Math in Focus is the U.S. version of the math curriculum taught in Singapore. Students in Singapore consistently score at the top of international mathematics comparison studies such as the TIMSS (Trends in International Mathematics and Science Study) and PISA (Program for International Student Assessment). The Singapore Math pedagogy was also one of the key research models used to guide the development of the Common Core State Standards. The following diagram shows the philosophy of the teachings of Singapore Math:

The center of the program revolves around mathematical problem-solving. All skills, processes and concepts develop problem-solving attitude and understanding. Students grow as thinkers as well as mathematicians.

Singapore Math teaches concepts using a concrete-to-pictorial-to-abstract learning progression, which anchors learning in real-world, hands-on experiences. The goal is to develop deep understanding through visualization. Manipulatives are a constant in the classroom, and teachers use them to demonstrate the concepts being taught. Examples include number bonds, 10 frames, place chips and charts, and bar models.

A typical lesson begins with making connections to previously learned concepts, learning something new through instruction and exploration, guided practicing of many levels of problems sets, and finally, independent problem solving. This process can take two to three days, because the students are studying for mastery. A parent may see, or hear about, some of the following:

• Teaching of the lesson – Direct instruction and exploration of the concept.
• Guided practice – Activities and practice with support from the teacher. Students are gradually led from the pictorial to the abstract.
• Let's practice – Simple to complex problems created to determine if students are ready to progress to independence. During this practice, teachers may address any reteaching necessary or establish enrichment groups.
• Workbook – Independent practice to create fluency and accuracy.
• Extra practice "homework" – Reinforces all the teachings of the lesson.

This Math in Focus Scope and Sequence brochure clearly defines and organizes the sequence of topics for grades K-5. Based on developmentally appropriate lessons, the chart reveals the expectations of mastery. Some overarching initiatives are constant throughout the curriculum. Two that are apparent in the classroom are:

1. A focused and coherent curriculum. Fewer topics in each grade allow more time to teach to mastery. Each subsequent grade teaches a concept at a higher level.
2. Content organized by big ideas, such as place value. The properties of operations are taught using place value materials so that students understand why the algorithms work.

All grade levels begin with the concept of number sense, which includes everything from understanding what the number 5 means (in kindergarten) to determining the patterns of place values (grade 5). Counting, comparing and ordering are all part of number sense.

The most important concept to understand in order to move into operations is the relationship between place values. Knowing that 1 ten equals 10 ones is essential to regrouping. This pattern of 10s is evident in all large number manipulations and throughout the decimal lessons:

10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand
10 tenths = 1 one
10 hundredths = 1 tenth

Learn more about place value in Math in Focus.

Throughout Math in Focus, the operations of addition, subtraction, multiplication and division are discussed. Each grade approaches an operation by discussing what is already known and understood. Then a larger place value may be added, or regrouping may be introduced. Nonetheless, each child has an idea of the pictorial representations of the operations.

A distinguishing characteristic of math taught in Singapore, and of Math in Focus, is the use of model drawing or "bar modeling," a systematic method of representing word problems and number relationships that is explicitly taught beginning in second grade.

In grades K-1, students draw pictures to represent a real-world problem. Discussion, predictions and finally mathematics all evolve from one picture. Once students become accustomed to discussing problems, they begin using cubes to represent the actions described. By combining or separating cubes, children get a clear sense of addition and subtraction. They have taken a concrete item such as a cube and created a picture of bundling or unbundling – concrete to pictorial.

In grade 2, students transition from cubes to drawing a rectangular bar that represents the cubes. The use of the rectangular bars and the identification of the unknown quantity with a question mark help students visualize the problem and know what operations to perform. The wording becomes a little trickier, so student must pay attention to the placement of the question mark; students must always be aware of answering the proper question. In grade 3, multi-step problems using multiplication and division become all the rage! Fourth graders gain a deep understanding of "before and after" problems, which can include up to three or four steps. Finally, fifth graders tackle problems involving fractions.

Learn more about Math in Focus bar modeling.

Problem examples from each grade.

Various websites are available for bar modeling help. Although rather simple in nature, they help students to build the basic skills of bar modeling.

Thinking Blocks - Can access via an app or PC.

Math Playground - A variety of bar modeling as well as quick fact recall games.

Math Buddies - A program through Marshall Cavendish that can be purchased for use at home. This digital supplemental program adopts the same principles of the Singapore Math approach.