Scale, Angles & Solids: 7th grade math in Kamchatka

Scale drawings, triangles, cross sections, circles, angle relationships, and area, surface area and volume.

Explore a wild peninsula of smoking volcanoes, boiling geysers and giant brown bears fishing for salmon. Characters here greet you with “Privet!” (hi in Russian), and eggs hatch into hybrids of animals like Kamchatka brown bear, Steller's sea eagle, sea otter and sable.

What your child practices

Follows Geometry (7.G).

• Scale drawings

  Turn lengths and areas on a map or plan into real ones, and real lengths into map lengths.

  7.G.A.1

• Which triangles can exist

  Two sides must add to more than the third, angles add to 180°, and some facts fix just one triangle.

  7.G.A.2

• Cross sections of solids

  Name the flat shape you get when you slice a prism, pyramid, cylinder or cone.

  7.G.A.3

• Area and circumference of circles

  Use π × d for the distance around a circle and π × r × r for the space inside, and work back from the circumference.

  7.G.B.4

• Supplementary, complementary, vertical and adjacent angles

  Use angle facts to find unknown angles, and write and solve equations for them.

  7.G.B.5

• Area of composite figures

  Find areas of shapes made of rectangles, triangles and trapezoids, adding parts or taking away cut-outs.

  7.G.B.6

• Surface area and volume of prisms

  Find the volume of rectangular and triangular prisms, the area of all their faces, and missing heights.

  7.G.B.6

Try a problem from Kamchatka

Every problem is a short story set in the world. These are real problems from the game. Kids get endless new ones with different numbers.

Common mistakes, and how to help

Every wrong answer in Mixmonde is planned: it points to a named mistake, and the tip after a miss explains it with that problem’s numbers. These are the mistakes this world watches for, grouped the way the grown-ups’ dashboard shows them.

• Ratio and scaling

  Adding when the situation multiplies: doubling a recipe by adding 2 to each amount, or taking a percent of the wrong total.

  Mistakes we catch: forgot the scale, scaled only one side, divided by the scale, scaled the area only once and multiplied going onto the map.

  Try at home: Compare prices at the shop per item or per 100 g. For percents, always ask “percent of what?” and start from 10% and 1%.

• Shapes and angles

  Shape properties: counting sides, corners or faces, symmetry, naming angles, measuring with a protractor or radius vs diameter.

  Mistakes we catch: thought a flat triangle works, misjudged the side rule, used the wrong angle total, mixed up what fixes a triangle, mixed up the slice direction, mixed up prisms and pyramids, mixed up cones and cylinders, named the wrong base shape, used the diameter as the radius, mixed up area and circumference, forgot to square the radius, mixed up radius and diameter, mixed up 90° and 180° and mixed up vertical and adjacent angles.

  Try at home: Unfold a cereal box to see its net. Measure angles with a protractor together, checking first whether the angle is smaller or bigger than a right angle.

• Choosing the operation

  The arithmetic is fine, but the wrong operation was picked: adding when the story takes away, or multiplying when it shares out.

  Mistakes we catch: multiplied instead of divided.

  Try at home: Have them say the plan in words first (“share 48 into groups of 6, so divide”). Swap in easy numbers to see which operation makes sense, then use the real ones.

• Reading the question

  The math works, but the answer is to a different question: a number already given, a halfway step, or only part of a two-step problem.

  Mistakes we catch: gave the angle, not x and left out a part.

  Try at home: Underline what the question asks for and list the steps (“first find …, then …”). Tick each step off before giving the answer.

• Units and measuring

  The number is fine but the unit is off: a missing conversion (cm and m), the ruler not started at zero, or area mixed up with perimeter.

  Mistakes we catch: forgot the cut-out part, forgot to halve, forgot the height, found the surface area, added the sizes instead of multiplying, missed some faces, found the volume and divided by one edge.

  Try at home: Before converting, ask whether the answer should be a bigger or smaller number. Fill a box with cubes to feel why volume uses cubic units.

More Grade 7 worlds: Proportions & Percent · Rational Numbers · Expressions & Equations · Sampling & Comparing Data · Probability