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.
Anonymous group code: __________ Date: __________
Before the sequence
Work independently. Write a number with its unit, and record the explanation requested. Your teacher will record the answer and the reasoning separately.
pre1. A parcel has mass 1 kg 8 g. Using 1 kg = 1000 g, enter its mass entirely in grams. Show the contribution from the kilogram and the leftover grams.
pre2. Strip A is 2 m 9 cm long and strip B is 190 cm long. Using 1 m = 100 cm, enter how many centimetres longer A is. Record both lengths in centimetres before comparing.
pre3. A rectangle has area 35 square cm and width 5 cm. Enter its missing length in cm, and write a multiplication equation that checks the area.
pre4. A rectangular plan requires area 40 square cm and width 5 cm. Only the rectangle's outside boundary receives edging, and at most 24 cm is available. Enter the extra centimetres of edging needed. Show the missing length, all four side lengths and whether the plan meets the limit.
pre5. A 2 cm × 2 cm × 1 cm prism and a 2 cm × 2 cm × 3 cm prism are stacked along one 2 cm × 2 cm face. Their interiors do not overlap. Enter their combined volume in cubic cm, give each part's volume and explain how the shared face is treated.
pre6. A base prism is 5 cm long, 2 cm wide and 1 cm high. A top prism is 2 cm long, 2 cm wide and 2 cm high; it sits above the leftmost 2 cm of the base, sharing a 2 cm × 2 cm face with no overlapping interiors. Enter the stepped solid's volume in cubic cm. Explain why the outer 5 cm × 2 cm × 3 cm dimensions do not describe a completely filled prism.
After the sequence
Use this set after the lessons. Work without a partner first. Explain your method; a correct number alone does not show every part of your reasoning.
post1. A parcel has mass 2 kg 5 g. Using 1 kg = 1000 g, enter its mass entirely in grams. Show the contribution from the kilograms and the leftover grams.
post2. Strip C is 3 m 6 cm long and strip D is 289 cm long. Using 1 m = 100 cm, enter how many centimetres longer C is. Record both lengths in centimetres before comparing.
post3. A rectangle has area 56 square cm and width 7 cm. Enter its missing length in cm, and write a multiplication equation that checks the area.
post4. A rectangular plan requires area 54 square cm and width 6 cm. Only its outside boundary receives edging, and at most 27 cm is available. Enter the extra centimetres of edging needed. Show the missing length, all four side lengths and whether the plan meets the limit.
post5. A 3 cm × 2 cm × 2 cm prism and a 3 cm × 2 cm × 3 cm prism are stacked along one 3 cm × 2 cm face. Their interiors do not overlap. Enter their combined volume in cubic cm, give each part's volume and explain how the shared face is treated.
post6. A base prism is 6 cm long, 2 cm wide and 1 cm high. A top prism is 2 cm long, 2 cm wide and 2 cm high; it sits above the leftmost 2 cm of the base, sharing a 2 cm × 2 cm face with no overlapping interiors. Enter the stepped solid's volume in cubic cm. Explain why the outer 6 cm × 2 cm × 3 cm dimensions do not describe a completely filled prism.
Transfer the reasoning
transfer. 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.