Math in Focus Manipulative Add-On Kit Bridging Grade 3-4

Countries around the world first became interested in Singapore's math curriculum when results of the Third International Math and Science Study (TIMSS) were published in 1995. Conducted by the International Study Center at Boston College, achievement tests in both math and science were administered to students in over 40 countries. Students from Singapore ranked highly in mathematics achievement: 1st in the fourth, seventh, and eighth grade levels and 2nd at the third grade level. Results for the U.S. were disappointing: 10th in the third grade, 11th in the fourth grade, 23rd in the seventh grade, and 27th at the eighth grade level. In a follow-up study in 1999, Singapore again ranked 1st in eighth grade math achievement while U.S. eighth graders ranked 19th. Although a first place ranking does not necessarily imply the best program, something about Singapore's math program was working.

"Singapore Approach Math" is a general term referring to a type of mathematical instruction (i.e. curriculum) developed from a syllabus designed by Singapore's Ministry of Education in the 1980s. There were a number of revisions and the 3rd edition was the last edition used in Singapore. The good test scores were associated with this material and all of our Singapore Approach Math programs are based primarily on the 3rd edition although it is no longer available for sale. Components from different editions are not interchangeable but a student can move between the editions in-between levels.

Primary Math US (1-6) is an adaptation of the 3rd edition for use in the U.S. Although a small amount of content (division of fractions) from the 2nd edition was added back into the US edition, it is almost identical to the 3rd edition. The US edition adds sections for U.S. customary measurements and uses U.S. spelling and conventions. We expect this edition to be available indefinitely. ©2003

Primary Math S/E (Standards Edition) (K-6) was adapted to meet the pre-Common Core CA math standards. An additional amount of content (probability, data analysis, negative numbers, coordinate graphing) from the 2nd edition was added back in and topics were rearranged but it is similar to the US edition. Cumulative Reviews at the end of each Unit and practice sets within each unit were added. Textbooks are in color. ©2008 This edition includes Earlybird Kindergarten Math.

Primary Math CC (Common Core) (K-5) is aligned to the Common Core State Standards and is another adaptation of the 3rd edition. Only minor changes were made to the scope and sequence. Unit Reviews are no longer cumulative and Practices were removed although some of the content was incorporated into the lessons. ©2014 Includes Earlybird Kindergarten Math CC. This edition will be available for the foreseeable future.

Primary Math 2022 Edition (K-5) is a completely new revision retaining all the excellent teaching methods of the earlier Primary Math programs. Incorporating both cumulative assessments and challenging problem solving, mastery learning is emphasized. The scope and sequence is similar to previous editions and topics are aligned to state and national standards. ©2021-2022

New Elementary Math (7-8) is a no-frills program based on an older Singaporian program and covering integrated algebra and geometry. It's considered a sequel to the Primary Math programs.

Math in Focus (K-8) was developed by Great Source (a division of Houghton Mifflin Harcourt) in conjunction with Marshall Cavendish (the original publisher in Singapore). Although the basic instructional sequences are similar and the content is very close to the SE, material added to the most recent editions brings it into alignment with CC. Math in Focus has a more American look and "feel." ©2010, 2014

View the Singapore Approach Math Comparison Chart.

NOTE: This is not the 2020 edition - - - Math in Focus is a program incorporating the widely-used Singapore approach to math. Two key ways that the Singapore approach differs from more traditional programs are:

• Consistent use of models that allow students to tackle concepts that are normally delayed until later grades
• An emphasis on application of math skills to real-world situations helps children become formidable problem solvers in real life

The question is not whether to use the Singapore approach, but which version you should choose: Primary Mathematics from SingaporeMath.com or this new Math in Focus?

The underlying philosophy of Math in Focus is the same as Primary Math. It has the same emphasis on integrating concepts and skills; the same approach of beginning with concrete, then to pictorial, then to abstract; the same extensive problem solving using the famous bar models to tackle the tough questions. The scope of the program is essentially alike, as well. On the whole, I would say there is a bit more material in MIF than PM. Sometimes this includes additional concepts, sometimes just going deeper into a topic. While the sequence of topics corresponds for the most part between the two programs, I found a few places where it was different in the two levels I compared. These differences seemed limited to order of presentation within a grade rather than movement of concepts from one grade to another. MIF is CCSS-aligned, but in a comparison between it and Singapore Math Standards Edition, there only appears to be about 10% new content at each grade level, and these are all minor concepts and topics. The general scope and sequence of the program has not been changed. If you have previously used Primary Math, the transition to Math in Focus should be a smooth one.

Basic materials also are similar: both have two levels (A and B) of teacher editions, non-consumable student texts, and workbooks per grade; and both have additional materials such as extra practice books, assessment (test) books, and enrichment (challenging) books.

The main differences between the two programs are:

• The format / content of the Teacher Editions
• The presentation of lessons
• The amount of instructional material in the student text
• The integration of concrete (hands-on) student activities into the programs
• The graphic content / layout
• The incorporation of enrichment activities into the MIF program
• The larger size of the MIF program
• The relative cost of the programs

First, the teacher editions. I think the authors of the PM teacher materials have done an outstanding job. It is difficult to write a teacher edition apart from the development of the student materials. Since these are not the actual teacher materials used in Singapore, or even translations of them, it is no surprise that they are not quite as coordinated with the student materials as the Math in Focus teacher editions are. These were written specifically for the MIF program and in tandem with the student editions. As such, the material relates directly to the student text and workbook pages. This is a significant difference. In contrast, most of the actual teaching in the PM Home Instructor guides takes place before you even open the student text. The work done in the student text is more reinforcement of concepts taught outside the scope of the text lesson itself. This puts a lot more of the teaching burden on the teacher. You must do the concept introduction, concrete modeling, and transition to pictorial before you "Have your student do tasks ___ , textbook pp.________".

The Math in Focus Teacher Editions begin, as most do, with a program overview, which describes components of the program, lists manipulatives (with suggested alternatives), includes a three-grade scope and sequence, and detailed Table of Contents. Each chapter begins with an overview. It contains background information for teaching the lessons, cross-curricular connections, and the location of "before" and "after" concepts for this topic. The Chapter Planning Guide is a tabular layout breaking the chapter into teaching units, showing for each the number of days it will take, instructional objectives, vocabulary, resources, materials needed, and how it fits into the NCTM standards. Its an "at a glance" overview. The actual lesson pages follow.

It is important to note that the Teacher Editions refer to online resources (specifically Think Central) that are not available to homeschoolers.

Unlike the PM program, the MIF Teacher Edition includes reduced images of both student text and workbook pages (with all answers printed in red). I find it difficult to teach effectively without my own copy of student materials, so I appreciate having it all in one place so Im not juggling books while teaching. Teaching instructions appear directly below the corresponding student text page. These include concept information, directions for teacher-led and/or student activities, and discussion (which is fairly scripted).

The lesson presentation is very organized, with several standard elements in each chapter, regardless of grade level. First, there is always a Chapter Introduction which coordinates with the introductory page in the student text. As an example, lets look at the Chapter Introduction to "Subtraction Facts to 10" in the 1A book: The student text page shows a boy in three frames: walking with five stickers in open hand; three of them dropping into an open grate in the sidewalk; with two of the five stickers (sadly) left in hand. It has a box at bottom left, delineating the chapter into four lessons and a "Big Idea" box at bottom right telling the student "Subtraction can be used to find how many are left." Next is a Recall Prior Knowledge section. These student text pages review concepts learned previously that are prerequisite to understanding material introduced in this chapter. Teaching instructions coincide, often including manipulative work for the student. Immediately following, theres a Quick Check with several questions to assess whether the student is ready to continue or needs additional review. (If needed, an additional pre-test is available in the Assessments book). When readiness is affirmed, chapter lessons begin. For each, the teacher edition details lesson objectives, coordinating resources, vocabulary, materials needed for each day, and provides a 5-minute Warm Up activity. The 5-minute Warm Up activity introduces and prepares students for the lesson. These generally involve work with concrete objects (linking cubes, counters, etc.) but, at higher levels can include "teaser" problems or questions. This is in sharp contrast to the heavy pre-text activities in PM. A lesson introduction in the student text states objectives and previews vocabulary. From here, lessons may vary, though the concrete to pictorial to abstract philosophy is ever-present and more integrated into the student text itself. Most lessons consist of several Learn and Guided Practice segments, interspersed with a variety of other components. Learn boxes introduce, explain, and model each concept. These correspond to lesson objectives and contain a heading revealing what the focal skill is. For example, In the "Ways to Subtract" Lesson, the first taught concept is: "You can subtract by taking away." The skill is then illustrated, modeled and explained, showing step-by-step the related math techniques.

Guided Practice segments almost always follow the Learn segments. At the lower levels, they usually photographically portray manipulative work used to solve problems. Correlating teacher edition instructions guide the teacher in use of corresponding manipulative work. At upper levels, these may be problems to work relating to the Learn segment. For example, in the Algebra chapter lesson (grade 5) "Using Letters as Numbers," the Learn teaches "how to write a numerical expression to show how numbers in a situation are related." It uses the example of computing a persons age next year and two years ago. It is followed by a second Learn segment explaining how to "Use variables to represent unknown numbers and form expressions involving addition and subtraction". This expands on the first segment as two students discuss how to compute their teachers age in these cases, without knowing his age now. It shows how a variable can be used to construct an algebraic expression to solve the problem. The Guided Practice follows up with a table presenting different situations (Now, 4 years from now, 10 years from now, 5 years ago, 8 years ago) and asking a student to supply the appropriate algebraic expressions (the x for Now is supplied). Other lesson components include several of the following:

• Lets Practice reinforces with addtional practice problems. When students can successfully solve these problems, they are ready for independent work in the student workbook
• Hands-On Activity reinforces skills, concepts and problem-solving strategies, using manipulatives. These show the items to use, how to use to solve problems, then provide several additional problems for independent work.
• Game breaks up the bookwork with a fun game using the target skill.
• Lets Explore! uses a discovery approach to learning. By working through the activity, the student will discern a concept, relationship, strategy, or principle.
• Math Journal helps children put math concepts into words. As you might expect, these require much less writing in the earlier grades.

Most lessons end with a Lets Practice leading into On Your Own assignments in the student workbook.

Chapters usually consist of 2-7 lessons and end with a Put on Your Thinking Cap! activity. These draw on both previous knowledge and skills acquired in the chapter to resolve challenging problems, combining problem-solving strategies with critical thinking skills. Its a little like pages from a Critical Thinking Press book were purposely bound in. Think of these as enrichment exercises built right into the course. Accompanying teacher instruction includes skills required to solve the problem and how to direct your child through the thought process as needed. These activities also have workbook follow-up pages. A Chapter Wrap Up recaps all of the concepts and skills learned in the chapter. At most levels, this is followed by a Chapter Review/Test right in the student text. At early levels, the chapter review/test is contained in the student workbook instead (probably to avoid having to rewrite the problems). The Assessments books also contain a test for each chapter in the student book.

A lot of the same components exist, in some form, in the PM program. Hands-on activities, games, enrichment, discussion, and exploratory exercises are all detailed in the teacher books, along with most of the lesson instruction. There is simply less reliance in the MIF program on the teacher getting skills and concepts across before using the text pages; in fact, teaching takes place alongside and corresponding to the student text. Because of this, the text has a more ordered and systematic feel compared to the PM texts. So, if you are not going to actually read through and teach from the instructor guides, you will be better off with this program. While it is not intended to be self-instructional, your student will have more complete guidance directly in the student materials. And, once you have finished the lesson, he will have more to refer back to, should he have a question or need clarification.

While both programs sport full-color student texts, Math in Focus uses more photographic, real-life images and fewer cartoonish renderings, giving them a more grown-up look. This is especially attractive where manipulatives are used to demonstrate a concept. As they say, "a picture is worth a thousand words." MIF has even replaced most of the Singrapore math signature "talking heads" (shoulder-up illustrations of children "talking" or "thinking" via word bubbles to identify concepts, explain processes, even provide instruction) with photographic images of real children instead. While lower-level student texts in both series are more heavily graphic, I feel that the balance is better in the MIF program. Too many large illustrations can overwhelm and distract.

Since all of the Primary Math books are smaller format, these more typically school-sized materials seem all the larger. MIF teacher editions are oversized, spiral bound books (increased width needed to fit student pages side by side). They are also much longer than the corresponding PM instructor guides, again largely because of the inclusion of reduced images of all student pages. The full-sized MIF student texts are hardbound, which not only makes them more durable, but makes them heftier. With so much more instructional material in them, they contain about double the pages of their PM counterparts. This page count difference does not carry over to the student workbooks, however, which are more similar in length (PMs may even have slightly more pages).

Reviews are also implemented differently in each series. Whereas MIF has a review of previously-learned material at the beginning of each chapter, PM (beginning in grade 2), generally has a cumulative review at the end of a unit, which is also echoed in the workbook. MIF has a distinct chapter review and test at the end of each chapter. Workbooks contain cumulative reviews after every two chapters (for only those two chapters). Each workbook also contains a cumulative test at the end of the book; Workbook A a Mid-Year and Workbook B an End-of-Year review. Both programs have an optional test book also. MIF calls this the Assessments book. It contains a diagnostic review for each chapter (mentioned earlier), "Benchmark" cumulative assessments to be taken midway through each text, and Mid- and End-of-Year cumulative tests.

A final difference between the programs is cost. While workbooks and student books are fairly close in price, the teacher editions are not. If you deduct the separate prices of student text and workbook from the Homeschool Kit price, youre still left with a considerable difference. Youre in the ballpark if you plan on using the more expensive Primary Math Teachers Guide instead of the Home Instructor Guide. Or, if you, like me, need a separate copy of student materials to teach with anyway, the remaining difference wont buy you a meal. You should also take into consideration whether you would need to use ancillary materials for either program. Homeschool Packages include the Student Book, Workbook and Teachers Edition for one semester of a grade level (A or B). The Kindergarten Homeschool Packages include Part 1 and 2 of the Student Book and the corresponding Teachers Edition. You might want to note that the Teachers Editions are not available separately; they are only found in the packages.

Full year packages are also now available with a parent answer key instead of the Teachers Editions. Answer keys (available for Grades K-5) contain reduced student pages and answers to the student textbook (in the front) and workbook (in the back). Packages with Answer Keys include Student Book A & B, Workbook A & B and the parent answer key. Answers for Grades 6-8 are only found in the Teacher's Editions. Student packs are also available. These packs include student textbooks and workbooks for both semesters and the assessments book. At the kindergarten level, the teacher edition is included because of the interactive nature of the lessons.

The 6th grade level has been added to the series, Course 1. Using the same approach and format found in the previous levels of the course, students will learn about positive and negative numbers, multiplying and dividing fractions and decimals, ratios and rates, percents, algebraic expressions, equations and inequalities, coordinate plane, perimeter, area, volume, statistics, and measures of central tendency. Each homeschool kit includes the hardcover teacher edition and hardcover student edition (nonconsumable text) for one semester. The assessment book is sold separately and includes content for both semesters. Extra Practice books for each semester and a Blackline Activities book is available but optional. This is a needed addition to the series before moving on to higher level math. The Reteach Workbooks correspond to the chapters in each level of the Student Book/Workbook. They provide examples with guided instruction along with additional practice problems. These serve the needs of some students who just need additional work on most concepts for mastery. Answers/Solutions are found in the back of each book. 210 pgs, pb.

In a nutshell, while the core content and philosophical approach of these Singapore programs is much the same, the implementation is not. So, my best advice? Get yourself to a curriculum fair and look at the programs side by side. Then you can decide the best fit for your teaching style and your child.

Note: Not included in the comparison above is the Math in Focus Kindergarten program, as it is much different in both format and presentation than the rest of the elementary program. The four-part student book is a worktext. Teaching instruction is all in the Teacher Edition, and consists of "Investigate," "Discover," "Explore," and "Apply" activities. As with the elementary levels, teaching instructions are correlated to student text pages. Lessons are detailed andscripted. Many reference a corresponding "Big Book." Some of the Big Book pages are larger reproductions of student text pages; for others, you can use the reduced copy in the teacher editions. Unlike the other MIF books, student books contain colorful illustrations rather than photographic images. The books have a "cute monster" theme carried throughout. Since there is no Primary Math kindergarten level, I cant really compare content or presentation. For a detailed scope and sequence, refer to the publishers website.

Also Note: We have assembled manipulative kits for all levels of this program.