math-2017:1.MD.1math-2017:1.MD.2
math-2017:1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
math-2017:1.MD.2 Express 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. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Learning goal: Order three objects by length, compare two lengths using a third object, and measure an object by laying equal-sized length units end to end without gaps or overlaps. Choose objects whose lengths are exactly spanned by a whole number of the selected units; fractional measurement is not required for this target.
Begin with three paper strips. Align their starting ends, compare the finishing ends and arrange them from shortest to longest. Reverse the order and use longest, middle and shortest in complete sentences. The strips’ colors or page positions are labels, not evidence for their lengths.
Sometimes two objects cannot be put directly side by side. Use a third strip or string as a comparison reference, keeping its length fixed. If table edge A is longer than the reference and table edge B is shorter than the same reference, A is longer than B. The reasoning depends on the particular relationships. If both are longer than the reference, that alone does not tell which is longer.
Measure using copies of one chosen shorter object. Place six equal tiles end to end along a strip with no gaps or overlaps. If those six tiles exactly span the strip, its length is six tile-length units. Count the lengths placed, not the boundary marks: six adjacent units create seven boundary positions including both endpoints.
The diagram shows a measured strip partitioned into six equal unit lengths. Each rectangular segment is one unit. The outer edges of the row, from the left end of unit 1 to the right end of unit 6, mark the object’s measured span. The lines between the rectangles separate units; they are not extra units to count. Explain what the word six refers to before writing the measurement.
Unit size matters. A shorter unit requires more copies to span the same object, while a longer unit requires fewer, when each fits exactly. Therefore “six units” is incomplete for comparing two measurements unless the unit is identified and kept consistent. Six small tiles and six long sticks represent different lengths when the tile and the stick are different sizes.
Identify errors in a proposed measurement. Gaps leave part of the object unmeasured, overlaps count part of the span more than once, and mixed-size units do not produce one consistent unit count. Repair the arrangement before accepting the numeral. This makes measurement a relationship between an object and a repeated equal unit rather than a picture with a number beside it.
Worked example 1: Order three strips. Three aligned strips measure four, six and three copies of the same unit. Their order is three-unit, four-unit, six-unit from shortest to longest. The numerical comparison works because the unit size is common.
Worked example 2: Indirect comparison with enough evidence. Strip A is longer than a reference string, and strip B is shorter than that same string. Therefore A is longer than B. If both A and B were longer than the string, more evidence would be needed to order them.
Worked example 3: Count spaces. A strip has six adjacent equal units with marks at both ends and between units. There are seven marks but six lengths. The measurement is six unit lengths, not seven.
Guided investigation: Order three real strips, then use an unchanged reference strip to compare two separated objects. Measure appropriate classroom objects with repeated equal tiles, ensuring whole-number fits. Partners check the endpoints and the absence of gaps or overlaps before recording a result.
Independent tasks: Order three objects, explain a supported indirect comparison, measure an object using identical repeated units, and correct a flawed measurement drawing. State the unit name with every recorded length. Choose examples fitting the whole-number restriction so uncertainty at a partial unit does not obscure the target.
Scoring and feedback: Award credit for correct order/comparison, consistent units, complete coverage and a correctly interpreted count. If a child counts marks, point inside each unit region while counting. If the unit changes midway, replace it with matching copies and remeasure. Extend by measuring the same object with two different uniform unit sizes that both fit exactly and explaining why the counts differ.
An adult may read the prompts aloud. Answer independently with words, objects, drawings or a demonstration before opening the answer guide. Award 1 point for a correct result or claim and 1 point for a matching explanation or demonstration; where a question asks only for a result (a corrected sentence, a spelling, a count), a fully correct result earns both points, and the answer guide shows what a complete response contains. Record prompting separately. The total (two points per question) is local practice feedback, not an Ohio proficiency level.
Three ribbons measure seven, five and nine of the same paper clip. Order the lengths from shortest to longest.
Five paper clips, seven paper clips, nine paper clips. The numbers can be compared because every ribbon was measured with the same unit.
A desk is shorter than a piece of string. A rug is longer than the same string. Which is longer, the desk or the rug?
The rug is longer than the desk, because the unchanged string lies between their lengths.
A shelf and a bench are both shorter than the string. Can you decide which of them is longer from that alone?
No. Both comparisons are with the string; neither one compares the shelf with the bench.
Eight paper clips of the same size are laid end to end along a pencil with no gaps or overlaps. The first clip starts at one end of the pencil and the last clip stops at the other end. How long is the pencil?
Eight paper clips long. The length is the number of same-size units that span the pencil, and the unit must be named.
A child lays five equal tiles end to end along a strip, with no gaps or overlaps, so that they cover it exactly from one end to the other. The child counts the six marks at the ends and between the tiles and says the strip is six tiles long. Repair the measurement.
The strip is five tiles long. Count the tile lengths that span the strip, not the marks; five tiles in a row have six marks.
Why do gaps invalidate an end-to-end unit measurement?
Part of the object’s length is left uncovered by the counted units.
Can measurements in different-size units be compared by numeral alone?
No. Identify and account for the unit size; the same numeral can represent different lengths.