 # Math

Singapore Math achieves the best results in the world by emphasizing conceptual understanding, problem solving, and mental math.

## Three Stage Process

Singapore math uses a three stage process to ensure students understand math concepts deeply: ### 1. Concrete

Students explore a mathematical idea or process using real objects.

### 2. Pictorial

Students represent mathematical thinking using pictures and diagrams.  ### 3. Abstract

Students represent mathematical thinking numerically.

## Problem Solving

Throughout these three steps, the Singapore Math method requires solving real-world math problems. These problems often ask students to use their understanding in new and challenging ways. There is always a lot of model-making, mathematical reasoning, and discussion involved.

## Math Fluency

All students in grades K-4 are expected to become fluent in the math facts for their grade level. Mathematical fluency involves the ability to make calculations quickly and easily. When students don’t have to struggle to figure out basic calculations, they can focus on higher-order thinking, such as problem solving. We consider knowing math facts similar to what knowing the letter sounds is to reading; it is a foundation on which higher-order skills are built.

In grades K-4, students need to be able to answer 20 questions per minute of the following types:

Kindergarten
• Adding with numbers up to 5
• For example: 1+2=3, 3+1=4, 5+0=5
• Subtraction with numbers up to 5
• For example: 4-3=1, 5-2=3, 3-1=2
1st
• Addition facts within 10 (the sum will not exceed 10)
• for example: 7 + 2 = 9, 3 + 5 = 8
• Subtraction facts within 10
• for example: 7– 4 = 3, 6 – 5 = 1
2nd
• Addition and Subtraction Facts 1-20
• For example: 5+7=12; 12+6=18; 8+12=20; 8-3=5; 15-7=8; 17-14=3
• Multiplication Facts 2, 3, 4, 5, & 10
• For example: 2x5=10; 3x4=12; 10x5=50
3rd
• Multiplication facts 2-12
• for example: 6 x 9 = 54, 8 x 5 = 40
• Division facts 2-12
• for example: 56 ፥ 8 = 7, 42 ፥ 7 = 6
4th
• Multiplication facts 0-12
• For example: 0x4 = 0, 9 x 12 = 108, 4x5 = 20
• Division facts 1-12
• For example: 14412=12, 72 8=9
• Simplifying Fractions
• For example: 2/4 = ½, 4/4 = 1

For more information on Singapore Math methods and what they look like in the classroom, Executive Director Dane Roberts hosted this in-depth discussion with parents:

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