SBA Math Test

Content Review Booklet

for the North Thurston Public Schools edited by Andrea Hicklin

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SBA Math Test Information: How many questions are on the test? It’s actually hard to get a straight answer on that because some of the questions on the test are “pilot” items, meaning that they’re being tested to see how well the question performs, not how well a student is doing. You’ll probably see between 42 & 48 questions, total, but: For the CAT (computer adaptive test, a.k.a. day 1), between 33 and 36 questions actually count. For the PT (performance task, a.k.a. day 2), 5 to 7 questions, but they usually have multiple parts. What score is needed to pass?

This year Previous years Level 2 2533 2543 Level 3 2614 2628 Level 4 2697 2718

To score as Proficient (level 3 and up), a student needs to score 2614 points. Then they’re considered “college and career ready”. But the minimum to graduate is still 2595. What will the test cover? The test is divided into “Claims”, which are then further divided into “Targets”. The target is a small group of related content expectations. Each target has many types of questions that could be asked. (So even if we know there are 2 questions from Target K, for example, we don’t know which two types of questions will be chosen.) Claim 1 has the content questions that don’t involve some sort of justification, explanation, or modeling from data. Claim 2 and Claim 4 both involve modeling/problem solving. Claim 3 has the “create or explain the reasoning” questions. Questions from Claims 2, 3, and 4 will to blend two or more different targets while Claim 1 will focus on a single target at a time. Can I use a calculator? Yes and no --- not all questions allow a calculator. For those that do, the test has the Desmos.com online calculator embedded in the question. However, a student with testing accommodations in their IEP or 504 plan could be allowed to use their own. The SBAC website has a place to practice working with both the calculator and the equation editor (in addition to a full practice test). The examples that you see in this document come directly from the item specification documents that are available at the SBAC website. Each section lists how many questions to expect from each target.

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Claims 2 & 4 6 questions on the computer adaptive test (reported as a combined score) 2 to 5 more on the performance task Like Claim 1, there are targets within Claims 2, 3, and 4. But the targets are about the different aspects of problem solving rather than specific content. Here are the Claim 2 Targets:

2A apply math to well-posed problems

2B use appropriate tools to solve problems

2C interpret results in context

2D identify and map important relationships Items in Claims 2, 3, and 4 usually blend together two different targets. For example, Target 2D is not assessed on its own, but instead are included in a question from Target 2A, 2B, or 2C. The Claim 2 & 4 items are drawn directly from the content standards. They often link to Claim 1 targets, but not always. Because the content of the item can be drawn from many topics, but the number of questions is fairly small, it’s impossible to predict exactly what will be tested. But there are some content areas that are only assessed in claims 2 & 4, so it’s likely that you will see items from those areas on the test. These are the standards that can be used in a Claim 2 question:

Standard label: Content involved:

N-Q.A Rational exponents

A-SSE.A Interpret the structure of expressions

A-SSE.B Write expressions in equivalent form

A-CED.A Create equations

A-REI.2 Solve simple rational and radical equations

A-REI.B Solve equations and inequalities

A-REI.C Solve systems of equations

A-REI.D Represent and solve equations & inequalities graphically

F-IF.A Functions & function notation

F-IF.B Interpret functions in context

F-IF.C Analyze functions in different representations

F-BF.A Build a function to model a relationship

G-SRT.C Solve problems involving right triangles

S-ID.C Interpret linear models for data

S-CP.A Understand independence and conditional probability 2-variable statistics is assessed only in Claims 2 & 4

Systems of equations is assessed only in Claim 2

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There isn’t room in this document to give you one of every type of question that you might see. Please understand that what’s here is only a sampling of the types of questions the test might ask. The sample questions were drawn from the item specifications that control the test, and also from the 2017 practice test available online at https://practice.smarterbalanced.org/student/ Here are some example questions from Claim 2, Target A (apply math to well-posed problems): 1. This one uses content from Claim 1, Target C (use units to solve problems) 2. This one draws from Claim 1, Target J (write & solve 2-variable equations or systems of equations)

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3. This one uses content from Claim 1 Target J as well: *** I think it’s highly likely that you will see at least 1 system of equations story problem on the test 4. This one uses content from Claim 1, Target O (right triangles) 5. This one uses content from Claim 1, Target N (write functions to fit 2-variable relationships)

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6. This one uses content from Claim 1, Target I (solve one-variable equations & inequalities): *** This question is also Target 2D (map important relationship) because it uses the diagram as the

way to answer the question. Here are some examples from Claim 2, Target B (use appropriate tools) 7. This one draws from S-ID.C (Statistics - Interpret Data: linear models for 2-variable statistics): * This particular question has target 2C (interpret results in context) as a secondary goal

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8. This one uses content from G-CO (Geometry – Congruence: translations and congruency) *** Geometric transformations are only assessed in Claims 2, 3, and 4 Here are some samples from Target 2C (interpret results in context) 9. This one uses content from F-BF.A (Functions –Building Functions: Write a function describing a

relationship between two quantities) 10. This one is from F-IF.A (Functions – Interpreting Functions: construct/compare models)

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11. This is from F-IF.B (Functions – Interpreting Functions: interpret functions in context) 12. This one is from F-IF.B also: Claim 4: part of a 6 question group on the CAT and 2 – 5 question group on the PT that are Claim 2/4 The hallmarks of Claim 4 questions are their “messiness” and use of real-world data (i.e. if the question starts with a scatterplot of statistical information). The question might have extra information that isn’t needed, or be missing information that you have to estimate. They are also marked by the use of open-ended wording and no scaffolding. Here is the list of targets for Claim 4:

4A apply math to real-world problems 4B construct chains of reasoning

4C state logical assumptions being used, including what information is needed to solve a problem

4D interpret results in context 4E analyze/improve a model for a situation 4F identify and map important relationships

Some of these sound the same as Claim 2’s targets. A single test question will not blend together targets from different claims. If it’s a Claim 4 question, then it’s a combination of claim 4 targets. The standards that are eligible to be used in Claim 4 are:

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Standard label: content covered:

N-Q.A Rational exponents

A-SSE.B Write expressions in equivalent form

A-CED.A Create equations

A-REI.A Understand equation solving as a process of reasoning

A-REI.B Solve equations and inequalities

A-REI.C Solve systems of equations

A-REI.D Represent and solve equations & inequalities graphically

F-IF.B Interpret functions in context

F-IF.C Analyze functions in different representations

F-BF.A Build a function to model a relationship

S-ID.A One-variable statistics

S-ID.B Two-variable statistics

F-LE.A Construct & compare linear, exponential, quadratic models

F-LE.B Interpret the parameters in a linear or exponential model

G-GMD.A3 Use volume formulas to solve problems

G-MG.A Apply geometric concepts in modeling situations Here are some sample questions from Claim 4, Target A (apply math to real-world problems) 1. This one uses content from G-MG (Geometry – Modeling with Geometry)

2-variable statistics is assessed only in Claims 2 & 4

F-LE is assessed only in Claim 4

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2. This one draws from G-MG also: *** where you see two choices in brackets is where there would be a drop-down menu of selections 3. This uses content from N.Q.A (Numbers – Quantity: Use units to solve problems)

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4. This one is from S.ID.B (Statistics – Interpreting Data: two-variable statistics) 5. This question is from S.ID.A (Statistics – Interpreting Data: one-variable statistics): *** where you see words in brackets is where there would be a drop-down menu of selections Claim 4, Target B is not assessed directly --- instead, it is mixed with one of the other Claim 4 targets.

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Here are some examples from Claim 4, Target C (construct a chain of reasoning): 6. This one uses content from S.ID.A (one-variable statistics) as well: 7. This question uses content from N.Q.A (Numbers – Quantities: Use units to solve problems) *** this is an example of the “tell what information is needed to solve the problem” part of Target 4C

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8. This question is from F.BF.A (Write a function to describe a relationship between two quantities) Here are some examples from Claim 4, Target D (interpret results in context). 9. This is from S.ID.A2 (use appropriate statistics to compare center & spread)

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10. This is also from S.ID.A: Here are some examples from Claim 4, Target E (analyze or improve a model): 11. This is from A.CED.1 ((Algebra – Create Equations to Describe: one-variable equations)

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12. This is from G.MG.1 (apply geometric concepts in modeling situations) Here are some examples from Claim 4, Target F (map important relationships): 13. This is from F.IF (Functions – Interpreting Functions) but it actually uses an 8th grade standard,

not a high school standard, about interpreting linear functions: *** The content for these questions can come from earlier grade levels, but the expectation is that the

required type of thinking about that content is elevated to a high-school level.

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14. This question comes from F.BF.A (Functions – Building Functions: write a function) Claim 3: 8 questions on the computer adaptive test Express Reasoning 1 or 2 more on the performance task Here are the targets for Claim 3:

3A test conjectures with specific examples

3B construct chains of reasoning

3C state logical assumptions being used, including what information is needed to solve a problem

3D break an argument into cases

3E distinguish correct reasoning from flawed

3F base an argument on a concrete referent such as an object, diagram, or drawing

Claim 3 is where a lot of Geometry topics end up. Only one Geometry topic --- right triangle trig --- is in Claim 1. Some of the measuring (i.e. surface area, volume) and modeling ideas are in Claims 2 and 4. But all of the proofs and theorems and postulates and “always/sometimes/never true” stuff ends up here in Claim 3. But even though about 80% of the items in the Claim 3 item bank are Geometry-related, that doesn’t mean Algebra is off-limits. And that makes the list of potential topics VERY long. Here are the standards that provide content for Claim 3:

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Standard label Content covered:

N-RN.A Rational exponents

N-RN.B Rational & irrational numbers

N-RN.B3 Sums & products of rational & irrational numbers

A-SSE.A2 Use structure of expressions to rewrite them

A-APR.A1 Polynomial operations

A-REI.A Equation solving as a process of reasoning

A-REI.A1 Explain steps in a solution using properties

A-REI.A2 Solve simple rational & radical equations

A-REI.C Solve systems of equations

A-REI.D10 Understand “solution” as a point on a graph

A-REI.D11 Find solutions for 𝑓𝑓(𝑥𝑥) = 𝑔𝑔(𝑥𝑥) on a graph

F-IF.A1 Function definition & notation

F-IF.B5 Domain & range

F-IF.C9 Compare functions in different representations

F-BF.B3 Connect changes in an equation to shifts in a graph

G-CO.A Transformations

G-CO.B Congruence in terms of rigid motion

G-CO.C Prove geometric theorems

G-CO.C9 Prove theorems about lines and angles

G-CO.C10 Prove theorems about triangles

G-CO.C11 Prove theorems about parallelograms

G-SRT.A Understand similarity in terms of transformations

G-SRT.B Prove theorems involving similarity Don’t be fooled by the fact that only 8 of the items listed here are specifically in a Geometry category. Consider how many different facts are included within those 8 items… test questions could ask about alternate interior angles, angles of a polygon, similarity, congruent triangle proofs, transformations, angles in a circle, equations for circles… There’s a lot there. Also, 6 of the 8 Geometry standards on the list are ONLY assessed in Claim 3, so it’s very likely that the test will include questions from these topics. (G-SRT.A and B are also assessed in Claim 1, under Target O.)

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Here are some examples from Claim 3, Topic A (test conjectures with specific examples). Expect 2 questions on the CAT. 1. This question is from G.C.A (theorems about circles): 2. This one is about circles, but also about the definition of function, so it’s from F.IF.A, not from G.C: 3. This one is all Algebra… N.RN.3 (Numbers – Real Numbers: rational vs irrational sums or products)

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4. Another Geometry one… G.CO.9 (Geometry – Congruence: theorems about lines and angles) Here are some examples from Claim 3, Target B (construct chains of reasoning). Expect 1 question on the CAT. 1. This one is from G.C.A (Geometry – Circles: apply theorems about circles)

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2. This one is a triangle / parallelogram proof problem from G.CO.11 (Geometry – Congruence: prove theorems about parallelograms)

3. This proof is algebraic, from A.APR (Algebra – Arithmetic with Polynomials and Rationals)

Ted claims that the two shaded triangles must be congruent. Is Ted’s claim correct? Show all work/reasoning necessary to either prove Ted’s claim or show that the two triangles are not congruent.

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4. This question is from F.BF.B (build new functions from existing functions) *** choosing the reasons (at the bottom of the item) qualify it as Target 3B (construct a chain of logic) 5. This is from F.IF.B (Functions – Interpret Functions: interpret key features) Here are some examples from Claim 3, Target C (state logical assumptions being used). Expect 1 question on the CAT. 1. This question is from A.APR (Algebra – Arithmetic with Polynomials and Rationals)

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2. This item draws from A.APR as well: 3. This is from A.REI.A (Reason with Equations & Inequalities: solving as a process of reasoning)

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4. Here is a Geometry example, from G.CO.11 (theorems about parallelograms): 5. Another Geometry one, from G. SRT.8 (use trig ratios to solve right triangles)

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Here are some examples from Claim 3, Target D (break an argument into cases). Expect 1 question on the CAT. 1. This one is from F.IF.C (Interpreting Functions: analyze functions using different representations: *** this qualifies as “breaks into cases” because each answer is considered in turn to see if it’s possible 2. This question is from A.SSE.A (Algebra – Seeing the Structure of Expressions) 3. This one is from A.REI.A (Reasoning with Equations and Inequalities)

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4. This one comes from G.SRT (right triangles) 5. This one comes from G.CO.5 (rotations and reflections that carry a figure onto another)

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6. This item draws from N.RN.1 (Real Number System: rational exponents) Here are some examples from Claim 3, Target E (distinguish correct reasoning from flawed). Expect 2 questions on the CAT. 1. This question uses content from A.REI (Reasoning with Equations and Inequalities) 2. This question is from A.REI as well:

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3. This item uses an 8th grade standard related to the Pythagorean Theorem: Here are some examples from Claim 3, Target F (base arguments on concrete referents). Expect 1 question on the CAT. 1. This uses content from A.REI.11 (solutions as intersection points on a graph)

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2. This is from G.C.2 (relationships among inscribed angles and chords in a circle) 3. And one more, from G.GMD (Geometry – Geometric Measurement and Dimension) Remember, as you prepare for Claims 2, 3, and 4, that the examples do NOT represent a complete list of all the possible types of questions on all the possible content areas.

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