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- Mathematics: Apprenticeship and Workplace Mathematics: Grade 10

# Yukon Territory - Mathematics: Apprenticeship and Workplace Mathematics: Grade 10

## WNCP Framework | Adopted: 2008

### 2: : Develop spatial sense.

2..B2: : Demonstrate an understanding of the Pythagorean theorem by:

2..B2.a: : identifying situations that involve right triangles

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Distance Formula

Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview

Pythagorean Theorem

Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview

Pythagorean Theorem with a Geoboard

Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

2..B2.c: : applying the formula

Circles

Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Distance Formula

Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview

Pythagorean Theorem

Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview

Pythagorean Theorem with a Geoboard

Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Surface and Lateral Areas of Pyramids and Cones

Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

2..B2.d: : solving problems.

Circles

Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Distance Formula

Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview

Pythagorean Theorem

Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview

Pythagorean Theorem with a Geoboard

Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Surface and Lateral Areas of Pyramids and Cones

Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

2..B4: : Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by:

2..B4.a: : applying similarity to right triangles

Sine, Cosine, and Tangent Ratios

Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview

2..B4.c: : applying the primary trigonometric ratios

Sine, Cosine, and Tangent Ratios

Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview

2..B4.d: : solving problems.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview

Tangent Function

2..B5: : Solve problems that involve parallel, perpendicular and transversal lines, and pairs of angles formed between them.

Constructing Congruent Segments and Angles

Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview

Triangle Angle Sum

Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview

2..B6: : Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex, by:

2..B6.b: : replicating and constructing

Segment and Angle Bisectors

Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview

2..B6.c: : bisecting

Concurrent Lines, Medians, and Altitudes

Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview

Segment and Angle Bisectors

Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview

### 4: : Develop algebraic reasoning.

4..D1: : Solve problems that require the manipulation and application of formulas related to:

4..D1.a: : perimeter

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview

4..D1.b: : area

Area of Parallelograms

Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview

4..D1.c: : the Pythagorean theorem

Circles

Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Tangent Function

Correlation last revised: 9/16/2020

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