# 5.4: New Page - Mathematics

5.4: New Page - Mathematics

## Fifth Grade Math Worksheets and Printables

By the time most kids reach fifth grade, life events begin to cross paths with school, and the biggest casualty is time. Whether it’s music lessons, sports practices and games, household chores, or simply increased social activities, fifth-graders usually have a lot on their plates — including increased homework responsibilities across all subjects.

This means there’s not a lot of time remaining to practice math, which gets more and more complicated with each passing year. But with middle school rapidly approaching, it’s absolutely essential for fifth graders to stay on top of the math game. The good news is we have hundreds of fifth grade math worksheets that can assist students with any math-related concept, regardless of skill level. So whether you need a review lesson on something that was taught in fourth grade or you have reached the point where you’re ready to tackle some algebra, our fifth grade math worksheets are here to help. All students have to do is carve out some practice time from their increasingly busy schedule!

## Saxon Math 5/4 through Calculus

The Saxon Math series as a whole is hugely popular among homeschoolers. It is important to be aware that the Math Intermediate series (for grades three through five) and the series reviewed here (Math 5/4 and up) are very different from the Saxon program for K-3. One reason Math Intermediate and other Saxon courses for fourth grade and above are used by so many homeschoolers is that they allow students to work independently. (Note that I will use the term Saxon Math in this review to refer only to Math Intermediate and the series of courses from Math 5/4 through Calculus.)

Homeschool kits include a non-consumable student edition textbook, either an answer key or solutions manual, and tests with answer keys. Some student books are hardcover and some softcover. For some high school courses, solutions manuals are available separately. There are no teacher editions for the Saxon program since each lesson in the student text provides the explanation of the concept to be learned. Each lesson includes an introduction and explanation of the new concept, examples and practice problems, then a set of problems that not only reinforces the new lesson content but also reviews previously-learned concepts. Parents might help students work through the beginning of the lesson, but most students will be able to work through lessons independently. Parents need to check daily assignments and tests, ensuring that students are understanding what they are learning. The program requires virtually no preparation time.

One significant feature of the Saxon series that sets it apart from many other math programs is the incremental, spiral method in which concepts are taught. Once a concept is introduced it is incorporated periodically into the mixed practice that students encounter every day. In later lessons, the concept is developed more fully. Over time and through repeated exposure to a developing concept, students gain understanding and mastery. Unlike most traditional math texts where one content strand is taught and fully explained over a few consecutive lessons (and not returned to unless the content is built on elsewhere), Saxon Math has students work with a concept many times over the course of study. They revisit concepts in what is called a spiral method for frequent review throughout each course.

In addition, practice problems review concepts taught in previous lessons, and the styles of the problems vary constantly. For some students, this works to strengthen their thinking ability and keeps things interesting while it’s just confusing for others. Be aware that some students might prefer arrays of similar problems that practice fewer topics, and they might not do as well with either Saxon Math's teaching approach or the mixture of practice problems.

Saxon Math leans more toward rules in its presentation (i.e., memorizing rules and math facts) rather than a hands-on, conceptual orientation like Math-U-See's or Saxon Math’s courses for the primary grades by Nancy Larson. Even though the program is not strong on teaching concepts, thinking skills get a good workout. This means that the program works best for students who do not need manipulatives and who tend to figure out mathematical concepts without a great deal of explanation. It is also good for those who like brain teasers like those troublesome time/rate/distance problems.

The newest editions of the texts correlate highly with Common Core math standards, having incorporated more about topics like statistics and probability, additional word problems to develop mathematical thinking skills, and topical investigations. For many years, Saxon has resisted the use of calculators at levels below Algebra 2 (third edition). But they now include calculator instruction in the fourth edition of Algebra 1.

A helpful addition in the newest Saxon textbooks is reference numbers in the mixed problems sets. If a student misses a problem, the reference number next to the problem provides the number(s) of the lesson(s) where the concept was taught. While new editions have added one color to the black-and-white presentation, Saxon Math books still lack visual pizzazz.

Saxon's two-digit, grade-level designations in the titles of the courses can help you figure out the correct grade level for each book, although free placement tests are available at their website. Typically the second of the two digits indicates the grade level usage for average to bright students. The first digit indicates the grade for students working a little below level. For example, Saxon Math 7/6 would be for average to bright sixth graders or for slower seventh graders.

The situation with Math 8/7 and Algebra 1/2 is a little confusing. Math 8/7 was a late addition to the Saxon lineup and was considered optional for a few years. However, with revisions to the other texts, Math 8/7 really replaces Algebra 1/2. Ideally, students will complete Math 8/7 in seventh grade and Algebra 1 in the eighth. If a student is not ready for algebra in eighth grade, consider using Algebra 1/2 at that point. There will be some repetition of content but struggling students will be better prepared to tackle Algebra 1 if they complete both courses.

Saxon texts Math 5/4 through Math 8/7 start each lesson with Warm Up activities. These generally include math-fact practice, mental math problems, and a word problem. A parent or teacher should present the mental math problems orally and listen for correct responses. Algebra 1/2 does not have Warm Up activities.

### Math 5/4 Third Edition

This textbook should be appropriate for most fourth graders and those fifth graders who lag slightly behind grade level. Among topics covered in Math 5/4 are addition (review), subtraction, multiplication (up to multiplying a three-digit number by a two-digit number), division (dividing by two-digit numbers), time, measurement, money, area, perimeter, fractions, mixed numbers, arithmetic algorithms, geometry, negative numbers, powers and roots, two-step word problems, decimals, averaging, estimation, patterns, sequences, statistics, probability, and Roman numerals. Saxon also sells Basic Fact Cards, an optional set of flashcards for working on addition, subtraction, multiplication, and division that might be useful at this level.

### Math 6/5 Third Edition

This text continues developing arithmetic skills through multiplication and division of fractions and decimals while reviewing and expanding concepts of place value, addition and subtraction, geometry, measurement, and probability. Powers and roots, prime and composite numbers, ratios, and order of operations are also taught. Extra math drills for each lesson are at the back of the book. A few students might have difficulty with this text because it requires them to work in more abstract ways than they might be ready for.

### Math 7/6 Fourth Edition

Math 7/6 is especially good at providing cumulative review and expansion upon topics covered in earlier grades. Among topics covered at this level are fractions, mixed numbers, decimals, percents, rounding, estimating, exponents, working with signed numbers, square roots, beginning algebraic expressions, volume, angles, circles, prime factorization, ratios, proportions, statistics, and probability. Especially notable are word problems that cause children to think of math concepts in a number of different ways to ensure understanding. These features make this a great choice for many students at this level.

### Math 8/7 Third Edition

Math 8/7 reviews material introduced in the prior texts, especially Math 7/6, and provides pre-algebra instruction. It covers word problems, scientific notation, statistics, probability, ratios, proportions, simplifying and balancing equations, factoring algebraic expressions, slope-intercept form, graphing linear inequalities, arcs, sectors, and the Pythagorean theorem.

### Algebra ½ Third Edition

This pre-algebra course can be used after completing Math 8/7. Plenty of review, a spiral learning process, thought-provoking word problems, and clear instruction that works for independent study make Algebra 1/2 one of my favorite options available for this level, even if it is no longer needed. As is typical of the upper-grade Saxon books, the level of difficulty rises sharply toward the end of the course. If your student starts to have more difficulty in the latter part of the course, consider doing only half a lesson each day.

Among topics covered are fraction, decimal, and mixed number operations scientific notation exponents radicals algebraic expressions solving equations with one variable order of operations ratios geometry fundamentals and graphing. Saxon Math has resisted the inclusion of calculator instruction even though most other texts for the pre-algebra level include it. While students can use calculators to solve problems when it is appropriate, they are not instructed to do so.

### Saxon Math High School Options

It is important to consider the design of the entire Saxon lineup of high school math courses before starting into Algebra 1. Fortunately, Saxon now has two options with two parallel series of textbooks.

Originally, Saxon Math took an unusual approach by integrating algebra, geometry, and trigonometry into three textbooks titled Algebra 1, Algebra 2, and Advanced Mathematics. (In contrast, most high schools teach one course in algebra, then geometry, then return to algebra with some trigonometry included.) Saxon has continued to offer the integrated approach with Algebra 1 and Algebra 2 third editions, as well as Advanced Mathematics second edition—these integrated texts are now referred to as the “Classic Editions.” But their Fourth Editions of Algebra 1 and 2 along with their relatively new Geometry text follow the more typical sequence. I will discuss the Third Editions first. Geometry required more space to review, so click here for that review.

### Algebra 1 and 2, Third "Classic" Editions

In Saxon Algebra 1, third edition, coverage is comparable to that in other first-year algebra texts. However, Saxon Math teaches the use of a graphing calculator sparingly compared to many other courses. The spiral method of presentation and constant review help students work fairly independently, a major advantage for parents who lack time and expertise.

Algebra 2, third edition, covers standard second-year algebra topics, although its inclusion of a significant amount of trigonometry is not a standard feature of all second-year courses. Students will need a scientific calculator for this course. You might want to invest in a graphing calculator while you are at it so it will be useful for future math courses.

Homeschool kits for both courses include the student text, an answer key (with only final answers), and a test book. A separate Solutions Manual with complete solutions and answers is available for each course. While the answer key might suffice, I recommend having the Solutions Manual in case students or parents cannot figure out how to arrive at a particular answer.

Saxon Algebra courses seem to work fine for students who grasp math fairly easily but not so well for those who struggle with the abstract thinking required. Overall, Algebra 1 is fairly easy for students to work through on their own. Interestingly, I have yet to find a text that does a better job with time/rate/distance problems than does this one, even though I know that students still struggle with them in Saxon Algebra 1.

If students have used Math 7/6 and Math 8/7, they might be ready for Algebra 1 in eighth grade. Although many eighth graders will have no problem with this book, there are many who will not be ready to begin algebra for another year or two. If you feel that your child is not ready for Algebra 1 at eighth-grade level, consider using Saxon’s Algebra 1/2 first. Or you might have your teen begin Algebra 1 in eighth grade, but move at a slower pace, taking one and a half to two years to complete it.

In the classic editions, Saxon Math does an excellent job with algebra, but the geometry is weak in my opinion. Geometry is scattered throughout Algebra 1 and 2, and it is presented very briefly in both books. By the time students have completed both books, they will have studied about one semester’s worth of geometry. They complete their geometry requirement with the Advanced Mathematics book. Explanation of geometry topics is fairly brief in Algebra 1 and 2 and does not begin to compare with the quality of presentation in such texts as Discovering Geometry.

A student planning to take only one year each of algebra and geometry (not recommended for college-bound students!) could use Saxon’s Algebra 1 third edition, possibly skipping over geometry instruction and problems, and then use Saxon's (or another publisher's) geometry text instead.

Students who complete both Algebra 1 and 2, but who do not intend to continue through Advanced Mathematics, will not have covered geometry sufficiently since Advanced Mathematics contains much of the geometry material. They would need to use another resource to complete geometry requirements. So this might be another instance where students might skip geometry activities within Saxon Algebra 1 and 2 if another geometry course will be used.

However, if a student is going to go through Advanced Mathematics, tackling a separate geometry course is likely to be redundant and overwhelming, so it would be better to stick with only the Saxon Math texts in that situation.

### Algebra 1 and 2, Fourth Editions

The fourth editions of Algebra 1 and 2 reflect a total rewrite rather than just modifications of the third editions. Both appearance and content are improved. The texts have added a little color with more graphic design. Each lesson begins with a Warm Up that includes one vocabulary question and five review problems. Investigations (mini lessons on specialized topics with their own problems to solve) follow every ten lessons. One of the most significant content changes is the early introduction and frequent use of a graphing calculator with graphing calculator labs. Also, probability and statistics receive far more attention in keeping with current math standards.

One feature lost in the transition over the last few editions is the tongue-in-cheek humor of some of the word problems. John Saxon, the original author, often incorporated historically anachronistic references or offbeat content such as “In a picaresque novel about the Spanish Main, the ratio of rascals to good guys was 13 to 5” (p. 149 Algebra 1 second edition). The fourth editions have plenty of word problems and real-life applications, but the humor has disappeared.

Other elements of Saxon’s methodology remain. Lessons are taught in increments followed by examples and a few practice problems. After that, students work on “Distributed and Integrated” practice problem sets with 30 problems per lesson.

The Homeschool Kits include the student text, a solutions manual with complete solutions for the Warm Ups and all practice problems, and a Homeschool Testing Book. The testing book has 23 cumulative tests plus reproducible test answer sheets. It also has the answers for all of the tests. In addition, a Test Analysis Form helps you identify lessons where concepts were originally taught so that students can review if needed for problems they missed. Note that the third editions have answers to odd-numbered problems in the back of each student text, but there are no answers in the fourth edition textbooks. All answers and solutions are in the solutions manuals.

The fourth edition of Algebra 1 introduces trigonometry and more extensive work with quadratic equations and functions than does the third edition. In keeping with the slightly advanced content of Algebra 1, the fourth edition of Algebra 2 does much less review in the early chapters than in the third edition. (A Skills Bank at the back of the book provides some review if needed.) Instead of a thorough review, this text jumps quickly into functions, matrices, and determinants. More attention is given to functions, while matrices and determinants are not even taught in the third edition. Geometry is reviewed through practice problems and incorporated into lessons that apply algebra and trigonometry. Students work with practical applications of concepts through word problems more than we find in many other second-year algebra courses. This text should be a great option for those who need a challenging course that will prepare them for advanced math.

The Saxon Math program has tended to be strong on skill development, but weaker on conceptual explanation and application. The inclusion of investigations in the fourth editions of Algebra 1, Algebra 2, and the new Geometry book (as well as in the newer texts for younger levels) reflects the publisher’s awareness of this problem. This particular feature, along with other improvements, makes the fourth editions my recommended option rather than third editions.

Advanced Mathematics should follow both the third and fourth editions of Algebra 2. This text is one of the easiest for most homeschoolers to work with to cover advanced algebra, geometry, and trigonometry. Originally envisioned as a one-year course, Saxon now recommends that students take at least a year and a half to complete the course unless they are very bright. However, because fourth editions of Algebra 1 and 2, as well as the Saxon Geometry course, are more advanced than the classic series, students are likely to find more material to be at a review level and might be able to get through the text in just one year.

Advanced Mathematics includes the equivalent of the second half of geometry, plus advanced algebra, pre-calculus, and trigonometry. In the revised second edition, much of the geometry was moved to the front of the book rather than being spread out. This should make it easier for students who need to get through the geometry lessons in preparation for PSAT tests in their junior year. In addition, geometric proofs are taught early in the course then used throughout the first half of the book.

Students will need a graphing calculator to use with this text, although the calculator is not used as much as in other texts for this level. Of course, parents can decide to allow students to use a calculator more than is required.

Among other topics covered are logarithms, conic sections, functions, matrices, and statistics. This text moves even further into the theoretical math realm than do earlier Saxon texts. By the time students complete Saxon’s Advanced Mathematics, they should be on a par with students who have completed a pre-calculus course. This course should be particularly good for preparing students to do well on college entrance exams.

### For extra help:

D.I.V.E. Into Math offers instruction for each Saxon text from Math 5/4 up through Calculus on CDs that play on your computer (discs for either Windows or Mac systems available).

Also see the review of Saxon Math Teacher, CD-ROM teaching presentations by an experienced teacher for selected Saxon textbooks.

You might want to check out the premade lesson plans from Homeschool Planet that are available for most of the Saxon Math courses.

Find lesson plans available for this product at Homeschool Planet. Sign up for a 30-day FREE trial.

### Pricing Information

When comparison prices appear, please keep in mind that they are subject to change. Click on links where available to verify price accuracy.

Problem: George owes his friend Jeanne $3. If he borrows another$6, how much will he owe her altogether?

Solution: This problem is quite simple: just add $3 and$6 and the result is $9. The problem above can be solved using addition of integers. Owing$3 can be represented by - 3 and owing $6 can be represented by - 6. The problem becomes: - 3 + - 6 = - 9 Look at the number line below. If we start at 0, and move 3 to the left, we land on - 3. If we then move another 6 to the left, we end up at - 9. Rule: The sum of two negative integers is a negative integer. Example 1: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.  Adding Negative Integers Integers Sum - 2 + - 9 = - 11 - 5 + - 8 = - 13 - 13 + - 7 = - 20 Do not confuse the sign of the integer with the operation being performed. Remember that: - 2 + - 9 = - 11 is read as Negative 2 plus negative 9 equals negative 11. Rule: The sum of two positive integers is a positive integer. Example 2: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.  Adding Positive Integers Integers Sum + 2 + + 9 = + 11 + 17 + + 5 = + 22 + 29 + + 16 = + 45 Do not confuse the sign of the integer with the operation being performed. Remember that: + 29 + + 16 = + 45 is read as Positive 29 plus positive 16 equals positive 45. So far we have added integers with like signs (either both negative or both positive). What happens when we add integers with unlike signs? How do we add a positive and a negative integer, or a negative and a positive integer? Procedure: To add a positive and a negative integer (or a negative and a positive integer), follow these steps: 1. Find the absolute value of each integer. 2. Subtract the smaller number from the larger number you get in Step 1. 3. The result from Step 2 takes the sign of the integer with the greater absolute value. We will use the above procedure to add integers with unlike signs in Examples 3 through 7. Refer to the number line to help you visualize the process in each example. We will use money as an alternative method for adding integers. Example 3: Find the sum of + 7 and - 4. Step 3: The number 3 will take a positive sign since + 7 is farther from zero than - 4. Solution 2: If you start with$7 and you owe $4, then you end up with$3.

Example 4: Find the sum of - 9 and + 5.

Step 3: The number 4 will take a negative sign since - 9 is farther from 0 than + 5.

Solution 2: If you owe $9 and you are paid$5, then you are still short $4. Example 5: Find the sum of + 6 and - 7. Step 3: The number 1 will take a negative sign since - 7 is farther from 0 than + 6. Solution 2: If you start with$6 and you owe $7, then you are still short$1.

Example 6: Find the sum of - 6 and + 7.

Step 3: The number 1 will take a positive sign since + 7 is farther from 0 than - 6.

Solution 2: If you owe $6 and you are paid$7, then you end up with $1. Example 7: Find the sum of + 9 and - 9. Step 3: The integer 0 has no sign. Solution 2: If you start with$9 and you owe \$9, then you end up with .

In Example 7 you will notice that the integers + 9 and - 9 are opposites. Look at the problems below. Do you see a pattern?

Rule: The sum of any integer and its opposite is equal to zero.

Summary: Adding two positive integers always yields a positive sum adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.

### Exercises

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

### Complex Numbers

Imaginary numbers become most useful when combined with real numbers to make complex numbers like 3+5i or 6−4i

### Spectrum Analyzer

Those cool displays you see when music is playing? Yep, Complex Numbers are used to calculate them! Using something called "Fourier Transforms".

In fact many clever things can be done with sound using Complex Numbers, like filtering out sounds, hearing whispers in a crowd and so on.

It is part of a subject called "Signal Processing".

### Electricity

AC (Alternating Current) Electricity changes between positive and negative in a sine wave.

When we combine two AC currents they may not match properly, and it can be very hard to figure out the new current.

But using complex numbers makes it a lot easier to do the calculations.

And the result may have "Imaginary" current, but it can still hurt you!

### Mandelbrot Set

The beautiful Mandelbrot Set (part of it is pictured here) is based on Complex Numbers.

The Quadratic Equation, which has many uses,
can give results that include imaginary numbers

Also Science, Quantum mechanics and Relativity use complex numbers.

## Applications & Interpretation SL

Revision Village was ranked the #1 IB Math Resources by IB Students & Teachers in 2020 & 2021.

Revision Village students scored 34% greater than the IB Global Average in their exams (2020).

###### 70% of IB Students

More and more IB students are using Revision Village to prepare for their IB Math Exams.

##### What are the assessment items in the IB Math AI SL course?

The IB Mathematics Applications and Interpretation SL course consists of three assessment items that contribute to a students overall score for the course. There are two exam papers, each worth 40%. Paper 1 (short response questions) and Paper 2 (long response questions) both encourage students to utilize their graphical display calculators. The third assessment item, worth the remaining 20% of the marks, is a ‘Mathematical Exploration’, where students complete a written assignment involving the investigation of an area of mathematics that interests them.

##### How should students prepare for IB Math AI SL exams?

There are two phases students progress through in their two-year IB Math AI SL course: the learning phase and the revision phase. The learning phase occurs in class, with their teacher and textbooks, where students first encounter and explore the mathematical concepts and consolidate their understanding by solving questions specific to that concept. The revision phase, which is what Revision Village is specifically designed for, is when students consolidate their understanding of all of the concepts in the AI SL course and appreciate how the concepts are connected. In the revision phase, the most effective strategy is to practice lots of IB Math AI SL exam questions, to build confidence, reach mastery, and be prepared for the AI SL examinations.

##### How does Revision Village support IB Math AI SL students?

Revision Village is specifically designed to support IB students in the revision phase of their IB Mathematics Applications and Interpretation Standard Level course. Revision Village has four main sections, each for different revision purposes: 1) Questionbank: a large library of IB Math AI SL exam questions categorised by topic and ordered by difficulty, 2) Practice Exams: a carefully designed set of quizzes and mock papers for students to use in their final phase of revision, 3) Past Paper Video Solutions: step-by-step video tutorials of past AI SL exam questions, taught by experienced IB Teachers, and 4) Key Concepts: short concise videos that recap the important theory in the AI SL course. Revision Village is the perfect place for IB Students to learn, practice and prepare for their IB Mathematics exam stress-free, with all of the resources they need in one place.

## Math Homework Help

Engage New York (ENY) Homework provides additional practice for math that is learned in class.

This site is intended to help guide students/parents through assigned homework. You will see a sample of what was done in class and how it was completed correctly. Below is an example of the top of the homework page for grades K-6. This example is for Grade 3 , Module 1 , Lesson 1 .

NYS COMMON CORE MATHEMATICS CURRICULUM

Begin by clicking on your student's GRADE , next select the MODULE , and finally select the LESSON .

The most common question students ask math teachers is
"When will I use math?" This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics.

For technical operation, usability problems with the OJUSD ENY Math Homework Help website, please use the Contact Webmaster Form .

## Practice

With Practice , students build competence in newly acquired skills and reinforce previously learned skills in preparation for tomorrow’s lesson. Together, Learn and Practice provide all the print materials a student uses for their core instruction.

Eureka Math contains multiple daily opportunities to build fluency in mathematics . Each is designed with the same notion—growing every student’s ability to use mathematics with ease . Fluency experiences are generally fast-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material.

Eureka Math fluency activities provide differentiated practice through a variety of formats—some are conducted orally, some use manipulatives, others use a personal whiteboard, or a handout and paper-and-pencil format.

Sprints: Sprint fluency activities in Eureka Math Practice build speed and accuracy with already acquired skills. Used when students are nearing optimum proficiency, Sprints leverage tempo to build a low-stakes adrenaline boost that increases memory and recall. Their intentional design makes Sprints inherently differentiated – the problems build from simple to complex, with the first quadrant of problems being the simplest, and each subsequent quadrant adding complexity.

## Selection Methods

How to answer that famous “tell me about yourself” question in an interview.

A clinical selection approach is probably the most common selection method, and it involves all who will be making the decision to hire a candidate. The decision makers review the data and, based on what they learn from the candidate and the information available to them, decide who should be hired for a job. Because interviewers have a different perception about the strengths of a candidate, this method leaves room for error. One consideration is disparate treatment, in which one’s biases may result in not hiring candidates based on their age, race, or gender. One way to handle this and limit the personal stereotypes and perceptions of the interviewers is to use a statistical method in hiring.

In the statistical method, a selection model is developed that assigns scores and gives more weight to specific factors, if necessary. For example, for some jobs, the ability to work in a team might be more important, while in others, knowledge of a specific computer program is more important. In this case, a weight can be assigned to each of the job criteria listed. For example, if the job is a project manager, ability to work with the client might be more important than how someone dresses for the interview. So, in the example shown in Figure 5.4 “Sample Selection Model, with Sample Scores and Weighting Filled In”, dress is weighted 1, while being able to give bad news to a client is weighted 5. In the example, the rating is multiplied by the weight to get the score for the particular job criteria. This method allows for a fairer process and can limit disparate treatment, although it may not limit disparate impact. A statistical method may work like this: you and the hiring team review the job analysis and job description and then determine the criteria for the job. You assign weights for each area and score ranges for each aspect of the criteria, rate candidates on each area as they interview, and then score tests or examine work samples. Once each hiring manager has scored each candidate, the hiring team can compare scores in each area and hopefully hire the best person in the best way. A sample candidate selection model is included in Figure 5.4 “Sample Selection Model, with Sample Scores and Weighting Filled In”.

With the statistical approach, there is more objectivity than with the clinical approach. Statistical approaches include the compensatory model, multiple cutoff model, and the multiple hurdle model. In the compensatory model , a similar method of scoring is used as the weighted model but permits a high score in an important area to make up for a lower score in another area. In our Figure 5.4 “Sample Selection Model, with Sample Scores and Weighting Filled In” example, ability to give bad news to a client might outweigh a test score. These decisions would be made before the interviews happen.

A multiple cutoff model requires that a candidate has a minimum score level on all selection criteria. In our Figure 5.4 “Sample Selection Model, with Sample Scores and Weighting Filled In” example, the candidate may be required to have a score of at least 2 out of 5 on each criteria. If this was the case, the candidate in Figure 5.4 “Sample Selection Model, with Sample Scores and Weighting Filled In” scored low on “bad news to a client,” meaning he or she wouldn’t get the job in a multiple cutoff model. In the multiple hurdle model , only candidates with high (preset) scores go to the next stages of the selection process. For example, the expectations might be to score a 4 on at least three of the items in Figure 5.4 “Sample Selection Model, with Sample Scores and Weighting Filled In”. If this were the case, this candidate might make it to the next level of the selection process, since he or she scored at least a 4 on three criteria areas.

Once the discussion on whom to hire has occurred and a person has been selected, the final phase of the process is to make an offer to the candidate. This is discussed in Section 5.5 “Making the Offer”.

Figure 5.4 Sample Selection Model, with Sample Scores and Weighting Filled In

## Explore the Multiplication Worksheets in Detail

Free printable multiplication tables and charts are available. Colorful tables are also provided to paste them in your study room.

Multiply numbers from 0 to 12. The numbers are arranged either horizontally or vertically in both and single and mixed digit facts.

Improve your knowledge by working on these colorful attractive exercises based on equal groups, arrays, area models and number lines.

Teach young learners the basics of multiplication with our unique collection of number line worksheets. Activities include writing multiplication sentences, drawing hops on the number line, MCQ's and much more are available on this page!

Basic multiplication worksheets on interesting picture multiplication, missing factors, comparing quantities, forming the product and a lot more.

Challenge your math skills by multiplying numbers from 3-digit to 8-digit. Word problems are also included in these worksheets.

Multiplication drills have 15, 25, 50, 75 and 100 problems per page. Options can be selected from horizontal/vertical and grids/no grids.

The students may practically apply the concepts given in the word problems in their day-to-day scenarios to find solutions.

Multiplication properties worksheets include commutative, associative, distributive, identity and inverse properties which are essential for kids.

Unravel our multiplication and division fact family worksheets to identify the fact family members, missing members of the fact family, complete multiplication and division facts, fact family houses and more!

Lattice multiplication is the best method to solve complex problems. Teacher templates are included to create their own worksheets.

According to the given value, enter the input/output in the table to satisfy the rule. This helps students to practice both multiplication and division.