Length tools and units
You have a small toy car that is about 6 inches long. Which tool from this list is best to measure it to the nearest inch: a ruler, a yardstick, or a meter stick? Explain why your choice is best.
The best tool to measure to the nearest inch is a ruler.
Look at a paperclip. Estimate its length in inches and in centimeters. Then explain one way you could check your estimate without using a measuring tool.
Here is a possible answer:
A possible answer could be:
I estimate the paperclip is about 1 inch long, which is about 2.5 centimeters.
I could check my estimate by comparing the paperclip to something I know the size of, like the width of my finger or the length of a dollar bill, and see how it matches up.
Another acceptable checking method might be lining several paperclips end to end and comparing them to a known object, like a sheet of paper.
When measuring two pencils, one is 6 inches, the other is 9 inches. How much longer is the second pencil? Show your subtraction and explain your method.
The pencil is 3 inches longer. 9-6=3 or 6+3=9
A bookshelf is 3 feet long. If one book takes up 3 inches on the shelf, how many such books will fit in a row along the entire shelf? Show your multiplication or repeated addition and explain.
12 books
I can fit 4 books in each foot. If I have 3 feet of space, then 4+4+4=12 books
You measured a pencil with a ruler and got 7 inches. Now measure the same pencil with a tape measure showing centimeters and got 18 centimeters. Explain why the two measurements are different and what that tells you about the size of the units.
They are different because the unit sizes are different. Centimeters are smaller than inches.
Two strips of ribbon look about the same length. One student estimates both are 12 inches. Describe a quick method to test whether the estimate is accurate and explain what it would mean if one ribbon measures 11 inches and the other measures 13 inches.
A possible answer could be:
A quick way to test the estimate is to place the two ribbons side by side and line up one end, then use a ruler or yardstick to measure each ribbon.
If one ribbon measures 11 inches and the other measures 13 inches, it means the ribbons are not the same length, even though they look similar. It also shows that the estimate of 12 inches was close on average, but not exact for either ribbon.
A ribbon is 24 inches long and another ribbon is 60 centimeters long. Which ribbon is longer? Explain how you decide and show any conversions or reasoning used.
A possible answer could be:
The ribbon that is 60 centimeters long is longer.
I know that 1 inch is about 2.5 centimeters, so 24 inches × 2.5 = about 60 centimeters.
Since 24 inches is about the same as 60 centimeters, and 1 inch is actually 2.54 centimeters, 24 inches is slightly more than 60 centimeters.
This means the 24-inch ribbon is just a little longer, but they are almost the same length.
Two students measured a rope. One measured 48 inches and the other measured 4 feet. Are their measurements the same? Explain and show work.
Their measurements are the same! Each foot is equal to 12 inches.
12+12+12+12=48 inches
4 feet = 48 inches
You need to measure the length of a classroom table that is about 4 feet long. Describe two different tools you could use and explain which would give the most precise measurement and why.
It makes sense to use a yard stick and a ruler to measure a table that is about 4 feet long. A tape measure would also be a wise tool. There may be more responses, but your teacher decides if it is a valid response.
You are given a classroom hallway to walk and estimate that it is about 20 meters long. Describe how you could use a known-length object (like your shoe or a meter stick) to test your estimate and explain how you would adjust your estimate if needed.
A possible answer could be:
I could test my estimate by using a known-length object, such as a meter stick, and count how many times it fits along the hallway. If it takes about 20 meter sticks, then my estimate is accurate.
If I use my shoe, I could find out how many shoes equal one meter and then count how many shoe lengths fit across the hallway. If the total is more than 20 meters, I would increase my estimate. If it is less than 20 meters, I would decrease my estimate.
You measured two toy cars: one is 12 cm and the other is 5 inches. Determine which is longer. Explain your steps and show any work.
A possible answer could be:
I know that 1 inch is about 2.54 centimeters.
To compare, I convert 5 inches to centimeters:
(5 \times 2.54 = 12.7) cm.
One toy car is 12 cm long and the other is 12.7 cm long, so the 5-inch toy car is longer.
A number line goes from 0 to 100. Each space is 1 inch. A pencil is 7 inches long.
Where the pencil would be on the number line?
Now the number line changes. Each space is 2 inches. Where the pencil would be now?
When 1 space = 1 inch, I count 7 spaces from 0 and stop at 7. That shows a pencil that is 7 inches long.
When 1 space = 2 inches, I know 7 inches is the same as 3½ spaces because 2 + 2 + 2 = 6 and one inch is left.
I would go to 3 and a half on the number line.
This works because changing the size of the spaces changes how many spaces the pencil takes up
A student uses a meter stick and measures a desk as 1 meter. Another student uses a yardstick and measures the same desk as 3 feet. Decide which measurement is larger, explain how you know, and show a quick conversion or comparison to justify your answer.
Your teacher will decide if your justification is valid.
Explain how the size of a unit (inch vs. foot or centimeter vs. meter) affects estimation. Provide an example where using a larger unit makes estimation easier and one where a smaller unit is better. Justify your choices.
A possible answer could be:
The size of the unit affects estimation because larger units cover more space, so fewer units are needed, while smaller units are more precise but require counting more units.
Using a larger unit makes estimation easier when measuring something long, like a hallway. Estimating in feet or meters is easier than inches or centimeters because you do not have to think about very large numbers.
Using a smaller unit is better for measuring something short, like the length of a pencil. Inches or centimeters give a more accurate estimate than feet or meters.
These choices make sense because the unit should match the size of the object being measured.
A student measures a shelf as 85 cm and another student measures it as 2 feet. Decide which measurement shows a longer shelf. Convert one measurement so you can compare, show your work, and explain your reasoning.
One student measured the shelf as 85 cm, and the other measured it as about 2 feet which is about 61 cm.
Since 85 cm is longer than 61 cm, the measurement of 85 cm shows a longer shelf.
A yard of fabric is 36 inches. You need two pieces: one is 24 inches and the other is 15 inches. Will one yard be enough? Explain how you determine this using addition and subtraction, and show your work.
No, one yard will not be enough.
24+15=39 inches. There is 36 inches in each yard.
You are given three objects: a book (about 25 cm), a pencil (about 18 cm), and a small stuffed animal (about 40 cm). Plan and describe a method to measure each object using only a ruler marked in inches. Explain how you will record measurements and how you will compare the lengths later.
Your teacher will determine if your plan and description of your method will be a valid response.
Two students estimate the length of their classroom table. Student A estimates 3 feet, Student B estimates 1 meter. Without measuring, explain who is likely closer and why. Show reasoning that compares the units and uses known relationships between inches, feet, centimeters, and meters.
A possible answer could be:
Student A is likely closer. A typical classroom table is usually a little under 4 feet long.
One foot is 12 inches, so 3 feet = 36 inches.
One meter is about 100 centimeters, and since 1 inch is about 2.5 centimeters, 1 meter is about 39 inches, which is a little more than 3 feet.
Because classroom tables are usually closer to 3 feet than 3¼ feet, Student A’s estimate of 3 feet is likely closer than Student B’s estimate of 1 meter.
You measure three boards: 1) 2 feet 6 inches, 2) 80 centimeters, 3) 90 inches. Order the boards from shortest to longest. Show conversions and explain each step you used to compare mixed units.
Order from shortest to longest:
Board 1 (2 feet 6 inches)
Board 2 (80 centimeters)
Board 3 (90 inches)
A student needs to pack three items into a box measuring 2 feet 6 inches long: a toy that is 45 cm, a book that is 10 inches, and a board that is 60 centimeters. Decide if the three items can fit end-to-end in the box. Show all conversions, calculations, and explain your final decision.
No, they will not fit. The items are longer than 50 inches long, but the box is only 30 inches long.