight of the

female elephant. 3. Determine if each statement is True (T) or False (F).

• An elephant that weighs 625 pounds would eat 375 pounds of vegetation.

• The equation is .w v= 0 6 .

• An elephant that eats 700 pounds of vegetation daily would weigh about 1,200 pounds.

• The equation is .v w= 0 6 .

• Female elephants eat approximately 60% of their weight in vegetation daily.

4. If an 86-pound girl ate at this rate, how much food would she eat in a day? Justify your answer.

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Supporting STAAR™ Achievement: Targeting the TEKS and ... · Supporting STAAR™ Achievement: Targeting the TEKS and Readiness Standards Grade 8 Mathematics Teacher Edition Product