Primary Mathematics Vs. Math In Focus

One of the most Frequently Asked Questions I get is, “What’s the difference between Primary Mathematics and Math in Focus?” (It usually comes right after “Wait, there’s more than one version of Singapore Math?”)

Primary Mathematics and Math in Focus are the two principle textbook options for schools considering the Singapore Math® program.

Primary Mathematics was the first series to be widely distributed in North America by Singapore Math Inc.® (beginning in 1998). As early adopting schools used Primary Mathematics with great success, that series gained attention and prominence in the U.S. and Canada, prompting more and more schools to use it.

Math in Focus is a more recent arrival on the scene (2009). Backed by Houghton Mifflin Harcourt, it has benefited from the favorable reputation that Singapore Math® materials enjoy and the marketing clout of a major publisher.

While both series are based on Math from Singapore, there are subtle but significant differences between the two. Below, I set out to explain these differences. But be forewarned: to provide a thorough comparison, there is a lot of ground to cover.

So let’s back up and set some things straight.

First, in Singapore, it’s just called MATHEMATICS.

Why Singapore?

Math from Singapore gained international attention as Singapore’s 4th and 8th grade students topped all others in the international TIMSS tests conducted in 1995, 1999 and 2003. Singapore’s students placed in the top three nations in the 2007 and 2011 TIMSS.

How did the term “Singapore Math” evolve?

From Singapore Math Inc.®, the Oregon company that since 1998 has sold textbooks from Singapore:

The term, “Singapore Math,” came into use in the U.S. around the year 2000 when U.S. academics, homeschoolers, schools and the media started referring to our books as Singapore Math® books. Since then, “Singapore Math” is the descriptive term used by customers, educators and the media to refer to our company and the math books that we distribute.

And there are different versions of Singapore Math® materials?

Yes, and this big picture view might help. In the early 1980s, Singapore wanted to develop strong mathematical students. Singapore’s Ministry of Education first published Primary Mathematics in 1982 and made slight revisions to the series periodically through 2001. Different editions of Primary Mathematics available from Singapore Math Inc.® are based on a 1999 Singaporean Syllabus.

In the mid-2000’s, Singapore changed their focus in math education to develop creative students and allowed the introduction of other syllabi, including My Pals are Here Maths. Houghton Mifflin Harcourt (HMH) adapted My Pals are Here Maths for the U.S. market and changed the name to Math in Focus.

Here’s a quick overview:

Series Title Primary Mathematics 

Math in Focus

Based on: Primary Mathematics  Principal curriculum available in Singapore from 1982-2007

My Pals are Here Maths One of several curricula available in Singapore 2007-Present

First available in US:

1998

2009

Current Editions:

U.S. Edition (2003) Standards Edition (2008) Common Core Edition (2014)

Math in Focus: Singapore Math (2014)

Singapore’s student results using series:

4th and 8th grade students were first in TIMSS tests in 1995, 1999 and 2003

4th and 8th grade students placed in the top three in TIMSS tests in 2007 and 2011

Now, I’m biased

Before continuing, I should say right up front that I prefer the Primary Mathematics series. My first contact with Math from Singapore was with the Third Edition of Primary Mathematics (the 1998 version) that included Singaporean names, metric measures and British English spellings.  I’ve worked with subsequent versions of Primary Mathematics (the U.S. and California Standards Editions) and I like the clean, easy to read pages and the coherent, focused sequence.

Recently, I’ve gained a solid understanding of Math In Focus as more and more schools have sought my help to effectively use it.

Jump directly to: top || Available Materials by Edition || Lesson Sequence by Book || Comparing Teacher’s Guides and a Lesson || Professional Development and Views from Schools || Summary and Conclusions || More Info

Available Materials by Edition

Let’s take a look at the materials available for the new Primary Mathematics Common Core Edition and Math in Focus.

• Primary Mathematics Common Core (2014)  from Singapore Math Inc.®
• Math in Focus (2013) from Houghton Mifflin Harcourt

Primary Mathematics Common Core

• Teacher’s Guides A & B
• Textbooks A & B
• Workbooks A & B
• Primary Digital Online
• Challenging Word Problems
• Extra Practice

And that’s all there is. Although I’d like to put in an official request for an update of the Intensive Practice books!

Math in Focus

• Teacher’s Guides A & B (Also available as an ebook)
• Textbooks A & B (Also available as an ebook)
• Workbooks A & B
• Assessments
• Reteach
• Extra Practice
• Enrichment
• School to Home Connections
• Online virtual manipulatives
• Interactive whiteboard lessons
• eLearning website
• Singapore Math Bar Models for iPad

Jump directly to: top || Available Materials by Edition || Lesson Sequence by Book || Comparing Teacher’s Guides and a Lesson || Professional Development and Views from Schools || Summary and Conclusions || More Info

So what are the components of each series?

Lesson Sequence by Book

Click below to expand each book. Included are the Units and Lessons from the Table of Contents from each series:

• Primary Mathematics Common Core (2014)  from Singapore Math Inc. ®
• Math in Focus (2013) from Houghton Mifflin Harcourt

1A Primary Math Common Core and Math in Focus

Primary Mathematics Common Core 1A

Unit 1 Numbers to 10 Counting

Unit 2 Number Bonds Making Number Stories

Unit 3 Addition Making Addition Stories Methods of Addition

Unit 4 Subtraction Making Subtraction Stories Methods of Subtraction

Unit 5 Ordinal Numbers Naming Position

Unit 6 Numbers to 20 Counting and Comparing Addition and Subtraction

Unit 7 Shapes Common Shapes

Unit 8 Length Compare lengths Measuring Length

Unit 9 Comparing Numbers Comparing Numbers Comparison by Subtraction

Unit 10 Graphs Graphs

Math in Focus 1A

Unit 1 Numbers to 10 Counting to 10 Comparing Numbers Making Number Patterns

Unit 2 Number Bonds Making Number Bonds

Unit 3 Addition Facts to 10 Ways to Add Making Addition Stories Real-World Problems: Addition

Unit 4 Subtraction Facts to 10 Ways to Subtract Making Subtraction Stories Real-World Problems: Subtraction Making Fact Families

Unit 5 Shapes and Patterns Exploring Planes Shapes Exploring Solid Shapes Making Pictures and Models with Shapes Seeing Shapes Around Us Making Patterns with Plane Shapes Making Patterns with Solid Shapes

Unit 6 Ordinal Numbers and Position Ordinal Numbers Position Words

Unit 7 Numbers to 20 Counting to 20 Place Value Comparing Numbers Making Patterns and Ordering Numbers

Unit 8 Addition and Subtraction Facts to 20 Ways to Add Ways to Subtract Real-World Problems: Addition and Subtraction Facts

Unit 9 Length Comparing Two Things Comparing More Than Two Things Using a Start Line Measuring Things Finding Length in Units

1B Primary Math Common Core and Math in Focus

Primary Mathematics Common Core 1B

Unit 11 Numbers to 40 Counting Tens and Ones Comparing Numbers Addition and Subtraction Adding Three Numbers

Unit 12 Multiplication Adding Equal Groups Making Multiplication Stories Multiplication Within 40

Unit 13 Division Sharing and Grouping

Unit 14  Halves and Fourths Making Halves and Fourths

Unit 15 Time   Telling Time Estimating Time

Unit 16 Numbers to 120 Tens and Ones Count past 100 Estimation Order of Numbers Comparing Numbers Addition Within 100 Subtraction Within 100

Unit 17 Money   Bills and Coins Shopping

Math in Focus 1B

Unit 10 Weight Comparing Things Finding the Weight of Things Find Weight in Units

Unit 11 Picture Graphs and Bar Graphs Simple Picture Graphs More Picture Graphs Tally Chart and Bar Graphs

Unit 12 Numbers to 40 Counting to 40 Place Value Comparing, Ordering and Patterns

Unit 13 Addition and Subtraction to 40 Addition Without Regrouping Addition With Regrouping Subtraction Without Regrouping Subtraction With Regrouping Adding Three Numbers Real-World Problems: Addition and Subtraction

Unit 14 Mental Math Strategies Mental Addition Mental Subtraction

Unit 15 Calendar and Time Using a Calendar Telling Time to the Hour Telling Time to the Half Hour

Unit 16 Numbers to 100 Counting to 100 Place Value Comparing, Ordering and Patterns

Unit 17 Addition and Subtraction to 100 Addition Without Regrouping Addition With Regrouping Subtraction Without Regrouping Subtraction With Regrouping Unit 18 Multiplication and Division Adding the Same Number Sharing Equally Finding the Number of Groups

Unit 18 Multiplication and Division Adding the Same Number Sharing Equally Finding the Number of Groups

Unit 19 Money Penny, Nickel , and Dime Quarter Counting Money Adding and Subtracting Money

2A Primary Math Common Core and Math in Focus

Primary Mathematics Common Core 2A

Unit 1 Numbers to 1,000 Looking Back Hundreds, Tens, and Ones Comparing Numbers

Unit 2 Addition and Subtraction Looking Back Addition Without Renaming Subtraction Without Renaming Addition With Renaming Subtraction With Renaming

Unit 3 Length Measuring Length Measuring Length in Meters Measuring Length in Centimeters Other Units of Measure

Unit 4 Mass Measuring Mass in Kilograms Measuring Mass in Grams Measuring Weight in Pounds and Ounces

Unit 5 Multiplication and Division Multiplication Division

Unit 6 Multiplication Tables of 2 and 3 Multiplication Table of 2 Multiplication Table of 3 Dividing by 2 Dividing by 3 Remainders

Math in Focus 2A

Unit 1 Numbers to 1,000 Counting Place Value Comparing Numbers Order and Pattern

Unit 2 Addition up to 1,000 Addition Without Regrouping Addition with Regrouping in Ones Addition with Regrouping in Tens Addition with Regrouping in Ones and Tens

Unit 3 Subtraction up to 1,000 Subtraction Without Regrouping Subtraction with Regrouping in Tens and Ones Subtraction With Regrouping in Hundreds and Tens Subtraction with Regrouping in Hundreds, Tens and Ones Subtraction Across Zeros

Unit 4 Using Bar Models: Addition and Subtraction Using Part-Part -Whole in Addition and Subtraction Adding On and Taking Away Sets Comparing Two Sets Real-World Problems: Two-Step Problems

Unit 5 Multiplication and Division How to Multiply How to Divide Real-World Problems: Multiplication and Division

Unit 6 Multiplication Tables of 2, 5, and 10 Multiplying 2: Skip-Counting Multiplying 2: Using Dot Paper Multiplying 5: Skip-Counting Multiplying 5: Using Dot Paper Multiplying 10: Skip-Counting and Using Dot Paper Divide Using Related Multiplication Facts

Unit 7 Metric Measurement of Length Measuring in Meters Comparing Lengths in Meters Measuring in Centimeters Comparing Lengths in Centimeters Real-World Problems: Metric Length

Unit 8 Metric Measurement of Mass Measuring in Kilograms Comparing Mass in Kilograms Measuring in Grams Comparing Mass in Grams Real-World Problems: Mass

Unit 9 Volume Getting to Know Volume Measuring in Liters Real-World Problems: Volume

2B Primary Math Common Core and Math in Focus

Primary Mathematics Common Core Edition 2B

Unit 7 Addition and Subtraction Finding the Missing Number Methods for Mental Addition Methods for Mental Subtraction

Unit 8 Multiplication and Division Multiplying and Dividing by 4 Multiplying and Dividing by 5 Multiplying and Dividing by 10

Unit 9 Money Dollars and Cents Adding Money Subtracting Money

Unit 10 Fractions Halves and Quarters Writing Fractions

Unit 11 Time Telling Time After the Hour Telling Time Before the Hour Time Intervals Other Units of Time

Unit 12 Capacity Comparing Capacity Liters Gallons, Quarts, Cups, and Pints

Unit 13 Tables and Graphs Picture Graphs Bar Graphs Line Plots Unit 14 Geometry Flat and Curved Faces Making Shapes Angles and Shapes

Math in Focus 2B

Unit 10 Mental Math and Estimation Meaning of Sum Mental Addition Meaning of Difference Mental Subtraction Rounding Numbers to Estimate

Unit 11 Money Coins and Bills Comparing Amounts of Money Real-World Problems: Money

Unit 12 Fractions Understanding Fractions Comparing Fractions Adding and Subtracting Like Fractions

Unit 13 Customary Measurement of Length Measuring in Feet Comparing Lengths in Feet Measuring in Inches Comparing Lengths in Inches Real-World Problems: Customary Length

Unit 14 Time The Minute Hand Reading and Writing Time Using A.M and P.M. Elapsed Time

Unit 15 Multiplication Tables of 3 and 4 Multiplying 2: Skip-Counting Multiplying 2: Using Dot Paper Multiplying 3: Skip-Counting Multiplying 4: Using Dot Paper Divide Using Related Multiplication Facts

Unit 16 Using Bar Models: Multiplication and Division Real-World Problems: Multiplication Real-World Problems: Division Real-World Problems: Measurement and Money

Unit 17 Picture Graphs Reading Picture Graphs with Scales Making Picture Graphs Real-World Problems: Picture Graphs

Unit 18 Lines and Surfaces Parts of Lines and Curves Flat and Curved Surfaces Symmetry

Unit 19 Shapes and Patterns Plane Shapes Solid Shapes Making Patterns

3A Primary Math Common Core and Math in Focus

Primary Mathematics Common Core 3A

Unit 1 Numbers to 10,000 Thousands, Hundreds, Tens and Ones Number Patterns Rounding Numbers

Unit 2 Addition and Subtraction Mental Calculation Looking Back: Addition and Subtraction Sum and Difference Word problems Adding Ones, Tens, Hundreds, and Thousands Subtracting Ones, Tens, Hundreds, and Thousands Two-Step Word Problems

Unit 3 Multiplication and Division Looking Back More Word Problems Multiplying Ones, Tens, and Hundreds Quotient and Remainder Dividing Hundreds, Tens, and Ones

Unit 4 Multiplication Tables of 6, 7, 8, and 9 Multiplying and Dividing by 6 Multiplying and Dividing by 7 Multiplying and Dividing by 8 Multiplying and Dividing by 9

Unit 5 Length Meters and Centimeters Kilometers Other Units of Length

Math in Focus 3A

Unit 1 Numbers to 10,000 Counting Place Value Comparing and Ordering Numbers

Unit 2 Mental Math and Estimation Mental Addition Mental Subtraction More Mental Addition Rounding Numbers to Estimate Using Front End Estimation

Unit 3 Addition up to 10,000 Addition Without Regrouping Addition with Regrouping in Hundreds Addition with Regrouping in Ones, Tens, Hundreds

Unit 4 Subtraction up to 10,000 Subtraction Without Regrouping Subtraction with Regrouping in Hundreds and Thousands Subtraction With Regrouping in Ones, Tens, Hundreds and Thousands Subtraction Across Zeros

Unit 5 Using Bar Models: Addition and Subtraction Real-World Problems: Addition and Subtraction Addition Subtraction

Unit 6 Multiplication Tables of 6, 7, 8, and 9 Multiplication Properties Multiply By 6 Multiply By 7 Multiply By 8 Multiply By 9 Division: Finding the Number of Items in Each Group Division: Making Equal Groups Subtraction

Unit 7 Multiplication Mental Multiplication Multiplying Without Regrouping Multiplying Ones, Tens and Hundreds with Regrouping

Unit 8 Division Mental Division Quotient and Remainder Odd and Even Numbers Division Without Remainder and Regrouping Division With Regrouping in Tens and Ones

Unit 9 Using Bar Models: Multiplication and Division Real-World Problems: Multiplication Real-World Problems: Two-Step Problems with Multiplication Real-World Problems: Division Real-World Problems: Two-Step Problems with Division

3B Primary Math Common Core and Math in Focus

Primary Mathematics Common Core Edition 3B

Unit 6 Mass and Weight Looking Back on Mass Measuring Mass in Kilograms Measuring Mass in Grams Kilograms and Grams Word Problems Measuring Weight in Pounds and Ounces

Unit 7 Capacity Comparing Capacity Liters Liters and Milliliters Gallons, Quarts, Pints, and Cups

Unit 8 Money Dollars and Cents Addition Subtraction

Unit 9 Fractions Fraction of a Whole Equivalent Fractions Fractions and Measurements Fraction of a Set

Unit 10 Time Hours and Minutes Other Units of Time

Unit 11 Data Analysis Presenting Data

Unit 12 Geometry Right Angles and Shapes

Unit 13 Area and Perimeter Area Perimeter Area of a Rectangle Composite Figures

Math in Focus 3B

Unit 10 Money Addition Subtraction Real-World Problems: Money

Unit 11 Metric Length, Mass, and Volume Meters and Centimeters Kilometers and Meters Kilograms and Grams Liters and Milliliters

Unit 12 Real-World Problems: Measurement Real-World Problems: Two-Step Problems Real-World Problems: One-Step Problems

Unit 13 Bar Graphs and Line Plots Making Bar Graphs with Scales Reading and Interpreting Bar Graphs Line Plots

Unit 14 Fractions Understanding Fractions Understanding Equivalent Fractions More Equivalent Fractions Comparing Fractions Adding and Subtracting Like Fractions Fraction of a Set

Unit 15 Customary Length, Weight, and Capacity Measuring Length Measuring Weight Measuring Capacity

Unit 16 Time and Temperature Telling Time Converting Hours and Minutes Adding Hours and Minutes Subtracting Hours and Minutes Elapsed Time Measuring Temperature Real-World Problems: Time and Temperature

Unit 17 Angles and Lines Understanding and Identifying Angles Right Angles Perpendicular Lines Parallel Lines

Unit 18 Two-Dimensional Shapes Classifying Polygons Congruent Figures Symmetry

Unit 19 Area and Perimeter Area Square Units cm2 and in2 Square Units m2 and ft2 Area and Perimeter More Perimeter

4A Primary Math Common Core and Math in Focus

Primary Mathematics Common Core 4A

Unit 1 Whole Numbers Numbers to 1,000,000 Approximation Factors Multiples Order of Operations

Unit 2 Four Operations of Whole Numbers Addition and Subtraction Multiplication by a 1-digit Number Division by Ones and Tens Multiplication by a 2-digit Number

Unit 3 Fractions Equivalent Fractions Adding and Subtracting Like Fractions Mixed Numbers Improper Fractions Fractions and Division

Unit 4 Operations on Fractions Adding and Subtracting Related Fractions Adding and Subtracting Mixed Numbers Multiplying a Fraction and a Whole Number Fraction of a Set

Unit 5 Measure Looking Back Multiplying and Dividing Compound Measures Measures and Fractions

Math in Focus 4A

Unit 1 Place Value of Whole Numbers Numbers to 100,000 Comparing Numbers to 100,000

Unit 2 Estimation and Number Theory Estimation Factors Multiples

Unit 3 Whole Number Multiplication and Division Multiplying by a 1-digit Number Multiplying by a 2-digit Number Modeling Division with Regrouping Dividing by a 1-digit Number Real-World Problems: Multiplication and Division

Unit 4 Table and Line Graphs Making and Interpreting a Table Using a Table Line Graphs

Unit 5 Data and Probability Average Median, Mode and Range Stem and Leaf Plots Outcomes Probability as a Fraction Real-World Problems: Data and Probability

Unit 6 Fractions and Mixed numbers Adding Fractions Subtracting Fractions Mixed Numbers Improper Fractions Renaming Improper Fractions and Mixed Numbers Renaming Whole Numbers when Adding and Subtracting Fractions Real-World Problems: Fractions

4B Primary Math Common Core and Math in Focus

Primary Mathematics Common Core Edition 4B

Unit 6 Decimals Tenths Hundredths Thousandths Rounding

Unit 7 Four Operations of Decimals Addition and Subtraction Multiplication Division

Unit 8 Geometry Points, Lines, Line Segments, Rays, and Angles Right Angles Measuring Angles Perpendicular Lines Parallel Lines Quadrilaterals Triangles Line Symmetry

Unit 9 Area and Perimeter Area of a Rectangle Composite Figures

Unit 10 Bar Graphs and Line Plots Bar Graphs Line Plots

Unit 11 Volume Cubic Units Volume of a Cuboid

Math in Focus 4B

Unit 7 Decimals Understanding Tenths Understanding Hundredths Comparing Decimals Rounding Decimals Fractions and Decimals

Unit 8 Adding and Subtracting Decimals Adding Decimals Subtracting Decimals Real-World Problems: Decimals

Unit 9 Angles Understanding and Measuring Angles Drawing Angles to 180° Turns and Right Angles

Unit 10 Perpendicular and Parallel Line Segments Drawing Perpendicular Line Segments Drawing Parallel Line Segments Horizontal and vertical Lines

Unit 11 Squares and Rectangles Squares and Rectangles Properties of Squares and Rectangles

Unit 12 Area and Perimeter Area of a Rectangle Rectangles and Squares Composite Figures Using Formulas for Area and Perimeter

Unit 13 Symmetry Identifying Lines of Symmetry Rotational Symmetry Making Symmetric Shapes and Pattern

Unit 14 Tessellations Identifying Tessellations More Tessellations

5A Primary Math Common Core and Math in Focus

Primary Mathematics Common Core Edition 5A

Unit 1 Whole Numbers Large Numbers Approximation and Estimation Factors & Multiples Prime Factorization Multiplying by Tens, Hundreds, or Thousands Dividing by Tens, Hundreds, or Thousands

Unit 2 More Calculations with Whole Numbers Order of Operations Methods for Mental Calculation Looking Back: Word Problems Multiplication by a 2-digit Whole Number Division by a 2-digit Whole Number

Unit 3 Fractions Looking Back Fractions and Division Addition and Subtraction of Unlike Fractions Addition and Subtraction of Mixed Numbers Product of a Fraction and a Whole Number Word Problems

Unit 4 Multiply and Divide Fractions Product of Fractions Word Problems Dividing a Fraction by a Whole Number Dividing by a Fraction More Word Problems

Unit 5 Perimeter and Area Square Units Area of Composite Figures – Rectangles and Squares Area of a Triangle Area of a Parallelogram

Unit 6 Ratio Finding Ratio Equivalent Ratio Combining Three Quantities

Math in Focus 5A

Unit 1 Whole Numbers Numbers to 10,000,000 Place Value Comparing Numbers to 10,000,000 Rounding and Estimating

Unit 2 Whole Number Multiplication and Division Using a Calculator Multiplying by Tens, Hundreds, or Thousands Multiplying by a 2-digit Number Dividing by Tens, Hundreds, or Thousands Dividing by a 2-digit Number Order of Operations Real-World Problems: Multiplication and Division

Unit 3 Fractions and Mixed Numbers Adding Unlike Fractions Subtracting Unlike Fractions Fractions, Mixed Numbers, and Division Expressions Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals Adding Mixed Numbers Subtracting Mixed Numbers Real-World Problems: Fractions and Mixed Numbers

Unit 4 Multiplying and Dividing Fractions and Mixed numbers Multiplying Proper Fractions Real-World Problems: Multiplying with Proper Fractions Multiplying Improper Fractions by Fractions Multiplying Mixed Numbers and Whole Numbers Real-World Problems: Multiplying with Mixed Numbers

Unit 5 Algebra Using Letters as Numbers Simplifying Algebraic Expressions Inequalities and Equations Real-World Problems: Algebra

Unit 6 Area of a Triangle Base and Height of a Triangle Finding the Area of a Triangle

Unit 7 Ratio Finding Ratio Equivalent Ratio Real-World Problems: Ratio Ratio in Fraction Form Combining Three Quantities Real-World Problems: More Ratio

5B Primary Math Common Core and Math in Focus

Primary Mathematics Common Core Edition 5B

Unit 7 Decimals Tenths, Hundredths, and Thousandths Approximation Add and Subtract Decimals Multiply and Divide Decimals by a 1-digit Whole Number Multiplication by Tens, Hundreds or Thousands Division by Tens, Hundreds or Thousands

Unit 8 More Calculations Multiplication by a 2-digit Whole Number Division by a 2-digit Whole Number Multiplication by a Decimal Division by a Decimal Conversion of Measures

Unit 9 Volume Cubic Units Volume of Rectangular Solids Finding the Volume of a Solid

Unit 10 Average, Plots and Graphs Average Line Plots Coordinate Graphs Line Graphs

Unit 11 Angles, Triangles and Quadrilaterals Looking Back Finding Unknown Angles Finding Unknown Angles in Triangles Finding Unknown Angles in Quadrilaterals

Unit 12 Percentage Percent Writing Fractions as Percentages Percentage of a Quantity

Unit 13 Rate Rate

Math in Focus 5B

Unit 8 Decimals Understanding Thousandths Comparing and Rounding Decimals Rewriting Decimals as Fractions and Mixed Numbers

Unit 9 Multiplying and Dividing Decimals Multiplying Decimals Multiplying by Tens, Hundreds or Thousands Dividing Decimals Dividing by Tens, Hundreds or Thousands Estimating Decimals Real-World Problems: Decimals

Unit 11 Graphs and Probability Making and Interpreting Double Bar Graphs Graphing an Equation Combinations Theoretical Probability and Experimental Probability

Unit 12 Angles Angles on a Line Angles at a Point Vertical Angles

Unit 13 Properties of Triangles and Four-sided Figures Classifying Triangles Measures of Angles in a Triangle Right, Isosceles, and Equilateral Triangles Triangle Inequalities Parallelogram, Rhombus, and Trapezoid

Unit 14 Three-Dimensional Shapes Prisms and Pyramids Cylinder, Sphere, and Cone

Unit 15 Surface Area and Volume Building Solids using Unit Cubes Drawing Cubes and Rectangular Prisms Nets and Surface Area Understanding and Measuring Volume Volume of a Rectangular Prism and Liquid

Jump directly to: top || Available Materials by Edition || Lesson Sequence by Book || Comparing Teacher’s Guides and a Lesson || Professional Development and Views from Schools || Summary and Conclusions || More Info

Comparing Teacher’s Guides and a Lesson

  

Let’s take a look at the materials…

The materials included are:

• Primary Mathematics U.S. Edition (2003)  from Singapore Math Inc ®
• Primary Mathematics Common Core (2014)  from Singapore Math Inc. ®
• Math in Focus (2013) from Houghton Mifflin Harcourt

The lesson that we’re comparing is from the 2A materials on addition with renaming or regrouping in the tens. Here’s the lesson sequence for the Addition with Renaming by book. All lessons are one class period, unless noted:

Primary Mathematics U.S. Edition

2.4a Add ones or tens to a 3-digit number 2.4b Add numbers within 1000, with renaming in the ones 2.4c Add numbers within 1000, with renaming in the tens 2.4d Solve word problems involving addition of 2-digit numbers with renaming once. 2.4e Add numbers within 1000 with renaming twice 2.4f Add three numbers within 1000 & Solve word problems which involve addition within 1000

Primary Mathematics Common Core

2.4a Add ones or tens to a 3-digit number 2.4b Rename ones 2.4c Rename tens 2.4d Rename ones and tens 2.4e Add more than two numbers

Math in Focus

2.2 Addition with Regrouping in Ones (2 days) 2.3 Addition with Regrouping in Tens 2.4 Addition with Regrouping in Ones and Tens Problem Solving (1/2 day)

U.S. Edition Teacher’s Guide for Lesson 2.4c Add numbers within 1000, with renaming in the tens

(Click images to enlarge)

OK, that wasn’t very helpful. You can see that the U.S. Edition Teacher’s Guides assume that you are teaching all the lessons and know what you need to do to teach a concept. Here’s the prior lesson, that teachers would use as guidance. It includes the number disc examples:

Ahh. That’s more helpful.

Common Core Edition Teacher’s Guide for Lesson 2.4c Rename tens

Here’s what is included in the Common Core Edition that the U.S. and CA Standards editions didn’t have: The textbook and workbook pages, right in the Teacher’s Guide. Hurray!

(Click images to enlarge)

Notice all of the guided questions? And when it is suggested to “Discuss with the students…” In the Common Core Edition, there are suggestions for discussion and emphasis, which is very helpful when working through word problems with the Bar Model in grades 3-5.

Math in Focus Teacher’s Guide for Lesson 2.3 Addition with Regrouping in Tens

(Click images to enlarge)

Some differences…

Concrete ->Pictorial -> Abstract. A key idea of the curriculum as designed in Singapore is this process of developing a student’ s full conceptual understanding through three stages identified by Jerome Bruner; the enactive, iconic and symbolic. Singapore refers to this as concrete – pictorial – abstract. (Common Core refers to the stages as concrete, representational, and abstract.)

When comparing materials, teachers should also look for applications of Zoltan Dienes’ Mathematical Variability Principle, which suggests that students need to be shown a concept with more than one manipulative. Younger students may believe that adding cubes together only works with cubes if they’ve never added crayons, animals, etc.

A major difference between Primary Mathematics and Math in Focus is seen in the actual content of the textbooks themselves. The Math in Focus student texts are very guided. Using the textbook, one gets the feeling that students are expected to teach themselves from the materials, however, in doing so, they lose the concrete portion of the lesson that is a hallmark of the Singapore approach.

Here’s a typical example of  the abstract before the concrete from the first lesson in Math in Focus 5A, Unit 3, entitled Adding Unlike Fractions:

And here’s another from the Math in Focus Teacher’s Guide in 2A, which includes the student textbook pages. I’ve taken the Teacher’s Guide page so you can see the original teacher-directed portion of the lesson skips over the concrete:

The lesson starts with:

“Explain the concept of multiplication as adding equal groups…Tell the children they can start by counting …Ask: How many groups are there?”

Compare that with the same lesson from Primary Mathematics. Note: This is from the Standards Edition as the Common Core Edition is not available yet.

This lesson starts with observing objects in groups. Then continues:

“Ask the students how many groups…Ask them how many counters in each…Ask students…Ask them…Lead students to see”

Manipulatives and Models: A difference with the use of manipulatives that you’ll see is that Primary Mathematics Common Core materials use the more abstract Place-value discs starting in grade 2, where the Math in Focus uses the more concrete Base-ten blocks (Place- value discs are introduced in grade 4 in Math in Focus). Additionally, Math in Focus incorporates the bar model into grade 2. Primary Mathematics introduces the bar model in grade 3.

In the Primary Mathematics Common Core materials, the teacher delivers the content of the lesson, then there is one example and some problems to work. What the teacher is doing with the students is important. I’m not sure a student would be able to figure these concepts out with just the textbook. (Nor should they be expected to. Isn’t this why we have schools?)

Some other differences: In the Common Core Edition, Teachers are reminded that students can use place value discs:

 

In the Math in Focus, only place value mats are suggested as a manipulative and designed  for struggling learners:

 

Where’s the concrete, hands-on learning for the student?  If you’re a teacher who is new to the materials, what would you do with these two sets of instructions? Does one edition emphasize the Concrete -> Pictorial-> Abstract learning trajectory better than the other? Which edition do you prefer?

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Professional Development and Views from Schools

The Singapore Math® approach is very different from other elementary math curricula that teachers have used. For this reason, I believe that it is critical for teachers to receive specific training in Singapore strategies as they begin to use it.

Singapore Math Inc. ® provides no professional development for Primary Mathematics or their secondary materials. They do provide a list of preferred training providers. (Full disclosure, I’m proud to be one of them.) Most people on that list provide full program and content-based professional development, as opposed to program proprietary training. (And some also work with Math in Focus)

The schools I have worked with tell me that Houghton Mifflin Harcourt includes a brief professional development session on how to use the Math in Focus materials. I’m spending a lot of time right now working with schools that are struggling with their Math in Focus implementations. Schools say they’ve been advised:

It’s ok if you don’t get to the ‘B’ books, most of the content is in the “A” books.

and conversely:

You can’t move on until all students have mastered a concept

The latter of which had a third grade working on front-end estimation for 2 weeks! (Math in Focus lists it as a one-day lesson.)

Here’s what schools that are using Math in Focus are finding their biggest challenges:

1. There is a distinct lack of concrete, hands-on lessons for which the Primary Mathematics materials are known. In addition, the abstract is frequently introduced before the concrete.
2. There isn’t as much bar modeling work as they expected. Instead there are logic-type puzzlers labeled “Thinking Skills.”
3. Teachers are fumbling their way through the materials. Because the books are expensive, schools don’t have funding to get the content-based professional development that they need.
4. There are just too many materials. (The Teacher’s Guides are particularly unwieldy)
5. The test books don’t correlate with the content taught, the tests are too hard, and there are too many.
6. There are many “American” concept lessons that have been added, making the program less-focused than Primary Mathematics. Even after four years of use, some schools still have trouble getting through the books in one year. Without a content specialist, most teachers just don’t know what to omit.

And here’s what schools using Primary Mathematics find challenging:

1. The materials look different and teachers need to study lessons to prepare.
2. The kindergarten books can be too easy for many children that attend a pre-k program.
3. The textbooks and workbooks look simple, so parents think the work is too easy. They don’t see what the teacher is doing in the classroom.
4. Teachers need to read and follow the Teacher’s Guides. They can’t just teach from the textbook.

Jump directly to: top || Available Materials by Edition || Lesson Sequence by Book || Comparing Teacher’s Guides and a Lesson || Professional Development and Views from Schools || Summary and Conclusions || More Info

Summary and Conclusions

I’ve worked with Primary Mathematics for 13 years and continue to prefer it over Math In Focus.

Why?

Primary Mathematics was THE Math Curriculum in Singapore for 25 years. Students there went from mediocre to the best in the world while using that series. The curriculum has withstood the test of time. Since its introduction in North America, thousands of schools have successfully used Primary Mathematics to help children become competent and confident math students.

Here’s what I tell schools about Primary Mathematics series:

• U.S. Edition – This edition provides the most focused, coherent and rigorous materials. It does lack tests and has minimal Teacher’s Guides. Aligned material includes challenging word problems, extra practice and intensive practice materials to supplement instruction.

• Common Core Edition – If your teachers struggle a bit, the Common Core Edition has more directed lessons with help teachers with good questioning and planning. The content has not been “dumbed” down to meet Common Core Standards. Instead, it includes more review lessons so that content is also covered in the year required by CCSS. For example, the Singapore Math® sequence has always had multiplication and division facts completed by the first half of third grade, while CCSS doesn’t expect that until the end of grade 4. Rather than move when facts are taught Primary Mathematics added on review lesson on facts in the fourth grade materials. This Edition also has a much more enhanced Teacher’s Guide to assist teachers who aren’t as strong in their math skills.

Math in Focus is based on My Pals are Here Maths, which is one of several programs currently used in Singapore as the country strives to develop more creativity in its students. In America, our students tend to be pretty darn creative, but struggle with computational understanding. Despite replacing Primary Mathematics with other options, Singapore’s students have continued to perform well in international tests in 2007 and 2011.

Here’s what I tell schools about Math In Focus.

• Math in Focus seems to have a lot of content that isn’t covered in Singapore. Because of this, it can be hard to find the most critical (and Singaporean) lessons. It also has many more materials in the series, making it overwhelming for teachers. The biggest difference I see with the actual  materials is in the overdone textbooks. Teachers who rely on these will be introducing the abstract before the concrete.

Bottom Line: I believe that a school is best served with any version of Primary Mathematics. If that’s not an option, then go with Math in Focus. That’s right.  A school is better served with Primary Mathematics first, then Math in Focus than with enVision, Saxon, Everyday Math or (insert your program here).

Finally, please be aware that I am not paid nor do I receive any financial gain by recommending one program or the other.

Jump directly to: top || Available Materials by Edition || Lesson Sequence by Book || Comparing Teacher’s Guides and a Lesson || Professional Development and Views from Schools || Summary and Conclusions || More Info

Additional Information

A definitive description of the evolution of the Primary Mathematics series is available at SingaporeMath.com.

– – – – –

Five years ago, I published a series of posts that compared four different versions of Singapore Math® materials that were available at that time (this was in 2009, prior to the introduction of Math in Focus).

• Primary Mathematics U.S. Edition (2003) from SingaporeMath.com
• Primary Mathematics Standards Edition (2008) from SingaporeMath.com
• My Pals Are Here Maths (2007) obtained in Singapore from Marshall Cavendish Education
• Shaping Maths (2007) obtained in Singapore from Marshall Cavendish Education

If you are interested in seeing content from My Pals Are Here Maths or Shaping Maths (direct from Singapore), take a look at these posts:

Part 1 – Teacher’s Guides Part 2 – Textbooks Part 3 – Workbooks

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