Reasoning · Grade 3-1 Applying Fractions
Problem
Fractions whose parts sum alike form one group.
Adding the top and bottom of a fraction is something a Grade 3 learner can do, and noticing the totals stay equal inside each block is just pattern-spotting.
3.NF.A.1Look For A PatternThe fractions are grouped by the total of their top and bottom, and inside one group that total never changes.
Every fraction has one definite top-plus-bottom total, so it belongs to exactly one group and the groups can be counted one after another.
Each group's total is one more than the group before it, so the groups march upward by a fixed step of one.
A group summing to s holds s − 1 fractions.
Testing the rule on the small groups I can actually see (1, 2, 3 fractions) makes me trust it before I use it on bigger groups.
3.OA.D.9Solve An Easier Related ProblemSince 4 + 11 = 15, it sits in the group summing to 15.
Once I know the rule is 'group by the sum,' I just add the two numbers to know which group the fraction belongs to.
3.NBT.A.2Look For A PatternThe earlier groups run 1 to 13, totalling 91.
Listing the group sizes in order and adding them is just careful counting; the pairing trick keeps the addition tidy.
3.OA.D.9Make A Systematic ListIt is fourth in its group: 91 + 4 = 95th.
Within a group the numerator IS the count from the start of that group, so numerator 4 means the 4th spot.
3.NBT.A.2Look For A PatternGroup the fractions by 'top plus bottom,' count the groups before yours, then add the numerator - only Grade 3 adding and pattern-spotting needed!