Problem
One day of Mr. Diaz plus one day of Mrs. Diaz adds 3/20 + 2/20 = 5/20 of the fence. Each Mr+Mrs pair contributes the same 5/20.
Adding fractions with the same denominator just adds the numerators — a Grade 4 same-denominator add.
4.NF.B.3Look For A PatternOne full pair of days — Mr. Diaz's day then Mrs. Diaz's day — always adds exactly 5/20 of the fence.
Mr. Diaz paints the same 3/20 on each of his days and Mrs. Diaz paints the same 2/20 on each of hers, so every such pair adds 3/20 + 2/20, which is 5/20.
Every twentieth is the same-size piece of the fence, so 3/20 is just three of those pieces and 2/20 is just two of them.
Putting three of those equal pieces together with two more of them makes five of the pieces, and five of the twenty equal pieces is 5/20 of the whole fence.
After 6 days there have been three complete Mr+Mrs pairs, so the painted amount is 3 × 5/20 = 15/20.
Repeating a fixed fraction is just adding it three times — 15/20 is still short of the whole 20/20.
4.NF.B.3Look For A PatternDay 7 is Mr. Diaz's turn, adding 3/20: 15/20 + 3/20 = 18/20. Not finished yet (18/20 less than 20/20).
Listing the next turn keeps the running total honest — we are 2/20 short.
4.NF.B.3Make A Systematic ListDay 8 is Mrs. Diaz's turn, adding 2/20: 18/20 + 2/20 = 20/20 = 1, the whole fence. The fence is finished on day 8.
Counting in units of 1/20, reaching 20/20 means the whole job is done.
4.NF.B.3Analyze The UnitsThis only needs Grade 4 same-denominator fraction adding — count in twentieths until you reach a whole!