Use the offset-ruler workbench to calculate a difference, compare a shifted span, and hold incomplete readings. The worked cards stay separate from blank hunt records for the real paper strip, notebook edge, and pencil.
Prepare objects and a suitable real ruler
This original planning packet proposes three teacher-approved, reachable objects:
| Hunt row | Object | Feature to measure | Actual estimate/readings |
|---|---|---|---|
| H1 | Straight paper strip | Stated end-to-end span | Blank |
| H2 | Notebook | Its stated long edge | Blank |
| H3 | Pencil | Stated tip-to-end span | Blank |
Use one declared unit per row. This packet uses centimeters. Do not take a start reading from an inch scale and an end reading from a centimeter scale.
This hunt concerns straight lengths only. It does not measure mass, curved paths, area, or converted units.
Make the estimate a separate record
Ask the learner to estimate the stated feature's length before measuring. Record the estimate with its unit in the estimate column.
Then keep it there. A measurement should not silently overwrite the estimate and make the earlier prediction disappear.
For each object, leave space for its ID and description, the feature measured, estimate, unit, start and end readings, calculated length, whether it is an illustrative card or an observed object, and anything still unclear. Leave classroom readings blank until learners measure.
An estimate is not a measured fact. A teacher can use a difference between estimate and measurement for discussion, but this packet does not mark every estimate wrong because it differs from an exact demonstration key.
Do not assign the same expected length to all actual paper strips, notebooks, or pencils. The source illustration supplies its own numbers; real objects require real readings.
Teach an offset ruler with an original card
Use authored ruler card M1: a fictional straight strip begins at 3 cm and ends at 9 cm on one declared centimeter scale.
| Record | M1 |
|---|---|
| Source | Illustrative card |
| Unit | cm |
| Start reading | 3 cm |
| End reading | 9 cm |
| Length | 9 − 3 = 6 cm |
The 9 cm label is an endpoint coordinate on the scale. The strip covers the distance between 3 and 9.
An answer of “9 cm” identifies the larger endpoint while ignoring the start. Keep that trial and point to the two readings needed for the difference.
For authored M2, the same model span begins at 0 cm and ends at 6 cm. Its length is 6 − 0 = 6 cm. Moving a fixed span along the scale changes its endpoint labels without changing its length.
These are fictional teaching-card values, not measurements already made of H1. The actual hunt row should say “Observed” only after a learner has used the real tool; the card row should say “Illustrative.”
Align the feature before reading the endpoints
Use the approved object's stated straight span and the actual ruler. Place the scale along that span and identify both endpoints on the same scale.
For the notebook, specify which long edge the row concerns. For the pencil, retain the declared tip-to-end span rather than switching to a different feature halfway through.
If the ruler is too short, an endpoint is obscured, or the feature is unclear, record the issue. Choose a suitable tool or clarify the feature before claiming a complete reading.
The pictured cards are schematic. Their screen width does not establish a physical centimeter, and printing the diagram does not make it a calibrated ruler. The real measuring tool remains separate.
Before learners begin, check the ruler's position, whether its graduations are readable, and whether its range covers the chosen feature. Check any printed activity sheet for legibility as well.
Give insufficient evidence its own outcome
Stage a card with start 3 cm, end hidden, and unit cm. The length is unknown; do not reuse M1's 9 cm endpoint to fill the gap.
In another card, show endpoint numbers 3 and 9 but omit the unit. The numerical difference is six scale intervals, but a centimeter length is not established. Ask for the unit before reporting a unit-bearing result.
For the bounded demonstration workbench, accept finite readings from 0 through 12 on the declared centimeter scale, with end greater than or equal to start. If end is smaller than start, hold the row for correction rather than taking an absolute difference silently.
Try the worked example
Calculate the default 9 − 3 = 6 cm. Shift the illustrative span to 0 and 6 and recalculate: its length remains 6 cm. Clear the end reading to see why the length cannot be established. Write estimates before measuring real objects, then preserve the estimate beside the actual readings. A missing endpoint is unknown, not zero.
Recreate this example
Build one complete self-contained HTML page for this task: calculate an illustrative straight span from two ruler readings and prepare a separate classroom observation sheet.
Use these exact original practice data and worked expectations: M1 starts at 3 cm, ends at 9 cm, length 6 cm. M2 starts at 0 cm, ends at 6 cm, same length. Teaching scale range 0–12; equal endpoints yield zero. Hunt objects: paper strip end-to-end, notebook long edge, pencil tip-to-end, with actual observations blank.
Implement the following useful local interactions: Provide start/end inputs and an explicit unit field, Calculate and Shift example buttons. Display differences rounded to ten decimal places, without trailing zeros. Require finite readings within 0–12 and end >= start; blank endpoint or missing cm unit withholds the unit-bearing result. Preserve a separate estimate and blank real observation rows. Preserve the supplied source text and distinguish an uncomputed state, a successful local result, and an invalid or incomplete input. Update output only from the current input snapshot. An input edit must retire stale feedback until the reader runs the relevant action again. Do not silently invent missing values or replace a failing case with a success.
Design the page as an orange-accented ruler activity sheet with a schematic scale and roomy labeled reading fields. Put a compact task heading, actual sample data, the main result, and usable controls early enough to be useful on a narrow screen. Use readable text of at least 16px, generous paragraph spacing, strong contrast, native labels, accessible buttons, and visible keyboard focus. Stack long records at 360px and wrap code without page-level horizontal overflow.
Use type=button and explicit querySelector-based click handlers rather than relying on form submission. If Enter is useful, handle it only on the relevant input and ignore isComposing. Keep effects within this open page; no remote dependencies, network calls, persistence, fake downloads, or automated sending. The screen ruler is schematic and not a calibrated measuring tool. Use a suitable real ruler for actual classroom observations. Place worked explanations beside their data and identify teacher or synthetic examples clearly. Output only the complete HTML document, with inline styles and script and LF line endings.
Review the ruler cards in NOS
Prepare the three object rows and confirm each straight feature before learners begin. A teaching-card explanation in NOS can keep both endpoint readings visible; eligible static instructions about which edge to measure can be revised in visual editing mode.