Early Math · Grade 1
Measuring Length with Units
Quick answer
Lengths can be put in order by lining things up at one end. Two things that cannot be put side by side can still be compared with a third thing, such as a string: if the string is longer than one and shorter than the other, the order is known. To measure a length, lay same-size units, such as cubes, end to end along it with no gaps and no overlaps, and count them. The count is the length in those units.
What you'll learn
- Order three objects by length
- Compare two lengths by using a third object
- Measure a length with same-size units laid end to end, with no gaps or overlaps
Put three in order
Here are a ribbon, a string and a rope. They are lined up at one end.
The string stops first, so it is the shortest. The rope goes the farthest, so it is the longest.
In order from shortest to longest: string, ribbon, rope.
Compare with a third thing
Is the door longer or shorter than the table? You can not put a door next to a table.
So use a string. Cut it as long as the table. Then hold it up to the door. The door is longer than the string.
The string is as long as the table. So the door is longer than the table, too.
Measure with units
To find how long a thing is, lay cubes along it, end to end.
Start at one end of the pencil. Stop at the other end. Count the cubes: .
The pencil is cubes long. Each cube is one unit of length.
Why the cubes must touch
A length in cubes tells how many cubes cover the object, from end to end. So the cubes must cover all of it, and each part only once.
If there are gaps, some parts are not covered. The count comes out too small.
If the cubes overlap, some parts get counted twice. The count comes out too big.
No gaps, no overlaps, all the same size. Then the count is the length.
Worked examples
Common mistakes
Practice problems
-
Put these in order from shortest to longest.
Three lengths Answer
Twig, yarn, tape
Full solution
They start at the same spot. The twig stops first, then the yarn, then the tape.
-
How many cubes long is the key?
A key and cubes Answer
Full solution
Count the cubes from one end to the other: , , .
-
A snake is longer than a worm. The worm is longer than an ant. Which is shortest?
Answer
The ant
Full solution
The worm is longer than the ant, and the snake is longer than the worm. So the ant is shortest.
-
A string is as long as a desk. The string is shorter than a rug. Which is longer, the desk or the rug?
Answer
The rug
Full solution
The rug is longer than the string, and the string is as long as the desk. So the rug is longer than the desk.
-
How many cubes long is the spoon?
A spoon and cubes Answer
Full solution
The cubes cover the spoon from end to end with no gaps. There are .
-
Is this a good way to measure? Why or why not?
Cubes under a stick Answer
No. The cubes overlap.
Full solution
Where the cubes overlap, parts of the stick are counted twice. The count would come out too big.
-
A shoe is cubes long. A sock is cubes long. Which is longer?
Answer
The shoe
Full solution
cubes is more than cubes, so the shoe is longer.
-
A shoe is cubes long. A sock is cubes long. How many cubes longer is the shoe?
Answer
Full solution
. The shoe is cubes longer.
-
Why do all the cubes need to be the same size?
Answer
So each one counts for the same length.
Full solution
If some cubes were big and some small, cubes could be a long thing or a short thing. Same-size cubes make the count mean one length.
-
Leo measures a pen with cubes. He leaves a space between each cube and says the pen is cubes long. Is the pen longer or shorter than cubes?
Hint
What happens to the parts of the pen under the spaces?
Answer
Longer. The spaces were not counted.
Full solution
Each space is part of the pen with no cube on it, so it was left out of the count.
With the spaces filled in, it takes more than cubes to reach the end.
Frequently asked questions
How do I put three things in order by length?
Line them up at one end. The one that goes the least far is shortest, and the one that goes the farthest is longest.
How can I compare two things that cannot be moved side by side?
Use a third thing, like a string. If the string is longer than the table but shorter than the door, the door is longer than the table.
How do I measure with cubes?
Lay cubes end to end along the object, starting at one end, with no gaps and no overlaps. Count the cubes to the other end.
Why can't there be gaps between the units?
A gap leaves part of the object uncovered, so it does not get counted. The count comes out too small.
Why must the units be the same size?
A length in units only means something if every unit is the same. 6 cubes tells you the length only when the cubes all match.
Standards alignment
This lesson covers the following Common Core State Standards for Mathematics.
- CCSS.MATH.CONTENT.1.MD.A.1Measurement and DataOrder three objects by length; compare the lengths of two objects indirectly by using a third object.
- CCSS.MATH.CONTENT.1.MD.A.2Measurement and DataExpress the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.