Mathematics · P7 · 3 weeks
Digging the Antonine Wall
Driving question
How much earth did Roman soldiers move to dig the Antonine Wall ditch across Scotland?
Having determined which calculations are needed, I can solve problems involving whole numbers using a range of methods, sharing my approaches and solutions with others.
TAUGHT IN Week 2, activity 1; Week 2, activity 3; Week 3, activity 1; Week 3, activity 2; Week 3, activity 3ASSESSED BY Solving Whole Number Problems
I can use my knowledge of rounding to routinely estimate the answer to a problem then, after calculating, decide if my answer is reasonable, sharing my solution with others.
TAUGHT IN Week 2, activity 2; Week 2, activity 3; Week 3, activity 2; Week 3, activity 4ASSESSED BY Estimation and Reasonableness
I can explain how different methods can be used to find the perimeter and area of a simple 2D shape or volume of a simple 3D object.
TAUGHT IN Week 1, activity 1; Week 1, activity 2; Week 1, activity 3; Week 2, activity 3; Week 3, activity 3ASSESSED BY Perimeter, Area, and Volume
Contains public sector information licensed under the Open Government Licence v3.0.
In this three-week unit, P7 pupils investigate the engineering of the Antonine Wall ditch. Working in small survey teams, pupils measure ditch and rampart profiles during fieldwork at Rough Castle using measuring tapes and simple clinometers. Back in class, they calculate cross-sectional areas using composite 2D shapes, scale up the volume along the wall's length, round to estimate reasonableness, and calculate total soldier workdays needed using historical digging rates. The unit culminates in presenting and defending their calculations to museum staff at Callendar House.
The teacher places a wooden Roman entrenching spade and a 1-metre measuring stick in the centre of the room. Pupils stand outside in the school grounds and mark out a ditch cross-section of 12 metres wide and 4 metres deep using skipping ropes to see the true size. The teacher asks how a Roman legion could dig that shape across the entire country.
- What shape was the ditch, and how big was it at Rough Castle?
- How do we find the area of the ditch cross-section?
- How long was the whole Antonine Wall in metres or kilometres?
- How much soil could one Roman soldier dig out in a single day?
- How do we know if our total volume and day counts are sensible?
Your lessons: 4 a week, 60 minutes.
Week 1
Measure the Antonine Wall ditch at Rough Castle and calculate its cross-sectional area.
Practise using measuring tapes and clinometers in the playground, recording slope angles and widths on profile sheets. Measure in threes, one on each tape end and one recording, and rotate roles at each of the three transects.
· 1 lessonVisit Rough Castle to measure ditch top width, base width, slope depth, and rampart height across three sample cross-sections. Walk the stretch of the wall in Callendar Park first so pupils see the ditch in town before we measure at Rough Castle.
· 2 lessonsSplit the measured ditch cross-section into simple shapes on squared paper to calculate the cross-sectional area in square metres. Have each group build a 1:50 card model of their measured cross section before they calculate the area.
· 1 lesson
Supports
Provide pre-drawn grid templates with visual boundaries for ASN pupils; pair EAL pupils with bilingual peers for field survey notes; encourage pupils ready for more to calculate the rampart volume alongside the ditch excavation.
Deliverable
A scaled, labelled cross-section diagram of the Rough Castle ditch with step-by-step area calculations.
Week 2
Calculate the total volume of earth moved along the full wall and estimate reasonableness.
Use maps of the Antonine Wall to establish total length in metres, converting kilometres to metres.
· 1 lessonRound length and area measurements to significant figures to create benchmark estimates of total soil volume.
· 1 lessonSplit the ditch cross section into a central rectangle and two right-angled triangles on squared paper to calculate total area, then multiply by wall length to find full volume and compare with estimates.
· 2 lessons
Supports
Offer place-value mats, squared paper templates, and multiplication grids for ASN pupils; provide dual-language mathematical glossaries for EAL pupils; pupils ready for more can adjust calculations to account for rocky sections along the route.
Deliverable
A volume calculation sheet showing rounding estimates, full calculations, and a written check on reasonableness.
Week 3
Calculate soldier workdays, critique findings, and defend calculations to Callendar House staff.
Use Roman military digging rates to calculate total soldier-days required, drafting an explanatory briefing board.
· 1 lessonRun a peer critique gallery walk using two stars and a wish on draft briefing posters, revising errors in calculation steps.
· 1 lessonPresent and defend ditch calculations and soldier-day estimates to visiting education staff from Callendar House.
· 1 lessonComplete an individual written reflection evaluating personal calculation strategies, rounding checks, and team methods.
· 1 lesson
Supports
Provide sentence starters for the presentation and reflection for EAL pupils; offer structured prompt cards for explaining methods for ASN pupils; pupils ready for more can calculate how winter weather or shift lengths would alter the completion timeline.
Deliverable
The finished calculation poster presented to museum staff and the completed personal reflection log.
Week 3, lesson 1
Teams display their draft calculation posters in a gallery walk during Week 3, lesson 2. Peers check calculations using a checklist focused on unit labels, rounding reasonableness, and step-by-step methods, leaving two stars and a wish before teams revise their work.
Student reflection
Pupils complete an individual exit reflection in Week 3, lesson 4, reviewing which calculation method worked best, how their initial rounded estimates matched their final total, and what was hardest about measuring real ground.
What they make
Teams produce an A2 illustrated engineering briefing poster showing the ditch cross-section, total volume calculations, and estimated soldier workdays needed to build the Antonine Wall.
Options
Teams choose whether to present their workings through hand-drawn scaled schematics or digital graph layouts, and choose whether to model digging rates based on peacetime or wartime legion conditions.
Who sees it
Education and heritage staff from Callendar House during Week 3, lesson 3.
Teams
Teams of three to four pupils, mixed by the teacher to balance practical surveying and calculation strengths.
| Criterion | beginning | developing | proficient | advanced |
|---|---|---|---|---|
Solving Whole Number Problems MNU 2-03a · individual | Solves simple single-step whole number calculations with prompting but misses multi-step stages for total volume or soldier days. | Solves multi-step calculations using written methods but shows arithmetic slips when calculating large soldier-day totals. | Determines correct operations and solves multi-step whole number calculations accurately for total volume and soldier workdays. | Solves complex whole number problems accurately using efficient methods and clearly explains multiple calculation strategies to others. |
Estimation and Reasonableness MNU 2-01a · individual | Rounds numbers only with support and does not use rounded figures to check if the final volume is reasonable. | Uses rounding to produce an initial estimate but struggles to explain whether the final calculated answer is sensible. | Rounds measurements systematically to estimate total volume beforehand and explains clearly why the final answer is reasonable. | Rounds flexibly to different degrees of accuracy to justify whether final answers are reasonable and identifies sources of measurement discrepancy. |
Perimeter, Area, and Volume MNU 2-11c · team | Measures dimensions but cannot divide the ditch cross-section into recognisable 2D shapes to find area. | Splits the cross-section into rectangles and triangles to find area but misapplies formulas when scaling up to volume. | Explains and applies methods to find the 2D cross-sectional area and correctly calculates the 3D volume of the wall ditch. | Compares multiple methods for calculating irregular cross-sectional area and 3D volume, evaluating which method gives the highest precision. |
Solving Whole Number Problems
MNU 2-03a · individualbeginning
Solves simple single-step whole number calculations with prompting but misses multi-step stages for total volume or soldier days.
developing
Solves multi-step calculations using written methods but shows arithmetic slips when calculating large soldier-day totals.
proficient
Determines correct operations and solves multi-step whole number calculations accurately for total volume and soldier workdays.
advanced
Solves complex whole number problems accurately using efficient methods and clearly explains multiple calculation strategies to others.
Estimation and Reasonableness
MNU 2-01a · individualbeginning
Rounds numbers only with support and does not use rounded figures to check if the final volume is reasonable.
developing
Uses rounding to produce an initial estimate but struggles to explain whether the final calculated answer is sensible.
proficient
Rounds measurements systematically to estimate total volume beforehand and explains clearly why the final answer is reasonable.
advanced
Rounds flexibly to different degrees of accuracy to justify whether final answers are reasonable and identifies sources of measurement discrepancy.
Perimeter, Area, and Volume
MNU 2-11c · teambeginning
Measures dimensions but cannot divide the ditch cross-section into recognisable 2D shapes to find area.
developing
Splits the cross-section into rectangles and triangles to find area but misapplies formulas when scaling up to volume.
proficient
Explains and applies methods to find the 2D cross-sectional area and correctly calculates the 3D volume of the wall ditch.
advanced
Compares multiple methods for calculating irregular cross-sectional area and 3D volume, evaluating which method gives the highest precision.
- 30-metre outdoor measuring tapes and simple handheld clinometers
- Centimetre squared graph paper and clipboards for field recording
- Map showing the complete route and length of the Antonine Wall across Scotlandcheck before use
- Archaeological summary sheet outlining typical Roman soldier daily excavation ratescheck before use
- A2 poster display boards and coloured markers