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A matrix for building, self-‐assessing and peer reviewing local assessment: Task Difficulty 1. Item: no task analysis, strategy, (Complexity, Autonomy, Context) Math Examples Cognitive Demand (Depth and breadth of thinking) or real performance required: a selected-‐response or fill-‐in test item. E.g. A multiple-‐ choice item requiring one-‐step solution. A. Recall: Accurate memory of familiar content. E.g. Recall a formula or a definition Qs: 1, 5 – 7% B. Basic: requires familiar, brief, and uncomplicated thinking, signaled by the way the challenge is scaffolded and worded. E.g. Infer which expression is correct from the options (but the correct choice is obvious and only a very simple ‘plug and chug’ is needed). Qs: 3, 4, 6, 7, 8, 9 – 22% C. Understanding: requires higher-‐order thought about content, strategy, and sequence. However, the challenge is scaffolded so that the thinking required should seem straightforward – i.e. ‘near transfer’ of thought. E.g. A slightly different problem or look than what was done in class: Analyze which math applies, which expression is correct, and perform some testing to determine & check the answer. D. Complex understanding: the challenge to thinking is significant: minimal or no scaffold is provided, so it is unclear which content and processes should be used, and what to make of ideas and facts that may seem to conflict or to be insufficient. Insight, analysis, and multiple steps of reasoning are needed – i.e. ‘far transfer’ of thought. E.g. A challenging word problem in which the problem seems initially unsolvable from what is given, and a substantial amount of thought and logic are demanded to find a solution path and solve it 2. Simple script: a routine, constructed-‐response task involving a familiar script, recipe, or process. (more like the “drill” than the “game”) E.g. A familiar and simplified constructed-‐response problem of 2-‐3 steps. 3. Complex performance: A non-‐ routine, complex task in a realistic context, requiring task analysis, strategy, and autonomy in the use of one’s repertoire, self-‐assessment, and self-‐ adjustment. (more like the “game” than the “drill”) E.g. A complex performance task in which minimal guidance is given about how to approach the task, and in which context matters. unlikely Qs: 2, 10, 14, 20, 21, 22, 27 26% Qs: 11, 12, 13, 15, 16, 17, 18, 19, 23, 24, 25 41% Q: 26 3% Place the number of total questions and % corresponding to each cell. E.g. There are 8 questions coded A.1 = 23%., 4 questions coded A.2. = 16%, etc. NOTE: coding the cognitive demand and task complexity often requires background knowledge. It requires you to know whether or not the students had studied and gone over with the teacher the questions/tasks on the assessment (or ones just like them). Just reading the assessment by itself might cause a rater other than the teacher to set the level of demand as high when in fact it is a recall question (i.e. the exact question was covered in class). © Grant Wiggins 2011 _____ _____ _____ Name: Class: Date: Algebra 1 ID: A CHAPTER 5 TEST Jdentfy the choice that best completes the statement or answers the question. Please record your answer with a capital letter in the space provided I) A rational number can A. be expressed as a quotient of integers. always B. sometimes C. never 2) Simpli C. Name the property the equation illustrates. 3) (ab)3a(b3) A. Inverse Property of Multiplication B. Associative Property of Addition C. Associative Property of Multiplication D. Commutative Property of Multiplication Name the property of real numbers illustrated by the equation. 4) —2(x + 11) = —2x 22 A. Associative Property of Multiplication — B. Distributive Property 5) -6+6=O A. Identity Property of Multiplication B. Inverse Property of Multiplication 6) The cross products of a proportion are A. always B. B. SI 2 --2 I -lu —8 Associative Property of Addition C. Associative Property of Addition D. Inverse Property of Addition I C. C. I CI 2 --8 D. III —6 -4 -2 SI 0 2 4 6 never —5xl I 8 —5xl I D. sometimes I 4 Commutative Property of Addition equal. 7) all real numbers at least —5 and at most I A. —5xl ii 4 C. 4 4 -2 III I I U 4 0 2 8 I I 10 2 —5<x<1 I I I I 8 0 ---10 -8 101 ---6 -4 —2 10—I 1) 2 I I I I 3 6 8 0 Name: ID:A 8) A relation is A. a function. always B. sometimes C. never 9) yx 2 ft I —3 10) Evaluatef(x) I I —2 I III 2 4 I x I III —4 —2 I • II 2 4 xforx=4. D.-12 2 x Name: ID: A For the remainder of the test, SHOW ALL OF YOUR WORK if you want to recieve credit. II) v —2x = - 3 + Make a table of values and then graph the function -.— — --- -— — - — — —••-- -. --—— -------- —— — ---- —— (, — 4 — — --- — — — — —— —— -4 I -2 —‘ — -.- -- ••—---• — — = 3xj —— 4 4 5 -v I — ._ — -----j rL —b- 12) y 3 —S — ••—L— — —— 1 — — —— —— - -- --. 1 —1—. Make a table of values and then graph the function -* _ 4 L1 .1 Lt.z --- - 13) I —5 --- -- -- — --- — --zrz 2 0 99 — —l 3 5 47 —6 = 14) Determine if the data is discrete or continuous. Explain your reasoning. A movie store sells DVDs for $15 each. The function (d) number purchased d. = l5d relates the total cost of movies to the ______ ___________ __ Name: IB: A 15) 16) What’s the rule for this table?____________________________ x —2 fix) —6 —1 —3 0 0 1 3 2 6 f(x) x 3 4 5 6 fixLj 71 91 8j iqj 17) Find the range of f(x) = —3x 18) f(x) 19) Suppose Given the = 4x — set of points — 2 and g(x) 2 for the domain {—2, 1, 5, 7}. Show your work. —2x + 1. Find the f(4) value of—. g( 1) [(—8,— 6)(—5, 2)(—8, 1)(7, 3)j, Draw a mapping diagram Domain Range_ Explain how you tell if this is a function { } ________________ ___________ ________ Name: ID:A 20) A taxi company charges passengers $2.00 for a ride, no matter how long the ride is. plus an additional $0.20 for each mile traveled, Let C cost and mmiles driven. a. independent variable b, dependent variable c. equation representing the situation a. What is the charge for a 1.4-mile ride? b. What is the charge for a 27-mile ride?___________ c. What set of numbers would best represent the domain 21) Hour Worked 2 4 6 8 Pay $15.00 $30.00 $45.00 $60.00 State the rule How much would you earn if you worked 10 hrs and 15 minutes? Hint (change 15 minutes into hours) 22) The french club is holding a car wash fundraiser. They are going to charge $12 per car, and expect between 60 and 80 cars. Identify the independent variable__________________________________________ dependent variable find a reasonable domain range and Name: ID: A 23) Solve and graph a. j3x7j 10 b. j2x+5j <9 24) Elaine is in the business of repairing home computers. She charges a base fee of $45 for each visit and $25 per hour for her labor. The price she charges depends on how many hours she works.Write a function rule to model this data. Use the function rule to make a table of values and a graph. (Put any scale you want on the ‘Y’ axis) x 0 c(x) , 3 c(x) - -. -1 zLLtzzz-..z: — — I__• -.. -l—. 1— —,. —4-—. --*.------H x 6 ______________________ Name: ID: A 25) A student scored 80 and 93 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 86 and 90. 26) A supertanker left port traveling north at an average speed of 10 knots (nautical miles). Two hours later a cruise ship leaves the same port, heading south at an average speed of 18 knots. How many hours has the cruise ship traveled when the two ships are 209 nautical miles apart? make a chart and draw a picture (if necessary) 27) An employee receives a weekly salary of $340 and a 6% commission on all sales. a. independent variable___________________________________ dependent variable___________________________________ b. Write a rule to describe the functionj(d) that gives weekly earnings in terms of d dollars in sales.________________________________________ c. Find the employee’s earnings for a week with $660 total sales._____________ d. What were the employee’s total sales for a week in which her earnings were $1300?_________________________