Mathematics 8th grade - Lead4ward

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Jul 25, 2013 ... STAAR Schoolhouse 2.0 Powerpoint and Handout Packet: ... STAAR Standards Snapshot - Grade 8 Math. Rptg. Cat. STAAR. ^d Z. D.
Mathematics th 8 grade STAAR :

Writing Secondary Math Assessments Northeast ISD | July 25, 2013

STAAR: Writing Secondary Math Assessments Northeast ISD | July 25, 2013

outcomes

Assessments are getting tougher…and, at the same time, quality resources for teachers are getting harder to find! School districts are meeting the challenge by creating their own tests— but where can we begin? What strategies can make assessments more effective in the classroom and the process more manageable for teachers? In this session, participants will: • Analyze samples of grade-specific items and activities. • Discuss what makes a task “stellar” (or, STAAR-like). • Develop methods to enhance and improve current tests already in use. • Learn strategies for creating your own assessments and activities. • Learn about three ways to adjust assessment: context, process, and rigor.

materials

Free tools at lead4ward.com/resources: • STAAR Standards Snapshots (Snapshots & Standards Tab) • TEKS Scaffolding Documents (Snapshots & Standards Tab) • STAAR Academic Vocabulary (Instructional Tools Tab) Teacher Field Guides: http://store.lead4ward.com/staar-field-guide-for-teachers-math/ New Math TEKS Resources: http://store.lead4ward.com/math-secondary/ STAAR Schoolhouse 2.0 Powerpoint and Handout Packet: http://lead4ward.com/workshops/logins/math-class/ password: STAAR-Ready-Math STAAR Schoolhouse (additional materials and activities): http://lead4ward.com/workshop-login-teacher-presentations/ password: staarteacher

contact

For questions about: • This session’s content • Workshop materials

Ward Roberts [email protected]

For questions about: • STAAR • Accountability • Technical assistance

Ervin Knezek [email protected] John Fessenden [email protected]

For questions about: • Workshop invoices • Registration information

Kim Lehman [email protected]

For questions about: • Follow-up presentations • Future staff development opportunities

Lee Rutledge [email protected]

Page 2



       



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Items—Comparisons 1

The probability of getting a red gumball from a gumball machine is 18 . The probability of getting a red piece of 1 gum from a candy machine is 6 . If both a gumball and a piece of candy are purchased, what is the probability that both are red?

2

Grade 8

Rufus has a box that contains cards of the same shape and size. There are 5 yellow cards, 4 red cards, and 1 purple card. He draws a card at random, replaces it, and draws a second card. What is the probability that both cards will be red? A

4 5

F

1 48

B

G

1 7

C

2 15 4 25

H

7 24

D

2 5

J

1 14

TAKS 2009, Grade 8

STAAR Release 2011, Grade 8

3. Use the spinner shown to find the probability of spinning a vowel. F G H J Holt Math, TAKS Prep Workbook

Compare & Contrast How are the items alike?

All: 8.11A

How are the items different?

Aligning Cognitive Level and Content The student is expected to:

write one-variable, two-step equations and inequalities to represent constraints or conditions within problems.

In this TEKS* Student Expectation: • Circle the verbs. • Put a box around the object nouns. • Underline any examples. Place these words in the graphic organizer. (Some may be used more than once.)

Verbs (Cognitive Level)

Nouns (Content)

Examples (including…such as…)

When are these skills covered in the math curriculum? * = New TEKS (7th Grade) beg. 2014-15

The student is expected to:

graph linear functions on the coordinate plane and identify the key features, including xintercept, y-intercept, zeros, and slope…

In this TEKS^ Student Expectation: • Circle the verbs. • Put a box around the object nouns. • Underline any examples. Place these words in the graphic organizer. (Some may be used more than once.)

Verbs (Cognitive Level)

Nouns (Content)

Examples (including…such as…)

When are these skills covered in the math curriculum? ^ = New TEKS (Alg. I) beg. 2015-16

Page 5

Aligning Cognitive Level and Content Graph

Linear functions

New Algebra I TEKS-SE Identify

coordinate grid

(1)

x-intercept

(2)

y-intercept

(3)

zeros

(4)

slope

(5)

Features

This student expectation has 5 possible alignments.

A

Match items A, B, and C (below) with one of these alignments.

A linear function is given by the equation 2x – 3y = 12. At what point will the graph of the function cross the y-axis?

Then, for items D and E, write questions to match the alignments that have not been used. Alignment: 1 2 3 4 5 (Circle one)

B

C

1. Identify the coordinates for any two points on the graph of this linear function.

Plot the graph of the equation: y = 2x – 3

2. Use these coordinates to determine the slope of the line. Alignment: 1 2 3 4 5 (Circle one)

D

Alignment: 1 2 3 4 5 (Circle one)

E

For the equation y = 4x – 7…

For the graph of the linear function…

Alignment: 1 2 3 4 5 (Circle one)

Alignment: 1 2 3 4 5 (Circle one) Page 6

Aligning Cognitive Level and Content Complete the organizer for each TEKS statement by writing the correct words in each box. 8.1A

compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals

8.1A Verbs (Cognitive Level)

Nouns (Content)

Examples (including…such as…)

(1)

Word bank

(2)

(3)

(4)

(5)

(6)

(7)

(8)

compare

decimals ( ±)

decimals ( ±)

fractions ( ±)

rational numbers

integers

percents

percents

order

fractions ( ±)

rational numbers

integers

Consider the 8 possible alignments above. Match one of these possibilities (or a combination!) to the items below.

1 What number is less than greater than 0.6? A

3 5

B

0.75

C

4 5

D

0.7

3 4 , but

Source: TxAIR, ID 490

Page 7

Source: TAKS 2006

Aligning Cognitive Level and Content Using the chart below, analyze one of more of the TEKS student expectations from your favorite grade level or course. A few samples are provided. TEKS (Student Expectations)

8.3B

A.2D

VERBS

NOUNS

EXAMPLES

(Cognitive Level)

(Content)

(including…such as…)

Estimate Find

Solutions

Collect Organize

Data

Make Interpret

Scatterplots

Model Predict Make

Decisions/Judgments

QUESTONS (Possible # of Ways)

Percents Proportions Similarity Rates

Positive correlation Negative correlation No correlation

2×1×4=

8 2×1 + 2×1×3 + 3×1 =

11

Think about various item stems that could be used to address each alignment of the student expectation. • What different questions could be asked to cover all the aspects of the given TEKS SE?

Page 8

Algebra Items (Tables, Graphs, Equations, Verbal Descriptions) Source: TEA, Released TAKS Items (2003-2009)

Item:

Grade:

% Correct

K ‘09

Item:

Grade:

% Correct

L ‘03

Item:

Grade:

M ‘04

Given (in Stem):

Given (in Stem):

Given (in Stem):

Find (in Choices):

Find (in Choices):

Find (in Choices):

Item:

Grade:

% Correct

N ‘03

Item:

Grade:

% Correct

O ‘09

Item:

Grade:

Given (in Stem):

Given (in Stem):

Find (in Choices):

Find (in Choices):

Find (in Choices):

Grade:

% Correct

Q ‘03

Item:

Grade:

% Correct

R ‘04

Item:

Grade:

Given (in Stem):

Given (in Stem):

Find (in Choices):

Find (in Choices):

Find (in Choices):

Grade:

T ‘06

% Correct

Item:

% Correct

S ‘09

Given (in Stem):

Item:

% Correct

P ‘09

Given (in Stem):

Item:

% Correct

Grade:

U ‘06

% Correct

Item:

Grade:

% Correct

V ‘09

Given (in Stem):

Given (in Stem):

Given (in Stem):

Find (in Choices):

Find (in Choices):

Find (in Choices):

Page 9

Multiple Representations (Tables, Graphs, Equations, Verbal Descriptions) Complete the chart for the table provided.

Table

Graph

x 0

y 425

1

375

2

325

3

275

4

225

7

75

Equation

Verbal Description

From this one set of representations… Consider: How many different ways are there to phrase question of each type? Table → Graph Graph → Table Equation → Table Table → Equation Graph → Equation Equation → Graph Table → Verbal Graph → Verbal Equation → Verbal Verbal → Table Verbal → Graph Verbal → Equation Page 10

Geometry Switch-Ups Complete the charts. Name

Description

3-D Figure

Triangular Prism

A solid figure with two triangular bases and three rectangular lateral faces

Net

A solid figure with two hexagonal bases and six rectangular lateral faces

Description

Figure

Shape Name

Formula

Dimensions

7 cm 15 cm

How many cubic centimeters of soda does it take to fill the can?

Cone

V = 31 Bh , or V =

1 3

(π r )h 2

12 in 20 in

S = Ph + 2B

r= 2 inches h = 3 inches

l= 12 inches w= 8 inches h = 20 inches P= ________ B = ________

8 in

Page 11

Measures of Central Tendency

A

Data (in order)

n

5, 5, 6, 7, 8, 8, 10, 10, 10, 12

10

B

1, 2, 3, 5, 7, 8, 8, 9, ____

C

10, 10, 12, ____ , ____ , 18, 20

7

D

____ , ____ , ____ , ____ , 50, 64, 64, 70

8

E

____ , ____ , ____ , ____ , ____

5

F

sum

Mean

Median

Mode(s)

54

Range

10

14

80

13

45

30

80

80

10

80

90

30

Page 12

Transformations on the Coordinate Plane Type of Transformation

Details

Original

A (-3, -1) B (-2, 2) C (1, -1)

1

Image

A’ ( __, -1) B’ ( __, 2) C’ (5, -1)

Rule (with coordinates)

Graph

B

Add 4 to the xcoordinates (x,y) → (x + 4, y)

A

C

Q 2

Reflection

Over the x-axis

P (-1, 1) Q (3, 4) R (5, 2)

P

R

3

Page 13

Probability

R

G R

R G

Y

G Y

B

4 red (R) 3 green (G) 2 yellow (Y) 1 blue (B)

In a jar are 10 marbles: 4 red marbles, 3 green marbles, 2 yellow marbles, and 1 blue marble. Without looking, a person is going to randomly select two marbles from the jar. Complete the chart to relate the probability of each outcome.

R

What’s the probability? First…

Then…

And next… Multiply

Answer

Pick another marble that is not red

3 3 × 5 5

9 = 36% 25

Pick a yellow marble

1 2 × 10 9

2 = 2.2% 90

Pick a red marble

Replace it

Pick a green marble

Pick a red marble

Do not replace it

Pick a green marble

Pick a marble that is red or yellow

Replace it

Pick a marble that is green or blue

Pick a marble that is not red

1 1 × 5 10

1 = 1% 100 Page 14

Varying the Context 1. The rectangle below is to be dilated by a scale factor of 2.5. What will be the area of the new (image) figure?

3. Which statement best describes the change in the area of a right triangle if all of its side lengths are multiplied by 4? A. The new area will be 4 times as large as the area of the original triangle. B. The new area will be 8 times as large as the area of the original triangle. C. The new area will be 12 times as large as the area of the original triangle. D. The new area will be 16 times as large as the area of the original triangle.

2 ft 6 ft

A. B. C. D.

30 square feet 40 square feet 60 square feet 75 square feet

2. A rectangle with an area of 16 cm2 is enlarged proportionally to create a new rectangle with an area of 144 cm2. What scale factor was used to enlarge the dimensions of the original rectangle? 1

A. 3 B. 3 C. 9 D. 19

TEKS: 8.10A Original

New (Image) Scale Factor (sides)

Sides

Area

Ratio (of areas) Sides

Area

1

2

3

Page 15

Varying the Context 1. The figure shows the net of a threedimensional solid.

• •

3.

What figure is represented by the net? Sketch the top, front and side views of the figure.

2. What three-dimensional figure has the given top, front, and side views?

Top

Front

Side

Sketch the 2-dimensional net for the figure.

TEKS: 7.8A-B name

3-D sketch

net

Top view

1

2

YOU TRY! -16-

Front View

Side View

Solved Problems 1.

Algebra I

The expression below could be used to find the slope between which pair of points?

−4−3 5+2

2.

A

(–4, –3) and (5, 2)

B

(5, –4) and (2, –3)

C

(5, –4) and (–2, 3)

D

(–4, 5) and (3, –2)

In point-slope form, a line is given by the equation y − 3 = 2( x + 7) . Which is the best description of this line?

3.

A

A line through (–3, 2) with a slope of 7

B

A line through (3, –7) with a slope of 2

C

A line through (–7, 3) with a slope of 2

D

A line through (2, 7) with a slope of –3

The expression below correctly uses the quadratic formula to solve which equation? x =

− 3 ± 3 2 − 4(5)(−1) 2(5)

2

A

5x – 3 x + 1 = 0

B

5x2 + 3x – 1 = 0

C

–3x2 + 5x – 1 = 0

D

3–x2 – 1x + 5 = 0

Page 17

Solved Problems 1.

Geometry

The expression below could be used to find the distance between which pair of points?

(−4 − 3)2 + (5 + 2)2

2.

A

(–4, –3) and (5, 2)

B

(5, –4) and (2, –3)

C

(5, –4) and (–2, 3)

D

(–4, 5) and (3, –2)

The expression below could be correctly used to find what?

2π (3)(6) + 2π (3)2 A

Volume of a cylinder with a radius of 3 and a height of 6

B

Surface area of a cylinder with a radius of 3 and a height of 6

C

Volume of a cone with a radius of 3 and a height of 6

D

Surface area of a cone with a radius of 3 and a height of 6

3.

The equation below is set up correctly using the Pythagorean theorem to find x, the unknown side length of a triangle. 62 + x2 = 92 Provide a sketch of this triangle, and label the length of each side.

4.

Consider the equation below. S = π(5)(8) + π(5)2

Fill in the blanks: This equation can be used to find the surface area of a

with a [What figure?]

that is equal to 5 units, and a

[What dimension?]

that is equal to 8 units. [What dimension?]

Sketch: Provide a sketch of this figure, and label each dimension.

Page 18

Error Analysis Where did each of these students go wrong? Item: A circular running track has a diameter of 42 meters. If an athlete can run at a rate of 3 meters per second, about how many seconds would it take her to complete one lap around the track? Arial

Corbel

Verdana

Franklin

C = 2π r

42 m

42 m

= 2π (42)

π r2 π (21)2

= 84π

C=πd C = 3.14 ⋅ 42 3.14 × 42 628 1256 18.84

C=πd C = 3.14 × 42 62.8 3 18.84

62.8 seconds

3.14 × 42 628 12560 131.88

3 m 84π = 1 sec ? 3x = 84π x =

3.14×441 1384.74

84π 3

= 28π = 87.9646...

About 132

d = 42 r = 21

1384.74 × 3 4154.22

About 88 sec.

Error Type:

Error Type:

Error Type:

P__________

A__________ C__________

Students lack skills or cannot complete specific step-by-step procedures.

Students cannot apply learning to a specific task. Although part of their work may be correct, the student may stop too soon, or not know where to start.

Students have misunderstanding about the underlying ideas or concepts behind the learning.

Other descriptions/examples:

Other descriptions/examples:

Other descriptions/examples:

Page 19

Error Analysis Classify each item according to potential student errors (Procedural, Application, or Conceptual). Then match each item to its answer choices, and classify each incorrect multiple-choice response as Procedural, Application, or Conceptual. 8.2B

1

Mrs. Bonner bought school clothes for her children at a local department store. The total cost of the items was $286.79. She put $50 down and will pay the remaining balance over the next 3 months. How much will each monthly payment be?

P

A

P

A

B

P

C D

8.2B

2

Circle one:

TxAIR, Item ID 1907

8.3B

Jody bought 2 CDs at $7.00 each. If the sales tax is 7.0%, what was the amount of tax on the total purchase?

P

A

C

A

P

A

C

B

P

A

C

C

C

P

A

C

A

C

D

P

A

C

P

A

C

P

A

C

4

A

C

8.3B

5

Circle one:

TxAIR, Item ID 1906

Tickets to a museum cost $6.95 for adults and $3.95 for students. One morning, the museum sold tickets for 12 adults and 34 students. What would be a reasonable estimate for the amount the museum collected, rounding to the nearest dollar?

P

A

P

A

C

B

P

A

C

C

P

A

C

D

P

A

C

A

C

3

Circle one:

TxAIR, Item ID 486

A bakery served 5 customers yesterday. Of these customers, 4 bought pies at a cost of $3 per pie. The 5th customer got a pie and ice cream deal, which costs more. The bakery made a total of $17.50 yesterday. What is the price of the pie and ice cream deal?

P

A

P

A

C

B

P

A

C

C

P

A

C

D

P

A

C

A

6

Circle one:

TxAIR, Item ID 1932

A model airplane has a length of 21 inches and a wing-span of 15.5 inches. If the real airplane has a length of 175 feet, how long is the real airplane’s wing-span?

P

A

C

A

P

A

C

B

P

A

C

C

P

A

C

D

P

A

C

8.3B

8.2B

Circle one:

TxAIR, Item ID 495

Circle one:

TxAIR, Item ID 495

The floor of a moving truck is 5 feet off the ground. If the ramp used to unload furniture from the truck is 15 feet long, then how far is the truck from the end of the ramp, rounded to the nearest foot?

P

A

C

A

P

A

C

B

P

A

C

C

P

A

C

D

P

A

C

C

Page 20

Distractors The correct answer to each item is provided below. Use your knowledge of Procedural, Application, and Conceptual errors to create three wrong (distractor) answer choices. 8

A library is selling used books in packages of 5 books for $8.00. Which proportion can be used to find b, the number of books that can be bought for $64.00?

10

F

A long-distance telephone company charges $3.05 for the first minute and $0.75 for each additional minute to call Rome, Italy. What would be the cost of a call to Rome that lasted 8 minutes? F

$8.30

G

G

H H J J

9

5 b = 8 64

A scientist needed to measure 2.3 × 10−3 milliliters of water. Which of the following is equivalent to this amount? F G H

0.0023 mL

J 8(8.3B): 8/64=b/5,5/8=64/b, 5/8=b/72| 9(8.1D): 2.3, 0.23, 0.00023| 10(8.2B): 9.05, 25.25, 30.40

Page 21

Varying the Process Read over the items on area and perimeter (1 – 6) or on solving equations (G – M). Place each item in one of the boxes below, depending on which type of process standards were used. Apply Mathematics • Everyday experiences • Other content areas

Select Strategies

• Look for a pattern • Tell examples from non-examples

Solve Problems • Understand the problem • Make a plan • Carry it out • Look back

• Draw a picture • Make a table • Guess and check • Work backward

Use Tools • Manipulatives • Models • Technology

Make Conjectures

Communicate Ideas • Use language • Validate conclusions • Give reasons

Page 22

Tools to Know | Ways to Show (Process Standards) 8

A right triangle is shown below.

6 cm 8 cm The triangle is dilated by a scale factor of 2.5 to create a new triangle. What is the perimeter of the new triangle? A

120 cm

B

24 cm

C

60 cm

D

150 cm

Process

Questions

Seeing Math in everyday situations (or, analyzing information from a problem)

How do you help students get started? How do you help them analyze and organize the information in the problem?

6.11A | 7.13A | 8.14A New: A.1A | G.1A | 2A.1A

Using problem-solving models and strategies 6.11B-C | 7.13B-C | 8.14B-C New: A.1B-C | G.1B-C | 2A.1B-C

Communicating mathematical ideas 6.12A | 7.14A | 8.15A New: A.1D-G | G.1D-G | 2A.1D-G

Coding: 8.6A and 8.14C Source: TEA (Released STAAR items)

My Strategies

What problem solving strategies would you encourage students to use?

What is your expectation for student responses if you asked them to “show your work” (or, “show what you know”)?

Page 23

Name: _______________________ From 2003 TAKS Math (Exit Level)

18 Olivero is choosing between two brands of AAA batteries for his graphing calculator. A package of three Brand M batteries costs $5.50, and a package of three Brand P batteries costs $3.85. What percent of the cost of Brand M batteries did Olivero save by buying a package of Brand P batteries? F 17% G 30% H 43% J 70%

5.50 − 3.85

Fill in the text bubbles with phrases from the word bank below. (Some choices are not used.) From 2003 TAKS Math (8th Grade)

Bobby saved $32 when he purchased a jacket at a clearance sale. If the sale price was 40% off the regular price, what was the regular price of the jacket? A $48 B $72 C $80 D $128

32 40 = x 100

1.65

1.65 x = 5.50 100

40 x = 3,200 x = 80 80 − 32 48

5.5 x = 165 x = 30

•Percent that was saved

•Rate of the discount

•Fraction that was saved

•Amount of the discount

•Amount that was saved

•Number of jackets purchased

•Cost of Brand M batteries

•Original price of the jacket

•Cost of Brand P batteries

•Sale price of the jacket Page 24

Name: _______________________ From 2003 TAKS Math (9th Grade)

A store sells milk in two different containers. The first container is a rectangular prism that has a height of 8 inches and a square base with a side length of 2 inches. The other container is a cylinder with a radius of 1.75 inches and a height of 8 inches. Which best describes the relationship between the two containers? A The prism has the greater volume. B The cylinder has the greater volume. C The volumes are equivalent. D The volumes cannot be determined.

Fill in the text bubbles with phrases from the word bank below. (Some choices are not used.)

•Base of the Prism

•Radius of circular Base

•Base of the Cylinder

•Circumference of circular Base

•Area of a circle

•Height of the Prism

•Area of rectangle

•Height of the Cylinder

•Side length of square Base

•Volume of the Prism

•Perimeter of square Base

•Volume of the Cylinder Page 25

Chickens and Cows A Poem: At Farmer Brown’s house Are just chickens and cows That he uses for milk and for eggs. Ten animals in all, As the Farmer recalls, But the group has just 28 legs.

How many chickens does Farmer Brown have? How many cows?

Lines Complete the tables for each linear function (A and B). Then sketch their graphs on the same grid provided. A) y = − x + 10

B) y = −

x

x

0

y

1 2

x+7

10

y

9 8

0

7

1

1

2

2

3

3

4

4

5

5

6 5 4 3 2 1 −1

0

1

2

3

4

5

6

7

8

9

10

−1

At what point would lines A and B intersect?

Page 26

Rigor/Relevance Framework A tool for analyzing the complexity of an academic task

KNOWLEDGE & SKILLS (Rigor)

Source: International Center for Leadership in Education (www.leadered.com)

APPLICATION (Relevance)

A

B

C

Acquisition

Application

Assimilation

Adaptation

Students extend and refine their acquired knowledge to be able to use that knowledge automatically and routinely to analyze and solve problems and create solutions.

Students have the competence to think in complex ways and apply their knowledge and skills. Even when confronted by perplexing unknowns, students are able to use extensive knowledge and skills to create solutions and take action that further develops their skills and knowledge.

Students gather and store bits of knowledge and information. Students are primarily expected to remember or understand this knowledge.

Students use acquired knowledge to solve problems, design solutions, and complete work. The highest level of application is to apply knowledge to new and unpredictable situations.

D

Page 27

Depth of Knowledge (DOK) Levels

Level One Activities • Recall elements and details of story structure, such as sequence of events, character, plot and setting. • Conduct basic mathematical calculations. • Label locations on a map. • Represent in words or diagrams a scientific concept or relationship. • Perform routine procedures like measuring length or using punctuation marks correctly. • Describe the features of a place or people.

Level Two Activities • Identify and summarize the major events in a narrative. • Use context cues to identify the meaning of unfamiliar words. • Solve routine multiple-step problems. • Describe the cause/effect of a particular event. • Identify patterns in events or behavior. • Formulate a routine problem given data and conditions. • Organize, represent and interpret data.

Level Three Activities • Support ideas with details and examples. • Use voice appropriate to the purpose and audience. • Identify research questions and design investigations for a scientific problem. • Develop a scientific model for a complex situation. • Determine the author’s purpose and describe how it affects the interpretation of a reading selection. • Apply a concept in other contexts.

Level Four Activities • Conduct a project that requires specifying a problem, designing and conducting an experiment, analyzing its data, and reporting results/solutions. • Apply mathematical model to illuminate a problem or situation. • Analyze and synthesize information from multiple sources. • Design a mathematical model to inform and solve a practical or abstract situation.

Webb, Norman L. and others. “Web Alignment Tool” 24 July 2005. Wisconsin Center of Educational Research. University of Wisconsin-Madison. 2 Feb. 2006. < http://www.wcer.wisc.edu/WAT/index.aspx >

Page 28

Leveling the Depth of Knowledge A tool for analyzing the complexity of an academic task Adapted for Secondary Mathematics

Is there more than one way to solve the question/task?

NO

Does the question/ task have more than one correct answer?

NO

Does the question/ task have more than one correct answer?

YES YES

NO

LEVEL 1

LEVEL 2

Recall facts, information, or procedures

Use information or conceptual knowledge, two or more steps, etc.

Easy Low Rigor

← Level

YES

NO

YES

LEVEL 3

LEVEL 4

Reason, develop a plan or a complex sequence of steps

Investigate, take time to process multiple aspects and conditions

Medium Moderate Rigor

Sample Task

Does the question/ task require extended thinking?

Hard High Rigor

Flowchart

Description



1

If x = 5, what is the value of 3x – 4 ?

NO/NO

One method, one answer

2

List pairs of numbers whose product is 24.

NO/YES

One method, many answers

YES/NO

Many methods, one answer

YES/YES/NO

Many methods, many answers

YES/YES/YES

Many methods, many answers, extended thinking.

2 3 4

Solve the system of equations y = 3x – 4 and 4x + 2y = 26. Create a system of equations that has as its solution an ordered pair for a point in Quadrant III. Which cell phone plan offers the best deal? Why?

Page 29

Assessment Items: What’s the Rigor? 8th Grade Math 1

Sam is cutting snowflakes out of paper to use for holiday decorations. He can cut out 5 snowflakes in 8 minutes. At this rate, about how many snowflakes could Sam cut out in 1 hour? A B C D

2

Algebra I 3

15 37 63 96

Freddy carries out groceries at a local market. On Saturdays, he carries out 12 loads of groceries each hour. If Freddy works a 6-hour shift on Saturday, which equation can he use to determine L, the number of loads of groceries he will carry out? A

) L = 12( 60 6

B

L = 12(6)

C

6 ) L = 12( 60

D

L = 12 ÷ 6

4

If the equation y = 2x + 5 is changed to y = 2x – 5, what effect will this change have on the graph of the equation? A

The graph will decrease from left to right (instead of going up).

B

The graph will be reflected over the x-axis.

C

The graph will be translated 10 units down.

D

The graph will not be as steep

Which table best describes the function y = −4x + 2? A

B

x

y

C

x

y

1

−6

1

−2

2

−10

2

−4

3

−14

3

−6

x

y

x

y

1

−2

1

6

2

−6

2

10

3

−10

3

14

D

Page 30

Increasing Item Rigor re-write the lower-level “Acquisition” item with more rigor. Use the Rigor/Relevance grid as a tool to re

Create a comparison →

New Item C

Create an Application → Original Item A

New Item B

The figure above shows a triangular prism. How many faces does the triangular prism have? A 4 B 5 C 6 D 9

Page 31

8th Grade

Increasing Item Rigor

You Try!

Use the Rigor/Relevance grid as a tool to re-write the lower-level “Acquisition” item with more rigor.

Create a comparison →

New Item C

Create an Application → Original Item A

New Item B

1 5

n Term

2 8

3 11

4 14

5 17

In the sequence above, n represents the number of the term in the sequence. Which number th would be the 8 term in the sequence? A B C D

26 20 8 3

STAAR Vocabulary Words extracted directly from the standard and/or associated with the instruction of the content within the standard.

(8.1)

The student understands that different forms of numbers are appropriate for different situations. The student is expected to







































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"









#









$

%

(A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals

(8.2)

Improper fractions; Standard form; Negative; Positive; Integer; No-negative; Comparison terms, Greatest to least, Fastest to slowest; Rational number

The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to







































!



















"









#









$

%

(B) use appropriate operations to solve problems involving rational numbers in problem situations (8.3)

Sum, Difference, Total, Change, Product, Dividend, Divisor, Quotient, Factor

The student identiÞes proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to

&













#







'











#

(





#









'

$











)



(





*





$

%

(B) estimate and Þnd solutions to application problems involving percents and other proportional relationships such as similarity and rates (8.4)

The student makes connections among various representations of a numerical relationship. The student is expected to

&













#







'











#

(





#









'

$











)



(





*





$

%

(A) generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description) (8.5)

Variable, Algebraic expression, Evaluate, Simplify

The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to

&













#







'











#

(





#









'

$











)



(





*





$

%

(A) predict, Þnd, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations (8.6)

Unit cost, Proportional, Non-proportional, Rate, Commission, Discount

+













,





#











'







#









$

%

Reasonable, Predict

The student uses transformational geometry to develop spatial sense. The

student is expected to (A) generate similar Þgures using dilations including enlargements and reductions (8.8)

-





#















Similar, Dilation, Enlargement, Reduction, Scale factor, Prime notation

The student uses procedures to determine measures of three-dimensional Þgures. The student is

%

expected to (C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume (8.9)

-





#















The student uses indirect measurement to solve problems. The student is expected to

%

(A) use the Pythagorean Theorem to solve real-life problems

Ʃ

Prism, Base, Volume, Cubic units, Cylinder, Base area, Lateral surface area, Total surface area

Hypotenuse, Side, Leg, Base, Pythagorean Theorem, Right angle, Square, Square root

.











































/

0

1

2

3





























8th Grade Math  TEKS Tree

8.2B •

Order

Rational numbers

Integers Percents Fractions Decimals

Use

Operations

Solve

Problems

Rational numbers

Estimate

Problem solutions

Percents Proportions

Problem solutions

Percents Proportions

Representations

Table Graph Equation Verbal description

8.9B •

8.11A •

8.3B• Find

8.4A •

8.5A •

8.6A •

Generate

Predict

Problem solutions

Tables Graphs Algebraic equations

Find

Problem solutions

Tables Graphs Algebraic equations

Justify

Problem solutions

Tables Graphs Algebraic equations

Generate

Similar figures

Dilations

Estimate

Measurements

Use

Formulas

Solve

Problems

8.8C •

Page 34

Lateral area Surface area Volume

Use

Pythagorean Theorem

Solve

Problems

Use

Proportional relationships

Find

Missing measurements

Find

Probabilities

8.9A •

Similar 2D figures Similar 3D figures

Independent events Dependent events

Readiness Standards

8.1A •

Compare

  Four Corners – Problem Solving   How could you turn the released test item below into a “four corners” activity? Mr. Barber wants to have the entire roof of his house replaced. A drawing of his prism-shaped house is shown below The cost of replacing the roof is $2.10 per square foot. What will be the cost for Mr. Barber to have the roof replaced? Source: TEA (Released STAAR Items, Grade 8)

How much will it cost Mr. Barber to have his roof replaced?

How much will it cost Mr. Barber to have his roof replaced?

How much will it cost Mr. Barber to have his roof replaced?

How much will it cost Mr. Barber to have his roof replaced?

Page 35

 

Four Corners – Problem Solving

Analyze the Problem

Q

What is the question? What are you asked to find?

E

Estimate the solution.

K

What do you already know?

A

What additional information might help you solve the problem?

The solution is probably between _____ and _____. (Maybe close to ______.)

Work the Problem Numbers/Information

Computation/Strategies

Page 36