Grade 2
  1. Number Sense and Operations  1.1. Counting and Number Sequences  1.1.1. Counting up to 100  1.1.2. Counting by 2s, 5s, and 10s  1.1.3. Counting Backward from 20  1.1.4. Odd and even numbers in counting sequences  1.2. Place Value  1.2.1. Understanding ones and tens  1.2.2. Comparing Two-Digit Numbers  1.2.3. Identifying the Value of Each Digit in a Number  1.2.4. Building numbers using tens and ones  1.3. Addition and Subtraction  1.3.1. Basic addition up to 20  1.3.2. Basic subtraction up to 20  1.3.3. Addition with Regrouping  1.3.4. Subtraction with Borrowing  1.3.5. Solving word problems involving addition and subtraction  1.3.6. Addition and Subtraction with Multiples of 10  1.4. Odd and Even Numbers  1.4.1. Identifying Odd and Even Numbers  1.4.2. Understanding patterns in odd and even numbers  1.4.3. Simple operations with odd and even numbers
  2. Fractions and Decimals  2.1. Introduction to Fractions  2.1.1. Understanding halves and quarters  2.1.2. Representing fractions visually  2.1.3. Simple Fraction Comparisons  2.1.4. Writing Simple Fractions  2.1.5. Fractions as part of a whole  2.2. Fraction Equivalency  2.2.1. Understanding Equal Parts  2.2.2. Identifying Equivalent Fractions
  3. Measurement and Data  3.1. Length Measurement  3.1.1. Measuring objects using rulers  3.1.2. Comparing lengths  3.1.3. Estimating lengths  3.1.4. Understanding units of measurement (centimeters and inches)  3.1.5. Relating Length Measurements to Real-World Objects  3.2. Weight and Mass Measurement  3.2.1. Comparing Weights of Objects  3.2.2. Estimating weight in grams and kilograms  3.2.3. Using balance scales for comparison  3.3. Volume and Capacity Measurement  3.3.1. Understanding capacity with cups and liters  3.3.2. Comparing capacities of containers  3.3.3. Introduction to Milliliters  3.4. Time  3.4.1. Reading analog and digital clocks  3.4.2. Understanding hours and minutes  3.4.3. Calculating elapsed time in hours  3.4.4. Days of the week and months of the year  3.4.5. Understanding AM and PM  3.5. Money  3.5.1. Recognizing coins and bills  3.5.2. Counting money up to $1  3.5.3. Simple Addition and Subtraction with Money  3.5.4. Making Change for a Dollar
  4. Geometry and Spatial Reasoning  4.1. Shapes and Their Attributes  4.1.1. Identifying basic shapes (circle, triangle, square, rectangle)  4.1.2. Understanding sides and corners  4.1.3. Distinguishing between 2D and 3D shapes  4.1.4. Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)  4.1.5. Composing and Decomposing Shapes  4.2. Symmetry  4.2.1. Understanding Lines of Symmetry  4.2.2. Drawing Symmetrical Shapes  4.2.3. Identifying Symmetrical Objects in the Environment  4.3. Patterns and Spatial Awareness  4.3.1. Recognizing and Creating Patterns  4.3.2. Extending Patterns  4.3.3. Understanding positions (left, right, above, below)  4.3.4. Using a grid to locate objects
  5. Data Handling and Probability  5.1. Collecting and Organizing Data  5.1.1. Using tally marks  5.1.2. Reading Bar Graphs  5.1.3. Simple Pictographs  5.1.4. Creating Bar Graphs from Given Data  5.2. Interpreting Data  5.2.1. Answering questions based on data  5.2.3. Identifying Most and Least in Data Sets  5.3. Introduction to Probability  5.3.1. Understanding likely and unlikely events

Grade 2 → Geometry and Spatial Reasoning → Shapes and Their Attributes ↓


Composing and Decomposing Shapes


In geometry, composing and decomposing shapes are fundamental concepts. These ideas help us understand how shapes are formed and how they can be taken apart. By learning about shape composition and decomposition, children can explore spatial reasoning, which is an essential part of mathematical understanding. In this discussion, we will take a deeper look at these concepts using simple language, textual explanations, and visual examples.

Creating shapes

Building shapes involves putting two or more simple shapes together to form a larger, more complex shape. This lets us know how different shapes can fit together. For example, if we take two triangles and put their bases together, we form a square.

Two triangles are joined to form a square.

Let us consider another example. Put three squares together in a row. This forms a rectangle. Mathematically, if each square has a side length s, the resulting rectangle will have a length of 3s and a height s.

Three squares together make a rectangle.

When drawing shapes, we explore and use various properties such as side lengths, angles, and symmetry. This develops a deeper understanding of geometry and helps us visualise how larger shapes and structures can be made from smaller components.

Disassembled shapes

Decomposing shapes is the opposite process of composition. It involves taking a complex shape and breaking it down into simpler shapes. This helps in understanding the components that make up complex structures.

For example, consider a rectangle. This shape can be divided into two triangles by drawing a diagonal line. Each triangle will have a right angle, and together, they join to form a rectangle.

A rectangle divided into two triangles.

Another example of a decomposition is the hexagon. A regular hexagon can be broken down into six equilateral triangles. Understanding this decomposition can help solve problems related to area and symmetry.

A hexagon divided into six triangles.

Combination of conjunction and disjunction

By combining composition and decomposition techniques, we gain versatility in solving a wide range of mathematical problems. For example, when determining the area of complex shapes, you can decompose the shape into simpler shapes, find the area of each, and then sum these areas.

Consider an irregular shape made up of a rectangle and a triangle. By identifying and separating these, you can find the area of each:

rectangle:

Area = length × breadth


Triangle:

Area = ½ × base × height

Exercises for practice

Understanding can be deepened with practice. Here are some exercises:

  1. Draw a large triangle and divide it into smaller triangles and rectangles.
  2. Construct a trapezoid using a square and a triangle. Confirm your construction by measuring the angles and sides.
  3. Divide a pentagon into a rectangle and a triangle. Find the area of each shape, then sum them for the overall area of the pentagon.

It is important in geometry to understand how shapes are formed and decomposed. These exercises will strengthen your spatial reasoning and problem-solving skills.

Conclusion

Composing and decomposing shapes are important skills that aid in understanding more advanced geometric concepts. They serve as building blocks for higher mathematical education and practical applications. Through visualization and practice, one can enhance their spatial awareness and use these skills effectively in both academic and real-world scenarios.


Grade 2 → 4.1.5


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Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)
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Symmetry

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Composing and Decomposing Shapes

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