Participant Viewing Guide Math Module 6: Spotlight on ... · =2 1 $20,000 $10,000 2 2 $40,000 $20,000 2 3 $80,000 $40,000 2 4 $160,000 $80,000 2 5 $320,000 $160,000 2 ACTIVITY 22

Participant Viewing Guide

Math Module 6: Spotlight on

Formative Assessment

1

Overview .................................................................................................. 3

BEFORE VIEWING: ACTIVATE PRIOR KNOWLEDGE

KWL on Formative Assessment .................................................................. 4

DURING VIEWING: CONSIDER AND DISCUSS Identifying Formative Assessment in Instruction The Research ......................................................................................... 5

Types of Formative Assessment ............................................................. 5

Recognizing Formative Assessment ........................................................ 6

Using Formative Assessment to Inform Instruction Formative Assessment in the Instructional Loop .................................... 7

Looking at a SpringBoard Lesson ............................................................ 7

Getting Ready Pages .............................................................................. 7

Adapting the Lesson .............................................................................. 7

AFTER VIEWING: APPLY AND REFLECT

Planning for Formative Assessment ...................................................... 11

Revisiting the Research ........................................................................ 14

KWL on Formative Assessment ............................................................. 14

SpringBoard Learning Strategies ........................................................... 15

Table of Contents

2

Spotlight on Formative Assessment

Overview

This module is designed to allow you to examine the multiple formative assessment opportunities within SpringBoard, as well as how to use those opportunities to inform instruction. You will also plan a lesson that incorporates formative assessment, which will prepare students to reach the expectations of the standards.

After viewing this module, you will be able to:

recognize the types of formative assessment opportunities within SpringBoardmaterials and create lesson plans that demonstrate how to use strategies toformatively assess during instruction.

examine how formative assessment can inform instruction through examining andapplying the plan, teach, assess, and adapt model.

reflect on formative assessment opportunities within a SpringBoard activity atyour level.

3

Spotlight on Formative Assessment BEFORE VIEWING: ACTIVATE PRIOR KNOWLEDGE KWL on Formative Assessment

Use the first two columns of the KWL chart to generate thoughts on the focus

question for this module shown below. A KWL chart allows us to activate prior knowledge by identifying what we Know, determining what we Want to learn, and having us reflect on what we Learned.

Focus Question:

How can we use SpringBoard strategies to provide opportunities for formative assessment, and use the data collected to inform instruction?

FORMATIVE ASSESSMENT

What I KNOW What I WANT to Learn What I LEARNED

4


DURING VIEWING: CONSIDER AND DISCUSS Identifying Formative Assessment in Instruction: The Research

Reflecting on the Quote: Use the paraphrasing strategy to restate in your ownwords the essential information in the quote below.

"The research shows very clearly that effective programs of formative assessmentinvolve far more than the addition of a few observations and tests to an existingprogram. They require careful scrutiny of all the main components of a teachingplan. Indeed, it is clear that instruction and formative assessment are indivisible."

Black and Wiliam

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

What types of formative assessment do you currently use in your classroom?

What types of formative assessment are available in SpringBoard?

Types of Formative Assessment

5


Recognizing Formative Assessment

Watch the video clip showing how one Algebra 2 SpringBoard teacher plans for anduses strategies as she formatively assesses students during a SpringBoard lesson.Consider the question below as you watch the video. Use the note taking strategyto record your thoughts on the Video Viewing Guide below. Refer to theSpringBoard Learning Strategies document on page 15 for support.

Video Viewing Guide – Formative Assessment

Focus Question: “How does the teacher plan for and use strategies as she formatively assesses students during the SpringBoard lesson?”

6


Using Formative Assessment to Inform Instruction: Formative Assessment in the Instructional Loop

Consider the relationship between formative assessment and the instructional loop.Record your thoughts in the space below.

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

Looking at a SpringBoard Lesson

Read through Algebra 1, Lesson 22-1 on Exponential Functions in order to get anidea of the types of questions and content addressed in the lesson. Discuss yourfindings with a small group if possible, otherwise simply proceed when ready. Thelesson can be found on pages 8-9 of this Participant Guide.

Getting Ready Pages

Determine which of these questions are prerequisite skills for Lesson 22-1. Circle theitem numbers. You may wish to refer back to the lesson as you do this. Again, if youare working with others, do this with a partner and then share ideas with the largergroup. The Getting Ready page is on page 10 of this Participant Guide.

Adapting the Lesson

Consider how you might use the data from the Getting Ready to inform yourplanning of Lesson 22-1. Discuss possible adaptations for those who did well on youridentified Getting Ready prerequisite questions, as well as those who did poorly. Besure to give very specific examples. Do this either in pairs or independently, byrecording adaptations on Lesson 22-1 (pages 8-9).

7

My Notes

Protecting Your InvestmentLesson 22-1 Exponential Functions and Exponential Growth

Learning Targets: • Understand the definition of an exponential function.• Graph and analyze exponential growth functions.

SUGGESTED LEARNING STRATEGIES: Marking the Text, Create Representations, Look for a Pattern, Interactive Word Wall, Predict and Confirm, Think-Pair-Share

The National Association of Realtors estimates that, on average, the price of a house doubles every ten years. Tony’s grandparents bought a house in 1960 for $10,000. Assume that the trend identified by the National Association of Realtors applies to Tony’s grandparents’ house.

1. What was the value of Tony’s grandparents’ house in 1970 and in 1980?

2. Compute the difference in value from 1960 to 1970.

3. Compute the ratio of the 1970 value to the 1960 value.

4. Complete the table of values for the years 1960 to 2010.

House Value

YearDecades

Since 1960Value of House

Difference Between Values of Consecutive

Decades

Ratio of Values of Consecutive

Decades

1960 0 $10,000 — —

1970

1980

1990

2000

2010

5. What patterns do you recognize in the table?

The ratio of the quantity a to the quantity b is evaluated by dividing a by b (ratio of a to b a

b= ).

MATH TIP

1970: $20,000 1980: $40,000

$10,000

Answers may vary. Differences of values from decade to decade are

different; differences of values increase; ratio of values from decade to

decade is constant.

$ ,

$ ,

20 000

10 0002=

1 $20,000 $10,000 2

2 $40,000 $20,000 2

3 $80,000 $40,000 2

4 $160,000 $80,000 2

5 $320,000 $160,000 2

ACTIVITY 22

Common Core State Standards for Activity 22

HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

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ACTIVITY 22

Investigative

Activity Standards FocusIn this activity, students explore exponential functions, their application, and their graphs. They learn how different values of the constant factor and the exponent affect the shape of the graph.

Lesson 22-1

PLAN

Pacing: 1 class periodChunking the Lesson#1–3 #4–5 #6–8#9–10 #11–13 #14–17Check Your UnderstandingLesson Practice

TEACH

Bell-Ringer ActivityTell students that their new boss offers them two pay schedules:Plan 1: $300 the first day, $303 the second day, $306 the third day, adding $3 each day.Plan 2: $0.03 the first day, $0.09 the second day, $0.27 the third day, and so on, tripling the rate each day.Ask students to choose which plan they believe is better. They should include a table or graph to support their conclusions.

1–3 Marking the Text, Think-Pair-Share The doubling pattern is introduced, and these questions provide an opportunity to ensure that the context is understood. Have students highlight “price of a house doubles every ten years” and discuss its meaning.

4–5 Create Representations, Look for a Pattern, Sharing and Responding Students use the information from Items 1–3 to complete the table. Be sure that students compute the ratio correctly. While patterns identified by students for Item 5 may vary, as groups share their thoughts, encourage connections to sequences and linear versus nonlinear relationships.

Activity 22 • Exponential Functions 3258

My Notes

Exponential Functions and Exponential Growth

6. Write the house values as a sequence. Identify the sequence as arithmetic or geometric and justify your answer.

7. Using the data from the table, graph the ordered pairs (decades since 1960, house value) on the coordinate grid below.

Decades Since 1960

House Value

Valu

e of

the

Hou

se (t

hous

ands

of d

olla

rs)

5 10

50

100

150

200

250

300

8. The data comparing the number of decades since 1960 and value of the house are not linear. Explain why using the table and the graph.

9. Make use of structure. Using the information that you have regarding the house value, predict the value of the house in the year 2020. Explain how you made your prediction.

10. Tony would like to know what the value of the house was in 2005. Using the same data, predict the house value in 2005. Explain how you made your prediction.

The increase in house value for Tony’s grandparents’ house is an example of exponential growth. Exponential growth can be modeled using an exponential function.

Exponential Function A function of the form f(x) = a ⋅ bx, where x is the domain value, f(x) is the range value, a ≠ 0, b > 0, and b ≠ 1.

$10,000, $20,000, $40,000, $80,000, $160,000, $320,000, …; this is a

geometric sequence because it has a common ratio of 2.

In the table, the rate of change is not constant. Graphically, the points

do not form a line.

$640,000. Following the pattern, the house value will double from 2010

to 2020.

Answers may vary. The value of the house in 2005 was about

$240,000. Since house value in 2000 = $160,000 and house

value in 2010 = $320,000, a linear relationship would give

Value in 2005 = $ , ,320 000 160 000

2

+, or $240,000.

continuedACTIVITY 22

Common Core State Standards for Activity 22 (continued)

HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

HSF-BF.A.1b: Combine standard function types using arithmetic operations.

HSF-LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

HSF-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.

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ACTIVITY 22 Continued

6–8 Discussion Groups, Look for a Pattern, Create Representations Students should identify the sequence of house values as a geometric sequence with a common ratio of 2. This should be reinforced as they graph in Item 7. Be sure that students graph the data from the appropriate columns in the table, columns 2 and 3. Students must address the noncollinear points on the graph and the nonconstant differences in the table when identifying the data as nonlinear.

9–10 Look for a Pattern, Discussion Groups, Construct an Argument, Predict and Confirm Students should have little difficulty extending the pattern to find the value of the house in 2020. In Item 10, students may assume linearity and find the average of 2000 and 2010, an incorrect response. It is not important to correct incorrect responses here as long as students can provide some justification for their responses. Students will revisit this response in later items as they develop the idea of exponential growth.

Developing Math LanguageThis lesson contains the terms exponential function and exponential growth. Have students add the terms to their math notebooks. Encourage students to include a sample scenario with drawings to clarify the definitions. Add the terms to the Word Wall.

Differentiating Instruction

Support students having difficulty understanding exponential functions by having the students choose two integers, a and b, that are greater than 1 and less than or equal to 6. Have them use a table to show a sequence by writing a for the first term, ab for the second, and then multiplying each successive term by b again to get the next term. Have students explain their sequences and how they developed them to another student. Then have them explain why the sequence they just wrote fits the definition.

326 SpringBoard® Mathematics Algebra 1, Unit 4 • Exponents, Radicals, and Polynomials

9

Getting Ready

Write your answers on notebook paper. Show your work.

1. Find the greatest common factor of 36 and 54. 2. List all the factors of 90.3. Which of the following is equivalent to

39 ⋅ 26 + 39 ⋅ 13? A. 139 B. 134 ⋅ 14 C. 132 ⋅ 32 ⋅ 2 D. 132 ⋅ 32

4. Identify the coefficient, base, and exponent of 4x5.

5. Explain two ways to evaluate 15(90 − 3).6. Complete the following table to create a linear

relationship.

x 2 4 6 8 10

y 3 5

7. Graph the function described in the table in Item 6.

8. Use ratios to model the following: a. 7.5 b. Caleb receives 341 of the 436 votes cast for

class president. Students in Mr. Bulluck’s Class

Girls Boys

12 19

c. girls to boys d. boys to total class members

9. Tell whether each number is rational or irrational. a. 25 b. 4

3 c. 2.16 d. π

10. Calculate. a. 1

238

+ b. 512

13

−

c. 32

25

d. 58

34

÷⋅

UNIT 4

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UNIT 4Getting Ready

Use some or all of these exercises for formative evaluation of students’ readiness for Unit 4 topics.

Prerequisite Skills• Factors and greatest common factors.

(Items 1, 2) 6.NS.B.4, 4.OA.B.4• Exponential expressions. (Items 3, 4)

6.EE.A.1, 6.EE.A.2c, 6.EE.A.2b• Distributive property. (Item 5)

3.OA.B.5• Linear functions. (Item 6) 8.F.B.4• Graph linear functions. (Item 7)

HSF-IF.C.7a• Ratios. (Item 8) 6.RP.A.1• Recognize rational and irrational

numbers. (Item 9) 8.NS.A.1• Fraction operations. (Item 10)

5.NF.A.1, 5.NF.B.4, 6.NS.A.1

Answer Key1. 182. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 903. D4. The coefficient is 4. The base is x.

The exponent is 5.5. Sample explanation: One way: First

subtract 90 − 3. Then multiply the difference by 15. Another way: Multiply 15 by 90. Multiply 15 by 3. Then subtract the second product from the first.

6.

7.

4

23

5

1

–4 –2–3–5 –1 2 31 4 5–2–3

–5–4

y

x

8. a. 7510

b. 341436

c. 1. 1219

2. 1931

9. a. rationalb. rationalc. rationald. irrational

10. a. 78

b. 112

c. 35

d. 56

x 2 4 6 8 10

y 3 5 7 9 11

Getting Ready PracticeFor students who may need additional instruction on one or more of the prerequisite skills for this unit, Getting Ready practice pages are available in the eBook Teacher Resources. These practice pages include worked-out examples as well as multiple opportunities for students to apply concepts learned.

286 SpringBoard® Mathematics Algebra 1, Unit 4 • Exponents, Radicals, and Polynomials

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AFTER VIEWING: APPLY AND REFLECT Planning for Formative Assessment

Look through a lesson at your level and determine opportunities for formativeassessment. You may choose a lesson you have already planned or a new lesson. Ifyou are planning a new lesson, use the second page of the lesson planning graphicorganizer on page 13 to record your ideas. You may do this independently or inpairs. (The first page is included for your reference.)

1. Select a SpringBoard lesson.

2. Determine which strategies you will use to providecontinuous opportunities for formative assessment.

3. Are there specific debriefing questions you will ask?

4. Will you include a mini-lesson?

11

Lesson Planning Graphic Organizer

Focus:

Level: Unit:

Embedded Assessment:

Explore the Embedded Assessment

Skills Knowledge

Activity:

Essential Question(s) addressed by this activity:

Prerequisite skills:

Embedded Assessment Skills/Knowledge Connections:

Unpacked Content and Practice/Process Standards:

12

Lesson Planning Graphic Organizer Continued….

Lesson:

Key Idea(s): Introduction/Transition:

Grouper: Group Roles:

Chunking: Key Strategies: Debriefing Questions/Formative Checks:

Differentiation: Early finishers:

13


Revisiting the Research

Reflecting on the Quote: Reread this quote from the beginning of the module andconsider how this module has informed your thinking on formative assessment.Record your thoughts below.

"The research shows very clearly that effective programs of formative assessmentinvolve far more than the addition of a few observations and tests to an existingprogram. They require careful scrutiny of all the main components of a teachingplan. Indeed, it is clear that instruction and formative assessment are indivisible."

Black and Wiliam

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

KWL on Formative Assessment

Consider these questions as you reflect on your new learning independently or in small groups. Then, return to your KWL chart on page 4 of this guide, and complete the last column.

How has your understanding of formative assessment changed?

Why is formative assessment important?

How will you use formative assessment to inform instruction in your classroom?

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SpringBoard Learning StrategiesREADING STRATEGIES

STRATEGY DEFINITION PURPOSE

Activating Prior Knowledge

Recalling what is known about a concept and using that information to make a connection to a new concept

Helps students establish connections between what they already know and how that knowledge is related to new learning

Chunking the Activity Grouping a set of items/questions for specific purposes

Provides an opportunity to relate concepts and assess student understanding before moving on to a new concept or grouping

Close Reading Reading text word for word, sentence by sentence, and line by line to make a detailed analysis of meaning

Assists in developing a comprehensive understanding of the text

Graphic Organizer Arranging information into maps and charts Builds comprehension and facilitates discussion by representing information in visual form

Interactive Word Wall Visually displaying vocabulary words to serve as a classroom reference of words and groups of words as they are introduced, used, and mastered over the course of a year

Provides a visual reference for new concepts, aids understanding for reading and writing, and builds word knowledge and awareness

KWL Chart (Know, Want to Know, Learn)

Activating prior knowledge by identifying what students know, determining what they want to learn, and having them reflect on what they learned

Assists in organizing information and reflecting on learning to build content knowledge and increase comprehension

Marking the Text Highlighting, underlining, and /or annotating text to focus on key information to help understand the text or solve the problem

Helps the reader identify important information in the text and make notes about the interpretation of tasks required and concepts to apply to reach a solution

Predict and Con!rm Making conjectures about what results will develop in an activity; confirming or modifying the conjectures based on outcomes

Stimulates thinking by making, checking, and correcting predictions based on evidence from the outcome

Levels of Questions Developing literal, interpretive, and universal questions about the text while reading the text

Focuses reading, helps in gaining insight into the text by seeking answers, and prepares one for group and class discussions

Paraphrasing Restating in your own words the essential information in a text or problem description

Assists with comprehension, recall of information, and problem solving

Role Play Assuming the role of a character in a scenario

Helps interpret and visualize information in a problem

Shared Reading Reading the text aloud (usually by the teacher) as students follow along silently, or reading a text aloud by the teacher and students

Helps auditory learners do decode, interpret, and analyze challenging text

Summarizing Giving a brief statement of the main points in a text

Assists with comprehension and provides practice with identifying and restating key information

Think Aloud Talking through a difficult text or problem by describing what the text means

Helps in comprehending the text, understanding the components of a problem, and thinking about possible paths to a solution

Visualization Picturing (mentally and/or literally) what is read in the text

Increases reading comprehension and promotes active engagement with the text

Vocabulary Organizer Using a graphic organizer to keep an ongoing record of vocabulary words with definitions, pictures, notes, and connections between words

Supports a systematic process of learning vocabulary

618 SpringBoard® Mathematics with Meaning™ Algebra 1

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SpringBoard Learning StrategiesCOLLABORATIVE STRATEGIES

STRATEGY DEFINITION PURPOSE

Critique Reasoning Through collaborative discussion, respond to the arguments of others; question the use of mathematical terminology, assumptions, and conjectures to improve understanding and to justify and communicate conclusions

Helps students learn from each other as they make connections between mathematical concepts and learn to verbalize their understanding and support their arguments with reasoning and data that make sense to peers

Debrie!ng T Discussing the understanding of a concept to lead to consensus on its meaning

Helps clarify misconceptions and deepen understanding of content

Discussion Groups Working within groups to discuss content, to create problem solutions, and to explain and justify a solution

Aids understanding through the sharing of ideas, interpretation of concepts, and analysis of problem scenarios

Group Presentation Presenting information as a collaborative group

Allows opportunities to present collaborative solutions and to share responsibility for delivering information to an audience

Jigsaw Reading different texts or passages, students become “experts” and then move to a new group to share their information; after sharing, students go back to the original group to share new knowledge

Provides opportunities to summarize and present information to others in a way that facilitates understanding of a text or passage (or multiple texts or passages) without having each student read all texts

Sharing and Responding

Communicating with another person or a small group of peers who respond to a piece of writing or proposed problem solution

Gives students the opportunity to discuss their work with peers, to make suggestions for improvement to the work of others, and/or to receive appropriate and relevant feedback on their own work

Think-Pair-Share Thinking through a problem alone, pairing with a partner to share ideas, and concluding by sharing results with the class

Enables the development of initial ideas that are then tested with a partner in preparation for revising ideas and sharing them with a larger group

WRITING STRATEGIES

Drafting Writing a text in an initial form Assists in getting first thoughts in written form and ready for revising and refining

Note Taking Creating a record of information while reading a text or listening to a speaker

Helps in organizing ideas and processing information

Prewriting Brainstorming, either alone or in groups, and refining thoughts and organizing ideas prior to writing

Provides a tool for beginning the writing process and determining the focus of the writing

Quickwrite Writing for a short, specific amount of time about a designated topic

Helps generate ideas in a short time

RAFT (Role of Writer, Audience, Format, and Topic)

Writing a text by consciously choosing a viewpoint (role of the writer), identifying an audience, choosing a format for the writing, and choosing a topic

Provides a framework for communicating in writing and helps focus the writer’s ideas for specific points of communication

Self Revision / Peer Revision

Working alone or with a partner to examine a piece of writing for accuracy and clarity

Provides an opportunity to review work and to edit it for clarity of the ideas presented as well as accuracy of grammar, punctuation, and spelling

Resources 619Resources 619


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Construct an Argument

Use mathematical reasoning to present assumptions about mathematical situations, support conjectures with mathematically relevant and accurate data, and provide a logical progression of ideas leading to a conclusion that makes sense

Helps develop the process of evaluating mathematical information, developing reasoning skills, and enhancing communication skills in supporting conjectures and conclusions

Create a Plan Analyzing the tasks in a problem and creating a process for completing the tasks by finding information needed for the tasks, interpreting data, choosing how to solve a problem, communicating the results, and verifying accuracy

Assists in breaking tasks into smaller parts and identifying the steps needed to complete the entire task

Create Representations

Creating pictures, tables, graphs, lists, equations, models, and /or verbal expressions to interpret text or data

Helps organize information using multiple ways to present data and to answer a question or show a problem solution

Guess and Check Guessing the solution to a problem, and then checking that the guess fits the information in the problem and is an accurate solution

Allows exploration of different ways to solve a problem; guess and check may be used when other strategies for solving are not obvious

Identify a Subtask Breaking a problem into smaller pieces whose outcomes lead to a solution

Helps to organize the pieces of a complex problem and reach a complete solution

Look for a Pattern Observing information or creating visual representations to find a trend

Helps to identify patterns that may be used to make predictions

Simplify the Problem Using “friendlier” numbers to solve a problem Provides insight into the problem or the strategies needed to solve the problem

Work Backward Tracing a possible answer back through the solution process to the starting point

Provides another way to check possible answers for accuracy

Use Manipulatives Using objects to examine relationships between the information given

Provides a visual representation of data that supports comprehension of information in a problem

SpringBoard Learning StrategiesPROBLEM-SOLVING STRATEGIES

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Documents

Participant Viewing Guide Math Module 6: Spotlight on ... · =2 1 $20,000 $10,000 2 2 $40,000 $20,000 2 3 $80,000 $40,000 2 4 $160,000 $80,000 2 5 $320,000 $160,000 2 ACTIVITY 22