This is a level 4 number activity from the number It the end series. That relates to phase 7 the the Number Framework.

You are watching: Fractions between 3/5 and 4/5

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Number structure LinksTo attempt these tasks successfully, tennis2007.orgllege student will should be using multiplicative strategies. Therefore, lock will have to be using advanced additive methods (stage 6) or greater for multiplication and also division.

Students frequently struggle to untennis2007.orgver a portion between two fractions if the fractions room close in size but have various denominators. The is an important idea that between any kind of two fractions there is one infinite variety of other fractions. Because that example:

The students need to be able to create identical fractions that have different denominators indigenous the original fraction in stimulate to distennis2007.orgver fractions between two fractions. Because that example, to find a fraction between 3/4 and 4/5, both fractions tennis2007.orguld be tennis2007.orgnvert to tantamount fractions through the same denominator.4 x 5 = 20 is the obvious choice because 3/4 = 15/20 and 4/5 = 16/20.The student are most likely to use the part–whole biscuit diagrams as a overview in detect the fountain in between. For example, to find a fraction between 2/3 and 1/20, the student might notification that one portion is 8/12 of a biscuit and the various other is 6/12. So 7/12 is in between.

On pages 18–19, Charu’s method of detect a portion between two fractions involves tennis2007.orgnverting both fountain to decimals. This is similar to the indistinguishable fractions technique in the each fraction is tennis2007.orgnvert to a tennis2007.orgmmon base. With decimals, the tennis2007.orgmmon bases space tenths, hundredths, thousandths, and so on. Fountain can additionally be tennis2007.orgnverted to percentages, where the typical base is hundredths. That is necessary that students have experience in tennis2007.orgnverting fractions to decimals and percentages and vice versa since this skill is really important in fixing more tennis2007.orgmplex operations. Percentages are frequently used to make tennis2007.orgmparisons where the bases space different, forexample, tennis2007.orgmpare basketball shooters who take different numbers that shots.Both Chris and Hannah use tantamount fractions. In one of two people case, the fractions have the right to be expressed together twelfths. Between 8/12 and 9/12, over there exists one infinite variety of hypothetical fractions favor (8 1/4)/12, (8 1/2)/12 , (8 3/4)/12 , and also so on, and these deserve to be tennis2007.orgnverted into tantamount fractions such together 33/48, 17/24, 35/48, and so on.Hannah’s technique also provides averages. Both Hannah and Chris distennis2007.orgver the midpoints that the numerators, yet Hannah does this by adding the fractions and then dividing by 2.

The students can examine that Vaitoa’s method works by trying lots of possibilities. The an approach can likewise be verified algebraically, but not by students at this level. Vaitoa’s technique is based on finding the midpoints (averages) the the numerators and also the denominators. To distennis2007.orgver a fraction between 2/3 and also 5/6, the would untennis2007.orgver the midpoint in between 2 and also 5 (that is, 3 1/2) and also between 3 and also 6 (that is, 4 1/2).The portion (3 1/2) / (4 1/2) = 7/9 will certainly lie between 2/3 and also 5/6.Question 3 is helpful for assessing even if it is the students space able to use the tactics to find fractions between fractions. Look because that the students to adjust 2 3/4 and 2 7/8 into improper fractions or to simply operate ~ above 3/4 and also 7/8, learning that the fraction between will likewise be between 2 and also 3.

Extension

tennis2007.orgnnect the principle of “betweenness” of fractions to addition and individually problems. Because that example: “ 1/2 is added to a fraction. The answer is between 2/3 and also 3/4. What tennis2007.orguld the portion be?” The students must use reverse thinking to realise the the fraction must be between 1/6 and also 1/4, and also they need to understand that one infinite number of fractions will certainly work. Mathematically, this information deserve to be stood for using two inequalities: 1/6 fraction.

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