Introduction
Making math meaningful
Exploring endless equations
A dedication to my area of specialization
The highs, lows and raised brows
This web quest will serve the purpose of empowering and embracing the ideology of Mathematics and its importance to everyday living. Mathematics is the science and study of quality, structure, space, and change. Through abstraction and logical reasoning mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences.
Task
Subject: Mathematics
Grade: 4
Unit title: Numbers
Topic: Addition of Fractions with unlike denominators
Focus questions:
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What do I need to know about fractions with unlike denominators?
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How can I add fractions with unlike denominators?
Pre-requisite knowledge: Students should already know how to
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Apply their conceptual understanding of a fraction
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Express their understanding of equivalent fractions
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Identify ‘like’ and ‘unlike’ fractions
Specific Objectives: At the end of this lesson, students should be able to:
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Apply equivalence to the addition of fractions with unlike denominators.
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Solve problems which require the addition of fractions with unlike denominators.
Process
Content Summary: A whole number is any number from zero upwards; the set of natural numbers and zero. Whole numbers are neither fractions or decimals. Examples of whole numbers include: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …}. A fraction may be described as a part of a whole object or a set of objects. A fractional number usually consists of two parts: a numerator and a denominator. The numerator is the top number in the fraction; the denominator is the bottom number in the fraction. For example, in the fraction ⅘, the 4 is referred to as the numerator, and the 5 is known as the denominator. In a mixed number there would be three parts and this entails the addition of a whole number to the preexisting fractional part. For example, in the mixed number 1 3/4, the 1 is the whole number, the 3 is the numerator, and the 4 is the denominator. Addition of two or more fractions will result in a sum that is greater than the addends. To add fractions with unlike denominators, the concept of equivalence needs to be applied so that all the addends can have the same denominator, i.e., the use of LCM. For example, 2/3 + 3/6 . The least common multiple (LCM) of 3 and 6 is 6, so both fractions need to be expressed having 6 as their denominator. Therefore, one would multiply both the numerator and denominator of 2/3 by 2, and multiply both the numerator and denominator of 3/6 by 1. These two operations would be joined by the addition sign. ( 2 ×2 / 3 ×2 ) + ( 3 ×1 / 6 ×1 ) = 4/6 + 3/6 . Now that there are like denominators, addition can be done seamlessly as required above. The numerators would be added and the new common denominators kept: 4/6 + 3/6 = 7/6 OR when expressed as a mixed number: 1 16 . In cases where the addition of unlike fractions occurred and the answer can be simplified, simplification is recommended.
Evaluation
