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Students approximate whether a fraction is closer to 0, 1/2 or 1. The purpose is to give the students an understanding of relative size of fractions.
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This is a great activity for getting students to think about fractions as a single quantity (ie half of 1 or half of something) and there relative size. All too often students see TWO numbers that form a thing called a fraction because one number is placed "over" another.
Time permitting, when discussing answers with the class, I like to ask students exactly how far each fraction is from the given benchmark. This can lead to interesting conversations about equivalent fractions and further division of the number line. E.g. with 4/9, 4.5/9 would be exactly half, so 4/9 is half of 1/9 from 1/2. So how does one think about half of 1/9, or .5/9?
I use this activity before we have talked about common denominators. The purpose to give the students a feel for the relative position of fractions on the number line.
Students create a line which they mark the beginning as 0 and the end as 1. They then place 1/2 in the middle. To approximate a fractions relationship to 0, 1/2 or 1, the students can divide the unit length into the appropriate number of pieces. Students also use their knowledge that a larger denominator means a smaller fraction. Hence 5/6 > 4/5 because 1/6 < 1/5.
This activity forces students to go beyond rules and employ critical thinking skills. Students are asked to determine if given fractions are closer to 0, 1/2 or 1. Many students are intimidated by the fact that other students know some formula to solve problems at hand. This type of problem will appeal to all students, as they can rely on their intuition for some answers. It also encourages the formulation of a rule based on their intuition. I will definitely be using this in my courses. I'll try to include visual interpretation of this exercise also.
I really like this. Think ahead to when students learn radians, and need to locate the fractions around the unit circle. This skill (being able to identify whether the fraction is close to 0, 1/2, or 1) is an important one. Great estimation practice.
This activity helps students understand that a larger denominator means each piece of a unit segment is smaller. The students can develop a rule for solving the problems at the top, where they determine if the fraction is closer to 0, 1/2 or 1, and then use that rule later when they need to write fractions that are close to 1/2 or 1. It also asks them to make the rule concrete with the questions "How do you know a fraction is closest to 1?' and "How do you know a fraction is closest to 1/2?"