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# reSolve: Quarter Cartons

This lesson challenges students to use algebra and proportional reasoning to investigate how changing the size of a paper square or rectangle impacts the dimensions of a box folded from that paper. Students apply knowledge about nets of 3D objects and explore algebraic relationships through a set of hands-on activities making origami boxes. The context of paper folding encourages students to physically manipulate objects to investigate relationships and demonstrate their findings. The sequence could serve as an introduction to geometric proofs. Each lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, discussion points and student resources. This sequence is part of the reSolve: Mathematics by Inquiry program.

Year level(s) Year 8
Audience Teacher
Purpose Teaching resource
Teaching strategies and pedagogical approaches Mathematics investigation
Keywords factors, area, volume, prisms, nets, origami, dilation, scale, simplification

## Curriculum alignment

Curriculum connections Numeracy
Strand and focus Algebra, Geometry, Build understanding, Apply understanding
Topics Proportion, rates and ratios, Patterns and algebra, Algebraic expressions, Area, volume and surface area
AC: Mathematics content descriptions
ACMMG198 Develop formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume
ACMMG202 Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
ACMNA191 Factorise algebraic expressions by identifying numerical factors
ACMNA192 Simplify algebraic expressions involving the four operations
National numeracy learning progression Number patterns and algebraic thinking
Understanding geometric properties
Understanding units of measurement - UuM7