GED 2014: An Inside Look at the Mathematics Test Participant Worksheet

Transcription

1 GED 2014: An Inside Look at the Mathematics Test Participant Worksheet How Does Webb s Depth of Knowledge differ from Bloom s Taxonomy? Record below a 1) definition and 2) an example of an: 1. Anchor Standard: Define Example: 2. Assessment Target: Define Example: 3. Indicator: Define Example: What are two Assessment Targets for the 2014 GED Math Test? 1) and 2) What changes have been made to the GED math test formula sheet? Formulas Removed: Formulas Added: Ready. Test. Go. Copyright

2 GED 2014: An Inside Look at the Mathematics Test Participant Worksheet One thing I will implement Two questions I have Three things I learned in this webinar Ready. Test. Go. Copyright

3 GED 2014: An Inside Look at the Mathematics Test Depth of Knowledge 2014 GED Mathematics Test Level 1 Level 2 Level 3 Requires students to recall or observe facts, definitions, or terms. Involves simple one-step procedures. Involves computing simple algorithms such as sum, quotient. Examples: Recall or recognize a fact, term or property Represent in words, pictures, or symbols in a math object or relationship Perform routine procedure like measuring Requires students to make decisions of how to approach a problem. Requires students to compare, classify, organize, estimate, or order data. Typically involves two-step problems Examples: Specify and explain relationships between facts, terms, properties, or operations Select procedure according to criteria and perform it Solve routine multiple-step problems Requires reasoning, planning, or use of evidence to solve a problem or algorithm. May involve activity with more than one possible answer. Requires conjecture or restructuring of problems. Involves drawing conclusions from observations, citing evidence, and developing logical arguments for concepts. Uses concepts to solve non-routine problems. Examples: Analyze similarities and differences between procedures Formulate original problem given situation Formulate mathematical model for complex situation Ready. Test. Go. Copyright

4 GED 2014: An Inside Look at the Mathematics Test Math Content Matrix Quantitative Problem Solving Math Content Domains Number Sense & Computation One-Step & Multi-Step Word Problems Rate, Ratio, & Percent Word Problems Approximate Percentage of Questions Per Form Foundation Progressing Advanced Q.1 Ordering and computing with rational numbers, simplifying numerical expressions, interpreting distance using a number line Q.2 Reasoning quantitatively to solve problems involving rational numbers Q.3 Solving problems involving a proportional relationship Common Core Standards Reference 6-7.NS, 3-5.NF 8.EE, N-RN 6-7.NS, K-5.OA, 7-8.EE, N-q 6.7.RP, 7.EE.3, 7-G, N-Q Quantitative Problems in Geometric Measurement Q.4 Computing perimeter, circumference, and area of plane figures Q.5 Computing volume and surface area of prisms and cylinders Q.6 Computing volume and surface area of cones, pyramids, spheres, and other shapes 3-8.G, 6.EE Quantitative Problems in Statistical Measurement Q.7 Reading and interpreting graphs, charts, and other data representations Q.8 Measuring the center of a statistical data set Q.9 Determining sample space and using probability models to interpret data 6-8.SP, S-CP.9, S-ID.1, S-MD.2 Ready. Test. Go. Copyright

5 GED 2014: An Inside Look at the Mathematics Test Math Content Matrix Algebraic Problem Solving Math Content Domains Approximate Percentage of Questions Per Form Foundation Progressing Advanced Common Core Standards Reference Transforming Expressions A.1 Simplifying, evaluating, and writing linear equations A.2 Simplifying, evaluating, and writing polynomial expressions A.3 Simplifying, evaluating, and writing rational expressions A-SSE, A-APR, 6-8.EE Solving Equations A.4 Writing and solving linear equations A.5 Writing and solving linear inequalities A.6 Writing and solving quadratic equations A-REI, A-CED, A-SSE, 6-8.EE Lines in the Coordinate Plane A.7 Graphing an equation in two variables in the coordinate plane; solving problems requiring knowledge of slope A.8 Determining the equation of a line A.9 Applying the slope criteria for parallel or perpendicular lines A-REI, G-GPE, 8.EE, A-CED Function Concepts A.10 Evaluating a function for a given point A.11 Comparing functions in different presentations A.12 Identifying features of a function from graphs or tables 8.F, 8.EE, F-IF Ready. Test. Go. Copyright

6 2014 GED Test An Inside Look at the Mathematical Reasoning Test Presented by Bill Walker

7 Common Core Standards Link Students with a shallow grasp of a wide range of topics are not as well prepared to succeed in postsecondary education, and are more likely to need remediation in mathematics, compared to those students who have a deeper understanding of more fundamental topics.

8 Common Core Standards Link Fundamentals: Quantitative problem solving Algebraic problem solving Conceptual understanding Mastery of procedural skill and fluency Apply fundamentals in realistic situations

9 Common Core Standards for Math Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure

10 The Mathematics Test 1¼-hour test Varied item types Measurement of procedural skill and fluency Range of complexity DOK 1-3 Virtual online calculator: Texas Instruments 30XS Detailed diagnostics Two performance levels

11 Cognitive Demands of GED Math Depth of Knowledge (DOK) GED Mathematics Level 1 Level 2 Level 3 Requires students to recall or observe facts, definitions, or terms. Involves simple one-step procedures. Involves computing simple algorithms such as sum or quotient. Requires students to make decisions of how to approach a problem. Requires candidates to compare, classify, organize, estimate, or order data. Typically involves two-step procedures. Requires reasoning, planning, or use of evidence to solve problem. May involve activity with more than one possible answer. Requires conjecture or restructuring of problems. Involves drawing conclusions from observations, citing evidence, and developing logical arguments for concepts. Uses concepts to solve non-routine problems. Examples: Perform routine procedure like measuring. Examples: Solve routine multi-step problems. Examples: Formulate original problem given situation. Recall or recognize a fact, term, or property. Select procedure according to criteria and perform it. Formulate mathematical model for complex situation.

12 DOK Level 3 Item Type your answer in the box. You may use numbers, a decimal point, and/or a negative sign in your answer. Hartley opened a food truck business to sell food on the street. On day 2, the business earned $112. On day 5, the business earned $367. Hartley assumes that his earnings will continue to increase at the same rate. How much will the business earn on day 10? $

13 DOK Level 3 Item Year TREE 1 Trunk Diameter in Inches GED Math Item A scientist creates an equation that models her data for Tree 1 so that she can predict the diameter in the future. Complete a linear equation that fits data for Tree 1, where x is the year and y is the trunk diameter. Click on the variables and numbers you want to select and drag them into the boxes. Equation for Tree 1 Y=

14 Solving a DOK Level 3 Item Slope of a Line Slope-Intercept Slope of a Line m= Y2-Y1 X2-X1 y= mx + b m= m=.6 2 m= 0.3 y= mx + b 18.6= 0.3(1) + b 18.6=

15 Math Assessment Targets Two major content areas: Quantitative problem solving Algebraic problem solving

16 Mathematics Content: Quantitative Problem Solving (45%) Math Content Domains Number sense and Computation One-Step and multi-step word problems Rate, ratio, and percent word problems Quantitative problems in geometric measurement Quantitative problems in statistical measurement Assessment Targets Foundation Progressing Advanced Q.1 Ordering and computing w/rational numbers, simplifying numerical expressions, interpreting distance using a number line. Q.2 Reasoning quantitatively to solve problems involving rational numbers. Q.3 Solving problems involving a proportional relationship. Q4. Computing perimeter, circumference, and area. Q.7 Reading and interpreting graphs, charts, and other data. Q.5 Computing volume and surface area of prisms and cylinders. Q.8 Measuring the center of a statistical data set. Q.6 Computing volume and surface area of cones, pyramids and spheres. Q.9 Determining sample space and using probability models. CCS References 6-7.NS, 3.5.NF, 8.EE, N-RN 6-7.NS, K-5.OA, 7-8.EE, N-Q 6-7.RP, 7.EE.3, 7-G, N-Q 3-8.G, 6.EE 6-8.SP, S-CP.9, S-ID.1, S-MD.2

17 Mathematics Content: Algebraic Problem Solving (55%) Math Content Domains Transforming Expressions Solving Equations Lines in the Coordinate Plane Function Concepts Assessment Targets Foundation Progressing Advanced A.1 Simplifying, evaluating, and writing linear expressions. A.4 Writing and solving linear equations. A.7 Graphing and equation in two variables in the coordinate plane, knowledge of slope. A.10 Evaluating a function for a given point. A.2 Simplifying, evaluating, and writing polynomial expressions. A.5 Writing and solving linear inequalities. A.8 Determining the equation of a line. A.11 Comparing functions in different presentations. A.3 Simplifying, evaluating, and writing rational expressions. A.6 Writing and solving quadratic equations. A.9 Applying the slope criteria for parallel or perpendicular lines. A.12 Identifying features of a function from graphs or tables. CCS References A-SSE, A-APR, 6-8.EE A-REI, A-CED, A- SSE, 6.8.EE A-REI, G-G-GPE, 8-EE, A-CED 8.F, 8-EE, F-IF

18 Assessment Targets: Quantitative Problem Solving Assessment Targets: Quantitative Problem Solving Q.1 Order and compute with rational numbers; simplify numerical expressions. Q.2 Use quantitative reasoning to solve problems with rational numbers. Q.3 Solve problems involving a proportional relationships. Q.4 Compute perimeter, circumference, and area of plane figures. Q.5 Compute volume and surface area or prisms and cylinders. Q.6 Compute volume and surface area of cones, pyramids, spheres, and other shapes. Q.7 Read and interpret graphs, charts, and other data representations. Q.8 Measure the center of a statistical data set. Q.9 Determine sample space and use probability models to interpret data.

19 Assessment Targets with Indicators: Quantitative Problem Solving CCS 7.G.6 8.G.7 7.G.4 6.EE.2c, 7.G.6 6.EE.2c, 7.G.5, 8.G.9 Q.4: Computing perimeter, circumference, and area of plane figures DOK Level Q.4.a: Complete the area and perimeter of triangles and rectangles. Determine side lengths of triangles and rectangles when given area or perimeter. 1-3 Q.4.b: Use the Pythagorean theorem to determine unknown side lengths in a right triangle. 1-3 Q.4.c: Compute the area and circumference of circles. Determine the radius or diameter when given the area or circumference. Q.4.d: Compute the perimeter of a polygon. Given a geometric formula, compute the area of a polygon. Determine the side lengths of the figure when given the perimeter or area. Q.4.e: Compute perimeter and area of 2-D composite geometric figures, which could include circles, given geometric formulas as needed

20 Assessment Targets: Algebraic Problem Solving Assessment Targets: Algebraic Problem Solving A.1 Simplifying, evaluating, and writing linear equations. A.2 Simplifying, evaluating, and writing polynomial expressions. A.3 Simplifying, evaluating, and writing rational expressions. A.4 Writing and solving linear equations. A.5 Writing and solving linear inequalities. A.6 Writing and solving quadratic equations.

21 Assessment Targets: Algebraic Problem Solving Assessment Targets: Algebraic Problem Solving A.7 Graphing an equation in two variables in the coordinate plane, solving problems requiring knowledge of slope. A.8 Determining the equation of a line. A.9 Evaluating the slope criteria for parallel and perpendicular lines. A.10 Evaluating a function for a given input. A.11 Comparing functions in different presentations. A.12 Identifying features of a function from graphs and tables.

22 Assessment Targets with Indicators: Algebraic Problem Solving A.7: Graphing an equation in two variables in the coordinate plane, solving problems requiring knowledge of a slope CCS DOK Levels 6.NS, 6c A.7.a: Locate points in the coordinate plane. 1 8.F.4 8.EE.5 A-CED.2, F-IF.7a A.7.b: Determine the slope of a line from a graph, equation, or table. A.7.c: Interpret unit rate as the slope in a proportional relationship. A.7.d: Graph two-variable equations

23 Mathematics Formula Sheet Area of a: Parallelogram A=bh Trapezoid A=½h(b1 + b2) Surface Area and Volume of a: Rectangular/right prism SA=ph +2B V=Bh Cylinder SA=2πrh+2πr² V=πr² Pyramid SA=½ps+2B V=1/3Bh Cone SA=πrs+πr² V=1/3πr²h Sphere SA=4πr² V=4/3πr³ π=3.14

24 Mathematics Formula Sheet Algebra Slope of a line m= Slope Intercept Form of the Equation of a Line Point-slope form of the equation of a line Standard form of a quadratic equation Quadratic formula Y = mx +b Y2-Y1 X2-X1 Y-Y1 =m(x-x1) ax² + bx + c = y Pythagorean Theorem a²+ b² = c² Simple Interest x= I = prt -b± b²-4ac 2a

25 Changes to Formula Page 2002 vs Formulas Removed Formulas Added 1. Area square, rectangle, triangle, circle 2. Perimeter/Circumference square, rectangle, triangle, circle 3. Volume cube, rectangular solid 4. Coordinate Geometry distance between points 5. Measures of Central Tendency mean, median 6. Distance 7. Total Cost 1. Surface Area 2. Volume 3. Algebra rectangular/right prism, cylinder, pyramid, cone, sphere Rectangular/right prism, sphere 1) slope-intercept form and 2) point-slope form of the equation of a line standard form quadratic equation quadratic formula

26 Virtual Online Calculator TI-30xs scientific calculator Features Dual power: solar and battery Classroom activities and exchange Preview kits and EZ Spot Teacher Pak Overhead version at Stokes Publishing Guidebook Online emulator at Atomic Learning Newsletter for instructors

27 What Can We Do Now? Join the Closeout Campaign - Lobby for infrastructure Plan and execute professional development Ask publishers about their plans

28 What Can We Do Now? Review the material supplied with this webinar Download the 2014 GED Resources: Test Item Sampler Tutorial Assessment Guides Chapters 1-3 Review the CCS for math and language arts

29 Bill Walker View our other webinars at Visit our blog at blog.wonderlic.com