Comparing lengths in 2nd grade

Answer. 4

The blue bar is $4$ cubes longer than the red bar.

1. 1Look at the two bars. The blue bar shows Maria's pencil. The red bar shows Carlos's pencil.
2. 2Count the cubes in each bar. The blue bar has $6$ cubes. The red bar has $2$ cubes.
3. 3To find how many cubes longer the blue bar is, subtract the red count from the blue count.

Common mistake. A common mistake is adding the two cube counts ($6 + 2 = 8$) instead of subtracting. To find how much longer one bar is than another, subtract the smaller count from the larger count.

The idea underneath. When you compare two lengths made of the same-size units, subtraction tells you how many units longer one is than the other.

Bar A is 5 units longer than Bar B. Bar A is 9 units long and Bar B is 4 units long, so $9 - 4 = 5$.

1. 1Look at the graph. Read where each bar ends. Bar A ends at 9, and Bar B ends at 4.
2. 2To find how much longer Bar A is, subtract the shorter bar from the longer bar.
3. 3Bar A is longer than Bar B by 5 units. So the true statement is 'Bar A is 5 units longer than Bar B.'

Common mistake. A common mistake is using one bar's length (like 9) as the answer instead of subtracting. To compare two bars, take the longer bar minus the shorter bar: $9 - 4 = 5$.

The idea underneath. To find how much longer one bar is, subtract the shorter length from the longer length. The bigger number minus the smaller number gives the difference.

The toothbrush is $7$ inches and the cookie is $3$ inches, so the true difference is $7 - 3 = 4$ inches. Sam said $5$, which is $1$ more than $4$. Sam counted one too many ticks to get the answer.

1. 1Look at the rulers. The toothbrush reaches the $7$ mark on the inch ruler, so the toothbrush is $7$ inches long. The cookie reaches the $3$ mark, so the cookie is $3$ inches long.
2. 2Find the true difference. The toothbrush is longer, so subtract the shorter length from the longer length:
3. 3The true difference is $4$ inches. But Sam said $5$. Notice that $5$ is exactly $1$ more than $4$. Sam counted one too many ticks.
4. 4When students count one too many ticks (often by counting the $0$ mark itself, or by counting both end ticks instead of the spaces between them), they get an answer that is $1$ more than the true difference. The statement that says Sam counted one too many ticks to get $5$ inches best describes Sam's measurement.

Common mistake. A common mistake is counting the $0$ tick when measuring distance. To find how much longer one object is than another, count only the spaces between tick marks, not the tick marks themselves. Counting an extra tick adds $1$ to the answer.

The idea underneath. When you find how much longer one object is than another on a ruler, count only the SPACES between tick marks, not the tick marks themselves. Counting both end ticks adds an extra count and gives a number that is $1$ too high.

The spoon is $2$ inches longer than the highlighter because $7 - 5 = 2$.

1. 1Read each object's length on its own ruler. Each object's left end starts at 0.
2. 2The spoon is 7 inches long and the highlighter is 5 inches long. Subtract the highlighter's length from the spoon's length to find the difference.
3. 3The spoon is 2 inches longer than the highlighter.

Common mistake. A common mistake is to add the two lengths instead of subtracting them. To find how many inches longer one object is than another, subtract the shorter length from the longer length.

The idea underneath. To find how many units longer one object is than another, subtract the shorter length from the longer length.