5th grade math: what your child learns this year

The best answer is: The student switched the x- and y-coordinates, because the checkpoint is at (2, 0) and the final point is at (2, 5) instead of the correct path to (5, 2).

1. Look at the graph. For the ordered pair (5, 2), the first move should be 5 units right from the origin, landing at (5, 0).
2. The checkpoint shown on the x-axis is at (2, 0), not (5, 0). The first move is already wrong—the student only moved 2 units right instead of 5.
3. The final point is at (2, 5). If the student had started from (2, 0) and moved up 5 units, they reached (2, 5)—which is exactly the reverse of the target (5, 2).
4. The graph shows the student started by moving 2 units right instead of 5 and then moved up 5 units instead of 2. That matches the description: the student switched the x- and y-coordinates.

Omar's conversion should use $90 \div 60$; the correct result is 1 hour 30 minutes, not 5,400 minutes.

1. Start by checking the goal and Omar's written conversion.
2. There are 60 minutes in 1 hour, so to find how many full hours are in 90 minutes, divide by 60.
3. The correct answer is 1 hour 30 minutes. Omar multiplied $90 \times 60 = 5{,}400$ instead of dividing. Multiplying by 60 converts in the wrong direction — it gives a much larger number of minutes, not hours and minutes.
4. Omar's error is using multiplication instead of division. To change a smaller unit to a larger unit, divide into groups of the conversion number (60).

The true statement is that moving the 7 one place to the left makes its value 10 times as much.

1. In 35.72, the 7 is in the tenths place, so its value is 0.7.
2. Moving one place left from tenths crosses the decimal point and puts the 7 in the ones place. Then its value is 7.
3. Compare the new value to the original value.
4. So the true statement is that the 7 would become 10 times as much.

Only Aaliyah is correct because Aaliyah rewrote both fractions correctly, but Liam changed $\frac{1}{6}$ to $\frac{1}{12}$ instead of $\frac{2}{12}$.

1. Multiplying a fraction's numerator and denominator by the same number splits its parts into smaller equal parts without changing its value. Multiply both by $3$ to rewrite $\frac{3}{4}$ as $\frac{9}{12}$. Multiply both by $2$ to rewrite $\frac{1}{6}$ as $\frac{2}{12}$. Now both fractions count twelfths. Subtract $2$ twelfths from $9$ twelfths to get $7$ twelfths. Check whether each student's rewrites and subtraction are correct.
2. Aaliyah uses twelfths. Check each rewrite and the subtraction.
3. Liam also uses twelfths but rewrites $\frac{1}{6}$ incorrectly. When the denominator is multiplied by $2$, the numerator must also be multiplied by $2$.
4. Aaliyah's chain is fully correct. Liam's chain is not correct because $\frac{1}{6}$ is not equivalent to $\frac{1}{12}$. The correct evaluation is: Only Aaliyah is correct.

The mistake is in Step 3: the student dropped the brackets and subtracted $2$ from $24$ before adding $7$, giving $29$ instead of the correct value $24 - [12 \div (8 - 2) + 7] = 24 - [2 + 7] = 24 - 9 = 15$.

1. Start with the original expression $24 - [12 \div (8 - 2) + 7]$. The innermost group is $(8 - 2)$, so that group must be simplified first.
2. Replace $(8 - 2)$ with $6$. Then divide inside the brackets: $12 \div 6 = 2$. The brackets still contain $2 + 7$, which has not been simplified yet.
3. Finish the work inside the brackets: $2 + 7 = 9$, so the expression becomes $24 - 9$. This is the step where the student went wrong: instead of adding $7$ inside the brackets first, the student dropped the brackets and subtracted $2$ from $24$ to get $(24 - 2) + 7$, which changes the order of operations.
4. Now do the outside subtraction: $24 - 9 = 15$. The correct value of the original expression is $15$, not $29$.