Reaching for the StarsReaching for the StarsUsing Data Analysis and Effective Teaching StrategiesUsing Data Analysis and Effective Teaching Strategies

to improve the achievement of to improve the achievement of ALLALL students students

Prepared for the Prepared for the Loudoun County Public Schools’ Loudoun County Public Schools’

Mathematics Instructional Team MeetingMathematics Instructional Team Meetingby Daniel Mulliganby Daniel Mulligan

Simply Achieve, Inc.Simply Achieve, Inc.October 2004October 2004

We’re not in Loudoun County anymore, Toto!

GGoooodd IInnssttrruuccttiioonn(Keep it Simple…Keep it Real)(Keep it Simple…Keep it Real)

““Good instruction is good instruction, regardless Good instruction is good instruction, regardless of students’ racial, ethnic, or socioeconomic of students’ racial, ethnic, or socioeconomic

backgrounds. To a large extent, good teaching backgrounds. To a large extent, good teaching – teaching that is engaging, relevant, – teaching that is engaging, relevant,

multicultural, and that appeals to a variety of multicultural, and that appeals to a variety of modalities and learning styles – works well modalities and learning styles – works well

with ALL children.”with ALL children.”Educating Everybody’s ChildrenEducating Everybody’s Children, ASCD, 1995., ASCD, 1995.

Part IPart I

The JustificationThe Justification

Reading/Language Arts Mathematics

Percentageof Students

Passed

Percentageof StudentsNot Tested

Percentageof Students

Passed

Percentageof StudentsNot Tested

All Students 79 1 82 2

Black 66 2 70 3

White 85 1 87 1

Hispanic 69 0 75 2

Disabled 51 4 57 4

Economically Disadvantaged

64 2 72 2

Limited English Proficient

65 0 75 2

2003-2004 Annual Measurable Objectives (AMO):for reading 61%for mathematics 59%

No Child Left BehindMandates accountability for student achievement by subgroup. Mandates accountability for student achievement by subgroup.

In VirginiaIn Virginia, , the major subgroups are:the major subgroups are:

ALL studentsALL students Black studentsBlack students Hispanic studentsHispanic students White studentsWhite students

LEP studentsLEP students Students with Students with

DisabilitiesDisabilities Low-socioeconomic Low-socioeconomic

studentsstudents

This year (2004-2005), the required pass rate for each subgroup in reading and math increases to

70%.

““A positive attitude may not A positive attitude may not solve all of your problems, but it solve all of your problems, but it will annoy enough people to will annoy enough people to make it worth it.”make it worth it.”

--Maya AngelouMaya Angelou

Part IIPart II

The Research-Based StrategyThe Research-Based Strategy

Opportunity to LearnOpportunity to Learn

Three types of math curricula were identified by SIMS:Three types of math curricula were identified by SIMS:The Intended CurriculumThe Intended Curriculum: content specified by the state, : content specified by the state,

division, or school at a particular grade level.division, or school at a particular grade level.The Implemented CurriculumThe Implemented Curriculum: content actually : content actually

delivered by the teacher.delivered by the teacher.The Attained CurriculumThe Attained Curriculum: content actually learned by : content actually learned by

the students.the students.

Intended Curriculum

Implemented Curriculum Attained

Curriculum

Has the Has the strongeststrongest relationship with student achievement of all relationship with student achievement of all school-level factors.school-level factors.

Virginia Curriculum Framework

•Math

The WHATThe WHAT

7.6 The student will use proportions to solve practical problems, which may include scale drawings, that contain rational numbers (whole numbers, fractions, and decimals) and percents.

UNDERSTANDING THE STANDARD(Teacher Notes)

ESSENTIAL UNDERSTANDINGSESSENTIAL KNOWLEDGE AND SKILLS

A proportion is a statement of equality between two ratios.A common property relates the numerators of the two ratios, and another common property relates the denominators of the two ratios. For example, both numerators relate to one property, such as length, while both denominators relate to another property, such as width. Alternatively, both numerators could relate to scale lengths, while both denominators relate to actual lengths.The dimensions of a scale model are proportional to the corresponding dimensions of the object (e.g., a blueprint of a house floor plan is proportional to the actual dimensions of the floor).A proportion can be written as = , •a:b = c:d, or a is to b as c is to d.A proportion can be solved by finding the product of the means and the product of the extremes. For example, in the proportion a:b = c:d, a and d are the extremes and b and c are the means. If values are substituted for a, b, c, and d such as 5:12 = 10:24, then the product of extremes (5 24) is equal to the product of the means (12 10).•continued

All students shouldUnderstand that a proportion is an equation showing that two ratios are equal.Understand how to set up a proportion, given the relationship between two items.Understand that when two quantities are proportional, a change in one quantity corresponds to a predictable change in the other.Understand that proportions are useful in solving many types of problems.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations toWrite proportions that represent equivalent relationships between two sets.Solve a proportion to find a missing term.Apply proportions to solve problems that involve percents.Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and/or decimals no less than tenths.

UNDERSTANDING THE STANDARD(Teacher Notes)

ESSENTIAL UNDERSTANDINGS

ESSENTIAL KNOWLEDGE AND SKILLS

•continuedIn a proportional situation, both quantities increase or decrease together.In a proportional situation, two quantities increase multiplicatively. Both are multiplied by the same factor.A proportion can be solved by finding equivalent fractions.There is a distinction between a proportion and the idea of equivalent fractions. Equivalent fractions are symbols for the same quantity or amount and they represent the same rational number in different forms.A rate is a special ratio that always has a denominator of 1. Examples of rates include miles/hour and revolutions/minute. A rate compares measures of different types.A percent is a special ratio in which the denominator is 100.Proportions are used in every-day contexts, such as speed, recipe conversions, scale drawings, map reading, reducing and enlarging, comparison shopping, and monetary conversions.

The HOWThe HOW

Classroom Instruction That Works Research-

based Strategies

Give One …Give One … Get One …Get One … On the Think Pad, write On the Think Pad, write one wayone way that being a math that being a math

teacher in Loudoun County using student achievement teacher in Loudoun County using student achievement data is like an astronaut on a walk in space. Think and data is like an astronaut on a walk in space. Think and be creative.be creative.

When signaled, circulate the room to meet a colleague. When signaled, circulate the room to meet a colleague. Give him/her your answer and get their answer.Give him/her your answer and get their answer.

You need a You need a total of 2 answerstotal of 2 answers. You may not get more . You may not get more than one idea from an individual. When you have than one idea from an individual. When you have completed your task, return to your seat.completed your task, return to your seat.

You have 90 seconds!You have 90 seconds! Enjoy!Enjoy!

CategoryCategory Ave. EffectAve. Effect

Size (ES)Size (ES)PercentilPercentil

e Gaine Gain

Identify similarities & differences

1.611.61 4545

Summarizing & note taking 1.001.00 3434

Reinforcing effort & providing recognition

.80.80 2929

Homework & practice .77.77 2828

Nonlinguistic representations .75.75 2727

Cooperative learning .73.73 2727

Setting objectives & providing feedback

.61.61 2323

Generating & testing hypotheses

.61.61 2323

Questions, cues, & advance organizers

.59.59 2222

What processes can students engage in to What processes can students engage in to identify similarities and differences?identify similarities and differences?

Comparing

The process of identifying and articulating similarities and differences among items.

Classifying

The process of grouping things into definable categories on the basis of their attributes.

Creating Metapho

rs

The process of identifying and articulating the underlying theme or general pattern in information.

Creating Analogie

s

The process of identifying relationships between pairs of concepts (e.g., relationships between relationships).

When I dieWhen I dieI hope it occurs I hope it occurs during a lecture during a lecture

because the because the transition from life to transition from life to

death will death will be sobe so slight that I slight that I

will hardly will hardly notice it.notice it.

Step 1:Step 1: Estimate the Estimate the medianmedian number of number of

years in years in education of the education of the participants.participants.

Write the number on a Post-it-Note. Write the number on a Post-it-Note. Caution:Caution: Make sure the glue is on top. Make sure the glue is on top.

Bring your estimates to the:Bring your estimates to the:Estimate Median Tenure Line PlotEstimate Median Tenure Line Plot

Place your estimates on the line-plotPlace your estimates on the line-plot

Teachers must recognize that “Reading comprehension Teachers must recognize that “Reading comprehension and achievement tend to be positively related. Almost and achievement tend to be positively related. Almost

without exception instruction in vocabulary and/or without exception instruction in vocabulary and/or reading skills paid off in terms of greater achievement, reading skills paid off in terms of greater achievement, especially in the area of problem solving” especially in the area of problem solving” (Earp, 1970, p. (Earp, 1970, p.

531).531).

Reading Comprehension in the Content Area

The Food Lion Theorem

Word Sort ApplicationsWord Sort ApplicationsClassify words based on student Classify words based on student

identified attributes.identified attributes.Match linguistic and nonlinguistic pairs Match linguistic and nonlinguistic pairs

that represent the same concept.that represent the same concept.Use a ‘Concentration Game’ approach to Use a ‘Concentration Game’ approach to

identifying similarities.identifying similarities.Create sentences that contain an Create sentences that contain an

identified word from the sort.identified word from the sort.Provide students with the previous years Provide students with the previous years

cards to check for prior knowledge.cards to check for prior knowledge.

Part IIPart II

The Focus The Focus

“People without information cannot act. People with information cannot help but

act.”~Ken Blanchard

SPBQ Key Questions SPBQ Key Questions Use the highlighters and your school’s SPBQ:Use the highlighters and your school’s SPBQ:

Highlight in red any objective with a pass rate Highlight in red any objective with a pass rate < 60%< 60% Highlight in yellow any objective with a pass rate Highlight in yellow any objective with a pass rate

Which Reporting Category(ies) reflect a lower level of student Which Reporting Category(ies) reflect a lower level of student achievement?achievement? When is this content taught (if at all) during the year? (Grade 6 – 7 – 8) When is this content taught (if at all) during the year? (Grade 6 – 7 – 8)

or (Algebra Part 1 – Part II).or (Algebra Part 1 – Part II). Does the curriculum pacing provide for time to spiral back to refresh Does the curriculum pacing provide for time to spiral back to refresh

students on these essential skills and content? students on these essential skills and content? How much time is provided for learning?How much time is provided for learning?

What level of thinking is reflected in the item description?What level of thinking is reflected in the item description? Prepare to share on the large Post-It Sheet the Reporting Prepare to share on the large Post-It Sheet the Reporting

Categories and objectives that will be your focus of Categories and objectives that will be your focus of improvement.improvement.

60 70x

Loudoun County Loudoun County - - Spring 2004 Grade 8 MATHSpring 2004 Grade 8 MATH

Core 1 – 2879 studentsCore 1 – 2879 studentsNumber/Number Sense – 8Q/60Q – 13% of testNumber/Number Sense – 8Q/60Q – 13% of test (25% of questions < 70% correct)(25% of questions < 70% correct)Identify prime numbers.Identify prime numbers. 2020Identify an irrational numberIdentify an irrational number 3939

Computation/Estimation – 7Q/60Q – 12% of testComputation/Estimation – 7Q/60Q – 12% of test (14% of questions < 70% correct)(14% of questions < 70% correct)Est. to solve multiplication prob. Involving whole #s.Est. to solve multiplication prob. Involving whole #s. 6464

Measurement/Geometry – 15Q/60Q – 25% of testMeasurement/Geometry – 15Q/60Q – 25% of test (13% of questions < 70% correct)(13% of questions < 70% correct)Identify equivalent measure of volume closest to volume in standard form.Identify equivalent measure of volume closest to volume in standard form. 5959Given lengths of 2 sides of a right triangle, find the length of the 3Given lengths of 2 sides of a right triangle, find the length of the 3 rdrd.. 6060

Probability/Statistics – 12Q/60Q – 20% of testProbability/Statistics – 12Q/60Q – 20% of test (33% of questions < 70% correct)(33% of questions < 70% correct)Determine the number of combinations possible.Determine the number of combinations possible. 6161Given a set of data, determine the probability of a simple event occurring.Given a set of data, determine the probability of a simple event occurring. 6262Identify the scatterplot that best represents a specific correlation. Identify the scatterplot that best represents a specific correlation. 6262Determine the probability for a given sample space.Determine the probability for a given sample space. 6666

Patterns/Functions/Algebra – 18Q/60Q – 30% of testPatterns/Functions/Algebra – 18Q/60Q – 30% of test (39% of questions < 70% correct)(39% of questions < 70% correct)Identify the graph of an equation.Identify the graph of an equation. 4747Identify an equation used to solve a problem.Identify an equation used to solve a problem. 5050Identify an equation equivalent to an equation.Identify an equation equivalent to an equation. 5858Identify a specific component of an equation.Identify a specific component of an equation. 5959Make a prediction based on a pattern.Make a prediction based on a pattern. 6464Identify the equation that represents a relationship presented in words.Identify the equation that represents a relationship presented in words. 6666Solve a problem using a proportion.Solve a problem using a proportion. 6969

Targeted ResourceTargeted Resourceto Improve Student Achievementto Improve Student Achievement

Virginia Department of EducationVirginia Department of Education

Enhanced Scope and Sequence DocumentsEnhanced Scope and Sequence Documents Organizing TopicsOrganizing Topics SOLSOL Essential Knowledge and SkillsEssential Knowledge and Skills Suggested Lesson BankSuggested Lesson Bank Released SOL test ItemsReleased SOL test Items

Sample: page 94Sample: page 94

Loudoun County Loudoun County - - Spring 2004 Algebra ISpring 2004 Algebra I

Core 1 – 2704 studentsCore 1 – 2704 studentsExpressions/Operations – 12Q/50Q – 24% of testExpressions/Operations – 12Q/50Q – 24% of test (42% of questions < 70% correct)(42% of questions < 70% correct)Divide a polynomial by a monomial.Divide a polynomial by a monomial. 4444Calculate a side of a square given its area.Calculate a side of a square given its area. 5353Factor a quadratic trinomial.Factor a quadratic trinomial. 5858Determine difference between two numbers in scientific notation.Determine difference between two numbers in scientific notation. 5858Evaluate a formula for given values of its variables.Evaluate a formula for given values of its variables. 6262

Relations/Functions – 12Q/50Q – 24% of testRelations/Functions – 12Q/50Q – 24% of test (42% of questions < 70% (42% of questions < 70% correct)correct)

Given the graph of a linear function, determine its range.Given the graph of a linear function, determine its range. 4040Identify a mapping diagram that represents a function.Identify a mapping diagram that represents a function. 5959Given its graph, identify the value of a function for a given domain element.Given its graph, identify the value of a function for a given domain element. 6666Determine range of a function given its domain.Determine range of a function given its domain. 6767Identify an equation that represents a direct variation for a given constant.Identify an equation that represents a direct variation for a given constant. 68 68

Equations/Inequalities – 18Q/50Q – 36% of testEquations/Inequalities – 18Q/50Q – 36% of test (17% of questions < 70% (17% of questions < 70% correct)correct)

Determine an equation for a line, given its slope and a point on a line.Determine an equation for a line, given its slope and a point on a line. 4747Recognize operation for which associative property is not valid.Recognize operation for which associative property is not valid. 6363Identify an equation written in slope-intercept form.Identify an equation written in slope-intercept form. 6767

Statistics – 8Q/50Q – 16% of testStatistics – 8Q/50Q – 16% of test (50% of questions < 70% (50% of questions < 70% correct)correct)

Given a scatterplot, identify equation for line of best fit.Given a scatterplot, identify equation for line of best fit. 5353Identify a matrix describing a given situation.Identify a matrix describing a given situation. 5555Determine the range for a set of data.Determine the range for a set of data. 6464Solve problems involving measures of central tendency.Solve problems involving measures of central tendency. 6666

Creating a Climate Creating a Climate for Learningfor Learning

For students to succeed, they need to believe that they:•can learn;

•are learning information and skills that is useful, relevant, and meaningful for them;

•are valued in the classroom;

•responsible for their learning; and

•responsible for their own behavior.

“Teachers’ beliefs in and about human potential and in the ability of all children to learn and achieve are critical.”

Caine & Caine, 1997

Loudoun County Loudoun County - - Spring 2004 GeometrySpring 2004 Geometry

Core 1 – 2574 studentsCore 1 – 2574 students

Lines/Angles – 11Q/45Q – 25% of testLines/Angles – 11Q/45Q – 25% of test (9% of questions < 70% correct)(9% of questions < 70% correct)Identify a construction from given arcs.Identify a construction from given arcs. 5858

Triangles/Logic – 12Q/45Q – 27% of testTriangles/Logic – 12Q/45Q – 27% of test (25% of questions < 70% correct)(25% of questions < 70% correct)Write a proportion describing the relationship of similar triangles.Write a proportion describing the relationship of similar triangles. 4747

Use relationships of a 60-30 triangle to solve a problem.Use relationships of a 60-30 triangle to solve a problem. 6262

Determine which theorem will prove two triangles congruent.Determine which theorem will prove two triangles congruent. 6464

Polygons/Circles – 10Q/45Q – 22% of testPolygons/Circles – 10Q/45Q – 22% of test (50% of questions < 70% correct)(50% of questions < 70% correct)Determine measure of an arc in a circle.Determine measure of an arc in a circle. 6060

Use properties of regular polygon to solve a problem.Use properties of regular polygon to solve a problem. 6060

Determine measure of segments of a secant.Determine measure of segments of a secant. 6262

Use properties of a parallelogram to solve a problem.Use properties of a parallelogram to solve a problem. 6464

Determine measure of an angle in a regular polygon.Determine measure of an angle in a regular polygon. 6969

Three-Dimensional Figures – 6Q/45Q – 13% of testThree-Dimensional Figures – 6Q/45Q – 13% of test (50% of questions < 70% correct)(50% of questions < 70% correct)Solve a problem involving volume of a pyramid.Solve a problem involving volume of a pyramid. 5757

Use similar triangles to solve a problem.Use similar triangles to solve a problem. 6161

Solve a problem involving surface area of a cone.Solve a problem involving surface area of a cone. 6464

Coordinate Rel./Transformations – 6Q/45Q – 13% of test (33% of questions < 70% correct)Coordinate Rel./Transformations – 6Q/45Q – 13% of test (33% of questions < 70% correct)Use distance formula to solve a problem.Use distance formula to solve a problem. 6060

Identify the transformation of figures shown.Identify the transformation of figures shown. 6868

Loudoun County Loudoun County - - Spring 2004 Algebra IISpring 2004 Algebra II

Core 1 – 1610 studentsCore 1 – 1610 students

Expressions/Operations – 10Q/50Q – 20% of testExpressions/Operations – 10Q/50Q – 20% of test (0% of questions < 70% correct)(0% of questions < 70% correct)n/an/a

Relations/Functions – 16Q/50Q – 32% of testRelations/Functions – 16Q/50Q – 32% of test (19% of questions < 70% (19% of questions < 70% correct)correct)

Evaluate a series given in Sigma notation.Evaluate a series given in Sigma notation. 3939

Use a line of best fit for a set of data to solve a problem.Use a line of best fit for a set of data to solve a problem. 6262

Determine equation that matches given data.Determine equation that matches given data. 6868

Equations/Inequalities – 10Q/50Q – 20% of testEquations/Inequalities – 10Q/50Q – 20% of test (0% of questions < 70% correct)(0% of questions < 70% correct)n/an/a

Analytical Geometry – 6Q/50Q – 12% of testAnalytical Geometry – 6Q/50Q – 12% of test (33% of questions < 70% (33% of questions < 70% correct)correct)

Given the equation for a conic section, describe its graph.Given the equation for a conic section, describe its graph. 5050

Given the x-intercepts of a polynomial function, identify its factors.Given the x-intercepts of a polynomial function, identify its factors. 6969

Systems of Equations/Inequalities – 8Q/50Q – 16% of test (50% of questions < 70% correct)Systems of Equations/Inequalities – 8Q/50Q – 16% of test (50% of questions < 70% correct)Given its graph, solve a system of equations.Given its graph, solve a system of equations. 6565

Identify the graphical solution to a system of inequalities.Identify the graphical solution to a system of inequalities. 6565

Match a matrix equation to a given system of equations.Match a matrix equation to a given system of equations. 6666

Write a matrix operation to describe a correct matrix combination.Write a matrix operation to describe a correct matrix combination. 67 67

““If an educator keeps using If an educator keeps using the same strategies over and the same strategies over and over and the student keeps over and the student keeps failing, failing,

who really is the slow who really is the slow learner?”learner?”

SPBQ Key Questions SPBQ Key Questions Use the highlighters and your school’s SPBQ:Use the highlighters and your school’s SPBQ:

Highlight in red any objective with a pass rate Highlight in red any objective with a pass rate < 60%< 60% Highlight in yellow any objective with a pass rate Highlight in yellow any objective with a pass rate

Which Reporting Category(ies) reflect a lower level of student Which Reporting Category(ies) reflect a lower level of student achievement?achievement? When is this content taught (if at all) during the year? (Grade 6 – 7 – 8) When is this content taught (if at all) during the year? (Grade 6 – 7 – 8)

or (Algebra Part 1 – Part II).or (Algebra Part 1 – Part II). Does the curriculum pacing provide for time to spiral back to refresh Does the curriculum pacing provide for time to spiral back to refresh

students on these essential skills and content? students on these essential skills and content? How much time is provided for learning?How much time is provided for learning?

What level of thinking is reflected in the item description?What level of thinking is reflected in the item description? Prepare to share on the large Post-It Sheet the Reporting Prepare to share on the large Post-It Sheet the Reporting

Categories and objectives that will be your focus of Categories and objectives that will be your focus of improvement.improvement.

60 70x

Effective Instruction for Effective Instruction for Students with Special NeedsStudents with Special Needs

Essential Characteristics of effective instruction -Essential Characteristics of effective instruction -ImprovesImproves through regular assessments and evaluations; through regular assessments and evaluations;focusesfocuses on essential knowledge and essential skills; on essential knowledge and essential skills;buildsbuilds on students’ prior knowledge; on students’ prior knowledge;integrates integrates higher level and basic skills;higher level and basic skills;providesprovides instruction on specific strategies; instruction on specific strategies;includesincludes the frequent review of key concepts; the frequent review of key concepts;consistently usesconsistently uses collaborative learning; collaborative learning;focusesfocuses on student-directed instruction; on student-directed instruction;strivesstrives to be culturally and linguistically relevant; and to be culturally and linguistically relevant; andreliesrelies on shared responsibility and collaboration. on shared responsibility and collaboration.

Office of Educational Research and Improvement (OERI), US DOE, 2000Office of Educational Research and Improvement (OERI), US DOE, 2000

7.6 The student will use proportions to solve practical problems, which may include scale drawings, that contain rational numbers (whole numbers, fractions, and decimals) and percents.

UNDERSTANDING THE STANDARD(Teacher Notes)

ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS

A proportion is a statement of equality between two ratios.A common property relates the numerators of the two ratios, and another common property relates the denominators of the two ratios. For example, both numerators relate to one property, such as length, while both denominators relate to another property, such as width. Alternatively, both numerators could relate to scale lengths, while both denominators relate to actual lengths.The dimensions of a scale model are proportional to the corresponding dimensions of the object (e.g., a blueprint of a house floor plan is proportional to the actual dimensions of the floor).A proportion can be written as = , •a:b = c:d, or a is to b as c is to d.A proportion can be solved by finding the product of the means and the product of the extremes. For example, in the proportion a:b = c:d, a and d are the extremes and b and c are the means. If values are substituted for a, b, c, and d such as 5:12 = 10:24, then the product of extremes (5 24) is equal to the product of the means (12 10).•continued

All students shouldUnderstand that a proportion is an equation showing that two ratios are equal.Understand how to set up a proportion, given the relationship between two items.Understand that when two quantities are proportional, a change in one quantity corresponds to a predictable change in the other.Understand that proportions are useful in solving many types of problems.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations toWrite proportions that represent equivalent relationships between two sets.Solve a proportion to find a missing term.Apply proportions to solve problems that involve percents.Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and/or decimals no less than tenths.

UNDERSTANDING THE STANDARD

(Teacher Notes)

ESSENTIAL UNDERSTANDINGS

ESSENTIAL KNOWLEDGE AND SKILLS

•continuedIn a proportional situation, both quantities increase or decrease together.In a proportional situation, two quantities increase multiplicatively. Both are multiplied by the same factor.A proportion can be solved by finding equivalent fractions.There is a distinction between a proportion and the idea of equivalent fractions. Equivalent fractions are symbols for the same quantity or amount and they represent the same rational number in different forms.A rate is a special ratio that always has a denominator of 1. Examples of rates include miles/hour and revolutions/minute. A rate compares measures of different types.A percent is a special ratio in which the denominator is 100.Proportions are used in every-day contexts, such as speed, recipe conversions, scale drawings, map reading, reducing and enlarging, comparison shopping, and monetary conversions.

The Essential Virginia The Essential Virginia Toy InvestigationToy Investigation

The Essential Questions:

If Barbie came to life, would Ken want to date her?

If Ken came to life, would Barbie want to date him?

Task: To create a Life-Size Scaled Task: To create a Life-Size Scaled Barbie and KenBarbie and Ken

Identify the tallest Identify the tallest person on your team.person on your team.

Select a Barbie or Select a Barbie or Ken for your team.Ken for your team.

Goal: To build a Goal: To build a scaled replica of scaled replica of Barbie or Ken the Barbie or Ken the same height as your same height as your tallest team member.tallest team member.

MeasureMeasure Original Original DollDoll

Life-Size Life-Size DollDoll

HeightHeight

Arm LengthArm Length

Leg LengthLeg Length

Body LengthBody Length

Foot LengthFoot Length

Part IIIPart III

The Focus:The Focus:

Drilling Down Drilling Down

“The real voyage of discovery exists not in seeking new lands but in seeing with new

eyes.”~R. Proust

My Personal My Personal Learning GoalsLearning Goals

I will understand the latest data on student I will understand the latest data on student achievement by subgroup as measured by SOL achievement by subgroup as measured by SOL tests. (achievement gaps?)tests. (achievement gaps?)

I will explore the latest research on improving I will explore the latest research on improving the performance of underachieving students.the performance of underachieving students.

I will practice effective learning strategies to I will practice effective learning strategies to boost the achievement of ALL students.boost the achievement of ALL students.

I will understand a differentiated lesson plan that I will understand a differentiated lesson plan that incorporates the research-based strategies.incorporates the research-based strategies.

I will enjoy learning in a non-threatening I will enjoy learning in a non-threatening environment.environment.

Essential Follow-up ActivityEssential Follow-up Activity In which areas/groups are we achieving our In which areas/groups are we achieving our

goal of improving the achievement of ALL goal of improving the achievement of ALL students?students?

In which areas/groups have we failed to In which areas/groups have we failed to achieve our goal of improving the achievement achieve our goal of improving the achievement of ALL students?of ALL students?

What will we do about this?What will we do about this?By when?By when?

Note: Note: GoalsGoals MUST BE MEASURABLE! MUST BE MEASURABLE!

CategoryCategory Ave. EffectAve. Effect

Size (ES)Size (ES)PercentilPercentil

e Gaine Gain

Identify similarities & differences

1.611.61 4545

Summarizing & note taking 1.001.00 3434

Reinforcing effort & providing recognition

.80.80 2929

Homework & practice .77.77 2828

Nonlinguistic representations .75.75 2727

Cooperative learning .73.73 2727

Setting objectives & providing feedback

.61.61 2323

Generating & testing hypotheses

.61.61 2323

Questions, cues, & advance organizers

.59.59 2222

Nonlinguistic RepresentationsNonlinguistic Representations

Approaches to this strategy in the Approaches to this strategy in the classroom:classroom:Graphic organizers,Graphic organizers,Pictographic representations,Pictographic representations,Mental images,Mental images,Physical models, andPhysical models, andKinesthetic representations.Kinesthetic representations.

COMPARING GRAPHIC ORGANIZERS

Characteristics Item 1 Item 2 Item 3 Comparisons

Similarities

Differences

Similarities

Differences

Similarities

Differences

Similarities

Differences

COMPARISON

MATRIX

VENN DIAGRAM

Place each Geometric Shape in the Venn DiagramPlace each Geometric Shape in the Venn Diagram

TriangleTrapezoid Rectangle Parallelogram Circle

All pairs of opposite

sides parallel

All interior angles

measure 90 degrees

Is a type of Quadrilateral

Graphic OrganizersGraphic Organizers

Use VisualsUse Visuals

Graphic organizers help Graphic organizers help students organize the students organize the information and retaininformation and retain 5 5 times more of the times more of the information.information.

Three Levels of LearningThree Levels of Learning Concrete ExperienceConcrete Experience

Without the concrete experience, the representation or symbol may Without the concrete experience, the representation or symbol may have little or no meaning no matter how much someone explains it to have little or no meaning no matter how much someone explains it to you.you.

This level of learning is often the most memorable for studentsThis level of learning is often the most memorable for students

Representational or Symbolic LearningRepresentational or Symbolic Learning Picture of concrete experiences are helpful BUT can not substitute Picture of concrete experiences are helpful BUT can not substitute

for the impact of concrete experience.for the impact of concrete experience.

Abstract LearningAbstract Learning This level of learning represents the use of words and numbers This level of learning represents the use of words and numbers

(democracy or culture). This learning depends on the ability of the (democracy or culture). This learning depends on the ability of the teacher to provide sufficient examples that relate to the students’ teacher to provide sufficient examples that relate to the students’ experiences.experiences.

Using the Visual and Auditory Using the Visual and Auditory Senses to Enhance LearningSenses to Enhance Learning

The eyes contain nearly 70 percent of the body’s The eyes contain nearly 70 percent of the body’s sensory receptors and send millions of signals every sensory receptors and send millions of signals every second along the optic nerves to the brain.second along the optic nerves to the brain.

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Create a mental picture of:

1 1

3 2X

YOUR TURN!!!!YOUR TURN!!!!

Using the Visual and Auditory Using the Visual and Auditory Senses to Enhance LearningSenses to Enhance Learning

Create a model the following:

1 1

3 4XExtra for Experts:

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3 8X

1. Describe it. (Describe its colors, shapes, and sizes. What does it look like?)

2. Compare it. (What is it similar or different from?)

3. Associate it. (What does it make you think of?)

4. Analyze it. (How is it made or what is it composed of?)

5. Apply it. (What can you do with it? How is it used?

6. Argue for or against it. (Take a stand and list reasons for supporting it.)

CUBING

Thank you for your Thank you for your commitment to children!commitment to children!

"It's your attitude, not just your aptitude that determines your ultimate altitude."

--Zig Ziglar

DanSimplyachieve@juno.com

757-754-5920