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🇨🇦 New Brunswick Department of Education and Early Childhood Development · Grade 10

Mathematics

Units follow the order of the New Brunswick Department of Education and Early Childhood Development programme. Pick a topic and start.

In the labEnglish
Units
1
Topics
6
Ready
0
No finished topic in this subject yet. The first topic's trial is open.

Course plan

Units and topics

Go in order, or start from any topic.

ReadyIn the labPlanned
Unit 1

Geometric Shapes

6 topics · 3 topics in the lab · Weeks 1–6

In the lab
1.1

Trigonometric Ratios and Identities

Two triangles of different sizes give the same number. Follow it from the four ratios to the exact values, the identities and the unit circle.

  • I can name the opposite side, the adjacent side and the hypotenuse for any acute angle.
  • I can write the sine, cosine, tangent and cotangent of an angle in a right triangle.
  • I can give the exact ratios of 30, 45 and 60 degrees without a calculator.
  • I can explain why the ratios stay the same when the triangle changes size.
  • I can prove the identities that come from the Pythagorean theorem.
  • I can read the ratios of an angle larger than 90 degrees from the unit circle.
ToolsRight triangleWritten inEnglish
In the labOpen the trial →
1.2

Pythagoras and the Primary Ratios

A right triangle has six measurements. Find how few you need before the other five are forced, then solve the whole triangle and check it.

  • I can find a missing side of a right triangle with the Pythagorean theorem.
  • I can test three lengths to decide whether a triangle has a right angle.
  • I can choose the ratio a question needs and say why I chose it.
  • I can find a missing side whether the unknown is above or below the line.
  • I can find an acute angle from a ratio of two sides.
  • I can solve a right triangle completely and check my answer.
ToolsRight triangleWritten inEnglish
In the labOpen the trial →
1.3

Indirect Measurement

You cannot climb the tree to measure it. Build a triangle you can measure, add your own eye height, and find out how wrong the answer might be.

  • I can say which lengths I can measure directly and which I must calculate.
  • I can turn a written situation into a labelled right triangle.
  • I can add the height of my own eye at the right moment.
  • I can solve a problem that needs two triangles sharing one side.
  • I can find the distance between two viewing points, not only the height.
  • I can explain how an error of one degree changes the answer.
ToolsRight triangleWritten inEnglish
In the labOpen the trial →
1.4

Auxiliary Elements of a Triangle

Four ways to draw a line from a corner, and each set of three meets at one point. Find the four centres and learn what each one is for.

  • I can name the four auxiliary elements of a triangle.
  • I can use the angle bisector as the set of points at equal distance from two arms.
  • I can use the interior and the exterior angle bisector theorems.
  • I can find the angle between two bisectors.
  • I can use the centroid and the two to one ratio on a median.
  • I can say where the circumcentre and the orthocentre lie in any triangle.
Written inEnglish
Planned
1.5

The Area of a Triangle

One triangle has three different bases, and every one of them gives the same area. Use that to split areas, compare them and scale them.

  • I can find an area from any of the three base and height pairs.
  • I can compare two areas that have the same height.
  • I can split an area with a line drawn from a corner.
  • I can show that sliding the top corner along a parallel line does not change the area.
  • I can use the medians to cut a triangle into equal parts.
  • I can scale an area by the square of the similarity ratio.
Written inEnglish
Planned
1.6

The Sine and Cosine Theorems

Two sides and the angle between them, and no height anywhere. One dropped altitude gives the area, the law of sines and the cosine theorem.

  • I can find an area from two sides and the angle between them.
  • I can compare two areas in the case where the sine cancels.
  • I can build the law of sines from the three area expressions.
  • I can prove the cosine theorem when the angle is acute and when it is obtuse.
  • I can use the sign of the cosine to say what kind of angle it is.
  • I can find the length of a median.
Written inEnglish
Planned

New units appear here as they are added. The order follows the New Brunswick Department of Education and Early Childhood Development programme.

In every topic

How a topic works

Four parts. You see it with a tool, then try it, then practise.

Learn

Starts with a scene. You move in short steps.

Explore

You use the tool yourself. Break it, fix it.

Practice

Easy, medium, hard. Questions with the same tool.

Summary

Rules, words and formulas on one page.

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