Singapore's 4th Grade "Year 4" Math Curriculum Overview

Singapore Math - problem-solving using the model method 

Singapore Math uses a three-step learning model called the Concrete-Pictorial-Abstract (CPA) method. This method starts with teaching students using hands-on objects, then moves on to drawing visuals, and finally to abstract learning

- Number and Operation

- Understanding 4-digit numbers, place value, expanded form, comparing and ordering numbers

- Addition and subtraction of 4-digit numbers, mental strategies, column addition and subtraction

- Multiplication of 2-digit and 3-digit numbers, multiplication tables up to 10 x 10, mental strategies, long multiplication

- Division of up to 3-digit numbers by 1-digit numbers, remainders, mental strategies, long division

- Fractions and decimals - fractions as parts of a whole, equivalent fractions, adding/subtracting fractions, decimals, converting fractions to decimals

- Measurement and Geometry

- Perimeter and area of regular and irregular shapes

- Comparing, estimating and measuring weight, capacity, time

- Properties of triangles, quadrilaterals, circles

- Symmetry, tessellations

- 3D shapes and nets, views of 3D shapes

- Data Analysis

- Pictographs, bar graphs, tables and line graphs

- Organizing, representing and interpreting data

- Algebra

- Number patterns and relationships

- Finding missing numbers in number sentences

- Solving simple algebraic equations

The curriculum focuses on building strong foundational math skills, with an emphasis on mental calculation strategies and problem solving. Students learn math concepts with the aid of concrete objects and visual models.

Here are some examples of how the Year 4 math concepts in Singapore are taught using concrete models and visual representations:

Place Value and Expanded Form:

- Students use place value blocks or discs to model 4-digit numbers, understanding each digit's value. They can trade 10 hundreds for 1 thousand, 10 tens for 1 hundred, etc.

- Students write numbers in expanded form, for example 3482 = 3000 + 400 + 80 + 2. The teacher provides place value charts for students to fill in the expanded form.

Addition and Subtraction:  

- To add multi-digit numbers without regrouping, students use place value mats with columns for thousands, hundreds, tens and ones. They add vertically in each place value.

- For problems involving regrouping, students use place value blocks and learn to trade a 10 in one place for a 1 in the next place. The teacher models this process step-by-step.

Multiplication:

- Students use arrays or grid paper to illustrate multiplication as repeated addition. For 3 x 4, they draw 3 rows with 4 boxes each and count the total number of boxes. 

- The teacher models using place value blocks to show multiplication involving larger numbers, trading 10 tens for 1 hundred, for example.

Fractions:

- Students fold paper strips into fractions or use fraction circles to compare unit fractions visually. They can see 1/4 is less than 1/3 because it is a smaller part of the whole.

- To add fractions, students use fraction strips to represent equivalent fractions with a common denominator before adding. 

Here are some more examples:

Division:

- Students use place value blocks or base 10 blocks to model division and understand remainders. For example, to divide 426 by 7, they trade 4 hundreds blocks for 40 tens blocks, and regroup 26 ones into 2 tens and 6 ones. They then distribute the blocks into 7 equal groups to see the quotient and remainder.

Perimeter and Area: 

- Students measure and calculate the perimeter and area of shapes drawn on grid paper. This allows them to count unit squares to find the area. The teacher emphasizes the formulas for rectangles and squares.

Time:

- Students use interactive online clocks or physical teaching clocks to read time in hours, minutes and seconds. They learn to convert between units of time, such as 2 hours 30 minutes = 150 minutes.

3D Shapes:

- Students examine and play with 3D shape models to learn their properties. They count the faces, vertices and edges.

- Students use nets of shapes like cubes and prisms to understand how they are formed from 2D shapes. They practice folding nets into 3D shapes.

Algebra:

- The teacher presents number sentences like 35 + ☐ = 53 or ☐ x 9 = 63. Students model the calculations with place value blocks and figure out the unknown number.

- Students also solve equations like ☐ + 9 = 16 using reasoning, trial and error and inverse operations.

Data Analysis:

- Students collect data on topics relevant to them, like favorite ice cream flavors in the class. They organize this data into pictographs and bar graphs.