welcome to module 7 computation of the Acadian math essential Workshop what is basic computation it's addition subtraction multiplication and division why is it important our nape results both in 2011 and the more recent napes indicate that a small percentage of students are at or above proficient on nape and 40% of the nape assessment in fourth grade really does focus on number properties and operations which typically are traditionally computation problems math computation plays a role in overall math achievement our computation measure is a standardized measure of basic computation skills really designed to assess skills from the following different domains so we have operations in algebraic thinking we have numbers and operations in base 10 numbers and operations with fractions and the number system so how did we design the computation measure depending on the grade level we're looking at assessing addition subtraction multiplication and division and in later grades we also include problems with fractions and decimals within those four operations we've done a number of research studies to determine our problem creation rules and also establish optimal timing for the measure at each grade level so for instance we have done uh with our item level studies the measures were administered untimed so we were able to tell exactly how long it takes students to finish the entire measure because we had teachers write the elapse time at the top of the page and then we actually don't want students to be able to complete the whole assessment so we want to be able to see growth across the year so we set time ranges in which a very small percentage of students would actually be able to complete the assessment during the winter so that was kind of where we where we looked was during the winter um and with the problem creation rules we really refined the ranges of numbers that we were asking um we really took a closer look at kind of the difficulty level of the problems and wanted to make sure the problems were consistent from worksheet to worksheet to worksheet so that the problem number two is going to be the same difficulty or at least a very similar difficulty level from you know progress monitoring 1 to progress monitoring 14 so we're able to look to see if student scores are increasing we can attribute that to student growth rather than difference in difficulty levels of the worksheets we also have a variety of problems that are included on each worksheet and each problem has a range of numbers to select from when we've randomly generated the numbers so another words there's a very specific set range of numbers that we can use for each problem and again that goes back to our item level studies that we've conducted and as I had said before the problems are stratified so they appear in the same place on each of the worksheets and this is really to control the difficulty level of the worksheets and make sure that those alternate forms are as close as possible without asking the exact same question over and over and over again because then you'd have practice effects so then students May recognize what type of question you're asking so again with computation we're really looking at that basic computation skill our Administration time ranges from 2 to 6 minutes per worksheet depending on the grade level it's given from the beginning of first grade all the way through the end of sixth grade we're going to be looking at correct digits in the final answer and we will spend a a large chunk of this module really digging deeper into how to score those problems we have no weight Rule and we have no discontinue rule because these measures are group administered measures here is what our computation Benchmark goals look like over the next few slides you'll be able to see exactly what they are we have our grade so what grade we're looking at we have our score level above Benchmark at Benchmark below Benchmark or well below Benchmark we have our need for support So core support strategic support or intensive support we have what time of year so beginning of year middle of year end of year then we have our bold numbers are The Benchmark goals and our italicized numbers are our cut points for risk so if you have a student who's scoring below that italicize number then they are going to have scores within that well below Benchmark range this is what the numbers look like for third and fourth grade and fifth and sixth grade computation is a group administered measure however if you have a student who would you feel would do better in an IND individually administered situation uh so they might be less distracted if they have the measure administered to themselves that's completely fine to do um but it is designed to be a group administered measure you as the assessor would provide a set of standard directions and then the time limits vary by grade our scores the total number of correct digits and we'll spend a lot of time in this module going over how to determine those those scores here are our grade level time limits for computation worksheets we have our time limit per worksheet with grade we're looking at and then the total time for Benchmark assessment because Benchmark assessment we're administering two worksheets and then taking the average of those two worksheets in grades one and two the time limit is 2 minutes per worksheet grade three is three minutes four is five minutes and five and six is 6 minutes per worksheet so if we're doing progress monitoring we're doing one work worksheet if we're doing a benchmark assessment we're doing two worksheets so there's always a form a and Form B and then then we would take the average of the two the materials that you'll need are copy the student worksheets for each student so again form a and Form B for The Benchmark assessment you'll need a copy of the Teacher Key a stopwatch and pencils for students you want to provide each student with a pencil and a student worksheet you want to hand out the worksheets face down to each students so they can't start before the time starts as you're handing out the worksheets you'll say I'm going to hand out a math worksheet please leave the paper face down and wait for further instructions some schools opt to pre-label their worksheets um and others don't so if you have not pre-labeled the worksheet with the student name um you can then give this following optional directions and the purpose of this step if you haven't pre-labeled is really to prevent students from taking the time to write their name during the timed test Administration so we just want them to be working on the math problems during the time to test Administration say leave the paper face down but write your name on the back and then we're going to read the following specific directions for the student and you will need to look up based on what grade level you're administering how long to say that the worksheet will take so for instance if we are looking at second grade it's 2 minutes so we'll say we're going to do a math worksheet that will take two minutes there will be several types of math problems look at each problem carefully before you answer it when I say begin Turn the Page over and start with the first problem continue working across the page before going on to the next row try to solve each problem if you cannot solve a problem skip it and go on to the next one if you reach the end of the page stop and put your pencil down are there any questions typically there aren't but we always ask and then when you say begin you'll start your stopwatch you'll want to monitor students especially if it's a larger group of students making sure to walk up and down rows of desks or however you have it structured and use reminders as needed at the end of the time limit so you look back again at the table depending on the grade level say stop and put your pencils down and then you'll want to collect all the computation worksheets during a benchmark assessment you're going to administer two worksheets so you administer the second worksheet immediately after the first so at administering the second worksheet you would say the following shorten directions so as you're handing out the second worksheet say I'm going to hand out a second math worksheet please leave the paper face down and if you haven't had them write their names on them and then you would also add and write your name on the back when I say begin Turn the Page over and start with the first problem then say begin and start your stopwatch again monitoring the students and using reminders as needed and then at the end of the time limit so again looking back at the grade level say stop and put your pencils down and then you'll want to collect all the computation worksheets it again it's very important that we read our directions for btim we start our timer after we say we monitor the students while they work and provide reminders as needed and when the time is up we say stop put your pencils down and then collect all the worksheets then distribute the second worksheet and repeat the procedures if you're doing a benchmark assessment we have several reminders that can be used as often as needed so if the students not attempting problems in order or skipping around without trying to solve them we can prompt them to say try to solve each problem if a student stops working before the test is done we can say keep doing the best work you can and if a student asks you for help with the task you'll say just do your best let's talk about the scoring rules for computation when you begin to score computation form you'll need a copy of the teacher key for that worksheet There are 16 to 25 problems on a worksheet each in individual boxes and there's going to be a lower right hand portion of the box you'll find a small legend that describes how to score the problem based on the number of correct digits in the answer we will go over many different examples of this in the next few slides all of the scoring should be done on the student worksheet and not the Teacher Key and then for each problem the student completed or attempted we want to write down the number of points received for that particular problem you want to make sure that you know which marks are yours especially if you are not the students teacher because likely the student teacher will go back to these worksheets because they contain a lot of very valuable instructional information in terms of how students are approaching the problems so you'll want to place your marks in a consistent location or Circle your marks or use a different color pen you'll want to add the total points possible in each row and note that number in the right margin by each row and then add the row totals together that get the students total score and record that score on the top of the page in the space provided the final score for the computation probe during a benchmark assessment is the average score from the two student worksheets so for example the scores of 27 and 35 the final score would be 31 so we're averaging the two scores together if the average ends up on a decimal such as 32.5 then we round up and the final score for the student would be 33 Acadian data management also will compute the final score for you so you don't need to go through and do this yourself if you don't want to so let's start to go through a few examples on the Teacher Key each problem includes a small chart in the lower right hand corner that displays the possible points for the problem this leftand column represents the number of digits that the student has correct in the answer answer potentially the right hand column displays the number of possible points the student can receive the arrow that you see here under the correct answer represents the direction to score the problem so we're always going to be consistent score this in a standardized way we're going to score right to left for addition subtraction multiplication and left to right for division if you note with fraction there may be some additional points awarded in parentheses and we'll go over examples of all of these different types of problems so our basic rules for scoring we're going to be looking at correct digits and this refers to correct digits in that final answer we're going to score each problem referring to the scoring Direction arrows on the Teacher Key so we're going to score in the direction that the arrows are the answer also must be completely correct in order to receive points for all of the correct digits um and this one was added a little bit later so initially we were just looking at the correct digits and rarely but but it did happen once in a while a student may have gotten credit for all of the correct digits but they didn't have the answer correct so it looked like they weren't having issues with that particular problem but they weren't arriving at the correct answer they just happened to get the digits correct so we wanted to make sure that did not happen so now the answers must be completely correct in order to receive points for all of the correct digits and we'll go through how to look at this in those rare circumstances when it may come up points really are determined by the difficulty level of the problems so the number of points possible for addition and subtraction of other simple problems typically is the same number of digits in the correct answer so for instance the student has one correct digit and that's worth one point however more complicated multiplication division fraction problems require more steps to complete typically take more time to complete and therefore they are going to be worth more points um so for instance with this long division problem three correct digits is now worth seven points we really are going to be looking at at the digits that are eligible for receiving points and it really is the digits in the answer that are displayed on the Teacher Key so this kind of goes through just some of the rules and again we are going to go over all of these in depth with all of our different examples in a few slides our remainder symbols are excluded from division problems but the remainder itself is eligible for receiving points decimal points are eligible for points and if fractions contain that only then the answer has to be exact to get the points the only is if students have successfully reduced the fraction we're we're not asking students to reduce the fraction um but they essentially get a bonus point if they do reduce the fraction so if the student doesn't answer exactly then look at the bottom answer and determine points based on that also with fractions the language may say or equivalent and in these instances it typically is the student has used a different number than the least common denominator and if the answer is correct then we still want to give the student credit for that they they've arrived at the correct answer they've just used a different denominator um and we will give them credit for that and correct digits are counted as the total digits in the answer that are correct and scored in the correct direction as indicated by the arrows on the answer key um so sometimes questions come up about why why why those directions why do we have to do it that way um number one it keeps things standardized so everyone is scoring it in the same fashion across the assessment so that way we're able to compare answers across classrooms across grade levels across schools districts you know States you can keep going out from there um and it also reflects if you were to solve the problem kind of an traditional way then you approach solving the the addition subtraction multiplication problems from right to left and you approach solving division from left to right this is not to say that students have to solve the problem in that way one of the wonderful things about looking at correct digits and the final answer is it doesn't necessarily matter how the student arrived at that answer it matters that they did arrive at that answer and then you as the teacher or if you are assessing and scoring and then giving that back to teachers but teachers can go back and look at the students work and determine exactly how they've arrived there and if they are having issues if they did get that problem in correct and they have made errors you can go back and take a look at their process in which they have arrived at that answer to determine kind of where that breakdown is occurring so when we start to determine points the thing that we are going to look at first is what the answer is so we can tell that this is an addition problem we're scoring this problem from right to left we can tell in this box down here there are going to be two possible correct digits and each digit is worth one point so with this first example the student wrote seven that's the first digit we look at that is correct the student wrote an eight the eight is correct they received two points for two correct digits so they had two digits correct that's worth two points in this next example the student wrote three and it should have been a seven the student wrote an eight which was supposed to be an eight so they have one digit correct and that is worth one point so this is how we look we're going to look at the arrow in which how we're scoring that and then we're going to evaluate in that way did the student write the correct digit and then once we have the number of correct digits we're going to look at this table at the bottom the chart at the bottom and say okay if the student had one digit correct how many points is that worth that's worth one point let's look at a more complex problem and determine correct digits first we're going to note that we're scoring these problems from right to left we'll also note that there are five potential correct digits worth a total of 17 points so in this first example we would look at the one first and that is correct the five that is correct the six that is correct the five correct seven correct so this student had all five digits correct and received a total score of 17 for this problem now let's look at example 2B this student made several errors when Computing this problem again we're just going to look at correct digits in the final answer the one is correct the seven is incorrect the six is correct the six is incorrect the eight is incorrect so this student had two correct digits and that is worth a total of six points a little bit later we're going to look at at the optional response pattern analysis which I think is is hugely important instructionally um to start taking a closer look at but in this student example 2B they would have gotten flagged as not having they had this problem correct and that's an indication that the teacher should go back and take a look at the student work and start to figure out okay where did that error occur and if you have common errors across a number of students you can always pull them together in a small group instructionally and ret that skill so let's take a look at fractions with fractions with this first example um with the Teacher Key we're going to note that there is an only so there's an opportunity for students to reduce the fraction remember with only they have to do it correctly so that's a worth a potential of three points if they've done it correctly if they haven't reduced or if they've reduced incorrectly we're going to evaluate it based on what's underneath this line what's underneath the or line so first with the first example the student wrote 1/2 now 1/2 is meeting that only rule so that student received three points for this problem in the next example they did not have the fraction reduced so they did not meet this Only Rule so we're going to evaluate it based on what's below that or line we look at the numerator and denominator separately so that's indicated by the arrows so if this were a multi-digit answer um you would you would want to especially evaluate it from right to left so first we'd look at the three the three is correct so they will receive credit for the correct digit in the numerator we'd look at the six the six is correct so they receive the credit for that correct digit in the denominator so they receive a total of two points for this problem in example 3C and this is a pretty common example from um all of the item level data that we've gotten back it's it's fairly common to see that this particular error but we would look first at the numerator and the three is correct so they're going to receive credit for one correct digit and next we're going to look at the denominator so we're going to look at that first digit again we're scoring from right to left and they wrote two should have been a six so they do not receive credit for the denominator they receive a total score of one for this particular problem let's take a look at another fraction uh this fraction has a whole number a numerator and a denominator and it has the text or equivalent so we know that if they choose a different common denominator rather than the least common denominator that's okay um and we're still going to give them credit if they have it correct so let's look at the first example I always typically look at the whole number first and then the num numerator and then the denominator but you can do it in any order that you'd like just know that you evaluate them separately so first the whole number should have been a nine we're evaluating from right right to left it is a nine so we know that's one correct digit next we're going to look at the numerator they wrote seven it should be seven again from right to left so they have two correct digits next we're going to evaluate the denominator the first number should be a two because we're evaluating it from right to left that is correct the second number should be a one that is correct they have all four correct digits and that's worth a total of 10 points in this next example we first look at the whole number the whole number is correct next we look at the numerator remember we evaluate these separately so the numerator they wrote two it should be seven it is incorrect then we're going to look at the denominator they wrote seven it should be a two that is incorrect so this student received one correct digit worth two points example 4 C here is an example of the or equivalent they have chosen a different common denominator than the least common denominator and that's fine so this student has all of the answers correct the whole answer is correct so we want to be able to award full points for this and I know you may be thinking but there's five digits there and there's only potential of four digits on the Teacher Key that doesn't matter we are just giving them full credit for the correct answer they've just chosen a different common denominator so this is an example of the or equivalent now decimals so with decimals the easiest way the best way to do this is just to ignore the decimal point at first so we know which direction we're scoring in we're scoring from right to left we know that there are four potential correct digits the decimal counts as a correct digit and this particular problem is worth a potential Four Points so when we're evaluating the answers we want to ignore the decimal first so we're going to look at the numbers first we say two is two the correct digit yes is zero a correct digit yes is nine a correct digit yes then we go to take a look to see if the decimal is in the correct position and in this case the decimal is in the correct position so that counts as a correct digit they have four correct digits and it's worth Four Points so let's take an second look at another example so this is example 1B again we are going to look at the numbers first ignoring the decimal so we say two yes the zero yes the nine yes now we go back to take a look and the decimal is not in the correct location so they do not get credit for that correct digit but they get credit for the three numbers so they have three correct digits and that is worth a total of three points let's look at a division example so for a division we're going to assign correct digits by looking at the student answer from left to right so the first correct digit we should see if we look from left to right on the teacher key is a seven the seven is correct the next is a five the five is correct the third is a five correct the fourth should be a seven and that is incorrect and then we would look at the remainder the remainder should be one and they wrote two so this student has a total of three correct digits and this is worth 12 points I alluded to this a little bit in the beginning but one of our other scoring rules includes extra digits so we want to take a look at the Teacher Key first so we know we're scoring from right to left we know that there should be two correct digits or two potential digits and that will be worth a potential of two points so what happens if students start to write additional digits we need to have two digits that are correct and scored in the correct direction and the extra digit to the left is only ignored if it's a leading zero otherwise it needs to be penalized since the final answer is not correct so this only comes into play when the answer otherwise would be receiving full credit but the student doesn't actually have the right answer so we're not going to worry about penalizing anything else just happens when the student would have gotten full credit but the student does not have the correct answer so let's look at the leading zero first so first we're going to look this should be a six and it is there should be a seven and it is and then the student wrote a zero a leading zero the leading zero on the left of the answer is not counted or penalized so the student has two correct digits worth a total of two points let's go back and take a look at example 1 a so the student wrote a six and that's correct the student wrote a seven and that's correct so really the student has two correct digits and it should be worth two points however the student wrote an extra digit so any additional digit to the left of the answer when the student would have otherwise received full credit is penalized since the final answer is not correct and all we need to do is reduce it by one correct digit so instead of receiving two correct digits for this we're penalizing it because the answer is not actually correct and the student would receive one point for this problem instead of two points and this this serves a purpose because we we still want to give the student credit for this but we also want to flag that problem as a problem that the student had as incorrect um and if we didn't penalize it then it wouldn't get flagged on that response pattern analysis and that that's an important piece we want to be knowing when students are making errors and this is a time that a student has made an error so let's take a look at additional digits within division so any additional digits to the right of the answer or to the right of the remainder when students otherwise would have received full credit for correct digits is going going to be penalized since the final answer is not correct so the total correct digits would be reduced by one correct digit again we are only doing this if the answer would have otherwise received full credit but it's not the right answer so for this example student 3D had this correct so this is what the correct answer should look like so the student wrote 7557 remainder one but then they added an additional zero to the right of the remainder now this otherwise would have received full credit however now they have an incorrect remainder we don't want to give them full credit for that problem I'm going to flip back a couple of slides but we would reduce this problem so they should have received five correct digits worth 20 points but they added another zero to that remainder and so now they got penalized they'll have four correct digits Worth 16 points let's take a look at the second example in this example they've added that additional digit to the right of the answer and again this makes the problem incorrect so we reduce the correct digits by one point otherwise they would have gotten complete credit because the Seven's correct the five the five the seven and then we'd look at the remainder and the remainder is one which is correct cor but they've added this additional digit in there and that makes the answer incorrect overall so if you do come across a student who adds a zero as a placeholder to the left of the answer it's not counted or penalized so we just want to ignore that leading zero um that the student had used as a placeholder and start looking when we're looking at our digits from left to right we would ignore that zero and say okay three yes zero yes remainder one yes they have three correct digits worth nine points this student had the three yes they wrote a one so that's not a correct digit and they do have a remainder of one yes so that's two correct digits worth six points now with erased digits if you can read what students wrote and they possibly could have gotten credit for it we want to give them credit for it so sometimes students May erase if they're not feeling confident in their answer if they're moving on um and if you can read it and give them credit for it please do with multiplication if you have a single line answer you really just need to use your best judgment to determine if that line was the first step in that calculation of the procedure or if that's the student's final answer and just score it according to that judgment some other scoring rules include remainders so the student can receive credit for a remainder whether it's written with a lowercase R an uppercase r or a fraction or decimal as long as it's correct it's fine when we're determining the final score we want to transfer the two Benchmark assessment scores to the front of the testing booklet and then compute the average and Acadian data management will also compute the average as well and the testing booklet contains an optional response pattern analysis I do find it's very helpful instructionally to start to take a look at the types of responses that students are making and then after that start to actually look back at the student work primarily I think that's one of the reasons why that the paper pencil assessments are still so valuable because you can go back and take a look at how students are responding not just the answer that they gave so let's review how many worksheets for a benchmark assessment there's two how long for each worksheet on a benchmark assessment it's a tricky question uh it depends on the grade so it ranges from 2 to six minutes what do I look at to determine points I want to look at the correct digit in the students answer and the basic scoring rule is the correct digits scored in the correct direction according to the arrow on the answer key so I would like you to look over this next practice activity piece I'm going to have you pause this module and complete the scoring for this Benchmark 3 Form B in grade four and then resume when we're ready to talk through the answers this is what the student worksheet looks like and this is what the Teacher Key looks like and when you're ready resume the module and then we will discuss what the answers are now that you've scored this assessment I'm hoping that your score was 31 or at least very close to 31 so let's go over what the answers are for the first question the student wrote 898 so first we would look at the eight then the nine then the eight the student had a potential of three correct digits they had all three correct digits and it is worth three points for question number two we score from right to left we look first at the two and that's correct the three is correct the six is correct and the three is correct that was four correct digits worth a total of four points for question number three we're looking at the whole number first they received credit for the six next we're going to look at the numerator it's two and that's correct the denominator is incorrect it should have been three so they have two correct digits worth total of two points for question number four the three is correct and the six is correct this is two correct digits for two points for number five the first number that they wrote was a four that is incorrect the next number is a two also incorrect they have zero correct digits for zero points number six the first digit is a the zero which is correct the four is correct and the three is correct that is a total of three correct digits for three points number seven the three in the numerator is correct the six in the denominator is correct they did not reduce the fraction so they don't get the only but they do get two correct digits for two points number eight the first number should be eight and they wrote two so that's incorrect the second number is incorrect should have been an eight the third number should have been a four and it's a five and the fourth number should have been a six and it's a seven so they received zero correct digits for zero points number nine they have the nine correct the six correct and the eight correct so total three correct digits for eight points number 10 we're going to look at the whole number first the one is correct and the one is correct next is the numerator the seven is correct and then with the denominator the eight is correct so they receive a total of four correct digits and that is worth Four Points number 11 so the first one that we see is should be a three they wrote an eight should be a one they wrote a zero and they have z.0 correct digits on this problem number 12 they wrote to three which is correct so they have one point for this particular problem next is number 13 this is incorrect it should be a four incorrect should be a zero incorrect should be a seven this is a correct digit the four is a correct digit so they have one digit correct and that's worth a total of two points one question that often comes up is you know does it matter where they write their numbers um and for this particular assessment when we're scoring in a direction it doesn't matter if they have the numbers spaced exactly where they need to be for instance in number 12 however if it's something that's coming up consistently uh definitely something that you can address instructionally but they would still receive credit for number 12 even though they wrote the three over the two instead of over the one so with the response pattern analysis what we're going to do is if the student has the problem correct then we're going to circle the number on the chart if they have the problem incorrect or partially correct we're going to mark an X over the number on the chart if they didn't reach the problem or if they skipped over it that we're going to leave that problem blank though if you notice a consistent pattern in skipping um specifically if students are always skipping division problems and that's a skill that's been taught um then that's definitely something that you'd want to go back and take a closer look look at uh with the last problem that the student completed on the sheet um if it's not completed we just want to leave it blank because we don't want to indicate that they got it wrong when they just ran out of time if students have left other problems partially done however we would mark an X over those numbers and for a benchmark assessment it's probably most helpful to use two different colored pens or some other way to distinguish form a and Form B because sometimes students may get a certain problem correct on form a and incorrect on Form B so let's take an example this is second grade and so when we're starting to look at the skills that are assessed the student is correctly answering the addition problems but has answered each of the subtraction problems incorrectly and so this response pattern analysis is a really quick way of saying okay this the students very solid with their addition skills however we may need some additional support built in for their subtraction skills and then we can go back and take a look at the actual student worksheet we can go back and take a look at the types of Errors the students are making and how they're what their thought process is behind how they're approaching those problems by going back and looking at the students work so let's do some individual practice I'd like you to pause this module and score the first and second worksheet and after completing each worksheet think about how the scoring went and then really answer the following following questions what was easy for you what was difficult what do you need to practice and how are the skills of the student you assessed and when you are ready you can resume the module and we will go over the answers to each of the sheets so for computation grade 5 Benchmark 2 form a you should have had a total score of 54 so let's go over how we arrived at that total score for this first question the student had the one the two the two and the nine that's four correct digits worth a total of four points in question number two the student had all four correct digits and that was worth a total of 11 points in question three the student let's take a look at this since the student did not have the correct answer overall the student did have the correct whole number so eight is correct this seven should have been a and this two should have been an eight so the student received one correct digit for that whole number and that was worth a total of three points question number four the student did not complete the answer they did receive zero points on this particular problem um I'm able to determine that they these were just the students work and the student didn't provide a final answer on this particular problem they've skipped question number five question number six was completely correct so that was four correct digits worth 11 points question number seven the whole number is correct the numerator is incorrect and the denominator is correct so the student received two correct digits worth a total of two points problem number eight was completely correct so the student received two correct digits for two points problem number n was also completely correct so they received four correct digits worth Four Points problem number 10 the seven is incorrect the four was correct the eight was incorrect and the two was correct so the student received two correct digits worth a total of two points they've skipped problem number 11 so if you notice they're skipping the division problems with problem number 12 the student has the two correct with the numerator so if we if we take a look at that the answer if you look under the or line is um 12 over 72 or equivalent this two is correct in the correct location so we uh are evaluating the numerator from right to left so the two would be the first number so they are going to get credit for the two now I know you may be thinking but clearly this student is not approaching this problem correctly ly um so even though they are getting two points for the two if you are filling out that response pattern analysis this problem would get flagged is a is a partially correct problem um so we would go back and take a look at closer look at this particular problem problem 13 they've skipped problem 14 the first correct digit should have been an eight and it was this should have been a four they wrote a six this should have been a six they wrote a five this is a zero which they wrote a zero and this is a one and they wrote a one so they have three correct digits worth a total of six points problem number 15 so with this one we are going to look at the numerator first should be a three they wrote a four should be a one they wrote an eight let's look at the denominator should be a four they wrote a nine should be a one and they wrote a one so they would receive credit for one correct digit worth a total of two points and problem 16 the two is correct the zero is correct the one is incorrect the zero is incorrect and the five is incorrect so they have a total of two correct digits worth five points on this one so this particular form a is worth 50 4 Points now let's take a look at Form B it should be worth 67 points so I'm hoping that you are either right on 67 or within a point of me with this first problem they had it completely correct the second problem they had completely correct the third problem the whole number is correct as well as this one so first we would look from right to left this first in the denominator should have been a zero they wrote a five the second should have been a one they wrote a one so they're going to get credit for the one they have two correct digits the numerator was incorrect they have two correct digits worth a total of four points let's take a closer look at number four so the zero is correct the four is correct the three is correct the one is incorrect and the three is incorrect so this student received three correct digits worth a total of eight points again they're skipping some of the division problems so with problem number six 21 remainder 1 is correct they received three correct digits worth nine points problem seven they have the whole number correct the numerator correct and the denominator correct were three points problem number eight the numerator is correct and then the two digits in the denominator are correct withth a total of three points problem number nine was completely correct so all four digits were correct worth Four Points problem number 10 all four digits correct worth Four Points 11 they've skipped problem number 12 the numerator is incorrect and the denominator the five is not correct but the one is correct they received two points for one correct digit they've skipped 13 problem number 14 the seven is correct The Nine's correct the one's correct the Zero's correct and the one's correct so all five digits are correct worth a total of 12 points problem 15 the whole number of eight is correct the numerator is not nor is the denominator so they received one correct digit worth a total of three points and then problem 16 they did not receive any correct digits with that problem so it is worth a total of zero points so that is how you score both form a and Form B of this assessment so now what I would like you to do is review the completed computation worksheet so the worksheets that we just did and then using a list of skills from The Benchmark scoring booklet it appears in your slides I want you to note the last item attempted Circle the correct items put the X on the incorrect items then leave blank any skipped or not attempted items and just think about a list of skills that the student has not yet mastered so let's pause this and when you're ready to go over what that response pattern analysis looked like you can resume the module so this is what this response pattern analysis looks like so we're able to very quickly say okay the student is fairly solid in the skills that we know that they've answered correctly in both worksheet a and worksheet B we can tell very quickly which skills they may need some additional support on if they've already been covered this year instructionally and we know that we have a couple of skills we may want to go back and take a closer look at because they had one is correct and one is incorrect so we want to make sure that they they have like a solid foundation with these particular skills so this is just one way of just starting to look and see kind of the overall picture of how students are responding now if I'm doing this with multiple people in my class I can see if I have a group of individuals who are really struggling with multiplying a two digit number by a three-digit number I can pull them together especially if I've covered this already and address that instructionally with a group of students who need similar support additionally I can go back and take a look at the students work and really start to determine how they're approaching solving these problems and where it's going wrong and that also will help me instructionally so even though these are brief measures we're getting a score we're comparing that score to the Benchmark goal they're still telling us a lot of really good information by going back and looking at the students work so to summarize with computation we are looking at correct digits to determine points and we need to remember that correct digits are scored in that correct direction as indicated by the arrows on the answer key and the answer must be completely correct in order to receive points for all of the correct digits