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Algebra 1 EOC Data Review and Recommendations Richland 2 District Webinar

Matt Owens, High School Mathematics Specialist Richland Two Teaching and Learning Department

High School Team

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▶ The opinions, questions, items, and scenarios discussed in this webinar are from my in depth interpretations from the Data Item Review Document developed by the State Department of Education and my work with SC College and Career Ready Standards Writing Panel.

▶ This information does not violate testing security regulations set forth by the Office of Assessment at the SC State Department of Education.

Public Disclaimer

▶ To acquire new generalizations of the new SCCCR Algebra 1 Standards

▶ To discover ways to target content standards that posed challenges during the 2015-16 EOC Testing administration

▶ To find assessment alternatives to provide similar testing environments for routine classroom assessments

Today’s Learning Objectives

▶ Tells you as an educator what students are doing cognitively with the mathematics.

Cognitive Demands (Verbs)

Cognitive Demand Example

Discuss

Solve

Graph

Write

Describe

2007 vs. 2015 Academic Standards

▶ Heavily procedural !!

2007 Algebra 1 Standards

Term/Word Frequency (from 2007 Standards)

Procedure

202

2007 Standards Tally Up!!

2007 Algebra 1 Cognitive Demands Tallies

▶ Cognitive Demands are very rigorous and are at least at an Depth Of Knowledge Level 2 or Higher;

▶ The only HS Math course that has the word procedure in it is Prob./Stats.

2015 SCCCR Math Standards

▶ Create 4 Analyze 2 Model 1 ▶ Solve 10 Rewrite 2 Compute 1 ▶ Interpret 9 Choose 3 Relate 1 ▶ Determine 2 Produce 1 Indicate 1 ▶ Understand 3 Describe 1 Translate 1 ▶ Justify 2 Label 1 Reveal 1 ▶ Use 8 Select 1 Show 1 ▶ Derive 1 Fit 1 Compare 1 ▶ Recognize 1 Write 1 Distinguish 1 ▶ Explain 5 Extend 1 Prove 1 ▶ Graph 4 Represent 1 Observe 1

Cognitive Demands for SCCCR Alg. 1 Standards

Alg. 1 from the Present to Future!

▶ The EOC is very wordy ! ▶ No surprises here! There is validity to this statement

Richland 2!

Latest Word on the Algebra Street

Verb Frequency

Context 9

Real World 7

Meaning 5

Interpret 11

Explain 6

Frequency Tallies from SCCCR Algebra 1 EOC Test Blueprint

Context, Relevance, and Mathematics with Meaning is a must!

When planning your lessons, think about CONTEXT before CONTENT. This will be the hook of your lesson. Since many of the test items have some sort of context, there are not many non-contextual math problems.

Algebra 1 is on FLEQ!! (LOL!) F U N C T I O N S

L I N E A R QUADRATIC EXPO.

F L QE

Approximate EOC Topics Ratios

▶ Consider these acronyms with visuals being posted somewhere in your classrooms.

4 Representations of Mathematics Tables Algebra/Analytical Graphical/Geometric Verbal Descriptions; Real World Situation; Explanations; Theorems Proofs

T + A + G + V = EOC Success

▶ 50 Items ▶ Computer Based Platform ▶ Question Types ◦ Multiple Choice (A-D Only) ◦ Technology Enhanced Items

⚫ Plot/Graphing ⚫ Drag and Drop ⚫Multi-Select ⚫ Table/Cell Select ⚫Matching ⚫ Numeric Response

The Algebra 1 EOC Overview

From Danial Camissa..

Plot/Graph Item Types

▶ Matt: Does this graphing plane have the possibility of converting into a real number line to graph solutions to a linear inequality in one variables or with it stay as a Cartesian Plane ?

▶ SDE: This is a static plane in this item.

Specialist to SDE Q&A

▶ Matt: In grading this item type, does it matter if the line drawn contains arrows (for a linear equation in two variables) ?

▶ SDE: No, they will not have access to all the different types of lines when they encounter an item. This item is there for students to have experience with all of the different tools.

▶ Create problems for students to use this Graphing/Plot Tool.

▶ Students can send screenshots to a Google Folder for your viewing.

▶ Give students this experience throughout the course, not just two weeks prior to the assessments.

Recommendations for R2 Teachers (Plot/Graphing Tool)

▶ This tool can be extended for students to drag anything!!

Drag and Drop Items

Drag/Drop from James/Osborne

▶ Create environments/item types that require students to drag: ◦ Equations ◦ Functions in Symbolic Form ◦ Graphs ◦ Parent Function ◦ Tables ◦ Terms/Words

Recommendations for R2 Teachers (Drag and Drop Tool)

▶ 5 Choices will be the minimum with 2, 3, or 4 possible answers;

▶ These items are scored as All or None.

Multi-Select Items

▶ Embed these item types in your classroom unit assessments. These items can really challenge students to critically evaluate as there’s more than one answer.

▶ 5 – 6 choices should be fair game.

Recommendations for R2 Math Teachers

Table Cell Select Item Types

▶ Table/Cell Selects are items that allow students to classify a construct into conditional categories.

▶ Think about other ways of incorporating this question type.

Recommendations for R2 Math Teachers (Table/Cell Selection)

More Considerations from your Content Specialist…

In what areas did the 2016 Algebra 1 EOC examinees perform well ?

Standard Code Language of the Standard

A1.AREI.1 Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

A1.AREI.10 Explain that the graph of an equation in two variable is the set of all its solutions plotted in the coordinate plane. (Featured in the Teacher’s Sample Items Guide)

A1.FIF.4 Interpret key features that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing……

A1.FIF.7 Graph functions from their symbolic representations. Indicate key features including intercept; intervals where the function is increasing, decreasing, positive, or negative; relative maximums , etc. (Graphing Caluclator is very supportive here.)

South Carolina’s Strengths

Standard Code

Language of the Content Standards

A1.ASE.1 Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear, quadratic, exponential.

A1.ASE.2 Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

A1.ASE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Think Quadratic.)

A1.FIF.1a Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

A1.NRNS.2 Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms.

SC’s Areas for Improvement

A water tank is leaking water at a constant rate. The equation models the amount of water in a water tank at any particular hour, t. Which statement below is a correct interpretation of this model? A. The water tank originally contained 2.5 gallons of water. B. The water is leaking out at a rate of 2.5 gallons per hour. C. The water is leaking out at a rate of 200 gallons per hour. D. All of the water has leaked out of the tank by t = 200 hours.

Standard Code Language of the Content Standards

A1.ASE.1 Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear, quadratic, exponential.

Standard Code Language of the Content Standards

A1.ASE.1 Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear, quadratic, exponential.

ADAPTED FROM: SOUTH CAROLINA ALG. 1 EOC TEACHER’S SAMPLE

ITEM GUIDE

Standard Code

Language of the Content Standards

A1.ASE.2 Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

Provide students with practice factoring polynomials. In particular, students should be able to factor a monomial with a variable out of a polynomial.

▶ In our Alignment Guides, Literal Equations comes in

our Linear Equations Unit. ▶ Extend this ideas to your Quadratics Unit also.

(Remember Alg. 1 is on FLEQ!!) ▶ SCDE Recommendation: Arrange to include literal

equations from other disciplines, eg. biology, physics, economics. See next slide.

Literal Equations (Spiral it.) A1.ACE.4 - Solve literal equations and formulas

for a specified variable including equations and

formulas that arise in a variety of disciplines.

Adapted from: North Carolina Algebra 1 EOC

(Access Database and Publishing System: EDUCAID)

A

B

C

D Answer

▶ Include problems where the result is given and the students must select an equation or a system of equations that could produce the same result.

SCDE Recommendation Cont’d

A direct link to the standards…..

A1.AREI.5 – Justify that the solution to a system

of linear equations is not changed when one of

the equations is replaced by a linear combination

of the other equation.

Table/Select Item Type!! YAY!!

X X X

▶ Present students with practice using radical bases raised to rational exponents. Then have them rewrite those expressions using only rational exponents.

SCDE Recommendation Cont’d

A direct link to the SCCCR Math standards…..

A1.NRNS.1 – Rewrite expressions involving

simple radicals and rational exponents in different

forms.

A1. NRNS.2 – Use the definition of the meaning of

rational exponents to translate between rational

exponent and radical forms.

Multiple Choice Again!!

A

B

C

D

▶ Teach verbal, tabular, algebraic, and visual representations of linear and exponential functions. Give students two or more functions in one or more of those representations and have them identify each as linear or exponential.

SCDE Recommendation Cont’d

A1.FLQE.1 – Distinguish between situations that can be

modeled with linear functions or exponential functions

by recognizing situations in which one quantity

changes at a constant rate per unit interval as opposed

to those in which a quantity changes by a constant

percent rate per unit interval.

▶ Ensure your assessments are strongly aligned to the new SCCCR Math Standards.

▶ I highly recommend teacher cohorts create common unit assessments to ensure that your school is strongly on target.

▶ Vary your item types. Now is the time. ▶ Remember the themes of Algebra 1. FLEQ ▶ Keep the 4 mathematical representations in your

minds as you provide instruction.

Final Wrap Up!!