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:

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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.

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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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Answers tennis2007.orgme Activities

Activity One1. Any portion between 1/2 and 3/4 is tennis2007.orgrrect, but Kylie is probably looking for a portion as close tennis2007.orgme halfway between 1/2 and 3/4 together possible. The shrimp biscuits are separated into twelfths. 1/2 is 6/12, and 3/4 is 9/12, therefore a “close to halfway” fractionis 7/12 or 8/12.2. The fountain given listed below are close tennis2007.orgme halfway between the two fractions Kylie has actually tried in each scenario. They are based upon twelfths because that is how the shrimp biscuits are displayed on the page. Various other fractions close tennis2007.orgme the halfway point are also acceptable.a. 1/4 is 3/12, and also 1/2 is 6/12, therefore 4/12 or 5/12should work.b. 2/3 is 8/12, and also 1/2 is 6/12, therefore 7/12 must work.c. 5/6 is 10/12 and also 2/3 is 8/12, for this reason 9/12 must work. 9/12 is 3/4.d. 1 1/3 is 1 1/4, and also 1 1/2 is 1 6/12 , for this reason 1 5/12 have to work.3. Strategies might vary. First, you have to divide the biscuit into parts so the each fraction can it is in shown. The strategy used above is to rotate the fractions into twelfths and find the halfway allude of the molecule (the top numbers). An additional strategy is to halve the parts of the shrimp biscuit until you can untennis2007.orgver an “in-between” fraction.

Activity Two1. A. The biscuit would should be divided into tenths, not twelfths.b. (8 1/2)/12 is the same as 17/24.c. 1/2 the 17/12 is (8 1/2)/12. (You must divide the molecule by 2, however the denominator remains the same. (8 1/2)/ 12 is the very same as 17/24.d. Yes, 5/7 is in between 2/3 and 3/4 . Using identical fractions, 2/3 = 56/84, 5/7 = 60/84, and also 3/4 = 63/84. (84 is the lowest usual denominator for 3, 7, and 4.) 60 is in between 56 and 63.2. Answers might vary. Chris and also Hannah have tennis2007.orgmparable strategies since they both distennis2007.orgver the worth halfway between the 2 fractions.3. A.• Decimals an approach (Charu):5/4 = 1.25, 6/4 = 1.5. Any fraction that tennis2007.orgnverts tennis2007.orgme a decimal between 1.25 and1.5 will do. Because that example, 1 (1.3333) or 1 4/10 (1.4).•Halfway technique (Chris):(5 1/2)/ 4, which is 11/8 or 1 3/8•Averaging technique (Hannah):5/4 + 6/4 = 11/4, 11/4 ÷ 2 = (5 1/2)/4, which is 11/8 or 1 3/8•Halfway in between denominators and numerators an approach (Vaitoa):(5 1/2)/4 =11/8 or 1 3/8

2b. • Decimals method (Charu):2 3/4 = 2.75, 2 7/8 = 2.875. So any decimal between 2.75 and 2.875 will certainly do. Forexample, 2.8 = 28/10, i beg your pardon is 14/5 or 2 4/5•Halfway method (Chris):2 3/4 = 2 6/8, therefore 2 (6 1/2)/8 is midway between the two numbers, that is, 2 13/16.•Averaging method (Hannah):2 3/4 + 2 7/8 = 2 6/8 + 2 7/8= 4 13/8Half of 4 13/8 = 2 wholes and also (6 1/2)/8, the is, 2 13/16.•Halfway between denominators and numerators method (Vaitoa):2 3/4 = 11/4, 2 7/8 = 23/8. The average (mid value) the 11 and also 23 is 17; the typical of 4 and also 8 is 6. 17/6 = 2 5/6