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    MMSTLC Session 17.4 SVSU 12/04/08

    OGAP Warm-up Task 12/08Marge Petit Consulting, MPC

    Jamie is in charge of purchasing pancake mix for the Clubs Annual Breakfastfundraiser. He is using the ratio table below to determine the amount of mix topurchase.

    Number ofPancakes 12 24 36 120 400

    Cups ofPancake Mix 1 3/4 3 1/2 5 1/4 17 1/2

    Milk 1 1/4 2 1/2 3 3/4 12 1/2

    The club expects to make about 400 pancakes. How many cups of mix does Jamie need? Explain your reasoning. Identify the structures of the problem, i.e., problem type, internal structure,

    multiplicative relationship, types of numbers, and representations.

    OGAP Pancake Problem

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    MMSTLC 1

    Michigan Department of Education www.michigan.gov/mdeGrade 4

    4 th GRADE LEVEL Math CONTENT EXPECTATIONS(Rational) NUMBER AND OPERATIONS

    Read, interpret and compare decimal fractions

    N.ME.04.15 Read and interpret decimals up to two decimal places; relate to money and place valuedecomposition.N.ME.04.16 Know that terminating decimals represents fractions whose denominators are 10,10 x 10, 10 x 10 x 10, etc., e.g., powers of 10.N.ME.04.17 Locate tenths and hundredths on a number line.N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places.N.MR.04.19 Write tenths and hundredths in decimal and fraction forms, and know the decimalequivalents for halves and fourths. * revised expectations in italics

    Understand fractionsN.ME.04.20 Understand fractions as parts of a set of objects.N.MR.04.21 Explain why equivalent fractions are equal, using models such as fraction strips or thenumber line for fractions with denominators of 12 or less, or equal to 100.N.MR.04.22 Locate fractions with denominators of 12 or less on the number line; include mixed numbers.* N.MR.04.23 Understand the relationships among halves, fourths, and eighths and among thirds, sixths,and twelfths.N.ME.04.24 Know that fractions of the form mn where m is greater than n, are greater than 1 and are called improper fractions; locate improper fractions on the number line.* N.MR.04.25 Write improper fractions as mixed numbers, and understand that a mixed number representsthe number of wholes and the part of a whole remaining, e.g., 5/4 = 1 + = 1 . N.MR.04.26 Compare and order up to three fractions with denominators 2, 4, and 8, and 3, 6, and 12,

    including improper fractions and mixed numbers.

    Add and subtract fractionsN.MR.04.27 Add and subtract fractions less than 1 with denominators through 12 and/or 100, in cases where the denominators are equal or when one denominator is a multiple of the other, e.g.,1/12 +5/12 = 6/12; 1/6 + 5/12 = 7/12; 3/10 23/100 = 7100 . * N.MR.04.28 Solve contextual problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100).* N.MR.04.29 Find the value of an unknown in equations such 1/8 + x = 5/8 or - y = *.

    Multiply fractions by whole numbersN.MR.04.30 Multiply fractions by whole numbers, using repeated addition and area or array models.

    Add and subtract decimal fractionsN.MR.04.31 For problems that use addition and subtraction of decimals through hundredths,represent with mathematical statements and solve.* N.FL.04.32 Add and subtract decimals through hundredths.*

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    MMSTLC 2

    Michigan Department of Education www.michigan.gov/mdeGrade 4

    Multiply and divide decimal fractionsN.FL.04.33 Multiply and divide decimals up to two decimal places by a one-digit whole number where theresult is a terminating decimal, e.g., 0.42 3 = 0.14, but not 5 3 = 1.6.

    5 th GRADE LEVEL Math CONTENT EXPECTATIONS

    Understand meaning of decimal fractions and percentagesN.ME.05.08 Understand the relative magnitude of ones, tenths, and hundredths and the relationship ofeach place value to the place to its right, e.g., one is 10 tenths, one tenth is 10 hundredths.N.ME.05.09 Understand percentages as parts out of 100, use % notation, and express a part of a wholeas a percentage.

    Understand fractions as division statements; find equivalent fractionsN.ME.05.10 Understand a fraction as a statement of division, e.g., 2 3 = 2/3 , using simple fractions andpictures to represent.N.ME.05.11 Given two fractions, e.g., and , express them as fractions with a common denominator, but not necessarily a least common denominator, e.g., =4/8 and = 6/8 ; use

    denominators less than 12 or factors of 100.*

    Multiply and divide fractionsN.ME.05.12 Find the product of two unit fractions with small denominators using an area model.* N.MR.05.13 Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions.*

    Add and subtract fractions using common denominatorsN.FL.05.14 Add and subtract fractions with unlike denominators through 12 and/or 100, using the common denominator that is the product of the denominators of the 2 fractions, e.g., 3/8 + 7/10; use 80 as the common denominator.*

    Multiply and divide by powers of tenN.MR.05.15 Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, 1,000; and identify patterns.N.FL.05.16 Divide numbers by 10s, 100s, 1,000s using mental strategies.N.MR.05.17 Multiply one-digit and two-digit whole numbers by decimals up to two decimal places.

    Solve applied problems with fractionsN.FL.05.18 Use mathematical statements to represent an applied situation involving addition and subtraction of fractions.* N.MR.05.19 Solve contextual problems that involve finding sums and differences of fractions with unlike denominators using knowledge of equivalent fractions.*

    N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness.* N.MR.05.21 Solve for the unknown in equations such as + x = 7/12.*

    Express, interpret, and use ratios; find equivalencesN.MR.05.22 Express fractions and decimals as percentages and vice versa.N.ME.05.23 Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3 : 5, 3/5 ;

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    MMSTLC 4

    Michigan Department of Education www.michigan.gov/mdeGrade 4

    decimal numbers. [Core]

    ALGEBRA

    Calculate ratesA.PA.06.01 Solve applied problems involving rates, including speed, e.g., if a car is going50 mph, how far will it go in 3 1/2 hours? [Core]

    Understand the coordinate planeA.RP.06.02 Plot ordered pairs of integers and use ordered pairs of integers to identifypoints in all four quadrants of the coordinate plane. [Core]

    Use variables, write expressions and equations, and combine like termsA.FO.06.03 Use letters, with units, to represent quantities in a variety of contexts, e.g., ylbs., k minutes, x cookies. [Core] A.FO.06.04 Distinguish between an algebraic expression and an equation. [Ext] A.FO.06.05 Use standard conventions for writing algebraic expressions, e.g., 2x + 1 means

    two times x, plus 1 and 2(x + 1) means two times the quantity (x + 1). [Fut] A.FO.06.06 Represent information given in words using algebraic expressions andequations. [Core] A.FO.06.07 Simplify expressions of the f irst degree by combining like terms, and evaluateusing specif ic values. [Fut]

    Represent linear functions using tables, equations, and graphsA.RP.06.08 Understand that relationships between quantities can be suggested by graphsand tables. [Ext]

    A.PA.06.09 Solve problems involving linear functions whose input values are integers;write the equation; graph the resulting ordered pairs of integers, e.g., given c chairs, the

    leg function is 4c; if you have 5 chairs, how many legs?; if you have 12 legs, how manychairs? [Fut] A.RP.06.10 Represent simple relationships between quantities using verbal descriptions,formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square,distance-time graphs, and conversions such as feet to inches. [Fut]

    Solve equationsA.FO.06.11 Relate simple linear equations with integer coeff icients, e.g., 3x = 8 orx + 5 = 10, to particular contexts and solve. [Core] A.FO.06.12 Understand that adding or subtracting the same number to both sides of anequation creates a new equation that has the same solution. [Core] A.FO.06.13 Understand that multiplying or dividing both sides of an equation by the samenon-zero number creates a new equation that has the same solutions. [Core]

    A.FO.06.14 Solve equations of the form ax + b = c, e.g., 3x + 8 = 15 by hand for positiveinteger coeff icients less than 20, use calculators otherwise, and interpret the results. [Fut]

    Seventh Grade

    The main focus in grade seven is the algebra concept of linear relationships, including ideas

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    MMSTLC 6

    Michigan Department of Education www.michigan.gov/mdeGrade 4

    graph, interpreting slope and y-intercept. [Fut] A.FO.07.08 Find and interpret the x- and/or y-intercepts of a linear equation or function.Know that the solution to a linear equation of the form ax + b=0 corresponds to the point atwhich the graph of y = ax+ b crosses the x-axis. [Fut]

    Understand and solve problems about inversely proportional relationships

    A.PA.07.09 Recognize inversely proportional relationships in contextual situations; knowthat quantities are inversely proportional if their product is constant, e.g., the length andwidth of a rectangle with f ixed area, and that an inversely proportional relationship is of theform y = k/x where k is some non-zero number. [Fut] A.RP.07.10 Know that the graph of y = k/x is not a line, know its shape, and know that itcrosses neither the x- nor the y-axis. [Fut]

    Apply basic properties of real numbers in algebraic contextsA.PA.07.11 Understand and use basic properties of real numbers: additive andmultiplicative identities, additive and multiplicative inverses, commutativity, associativity,and the distributive property of multiplication over addition. [Core]

    Combine algebraic expressions and solve equationsA.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the f irst degree,e.g., (92x + 8y) 5x + y, or x(x+2) and justify using properties of real numbers. [Core] A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b= c and ax + b = cx + d, and interpret solutions. [Fut]

    Solve problemsN.MR.08.07 Understand percent increase and percent decrease in both sum and product form, e.g., 3%

    increase of a quantity x is x + .03x = 1.03x.N.MR.08.08 Solve problems involving percent increases and decreases.N.FL.08.09 Solve problems involving compounded interest or multiple discounts.N.MR.08.10 Calculate weighted averages such as course grades, consumer price indices, and sports

    ratings.N.FL.08.11 Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons

    per square mile.* revised expectations in italics

    Understand the concept of non-linear functions using basic examplesA.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions

    including inversely proportional relationships (y = k/x); cubics (y = ax3); roots (y = x ); and exponentials(y = ax , a > 0); using tables, graphs, and equations.*

    A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and populationgrowth, describe how changes in one variable affect the others.

    A.PA.08.03 Recognize basic functions in problem context, e.g., area of a circle is r2, volume of asphere is r3, and represent them using tables, graphs, and formulas.

    A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable.

    Understand and represent quadratic functionsA.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa;

    in particular, note that solutions of a quadratic equation are the x-intercepts of the correspondingquadratic function.

    A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and thecoordinates of the vertex; use words parabola and roots; include functions in vertex form and thosewith leading coefficient 1, e.g., y = x2 36, y = (x 2)2 9; y = x2; y = (x 3)2.

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    MMSTLC 7

    Michigan Department of Education www.michigan.gov/mdeGrade 4

    Recognize, represent, and apply common formulasA.FO.08.07 Recognize and apply the common formulas:(a + b)2 = a2 + 2 ab + b2(a b)2 = a2 2 ab + b2(a + b) (a b) = a2 b2 ; represent geometrically.

    A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g., x2 + 6x + 9, x2 + 2x 3,and x2 4; solve simple quadratic equations, e.g., x2 = 16 or x2 = 5 (by taking square roots);x2 x 6 = 0, x2 2x = 15 (by factoring); verify solutions by evaluation.

    A.FO.08.09 Solve applied problems involving simple quadratic equations.

    Understand solutions and solve equations, simultaneous equations, and linearinequalities

    A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which theequation is true, e.g., determine whether a given value, or values from a given set, is a solution of anequation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution).

    A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and bylinear combination; estimate solutions using graphs; include examples with no solutions and infinitelymany solutions.

    A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets.A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear

    inequalities. * revised expectations in italics .

    Each expectation is labeled [Core] , [Ext] (Extended Core), [Fut] (Future Core) or [NASL] (NotAssessed at the State Level); NC designates a N on- Calculator item

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    MMSTLC Session 17.5 SVSU 12/04/08

    A derivative OGAP product created for MMSTLC November 2008. Original materials were developed as a part of TheVermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award NumberS366A020002) and the National Science Foundation (Award Number EHR-0227057) November 2008

    Progam Review Task page 1 of 3

    Scan Across a Unit and a Year

    Step 1: Review the table of contents of your mathematics program. Highlight theproportionality topics/contexts on the OGAP Proportionality Framework (use the copyattached) that are addressed in your mathematics program.

    Step 2: Select a MAJOR unit that focuses on developing proportional reasoning. Scan theunit and then highlight the structures evidenced in the problems across the unit. Indicatemultiple hits on a structure with tic marks.

    Particularly look for:

    Mathematical topics and contexts Problem types Multiplicative relationships Internal structures For ratio problems Referents (implied vs. explicit) Numbers Representations

    Step 3: Given the GLECS at your grade level and the OGAP Framework answer thefollowing questions.

    1) What surprised you?

    2) In what ways does your program support the GLECS at your grade level? In whatways does your program support the OGAP Framework Problem Structures?

    3) In what ways does the unit (s) you reviewed provide opportunities for students tosolve different types of problems with varying problem structures?

    4) What gaps, if any, did you find between your program and the OGAP FrameworkProblem Structures?

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    MMSTLC Session 17.5 SVSU 12/04/08

    A derivative OGAP product created for MMSTLC November 2008. Original materials were developed as a part of TheVermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award NumberS366A020002) and the National Science Foundation (Award Number EHR-0227057) November 2008

    Progam Review Task page 2 of 3

    STEP 4 :

    1) Join the other groups at your grade and program and complete the flip chart paperprovided to you. Place your completed chart on the wall with the charts for othergrades and your program.

    (Note: We will come back to these analyses after you have analyzed the student work fromthe OGAP pre-assessment that you administered to your students. At that point you willknow what strategies your students used to solve the problems and how problem structuresdid or did not affect their solution path.)

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    M M S T L C

    S e s s

    i o n

    1 7 . 5

    S V S U 1 2 / 0 4 / 0 8

    A d e r i v a

    t i v e

    O G A P p r o d u c

    t c r e a t e d

    f o r

    M M S T L C N o v e m

    b e r 2

    0 0 8 . O r i g i n a

    l m a t e r

    i a l s w e r e

    d e v e

    l o p e

    d a s a p a r t o f

    T h e V e r m o n

    t M a t

    h e m a t

    i c s

    P a r t n e r s

    h i p

    f u n d e d

    b y a g r a n

    t p r o v i d e

    d b y t h e

    U S D e p a r

    t m e n

    t o f E d u c a

    t i o n

    ( A w a r

    d N u m

    b e r

    S 3 6 6 A 0 2 0 0 0 2 ) a n d

    t h e

    N a t

    i o n a

    l S c i e n c e

    F o u n

    d a t i o n

    ( A w a r

    d N u m

    b e r

    E H R -

    0 2 2 7 0 5 7 ) N o v e m

    b e r 2 0

    0 8

    P

    R v

    i w

    T

    k

    3 f

    3

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    S e s s

    i o n

    5 . 1 - S

    t r a n

    d s o f M a t

    h e m a t

    i c a l

    P r o

    f i c i e n c y

    ( N

    R C )

    C h a p t e r

    4 A d d i n g

    i t U p

    1 (

    T h e s e m a t e r

    i a l s w e r e c r e a

    t e d b y t h e

    V e r m o n

    t M a t

    h e m a t

    i c s

    P a r

    t n e r s

    h i p

    f u n d e d

    b y t h e

    U S D e p a r

    t m e n

    t o f E d u c a

    t i o n

    ( A w a r

    d N u m

    b e r

    S 3 6 6 A 0 2 0 0 0 2 ) a n

    d t h e

    N a t

    i o n a

    l S c i e n c e

    A

    b

    V

    A

    V

    S t r a n

    d :

    M a j o r

    f e a

    t u r e s o

    f t h i s s

    t r a n

    d

    E x a m p

    l e s o

    f t h e

    f e a

    t u r e s y o u

    i d e n

    t i f i e

    d

    H o w

    d o e s

    t h i s s

    t r a n

    d r e

    l a t e t o t h e o t

    h e r s

    t r a n

    d s

    ?

    S t r a n

    d___________________

    S t r a n

    d___________________

    S t r a n

    d___________________

    S t r a n

    d___________________

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    MMSTLC Session 17.7 SVSU 12/4/08

    A derivative OGAP product created for MMSTLC November 2008. Original materials were developed as a part of The VermontMathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and theNational Science Foundation (Award Number EHR-0227057)

    Evidence in Student Work to Inform Instruction

    In this activity you wlll be using the OGAP Framework to help describe evidence

    in over 20 student solutions to problems that you have encountered in previousOGAP work.

    Questions to keep in mind: What is the solution strategy that the student used? What is the evidence of that strategy? What structure (s) in the problem facilitated the use of a proportional

    strategy or may have resulted in a student using either a transitional ornon-proportional strategy?

    What might your next instructional/assessment step be given the studentsolution? (e.g., what evidence of understanding can be built on? Whatelse do you need to know to help make decisions about the nextinstructional step? What questions can you ask to build on understanding?What activities or models can be used?)

    There are some underlying assumptions when asking about nextinstruction steps:

    A student solution usually provides evidence of understanding that can be

    built upon; One might need to collect additional information about the student

    understanding as a part of the next step; While you are identifying next instructional steps in response to one

    student response in this activity, these evidences are common acrossclassrooms. So when you answer questions about individual pieces ofstudent work in this activity think about this being an example of commonerrors across groups of students that can be applied to full classrooms ofstudents.

    Even when a student correctly solves a problem, there are instructionalnext steps to consider.

    Important Note: The purpose of reviewing this work is NOT to spend time toreliably agree about the evidences, but to give us a way to describe the evidencethat will inform instruction.

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    MMSTLC Session 17.7 SVSU 12/4/08

    A derivative OGAP product created for MMSTLC November 2008. Original materials were developed as a part of The VermontMathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and theNational Science Foundation (Award Number EHR-0227057)

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    M M S T L C S e s s

    i o n

    1 7 . 8

    O G A P P r o p o r

    t i o n a l

    R e a s o n i n g

    I t e m

    A n a

    l y s i s

    S h e e

    t

    T h e V e r m o n

    t M a t

    h e m a t

    i c s

    P a r t n e r s h

    i p i s f u n d e d

    b y a g r a n

    t p r o v i

    d e d b y t h e

    U S D

    e p a r

    t m e n

    t o f E d u c a

    t i o n

    ( A w a r

    d N u m

    b e r

    S 3 6 6 A 0 2 0 0 0 2 ) a n

    d t h e

    N a t

    i o n a

    l S c i e n c e

    F o u n

    d a t i o n

    ( A w a r

    d N u m

    b e r

    E H R -

    I t e m

    B a c

    k g r o u n

    d :

    P r o p o r t

    i o n a

    l S t r a t e g

    i e s

    T r a n s

    i t i o n a l

    P r o p o r t

    i o n a

    l S t r a t e g

    i e s

    N o n - p r o p o r t

    i o n a

    l S t r a t e g i e s

    D e s c r

    i p t i o n o f e v

    i d e n c e

    t o i n f o r m

    i n s t r u c t

    i o n :

    F i n d s a n

    d a p p l

    i e s u n

    i t r a t e

    t o s i

    t u a t

    i o n

    C o m p a r e s s i m p l

    i f i e d f r a c

    t i o n s , r

    a t e s , o

    r

    r a t i o s

    A p p

    l i e s m u l

    t i p l i c a t

    i v e r e

    l a t i o n s

    h i p

    S e t s u p a p r o p o r

    t i o n a n

    d u s e s c r o s s

    p r o d u c

    t s

    U s e s y = m x

    O t h e r

    F o r r a

    t i o p r o b

    l e m s :

    A p p

    l i e s

    t h e c o r r e c

    t r a t i o r e

    f e r e n t

    D e s c r

    i p t i o n o f e v

    i d e n c e

    t o i n f o r m

    i n s t r u c t

    i o n :

    B u i

    l d s u p

    / d o w n

    F i n d s e q u i v a

    l e n t

    f r a c

    t i o n s

    / r a t

    i o s w

    i t h a n e r r o r

    U s e s m o d e l s

    M a k e s a c r o s s p r o d u c

    t e r r o r

    M a k e s a n e r r o r

    i n a p p l y i n g a m u l

    t i p l i c a t

    i v e

    r e l a t i o n s

    h i p

    O t h e r

    D e s c r

    i p t i o n o f e v

    i d e n c e

    t o i n f o r m

    i n s t r u c t

    i o n :

    G u e s s e s o r u s e s r a n d o m a p p l

    i c a t

    i o n

    o f n u m

    b e r s ,

    o p e r a t

    i o n s , o

    r s t r a

    t e g i e s

    U s e s a d

    d i t i v e r e a s o n

    i n g

    U s e s w

    h o l e n u m

    b e r r e a s o n

    i n g

    S o l v e s a n o n - p r o p o r

    t i o n a

    l s i t u a t

    i o n

    p r o p o r

    t i o n a

    l l y

    M i s u n

    d e r s

    t a n d s v o c a

    b u l a r y a n

    d r e l a t e d c o n c e p

    t ( e . g .

    r a t i o

    , s i m i l a r i

    t y )

    N o t e n o u g h

    i n f o r m a t

    i o n

    t o d e t e r m i n e

    / l a c k s

    s u p p o r

    t i n g e v

    i d e n c e

    N o a t

    t e m p t

    O t h e r

    U

    n d e r

    l y i n g

    C o n c e r n s /

    E r r o r s

    U n d e r

    l y i n g

    i s s u e s o r c o n c e r n s

    i n s t u d e n

    t s o l u t

    i o n s :

    E r r o r

    i n t h e a p p l

    i c a t

    i o n o f c r o s s p r o d u c

    t s

    U s e s a d

    d i t i v e s t r a

    t e g i e s r a

    t h e r

    t h a n m u l

    t i p l i c a t

    i v e s t r a t e g y

    ( e . g . ,

    u s e s

    r e p e a t e d a d

    d i t i o n

    i n s t e a

    d o f m u l

    t i p l i c a t

    i o n )

    U n i

    t s i n c o n s

    i s t e n t o r a b s e n t

    M i s i n t e r p r e

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    i n g o f

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    M M S T L C S e s s

    i o n

    1 7 . 8

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    MMSTLC Session 17.8 SVSU 12/4/08

    A derivative OGAP product created for MMSTLC November 2008. Original materials were developed as a part of The VermontMathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and theNational Science Foundation (Award Number EHR-0227057)

    The OGAP Student Work Sort Process

    There are three steps to the OGAP Student Work Sort Process. For a singlequestion:

    STEP 1: Review and then sort the work for the class into three piles consistent

    with the OGAP Proportionality Framework.

    Proportional Strategies Transitional Proportional Non-Proportional

    STEP 2: Record the evidence on an OGAP Item Analysis Sheet by piles.

    We suggest starting with the Proportional Strategy pile of student work first andthen repeat the process for each of the other piles.

    A) Record the strategy (you may want to sub sort the work first (e.g., All thatuse multiplicative relationships, or unit rate) by placing the students #s (inyour case name, initials) that corresponds with the strategy.

    B) Record any underlying issues, errors, or misconceptions evidencedin the work by placing the students #s (in your case name, initials) thatcorresponds with the error et al.

    STEP 3 : In the Instructional notes section or on the back make some quicknotes about trends in the class or instructional ideas that you may have afterreviewing the work.

    Student 11

    Student 1

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    1 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    2 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    4 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    5 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    7 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    9 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    12 These materials were created by the Vermont Mathematics Partnership funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)

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    9.2 Analyzing Pre-assessment Participant Directions

    2 A derivative OGAP product created for MMSTLC November 2008. Original materials were developed as a part of The

    2) Complete the OGAP Sort and collect evidence in the OGAP Item Analysis Sheet.IMPORTANT: We suggest that you actually put the students initials on the itemanalysis sheets. That way you wont loose important individual student data asyou analyze items across the classroom of students.

    3) Write comments on the Instructional Notes section of the OGAP Item AnalysisSheet before moving onto the analysis of the next item.

    Complete analysis of all five items in this way.

    Part II: Telling the Story

    After you complete the analysis of all the items in the pre-assessment address these threequestions on the Telling the Story template (9.3).

    1) What are some strategies evidenced in the student work that you can build upon?

    2) What are some underlying issues or concerns evidenced in the student work?3) What are some implications for instruction?You will use the information from this activity in the next session as you do unitplanning.

    Part III: Telling the story across grades

    1) Return to your school level team. In a round robin have each teacher Tell theStory for the group of students that they analyzed their pre-assessments (about 5minutes each).

    2) Be prepared to discuss general observations, findings, and implications for yourschool.