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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
  • 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:

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

PMUS 4A 3a PM TG MIF 2A TG cover

Let’s take a look at the materials…

The materials included are:

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

2A 2.4c TG p. 46
(Click images to enlarge)
2A 2.4c TG p. 46

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:

2A 2.4c TG p. 45

Ahh. That’s more helpful.

2A 2.4c TG p. 46

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!

PMCC_tg_p.62
PMCC_tg_P._63
PMCC_tg_P._64
(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

mIf_2a_tg_P._46

MIF_tg_P._47

MIF_tg_p._48

(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:

MiF_5A_text_3.1_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:

mIf_2a_tg_P._46The 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.PM 2A TG mult

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:

PMCC_materials 
PMCC_PV_discs

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

MiF_Materials MiF_PV_rods

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.

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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.


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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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Throwback Thursday – It can’t all be Singapore Math…

Over the summer, we thought it would be fun to run some of the most popular posts from the past. Here’s a look at some misconceptions around Singapore Math and Common Core Standards. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


It can’t all be Singapore Math…

Originally published 12/29/2014

This tweet posted by the National Council on Teacher Quality (@NCTQ) caught my eye:

NCTQ_Tweet

Now, I’ve heard decomposing called “branching” but can’t remember ever seeing this in a Singapore textbook. Where did this problem come from?

It’s nice that NCTQ recognizes Singapore’s Math as “tops in the world.” But it’s discouraging to see methods and terminology that are not a part of the Singapore curriculum attributed to it. Especially in the context of the nasty debate about CCSS. And especially since Singapore’s math curriculum–with its rigor, coherence, and focus–is often cited as a basis for more rigorous standards, including CCSS.

The problem posted is based on the concept of “Number Bonds,” which calls for students to decompose numbers (this is the term used in Singapore and in all major Singapore Math® textbooks distributed in the U.S.). Below, I’ve posted some examples of how this concept is presented in Singapore Math® series available in both the U.S. and Singapore.

This matter points to my BIG concern: As publishers and others adapt Singapore’s Math for the American market, new approaches creep in. These often are not based on the curriculum that helped Singapore’s students go from mediocre to best in the world in a dozen years. I’ve written about this in my comparison of Singapore math textbook series available in the United States.

So my plea to NCTQ: please use examples from an actual Singapore mathematics text when citing the components that make it so successful. And feel free to ask if I can help you find those examples.

Number Bonds problems in Singapore Math® textbooks

Here are some materials covering Number Bonds and “decomposing” numbers from actual Singapore textbooks:

From My Pals are Here, the most-used materials in Singapore:

MPAH 3A Mental Addition

From the U.S. Edition of Primary Mathematics, available in North America since 2003:

PM US 3A Mental Addition

From the Common Core Edition of Primary Mathematics, released in the U.S. market in 2014:

PM CC 3A Mental Addition_0001

And finally, from Math in Focus:

MiF_3a_mental_math

 

UPDATE:

Ugh! One more similar tweet from NCTQ.

NCTQ_tweet_#2

 

 

 

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Best Books to Support Singapore Math in the Classroom

Best Books to Support Singapore Math in the ClassroomLooking for materials to supplement your Singapore Math® curriculum?  Here are some ideas along with why I recommend (or don’t recommend) them:

 

Challenging Word problems Common Core 4Challenging Word Problems US & Standards Edition and Challenging Word Problems Common Core Edition – What’s great about this series is that it includes samples & on-grade level problems PLUS samples & challenge problems.

Intensive Practice books – Great for advanced students. There’s computation practice, problem solving practice and logic problems.

 

Extra Practice U.S. Edition and Extra Practice Common Core Edition – No instruction, but extra worksheets to use for practice, home enjoyment, etc. I really like the friendly notes in the Common Core Edition to share with parents.

 

Marshall Cavendish has a couple of new series’ available:

Problem Solving Beyond the ClassroomProblem Solving Beyond the Classroom – More problem solving using multiple heuristics, not just bar modeling. A great addition to the classroom and would probably replace Process Skills in Problem Solving on my classroom bookshelf.

 

Math Practice the Singapore Way 3Math Practice the Singapore Way – Some schools are using this book as summer review work for students to keep up their math skills. It’s one year’s worth of review in one book.

 

Math Challenge The Singapore Way 2 Math Challenge the Singapore Way – Haven’t delved too deeply, but this one looks good! I definitely want a copy on my shelf.

 

 

Visible Thinking in Mathematicsvisible-thinking-in-mathematics-3bVisible Thinking in Mathematics – I love these as they provide great additional visual examples. I’d buy a set for resource library/room/Special Ed. Dep’t.

 

And some books straight from Singapore. Expect to find durian fruit or rambutans, but no U.S. measurement or money.

Speed Maths Strategies – Not necessary as they teach the strategies incorporated into the curricular materials, but many grade 4 & up teachers like the level 2 & 3 books to backfill Mental Math strategies. You probably don’t need above level 4. Each strategy includes a week worth of learning & practice:

  • Challenge page (Can you answer 2 problems in 10 seconds?)
  • Two pages of explanation
  • a page of practice problems
  • a page of word problems applying the strategy
  • A speed & accuracy test

Process Skills in Problem Solving level 4 Process Skills in Problem Solving – Replaced my favorite iExcel Heuristic and Model Approach books. Solid content, yet visual formatting makes the books challenging.

 

Math Works Foundations  – This is a full series designed for grade 5 & 6 students that struggle with the grade level content. It reteaches many concepts from grades 1-4 incorporating them into the grade 5-6 content. I find they’re a great resource for your Resource Room, Spec. Ed (or whatever you’re calling that department.)

i-Excel Heuristic and Model Approach– These are great, but out of print. you might luck out on eBay.

 

 

SprintsDifferentiated Math Sprints – The Singapore Math® curriculum stresses the use of mental math. These sprint books are written with that in mind and are useful to all elementary teachers interested in developing mental math fluency in their children. They take the place of Rocket Math or other pencil and paper fluency programs.

 

Placement tests on Singapore Math.com – These are used by homeschoolers to determine which books their student should start in. Most schools use these to locate gaps in students background knowledge.

Carson Dellosa books (available at Barnes & Noble & Costco). If you have nothing better to spend a gift card on, I guess you could buy these.

carson Dellosa Singapore Math Practice 3aSingapore Math Practice – So which level do you buy? 3A for students in Grade 4? or for students in Grade 3? If you’re using a Singapore based curriculum, you’d buy 3A for a 3rd grader. I’d buy the Marshall Cavendish series: Math Practice the Singapore Way instead.

 

Singapore Mental Math 4Singapore Math Mental Math  – One example, ten problems for 52 weeks. Too much work, not enough focus on a strategy. Buy Speed Maths Strategies  instead.

 

Step by step problem solving 3

Again, I’d go with the Singapore versions, either Challenging Word Problems or Problem Solving Beyond the Classroom

 

Free previews of the  series from Frank Schaffer Publications based on the Singapore syllabus are available here.

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It can’t all be Singapore Math…

This tweet posted by the National Council on Teacher Quality (@NCTQ) caught my eye:

NCTQ_Tweet

Now, I’ve heard decomposing called “branching” but can’t remember ever seeing this in a Singapore textbook. Where did this problem come from?

It’s nice that NCTQ recognizes Singapore’s Math as “tops in the world.” But it’s discouraging to see methods and terminology that are not a part of the Singapore curriculum attributed to it. Especially in the context of the nasty debate about CCSS. And especially since Singapore’s math curriculum–with its rigor, coherence, and focus–is often cited as a basis for more rigorous standards, including CCSS.

The problem posted is based on the concept of “Number Bonds,” which calls for students to decompose numbers (this is the term used in Singapore and in all major Singapore Math® textbooks distributed in the U.S.). Below, I’ve posted some examples of how this concept is presented in Singapore Math® series available in both the U.S. and Singapore.

This matter points to my BIG concern: As publishers and others adapt Singapore’s Math for the American market, new approaches creep in. These often are not based on the curriculum that helped Singapore’s students go from mediocre to best in the world in a dozen years. I’ve written about this in my comparison of Singapore math textbook series available in the United States.

So my plea to NCTQ: please use examples from an actual Singapore mathematics text when citing the components that make it so successful. And feel free to ask if I can help you find those examples.

Number Bonds problems in Singapore Math® textbooks

Here are some materials covering Number Bonds and “decomposing” numbers from actual Singapore textbooks:

From My Pals are Here, the most-used materials in Singapore:

MPAH 3A Mental Addition

From the U.S. Edition of Primary Mathematics, available in North America since 2003:

PM US 3A Mental Addition

From the Common Core Edition of Primary Mathematics, released in the U.S. market in 2014:

PM CC 3A Mental Addition_0001

And finally, from Math in Focus:

MiF_3a_mental_math

 

UPDATE:

Ugh! One more similar tweet from NCTQ.

NCTQ_tweet_#2

 

 

 

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Singapore Math Source Quick Start Guide

Since 2008, I’ve worked as Singapore Math® Trainer and Consultant. Each year, I have the pleasure of introducing the curriculum to thousands of teachers, administrators and parents and help dozens of schools implement and use Math from Singapore.

Without hesitation, I can say that the Singaporean curriculum provides a great foundation for elementary math success. But it is not a silver bullet. A school or district implementing the curriculum requires leadership and community-wide support, willingness to learn a new approach and specific training in the Singapore Math® Method. SingaporeMathSource.com is chock full of tools and tips to help teachers and students, administrators and parents to understand and use the curriculum successfully. If you need help or advice as you consider the curriculum, don’t  hesitate to get in touch with me.

In the meantime, consider taking a look at a few of the posts and pages that visitors tell me are the most valuable:

General Information on the Curriculum

For Teachers

For Teachers and Parents

For Teachers, Parents and Students

Cassy’s Adventures

If you have any suggestions or comments, please let me know. Enjoy your exploration.

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