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 → Fractions and Decimals ↓


Fraction Equivalency


In math, a fraction represents a part of a whole. It consists of two numbers: the numerator, which is above the line, and the denominator, which is below the line. For example, in the fraction 1/2, 1 is the numerator, and 2 is the denominator. When talking about fraction equivalence, we are exploring the concept of how different fractions can actually represent the same value.

Understanding fractions

Let's start by considering the fraction 1/2. This fraction means that something is divided into 2 equal parts, and we are taking 1 of those parts. If we have a pizza, and we cut it into 2 equal pieces, 1/2 will be one of those pieces.

      ,
     ,
    | 1 |
    , 
    ,
    (Visual representation of a pizza with one of the two slices highlighted)

Now, let's look at another example: the fraction 2/4. This fraction shows that something is divided into 4 equal parts, and we take 2 of it. If we cut a pizza into 4 slices and take 2 slices, we'll look at the fraction 2/4.

      ,
     ,
    | 1/4 |
    | 1/4 |
    | 1/4 |
    | 1/4 |
    (Visual representation of a pizza with two of the four slices highlighted)

What is fraction equivalence?

Fraction equivalence means that different fractions can describe the same quantity. In the examples above, the fractions 1/2 and 2/4 describe the same portion of pizza. This means that they are equivalent fractions. When we say that fractions are equivalent, they are equal in value.

An easy way to check if two fractions are equal is to multiply or divide both the numerator and denominator by the same number. For example:

    ,
    frac{1}{2} equiv frac{1 times 2}{2 times 2} = frac{2}{4}
    ,

    ,
    frac{3}{6} equiv frac{3 div 3}{6 div 3} = frac{1}{2}
    ,

Examples of equivalent fractions

Let's look at these examples through some diagrams:

Consider a chocolate bar:

        Chocolate Bar:
        ,
       ,
       | 1/2 |
       ,

The whole is divided into two parts, and one part is colored. This fraction is 1/2.

        ,
       | 1/4 | 1/4 |
       ,

Now, the whole is divided into four parts, and 2 parts are colored. This fraction is 2/4.

        ,
       | 1/3 | 1/3 | 1/3 |
       ,

Again, all the parts together also make a whole. Note that in the previous example, if 2 parts of 3 are colored it will be a fraction of 2/3 which is not equal to 1/2.

Using these examples, you can see that 1/2 and 2/4 have the same value because they take up the same space in the chocolate bar, even though they are divided differently.

Equivalence of fractions with some numbers

It's important to practice creating equivalent fractions. Let's take 1/3 :

    ,
    frac{1}{3} equiv frac{1 times 2}{3 times 2} = frac{2}{6}
    ,

    ,
    frac{1}{3} equiv frac{1 times 3}{3 times 3} = frac{3}{9}
    ,

    ,
    frac{1}{3} equiv frac{1 times 4}{3 times 4} = frac{4}{12}
    ,

All these fractions represent the same value, such as dividing something into parts and taking equal parts. It is important to note that as long as we multiply the numerator and denominator by the same number, they will be equal.

Using fraction equivalence in decimals

Fractions can also be converted to decimals. This is often done by dividing the numerator by the denominator. For example:

    1/2 = 0.5
    3/4 = 0.75
    2/5 = 0.4

Understanding equivalence is helpful when comparing decimals and fractions. Knowing that 1/2 = 0.5 and 2/4 = 0.5, they are equivalent in either fraction or decimal form.

Practical exercises to understand equivalence

Here are some simple exercises to strengthen understanding:

  1. Find the equivalent fraction for 1/4.
  2. Compare visually if 2/4 equals 1/2.
  3. Convert 1/8 and 2/16 to decimals and compare the values.

Why learn about fraction equivalence?

Understanding equivalence of fractions is important because it helps us simplify fractions, make calculations easier by converting them to whole numbers, and understand relationships between different measurements.

When students understand the equivalence of fractions at an early age, it lays the groundwork for more complex math topics and problem solving. It creates a way to simplify and compare fractions without actually doing arithmetic on them.

After all, fraction equivalence also helps in everyday life, such as cooking recipes, working with money, measuring distances, or dealing with time. Knowing fractions means knowing how much and what amounts to make better decisions.

Conclusion

Fraction equivalence is a valuable skill in everyday life and in advanced mathematics. It allows us to see that different fractions can tell the same story or represent the same part of a whole. Whether learning with numbers or a visual aid, understanding equivalence gives insight into the flexibility and versatility of fractions. It is a stepping stone to mathematical learning and practical applications in the world around us.


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Fractions as part of a whole
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Fraction Equivalency

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