IPT- Algebra1

Mathematics A L G E B R A I

INSTRUCTIONAL PLANNING TOOL

STAAR™

Acknowledgements:

Ed VaraDeputy Director of Academic Services

Jennifer DrummSenior Coordinator of Curriculum and Instruction

Clee UpchurchCoordinator of Communication and Production

Cindy HamiltonCoordinator of Teaching and Learning

Emily Gray Secondary Mathematics Education Specialist

Haley StanfieldCommunication and Production Specialist

TEKS and STAAR example questions are copyrighted by the Texas Education Agency.Copyright © by the Texas Education Agency.

The materials are copyrighted © as the property of the Education Service Center Region XIII and may not be reproduced without written permission of ESC Region XIII.

Copyright©2011 Education Service Center Region XIII3

Instructional Planning Tool User Guide

Overview This tool is designed to support teachers in instructional planning, by providing a means to process the sampling of assessed standards on the released STAAR items. Using this process, educators will:

review historical assessment data; read and solve sample STAAR items; analyze assessment prompts in order to consider the multiple steps required to generate a response; anticipate varying approaches and steps students might take; and reflect on his or her current classroom instruction.

The goal of this tool is to guide effective planning, including probing questions, and monitoring of student progress, which support student success. The Instructional Planning Tool is organized by the learning standards assessed on STAAR. Each standard is labeled as Readiness, Supporting, or Process.

As you work through the tool, keep in mind that the intent is to help think through the instructional implications of each standard. This tool provides an option to work through this thought process and can be customized to fit the needs of each campus.

Contents Each booklet contains:

all learning standards assessed on STAAR for a grade and content area; table to insert state, region, district, and grade TAKS performance data; sample STAAR items; example solution steps; reflection questions to assist educators in increasing the rigor of classroom instruction.

In addition to the booklet, this tool contains a CD with modifiable files so campuses may modify the documents to meet their needs.

READINESS STANDARDS: SUPPORTING STANDARDS: PROCESS STANDARDS: are essential for success in the

current grade or course; are important for preparedness for

the next grade or course; support college and career

readiness; necessitate in‐depth instruction; address broad and deep ideas.

may be emphasized in a subsequent year (although introduced in the current grade or course);

may be emphasized in a previous year (although introduced in the current grade or course);

play a role in preparing students for the next grade or course but not a central role;

address more narrowly defined ideas.

will be assessed in context, not in isolation in the content areas of Social Studies, Science, and Math;

will allow for a more integrated and authentic assessment.

Copyright©2011 Education Service Center Region XIII 4

Instructional Planning Tool – COMPLETED SAMPLE Algebra I Math

Copyright©2011 Education Service Center Region XIII

Read: Student Expectation (SE): Highlight the verb(s) and concept(s).

A.1A: The student is expected to describe independent and dependent quantities in functional relationships. [Supporting Standard; Reporting Category 1]

Read:

Think/Analyze:

State* Region* District* Grade* 70% 69% 71% 73% *Reminder: Use previous year’s spring administration data.

What is the question?

What is the relationship between tax rate and price? Which variable is independent and which is dependent?

What part of the standard is being assessed? Describe dependent quantity from a relationship presented verbally.

How else might this SE be assessed? Student may be expected to describe the independent quantity. Also, the functional relationship could be presented in another representation, such as a table, graph, or equation. SAMPLE



Apply: Possible Solution Steps: Recognize key phrase “Sales tax on an item is a function of its price.” This means that the tax charged on an item depends on its price, therefore the amount of tax is the dependent quantity Instructional Considerations: What prior knowledge is being built upon? In grades 6, 7, and 8, students learned how a change in one quantity can cause as change in another quantity, and they explore this change through multiple representations. In middle school and high school science, students learn about independent and dependent quantities. How do I currently teach this SE concept/content?

Currently, I use…

How do I need to adjust my instruction based on this analysis? I need to use a variety of ways to describe dependency (e.g., “is a function of”, “depends on”, etc…). I need to present functional relationships using multiple representations. What formative assessment will I use to be sure it’s working? Have students highlight the independent quantity in one color and the dependent quantity in another color. Ask students to write examples of functional relationships from their life and identify the independent and dependent quantities. What are some probing questions to use with students?

How does the phrase “Sales tax is a function of price” help you identify the dependent quantity? What might be another way to say the same thing?

What is a situation from your life that has an independent and dependent quantity? If an item costs x dollars, how would you calculate its total cost including tax?

Extension‐Write another question on a separate sheet of paper that addresses a different part

(different content) of the standard.

Correct Answer

C

SAMPLE


Instructional Planning Tool Algebra I Math




Read:

Think/Analyze:

State* Region* District* Grade* *Reminder: Use previous year’s spring administration data.


What part of the standard is being assessed?

How else might this SE be assessed?



Apply: Possible Solution Steps:

Instructional Considerations: What prior knowledge is being built upon?

How do I currently teach this SE concept/content?

How do I need to adjust my instruction based on this analysis?

What formative assessment will I use to be sure it’s working?

What are some probing questions to use with students?

Extension‐Write another question on a separate sheet of paper that addresses a different part (different content) of the standard.

Correct Answer




Read: Student Expectation (SE): Highlight the verb(s) and concept(s)..

A.1B: The student is expected to gather and record data and use data sets to determine functional relationships between quantities. [Supporting Standard; Reporting Category 1]

Read:

Think/Analyze:














Correct Answer





A.1E: The student is expected to interpret and make decisions, predictions and critical judgments from functional relationships. [Readiness Standard; Reporting Category 1]

Read:

Think/Analyze:














Correct Answer





A.2B: The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. [Readiness Standard; Reporting Category 2]

Read:

Think/Analyze:














Correct Answer





A.4A: The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations and factor as necessary in problem situations. [Readiness Standard; Reporting Category 2]

Read:

Think/Analyze:














Correct Answer





A.5C: The student is expected to use, translate and make connections among algebraic, tabular, graphical or verbal descriptions of linear functions. [Readiness Standard; Reporting Category 3]

Read:

Think/Analyze:














Correct Answer





A.6A: The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables and algebraic representations. [Supporting Standard; Reporting Category 3]

Read:

Think/Analyze:














Correct Answer




Read: Student Expectation (SE): Highlight the verbs and concepts.

A.6F: The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations. [Readiness Standard; Reporting Category 3]

Read:

Think/Analyze:














Correct Answer





A.8A: The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems. [Supporting Standard; Reporting Category 4]

Read:

Think/Analyze:















Correct Answer





A.8B: The student is expected to solve systems of linear equations using concrete models, graphs, tables and algebraic methods. [Readiness Standard; Reporting Category 4]

Read:

Think/Analyze:














Correct Answer





A.9D: The student is expected to analyze graphs of quadratic functions and draw conclusions. [Readiness Standard; Reporting Category 5]

Read:

Think/Analyze:















Correct Answer





A.10A: The student is expected to solve quadratic equations using concrete models, tables, graphs and algebraic methods. [Readiness Standard; Reporting Category 5]

Read:

Think/Analyze:














Correct Answer




Read: Student Expectation (SE): Highlight the verbs and concepts.

A.11C: The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs or algebraic methods. [Supporting Standard; Reporting Category 5]

Read:

Think/Analyze:














Correct Answer




Algebra I Solution Steps Recognize key phrase “Sales tax on an item is a function of its price.” This means that the tax charged on an item depends on its price, therefore the amount of tax is the dependent quantity.

1. Recall that for a relation to be a function each input much have exactly one possible output.

2. Analyze each of the given relations. This relation is NOT a function, since 0 as an input gives more than one output. This relation is a function. This relation is a function. This relation is NOT a function, since 1 as an input gives more than one output.

3. Therefore the correct answer choice is C, since we have determined that only relations II and III are functions.

1. Analyze the meaning of each component of the function given. c=0.40(m-500)+39.99

2. Based on this analysis, we see that B, C, and D are incorrect, and only A represents a statement that appropriately describes this function.

Recall that domain refers to possible values for the independent variable, x. From the graph, we can see that the correct answer is A. Notice that answer choice C represents the numerical values that comprise the range (although it should be written as 0≤y≤4). Substitute x=-3 for x, and then solve the resulting equation for c.

(-3)^2-(-3)+c=0 9+3+c=0 12+c=0 c=-12

1. By looking at the equation that is given, we see that the slope of this line is �2 and the

y-intercept (and therefore one of the points on the graph) is (0, �7). 2. To determine additional points, input the equation into a calculator and look at the table

of values, or substitute the given x-values into the equation to determine if they give the corresponding y-values.

Fee for 1st 500 minutes

Total charge

Cost per minute after 500

# of minutes past 500

A.1A (Question 1) pg. 6

A.1B (Question 2) pg. 8

A.1E (Question 3) pg. 10



A.5C (Question 6) pg. 16



3. Through this analysis, we see that A, B, and C all represent correct descriptions of the graph. Only choice D, with the incorrect point (3, �1) does not describe the given function. (3, �13) is a point on the graph of this function, not (3, �1).

1. Find the slope formula from the reference materials. m=(y_2-y_1)/(x_2-x_1 )

2. Substitute the points given and simplify to determine the slope. m=(4k-k)/(3k-2k)=3k/k=3

Realize that the change from the old equation to the new was an increase in the y-intercept, or starting value, by $10. This change will result in the overall amount increasing by $10, and will not impact the hourly charge. Therefore, the answer is A.

1. Draw the two figures, and recall that perimeter is the sum of the lengths of all the sides of a figure.

2. Now that the perimeters of each square have been determined, translate the two sentences into symbolic form. Note that choice B (the correct response) is the only one with the two perimeters expressed correctly.

Recognize that the solution to this system will be represented by the one point that is contained in both tables. This point, (5, 11), is the correct answer choice. Carefully read each answer choice and determine which are true. Choices A, B, and C are all true statements. Choice D is false because the actual line of symmetry is the line x=-1, not the y-axis.

1. Draw in the horizontal line y=8. 2. Notice that this line appears to intersect the given function at x=-3 and x=7. Select the

positive value, since this is the one requested. Recognize that the percent change each year is (1-0.015), therefore the correct answer must be choice A. Notice that choices C and D both represent an increase in population instead of a decrease, and choice B cannot correctly satisfy the value given for year 10.

� � ��

��


A.6F (Question 8) pg. 20



A.9D (Question 11) pg. 26


A.11C (Question 13) pg. 30



Notes:



Notes:


Instructional Planning Tool User Guide

Overview This tool is designed to support teachers in instructional planning, by providing a means to process the sampling of assessed standards on the released STAAR items. Using this process, educators will:

review historical assessment data; read and solve sample STAAR items; analyze assessment prompts in order to consider the multiple steps required to generate a response; anticipate varying approaches and steps students might take; and reflect on his or her current classroom instruction.

The goal of this tool is to guide effective planning, including probing questions, and monitoring of student progress, which support student success. The Instructional Planning Tool is organized by the learning standards assessed on STAAR. Each standard is labeled as Readiness, Supporting, or Process.

As you work through the tool, keep in mind that the intent is to help think through the instructional implications of each standard. This tool provides an option to work through this thought process and can be customized to fit the needs of each campus.

Contents Each booklet contains:

all learning standards assessed on STAAR for a grade and content area; table to insert state, region, district, and grade TAKS performance data; sample STAAR items; example solution steps; reflection questions to assist educators in increasing the rigor of classroom instruction.

In addition to the booklet, this tool contains a CD with modifiable files so campuses may modify the documents to meet their needs.

READINESS STANDARDS: SUPPORTING STANDARDS: PROCESS STANDARDS: are essential for success in the

current grade or course; are important for preparedness for

the next grade or course; support college and career

readiness; necessitate in‐depth instruction; address broad and deep ideas.

may be emphasized in a subsequent year (although introduced in the current grade or course);

may be emphasized in a previous year (although introduced in the current grade or course);

play a role in preparing students for the next grade or course but not a central role;

address more narrowly defined ideas.

will be assessed in context, not in isolation in the content areas of Social Studies, Science, and Math;

will allow for a more integrated and authentic assessment.


Instructional Planning Tool – COMPLETED SAMPLE Algebra I Math




Read:

Think/Analyze:

State* Region* District* Grade* 70% 69% 71% 73% *Reminder: Use previous year’s spring administration data.


What is the relationship between tax rate and price? Which variable is independent and which is dependent?

What part of the standard is being assessed? Describe dependent quantity from a relationship presented verbally.

How else might this SE be assessed? Student may be expected to describe the independent quantity. Also, the functional relationship could be presented in another representation, such as a table, graph, or equation. SAMPLE



Apply: Possible Solution Steps: Recognize key phrase “Sales tax on an item is a function of its price.” This means that the tax charged on an item depends on its price, therefore the amount of tax is the dependent quantity Instructional Considerations: What prior knowledge is being built upon? In grades 6, 7, and 8, students learned how a change in one quantity can cause as change in another quantity, and they explore this change through multiple representations. In middle school and high school science, students learn about independent and dependent quantities. How do I currently teach this SE concept/content?

Currently, I use…

How do I need to adjust my instruction based on this analysis? I need to use a variety of ways to describe dependency (e.g., “is a function of”, “depends on”, etc…). I need to present functional relationships using multiple representations. What formative assessment will I use to be sure it’s working? Have students highlight the independent quantity in one color and the dependent quantity in another color. Ask students to write examples of functional relationships from their life and identify the independent and dependent quantities. What are some probing questions to use with students?

How does the phrase “Sales tax is a function of price” help you identify the dependent quantity? What might be another way to say the same thing?

What is a situation from your life that has an independent and dependent quantity? If an item costs x dollars, how would you calculate its total cost including tax?



Correct Answer

C

SAMPLE






Read:

Think/Analyze:














Correct Answer

Documents

IPT- Algebra1