A three-lesson teacher plan connecting existing investigations: establish common units, recover a rectangle side and test its boundary, then account for a joined solid using non-overlapping parts.
Get assessments and teacher materialsGoal: Help learners build measurement records that name the quantity and unit, check every stated constraint and count each occupied region once. Use item-level evidence to decide which representation or calculation needs further teaching.
Materials: The existing c905, c906 and c908 investigation materials; paper, squared paper, pencils and two colours. Display the exact keys 1 m = 100 cm and 1 kg = 1000 g. Formula key: rectangle area = length × width; rectangle perimeter = 2 × (length + width); rectangular-prism volume = length × width × height. Use exact labelled mathematical sketches rather than measuring screen or print size. Keep a teacher record with separate columns for the numerical response and the explanation evidence for each assessment item.
Use the pre-assessment before the sequence and record each item's numerical correctness separately from its lookFor explanation evidence. Common-unit and rectangle-constraint work belongs to Grade 4; additive volume belongs to Grade 5. For Grade 4 learners who have not studied volume, record the solid-accounting items as not yet introduced, teach the first two lessons and schedule the third after its volume prerequisites are available. Before Lesson 3, learners need to explain cubic units and find a single rectangular prism's volume from three dimensions. If that prerequisite is absent, use the existing volume-as-equal-layers workshop first and ask the learner to explain why a 4 cm × 3 cm × 2 cm prism occupies 24 cubic cm. Resume this sequence when that explanation is available. Within each scheduled 40-minute lesson, use the linked investigation's support or ready route; secure learners explain or check an alternative record while classmates receive the targeted representation. The three planned lessons total 120 minutes; prerequisite work is scheduled separately. Use evidence by skill rather than a total-score threshold.
Use these six questions independently. Keep the numerical answer and the requested explanation as separate observations.
1008 · One kilogram contributes 1000 g and the leftover mass contributes 8 g, giving 1008 g.
Reasoning evidence: Labels 1000 g and 8 g as separate contributions, adds the remainder once and states that the measurement stays unchanged when renamed in grams.
19 · A is 209 cm and B is 190 cm; the common-unit difference is 19 cm.
Reasoning evidence: Writes 209 cm and 190 cm before subtraction, preserves the 9 cm remainder and identifies A as the longer strip.
7 · The length is 35 ÷ 5 = 7 cm, and 5 × 7 reconstructs the required 35 square cm.
Reasoning evidence: Uses 5 × unknown length = 35, solves by division and labels the side in cm rather than square cm.
2 · The required length is 8 cm. Its full perimeter is 8 + 5 + 8 + 5 = 26 cm, which exceeds the 24 cm allowance by 2 cm.
Reasoning evidence: Recovers 8 cm from the area, counts both pairs of opposite edges and explains that a correct area can accompany a boundary that exceeds its limit.
16 · The separate volumes are 4 and 12 cubic cm, so the total is 16 cubic cm. The contact face has area 4 square cm and no thickness; it does not remove a filled region from either part.
Reasoning evidence: Adds both non-overlapping interiors once, uses cubic units for volume and explains why subtracting the contact-face area would mix different quantities.
18 · The base contributes 10 cubic cm and the top contributes 8, giving 18. Above the rightmost 3 cm of the base is empty space 3 cm × 2 cm × 2 cm, with volume 12 cubic cm; the containing box would include it.
Reasoning evidence: Uses each part's own height, identifies the empty upper-right region and explains why adding the two occupied parts counts the solid once.
Before: Prepare the conversion key and an object/original/common-unit record. Read pre1 and pre2 separately: pre1 tests preservation of the smaller-unit remainder, while pre2 tests comparison after conversion. A correct number without a unit-based explanation still needs a brief follow-up. Bring learners' records, rather than a combined assessment score, into the investigation's diagnostic.
Focus: Run the existing investigation's 5-minute diagnostic, 10-minute model, 15-minute differentiated practice and 10-minute independent/transfer routine. Learners replace each larger unit using the exact key, add the smaller-unit remainder once and compare matching units. Have partners reverse a conversion to reconstruct the original record. Connect this to the next lesson: a boundary and its edging allowance can only be compared after their units match.
Collect: Collect the investigation's independent record and the learner's reverse check. Look for both measurements in the same unit, preservation of the leftover smaller units and a difference labelled with the requested unit. Record the numerical answer separately from these explanations; a plausible difference alone does not show which units were compared.
If secure: Move to the rectangle investigation. Ask the learner to label which numbers describe length, area and an edging allowance before calculating; the common-unit record becomes part of the final feasibility check.
If more support is needed: Use a larger-unit box labelled with its smaller-unit count and write leftover units outside it. Complete the common-unit routing recheck and ask the learner to reverse it. Keep the conversion key visible during Lesson 2; postpone an independent mixed-unit comparison until the learner can explain the conversion.
Before: Prepare a labelled rectangle with one missing side and distinct spaces for area, side lengths, perimeter and the edging limit. Use pre3 to check the missing-factor relationship and pre4 to check all four outside edges and the limit. If multiplication and division are not connected, prepare rows of unit squares before the investigation's diagnostic.
Focus: Run the linked 5/10/15/10-minute routine. Learners recover the missing side from area ÷ known side, multiply to verify the area and then add both pairs of opposite sides. They compare the complete boundary with the edging allowance. Discuss a plan that meets one requirement but fails another. Connect to Lesson 3 by distinguishing a filled two-dimensional region from its boundary; a solid likewise needs a record of occupied space rather than its outline alone.
Collect: Collect a labelled rectangle, its missing-factor equation, the reconstructed area, the four-edge perimeter and the feasibility decision. Distinguish a correct side with an incomplete boundary from an incorrect side. Check whether the learner states exactly how much edging is left or missing, including the possibility of meeting a limit exactly.
If secure: Move to the joined-solid investigation once the single-prism volume prerequisite is available. Ask the learner to name the area units used for a face and the cubic units used for filled space before adding any prism volumes.
If more support is needed: For a missing-factor error, rebuild complete unit-square rows and connect multiplication to division. For a boundary error, mark and trace all four edges before comparing with the limit. Use the rectangle-constraint routing recheck and retain separate evidence for the recovered side, perimeter and decision.
Before: Confirm the learner can explain a cubic unit and calculate one prism's volume, using volume-as-equal-layers first if needed. Prepare two colours and a base/top record. Use pre5 to identify subtraction of a contact-face area and pre6 to identify multiplication of outer dimensions despite empty space. Grade 4 learners join this lesson as a supported extension after the prerequisite, while it is the Grade 5 additive-volume lesson in this plan.
Focus: Run the existing investigation's 5/10/15/10-minute routine. Colour two parts with non-overlapping interiors, record each part's own dimensions and add their volumes. Contrast a shared face with a genuinely overlapping filled region. Use the challenge to repair overlapping region labels into a disjoint partition. Connect back to the earlier lessons: label the quantity and unit first, then ensure that the record describes the complete object exactly once.
Collect: Collect a coloured partition, both part-volume calculations and the combined volume in cubic units. Ask the learner to point to the contact face and explain why it has area but contributes no duplicate filled volume. Use a containing-box check to see whether an empty region has been included. Record calculation success and coverage explanations separately.
If secure: Administer the post-assessment and the integrated transfer. Ask the learner to compare two valid disjoint partitions or use a containing box with its empty prism identified. Describe readiness only for the skills shown by the current work.
If more support is needed: If the learner cannot calculate a single prism, return to the prerequisite before repeating joined-solid work. If the problem is double coverage or empty space, colour occupied regions and create one record row per disjoint part. Use the solid-accounting routing recheck and require the shared-face explanation alongside the number.
If the smaller-unit remainder disappears or changes size, use a labelled larger-unit box plus separate remainder marks. If conversion is correct but the comparison is wrong, place both common-unit records side by side before subtracting. Ask for the unit explanation even when the numerical response is correct.
Revisit the model and teaching sequence
Fresh check: A parcel has mass 3 kg 6 g. Using 1 kg = 1000 g, enter the mass in grams and explain each contribution. Reverse your conversion to recover the original record.
3006 · Three kilograms contribute 3000 g and the remainder contributes 6 g. Splitting 3006 g into those parts reconstructs 3 kg 6 g.
For an incorrect missing side, tile equal rows and connect the area equation to its inverse division. For a correct side with an incorrect perimeter, label both pairs of opposite sides and trace the complete boundary. For an incorrect decision, compare that perimeter with the stated allowance and name any surplus or shortage.
Revisit the model and teaching sequence
Fresh check: A rectangle requires area 18 square cm and width 3 cm. Exactly 18 cm of edging is available for its complete outside boundary. Enter the perimeter in cm, show the missing side and explain whether the edging is enough.
18 · The missing side is 6 cm because 18 ÷ 3 = 6. The boundary is 6 + 3 + 6 + 3 = 18 cm, so the edging fits exactly with none left.
First distinguish difficulty with one prism from difficulty partitioning a joined solid. Use volume-as-equal-layers for the single-prism prerequisite. For contact-face subtraction, compare square and cubic units. For an outer-dimensions product, colour the occupied regions and identify the empty part of the containing box. Resume the joined-solid lesson with one record row per disjoint interior.
Revisit the model and teaching sequence
Fresh check: A base prism is 3 cm × 2 cm × 1 cm. A 1 cm × 2 cm × 2 cm top prism sits above the leftmost 1 cm of the base, sharing a 1 cm × 2 cm face with no overlapping interiors. Enter the total volume in cubic cm and explain why the shared face is not subtracted.
10 · The base occupies 6 cubic cm and the top occupies 4, so together they occupy 10. The shared face has area 2 square cm and no thickness; each occupied interior is already counted once.
The skills match the first set; the quantities change. Compare the explanation for each skill as well as the number.
2005 · The two kilograms contribute 2000 g and the leftover mass contributes 5 g, giving 2005 g.
Reasoning evidence: Shows 2 × 1000 g and 5 g separately, preserves the small remainder and reconstructs 2 kg 5 g from 2005 g.
17 · C is 306 cm and D is 289 cm; subtracting matching units gives 17 cm.
Reasoning evidence: Writes 306 cm and 289 cm before subtraction and explains that the original numerals describe different-sized units.
8 · The length is 56 ÷ 7 = 8 cm, and 7 × 8 reconstructs the required 56 square cm.
Reasoning evidence: Represents the unknown as a factor, uses division to recover it and distinguishes the length unit from the area unit.
3 · The required length is 9 cm. The complete perimeter is 9 + 6 + 9 + 6 = 30 cm, exceeding the 27 cm allowance by 3 cm.
Reasoning evidence: Verifies the 54-square-cm area, counts all four edges and states that the area and width can be correct while the edging constraint is unmet.
30 · The separate volumes are 12 and 18 cubic cm, giving 30. Their contact face has area 6 square cm and no thickness, so no duplicated filled volume is subtracted.
Reasoning evidence: Adds 12 and 18 cubic cm, distinguishes the 6-square-cm boundary from a volume and explains the non-overlapping-interior condition.
20 · The base contributes 12 cubic cm and the top contributes 8, giving 20. The empty region above the rightmost 4 cm of the base is 4 cm × 2 cm × 2 cm, with volume 16 cubic cm; the containing box's 36 cubic cm includes it.
Reasoning evidence: Labels the two occupied parts and their own heights, excludes the empty upper-right prism and explains why a containing box includes extra space.
Ready to continue: Review the post-assessment and relevant rechecks by skill. A learner is ready to use that skill in the transfer when the current work includes both a correct calculation and its requested explanation: equivalent common-unit records, an area check plus all-edge boundary check, or a disjoint volume partition with cubic units. Record the evidence actually observed; this is a decision about the next task rather than a claim of general mastery.
More support: Route each unmet explanation or calculation to its matching lesson and recheck. A numerical error with a sound representation calls for checking the calculation; a correct number without a quantity, unit or coverage explanation calls for a follow-up representation. Keep solid-accounting work marked not yet introduced for learners awaiting the volume prerequisite. Retain item-level records and use the two parallel forms to compare the calculations and explanations observed at each point.
Extend: Have learners produce a second valid record for the transfer: reverse the metric conversion, verify the rectangle's area and boundary, then repartition the solid vertically. Compare the two volume sums and explain why equal totals are supported by coverage of the same occupied region. Change one constraint and state which conclusion must be recalculated.
These original checks support teaching decisions. They are not a standardised assessment or a measure of classroom effectiveness.
Create one complete record for a stepped display model. Its rectangular base has footprint area 900 square cm, width 15 cm and height 2 cm. Only the base's rectangular footprint receives edging; 1 m 55 cm is available, with 1 m = 100 cm. A top prism is 20 cm long, 15 cm wide and 1 cm high. It sits above the leftmost 20 cm of the base, sharing a 20 cm × 15 cm face, with no overlapping interiors. Find the missing base length, the complete base boundary, whether the edging is sufficient and by how much, and the total volume. Explain the units and how the parts cover the solid once.
The base length is 900 ÷ 15 = 60 cm. Its full boundary is 60 + 15 + 60 + 15 = 150 cm. The available edging is 155 cm, so it is sufficient with 5 cm left. The base volume is 60 × 15 × 2 = 1800 cubic cm and the top volume is 20 × 15 × 1 = 300 cubic cm. Their non-overlapping interiors give a total of 2100 cubic cm. The 300-square-cm shared face is a boundary, not a volume to subtract. · The decision connects the three lesson records: convert the allowance to the boundary's unit, use area to recover a side and check all four edges, then add occupied prism volumes in cubic units. A second valid partition is a 20 cm × 15 cm × 3 cm left prism and a 40 cm × 15 cm × 2 cm right prism, giving 900 + 1200 = 2100 cubic cm.
Use an anonymous group code. For each question, record numerical correctness and the requested explanation in separate columns. Leave a short next step tied to the skill.
Download the blank group record (CSV)The file contains blank assessment rows. Keep any completed classroom record in your own storage.
Student pages contain both assessment sets. Teacher pages add answers, evidence criteria, lesson routing and fresh checks.
This plan connects the linked lessons. Each lesson records its curriculum scope and original models; the sequence adds parallel checks and teaching decisions.
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