India/Knowledge Base/Maths/Fractions and Decimals

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Std 2.14 They understand using concrete material and pictures- the meaning of fraction as part of a whole or of a collection where whole or collection is divided into equal parts. They recognize and name the following fractions of a whole or a small set of objects - half, one-third, one fourth etc. and two-third, three-fourth using concrete objects and pictures. They know their symbolical representation and the terms numerator and denominator. They compare and order these fractions using concrete objects and pictures. They are explained the representation of these fractions on a number line. They understand concretely, pictorially that when all fractional parts are included such as two halves or four one-fourths, the result is the whole or the complete set.

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Std 3.14 They understand the meaning and concept of fractions as part of a whole or a collection where the whole or collection is divided into equal parts using concrete objects and pictures. They understand naming and notation of fractions and know the terms- numerator and denominator.
 * 1) / SWBAT identify (visually) and write simple fractions (with denominator up to 15) /
 * 2) / SWBAT identify the numerator and denominator of a fraction /

Std 3.17 They understand the relative sizes of unit fractions (1 or 2 to 1 or 12) and other simple fractions (2 or 3, ¾) using one long object (e.g. sugarcane), a collection of say 12 objects or their pictures. They are explained the representation of these fractions on a number line
 * 1) / SWBAT order unit fractions and fractions with the same denominator /

Std 3.20 They thus understand that decimals are fractions and know decimal and fraction equivalents of tenth, hundredth etc /]]
 * 1) / SWBAT represent parts of a whole as decimals (only to tenths) and convert between fractions and decimals /

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Std 4.12 They understand the meaning of proper/improper fractions and mixed numbers concretely, pictorially and symbolically. They convert improper fractions to mixed numbers and vice-versa and understand their equivalence.
 * 1) / SWBAT identify proper and improper fractions (including showing them visually) /
 * 2) / SWBAT identify and represent mixed numbers /
 * 3) / SWBAT convert between improper fractions and mixed numbers. /

Std 4.14 Using LCM, they are also able to compare unlike fractions with denominators less than 12 or 20 (for the sake of simplicity) and add/subtract them. They compare or add/subtract mixed numbers by comparing or adding/subtracting whole parts and then fractional parts (like or unlike).
 * 1) / SWBAT identify like and unlike fractions (EI 3.16) /
 * 2) / SWBAT compare fractions with the same denominator (EI 3.17) /
 * 3) / SWBAT arrange fractions with the same denominators in ascending/descending order (EI 3.17) /

Std 4.15 They summarize methods of comparing and adding/subtracting fractions and mixed numbers.
 * 1) / SWBAT add/subtract fractions with like denominators (both arithmetically and visually) /
 * 2) / SWBAT add/subtract mixed numbers with equal denominators /
 * 3) / SWBAT to identify 1/2, 1/3, and 1/4 of a given number (resulting in a whole number) /

Std 4.16 They compare like/unlike decimals to thousandth place and beyond. They understand and know addition/subtraction of like/unlike decimals to thousandth place and beyond.
 * 1) / SWBAT represent parts of a whole as decimals (only to hundredths) and convert between fractions and decimals /
 * 2) / SWBAT identify place value of decimals (up to hundredths place) /
 * 3) / SWBAT add/subtract decimals (up to hundredths place) /

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Std 5.6 Besides parts of a whole or a collection when whole or collection is divided in equal parts, they understand fraction from another point of view also as – division of two whole numbers. They understand equivalence of these interpretations and associate a proper fraction to a number between 0 and 1 on the number line.
 * 1) / SWBAT order fractions on a number line (natural extension of comparing fractions) /
 * 2) / SWBAT identify equivalent fractions (3rd EI) /
 * 3) / SWBAT create equivalent fractions with a missing number. (3rd EI) /
 * 4) / SWBAT reduce fractions to their lowest form (3rd EI, 4th IGCSE) /
 * 5) / SWBAT compare fractions with unlike denominators (4th EI, 5th 4th IGCSE) (by creating equivalent fractions with like denominators) /

Std 5.7 They know representation of a whole number as a fraction and a decimal and understand that division can be regarded as multiplication by reciprocal.
 * 1) / SWBAT write a whole number as a fraction. /

Std 5.8 They understand the meaning and effect of multiplication and division of fractions by a whole number, by a fraction or a mixed number/improper fraction and know how to carry out multiplication and division of fractions by these.
 * 1) / SWBAT multiply a fraction by a whole number /
 * 2) / SWBAT multiply fractions /
 * 3) / SWBAT identify recipricols of fractions /
 * 4) / SWBAT divide fractions /
 * 5) / SWBAT divide fractions by whole numbers /

Std 5.13 They understand the equivalence of the concepts of fractions and decimals. They know that all decimals can be represented in fractional form and all fractions in decimal form by dividing the numerator by the denominator including terminating and repeating decimals.
 * 1) / SWBAT identify decimal fractions and their decimal conversions for fractions up to denominator of 1000 (EI 3.19 and 3.20) /
 * 2) / SWBAT convert a decimal into a fraction to the thousandths place. /
 * 3) / SWBAT identify and create equivalent decimal fractions (ex. 6/10, 60/100, 600/1000) /

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