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Measures and solids, grade 6

Sixth-grade measures, solids, circles and volumes.Subjects

The topics, in order:

  • units of length, weight and money;

  • units of area and volume;

  • solids: the prism, the pyramid, the cylinder and the cone, and their nets;

  • circle and disc: the circumference and the area;

  • volumes: the box, the cylinder and the cone, the prism, the pyramid and the sphere.

  • Learning lessons explain a topic with examples, and have a few questions to try.

  • Practice lessons are all questions.

  • Go in order.

How the page works: Using a page.

  1. Units of length, weight and moneyLearningmm, cm, m and km; g, kg and tons; agorot and shekels – and converting between them, in decimals too.
  2. Units of area and volumeLearningA metre is 100 cm, but a square metre is 10,000 cm²; cm³, litres and m³.
  3. Practice: measuresPracticeConverting units of length, weight, money, area and volume, and word problems.
  4. The prism and the pyramidLearningSolids; faces, edges and vertices; the right prism and the pyramid, their bases and lateral surface; counting faces, edges and vertices.
  5. Nets of prisms and pyramidsLearningA solid's net; nets of a prism and of a pyramid; sides that meet when folded; counting edges in a net.
  6. The cylinder, the cone and the sphereLearningSolids with a curved surface: the cylinder and the cone – bases, lateral surface and net; the sphere; cross-sections of solids.
  7. The regular polyhedraLearningA regular polygon; a regular polyhedron; the five regular polyhedra, why there are only five, and their nets.
  8. Circle and discLearningCentre, radius, diameter and chord; a circle and a disc; drawing a circle with a compass.
  9. The circumference and πLearningMeasuring shows the circumference is a bit more than 3 times the diameter; the number π; the circumference from the diameter and from the radius.
  10. The area of a discLearningA disc is a bit more than 3 squares whose side is the radius; the area of a disc; twice the radius – 4 times the area; half discs, rings and combined shapes.
  11. Practice: circle and discPracticeThe circumference and the area of a disc, combined shapes and word problems.
  12. The volume of a boxLearningEstimating volume; the volume of a box – length times width times height, or the base's area times the height; solids with the same volume; changing the edges; volume and surface area.
  13. The volume of a cylinder and a coneLearningThe volume of a cylinder – the base's area times the height; the volume of a cone – a third of the cylinder with the same base and height.
  14. The volume of a prism, a pyramid and a sphereLearningThe volume of a prism – the base's area times the height; a pyramid – a third of the prism; a sphere – two thirds of the cylinder around it; designing solids with a given volume.
  15. Practice: volumesPracticeThe volume of a box, a prism, a cylinder, a cone and a pyramid; units of volume; word problems.
  16. Review: measures and solidsPracticeQuestions on the whole course: units of measure, solids, circle and disc, volumes.
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