Reasoning · Grade 4-2 Adding and Subtracting Decimals
Problem
Mia's final score is 25.93.
Lining the five numbers up smallest to largest makes 'the highest' and 'the lowest' the two on the ends, so there is nothing to hunt for — you just chop off both ends of the list.
5.NBT.B.7Make A Systematic ListLiam scores 25.75.
Adding decimals to hundredths is just column addition with the decimal points lined up, exactly like adding whole numbers of cents.
5.NBT.B.7Make A Systematic ListNoah scores 24.43.
All three gymnasts get the same treatment, so the three totals are fair to compare — that is why the rule exists in real gymnastics scoring.
5.NBT.B.7Make A Systematic ListThe order is Mia, Liam, Noah.
Comparing decimals is place-value work you already do with money: check the biggest place first and only move right when there is a tie.
4.NF.C.7Make A Systematic ListIn (2) the three certain scores add to 26.68.
You do not need to know the missing number to know it cannot make 8.52 or 8.89 or 9.27 into the biggest or the smallest of the six — those three are already sandwiched between 7.06 and 9.75.
4.NF.C.7Eliminate PossibilitiesSubtracting back leaves 7.08.
Working backwards turns 'add four things to get 33.76' into one subtraction, because three of the four are already known.
5.NBT.B.7Work BackwardsTaking the three certain scores away from the final total leaves exactly the fourth counted score.
The final score is the four counted judges added together, with the highest and lowest already thrown out.
With the whole and three of the four parts known, subtracting hands back the missing part.
That score belongs to Judge 4.
There were only three ways the blank could behave, and checking all three by hand is quick — two of them give the wrong total, so the middle one is the answer and nothing was overlooked.
5.NBT.B.7Eliminate PossibilitiesSort the scores first — then the two you throw away are simply the two on the ends, and the score you cannot see is just the total minus the ones you can.