Problem
One day of Mr. Diaz plus one day of Mrs. Diaz adds + = of the fence. Each Mr+Mrs pair contributes the same .
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 of the fence.
Mr. Diaz paints the same on each of his days and Mrs. Diaz paints the same on each of hers, so every such pair adds + , which is .
Every twentieth is the same-size piece of the fence, so is just three of those pieces and 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 of the whole fence.
After 6 days there have been three complete Mr+Mrs pairs, so the painted amount is 3 × = .
Repeating a fixed fraction is just adding it three times — is still short of the whole .
4.NF.B.3Look For A PatternDay 7 is Mr. Diaz's turn, adding : + = . Not finished yet ( less than ).
Listing the next turn keeps the running total honest — we are short.
4.NF.B.3Make A Systematic ListDay 8 is Mrs. Diaz's turn, adding : + = = 1, the whole fence. The fence is finished on day 8.
Counting in units of , reaching 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!