These draft test specifications and sample items and other materials are just that drafts. As such, they will systematically evolve over time.

Transcription

1 t h e reesigne sat These raft test specifications an sample items an other materials are just that rafts. As such, they will systematically evolve over time. These sample items are meant to illustrate the shifts in the reesigne SAT an are not a full reflection of what will be teste. Actual items use on the exam are going through extensive reviews an pretesting to help ensure that they are clear an fair, an that they measure what is intene. The test specifications as well as the research founation efining what is measure on the test will continue to be refine base on ongoing research.

2 Problems Groune in Real-Worl Contexts In response to evience about essential prerequisites for college an career reainess an success, the reesigne sat s Math Test requires stuents to apply their mathematics knowlege, skills, an unerstanings in challenging, authentic contexts. Stuents taking the Math Test will encounter a range of isciplines an will be aske to aress real-worl problems rawn from science, social stuies, an careers an emonstrate a capacity for sustaine reasoning over the multiple steps require to answer many of the questions on the exam. In these ways, the Math Test also rewars an incentivizes valuable work in the classroom. Applications on the reesigne sat s Math Test require stuents to emonstrate the ability to analyze a situation, etermine the essential elements require to solve the problem, represent the problem mathematically, an carry out a solution. These applications often also require linking topics within the mathematics omain (e.g., functions an statistics) an across isciplines (e.g., math an science). Learning to moel an problem solve is enhance when stuents use the same mathematics (e.g., linear equations) to solve problems in ifferent contexts (e.g., science, social stuies, or careers). The following questions help illustrate two important ways in which stuents are aske to emonstrate skill in working within real-worl contexts on the reesigne sat. The first question is set in a science context, base on real-worl methos (synoptic counts, or aerial observations of wintering spots) use by the U.S. Fish an Willife Service to count manatees, a type of sea mammal. 1

3 EXAMPLE 1 6,000 Count of Manatees Number of Manatees 5,000 4,000 3,000 2,000 1, Year The scatterplot above shows counts of Floria manatees, a type of sea mammal, from 1991 to Base on the line of best fit to the ata shown, which of the following values is closest to the average yearly increase in the number of manatees? A) 0.75 B) 75 C) 150 D) 750 This question is an excellent way of connecting linear functions to statistics an using math within a science context. In this question, stuents are not require to moel the line of best fit completely, but they are require to analyze the question to unerstan that they must compute the slope of the line of best fit to get the correct answer, 150 (choice C). The secon example helps show how stuents might be aske to emonstrate algebraic, proportional, an quantitative reasoning while solving real-worl problems on the reesigne sat. 2

4 EXAMPLE 2 An international bank issues its Traveler creit cars worlwie. When a customer makes a purchase using a Traveler car in a currency ifferent from the customer s home currency, the bank converts the purchase price at the aily foreign exchange rate an then charges a 4% fee on the converte cost. Sara lives in the Unite States, but is on vacation in Inia. She use her Traveler car for a purchase that cost 602 rupees (Inian currency). The bank poste a charge of $9.88 to her account that inclue the 4% fee. part 1 What foreign exchange rate, in Inian rupees per one U.S. ollar, i the bank use for Sara s charge? Roun your answer to the nearest whole number. part 2 A bank in Inia sells a prepai creit car worth 7,500 rupees. Sara can buy the prepai car using ollars at the aily exchange rate with no fee, but she will lose any money left unspent on the prepai car. What is the least number of the 7,500 rupees on the prepai car Sara must spen for the prepai car to be cheaper than charging all her purchases on the Traveler car? Roun your answer to the nearest whole number of rupees. solution Part 1: $9.88 represents the conversion of 602 rupees plus a 4% fee on the converte cost. To calculate the original cost of the item in ollars, x: 1.04x = 9.88 x = 9.5 3

5 Since the original cost is $9.50, to calculate the exchange rate r, in Inian rupees per one U.S. ollar: 9.50 ollars r rupees 1 ollar answer: 63 = 602 rupees r = ª 63rupees part 2: Let ollars be the cost of the 7,500-rupee prepai car. This implies that the exchange rate on this particular ay is ollar per rupee. 7,500 Suppose Sara s total purchases on the prepai car were r rupees. The value of the r rupees in ollars is ( 7,500 ) r ollars. If Sara spent the r rupees on the Traveler car instea, she woul be charge ( 1.04) ( 7,500 ) r ollars. To answer the question about how many rupees Sara must spen in orer to make the Traveler car a cheaper option (in ollars) for spening the r rupees, we set up the inequality 1.04( 7,500 ) r. Rewriting both sies r reveals 1.04( 7,500 ) (1), from which we can infer 1.04 r ( 7,500 ) 1. Diviing on both sies by 1.04 an multiplying on both sies by 7,500, finally yiels r 7,212 Hence the least number of rupees Sara must spen for the prepai car to be cheaper than the Traveler car is 7,212. answer: 7,212 Example 2 is an extene-thinking question that requires stuents to go through multiple steps to prouce the solution. Such extene-thinking questions on the reesigne sat require stuents to eeply think through the process of solving problems. Set within a range of real-worl contexts, extene-thinking questions require stuents to make sense of problems an persevere in solving them; make connections between an among the ifferent parts of a stimulus; plan a solution approach, as no scaffoling is provie to suggest a solution strategy; abstract, analyze, an refine an approach as neee; an prouce an valiate a response. These types of questions require the application of complex cognitive skills an will require a little more thinking time for stuents. Stuents will generally be seeing longer problems in their postseconary work. By incluing extenethinking questions, the reesigne sat rewars an incentivizes aligne, prouctive work in classrooms The College Boar. College Boar, SAT, an the acorn logo are registere traemarks of the College Boar. Visit the College Boar on the Web: 4