E. Spatial Sense · Spatial Sense: Shapes, Grids, Angles, Area and Surface Area

Spatial Sense: Shapes, Grids, Angles, Area and Surface Area: Unit Review

A1 E1.1 E1.2 E1.3 E1.4 E2.1 E2.2 E2.3 E2.4 E2.5 E2.6About 40 minutes

Learning goals

I can describe quadrilaterals by their sides, angles, diagonals and symmetry, and build objects from their views.
I can plot points in all four quadrants and perform and combine transformations.
I can convert metric units, and measure, draw and reason about angles up to 360°.
I can find the areas of trapezoids, rhombuses, kites and composite polygons, and the surface areas of prisms and pyramids.

Words to know

diagonal
A line segment joining two vertices that are not next to each other.

rotational symmetry
A shape fits onto its own outline after a turn of less than 360°.

quadrant
One of the four parts of the Cartesian plane, numbered I to IV counterclockwise from the top right.

reflex angle
An angle greater than 180° and less than 360°.

supplementary / complementary
Two angles that add to 180° / two angles that add to 90°.

surface area
The total area of all the faces of a 3D object.

Let's review!

In this unit you listed the properties of quadrilaterals, including their diagonals and symmetry, and built 3D objects from their views. You plotted points in all four quadrants and combined transformations. You converted metric units both ways, measured and drew angles up to 360°, and used complementary, supplementary, opposite, interior and exterior angles to find unknown angles. Finally, you found the areas of trapezoids, rhombuses, kites and composite polygons, made nets, and calculated surface area.

This review has a few questions from every lesson. Try each one, then press Show answer to check.

Quadrilaterals: Sides, Angles and Diagonals

Which quadrilaterals have diagonals that bisect each other?

A quadrilateral's diagonals are perpendicular, and only one of them is cut in half. Name it.

The diagonals of a rectangle cross at M. One diagonal is 18 cm. How far is M from each corner?

Line Symmetry and Rotational Symmetry

How many lines of symmetry does a rhombus (not a square) have, and where are they?

What is the order of rotational symmetry of a parallelogram?

A shape has rotational symmetry of order 8. What is the smallest turn that makes it fit?

Building 3D Objects from Top, Front and Side Views

A top view with numbers has a front row of 2, 1 and a back row of 1, 3. How many cubes are there?

For the same structure, describe the front view and the right side view.

In a right side view, where is the front of the structure?

The Cartesian Plane: All Four Quadrants

In which quadrant is (−7, −2)?

Describe the translation from (−4, 1) to (2, −3).

Start at (3, −5) and move 7 units left and 6 units up. Where do you land?

Quick review: the signs of the coordinates tell you the quadrant without plotting the point.

Reflections and Rotations in Four Quadrants

Reflect (−2, 6) in the x-axis.

Rotate (5, 1) 90° counterclockwise around the origin.

Rotate (−3, 4) 180° around the origin.

Combining Transformations and Predicting Results

Start at (1, 3). Reflect in the y-axis, then translate 4 units down.

Which single transformation does the same as reflecting in the x-axis and then in the y-axis?

A point is translated 5 units right and then reflected in the x-axis. It ends at (2, 4). Where did it start?

Metric Units: Measuring and Converting Both Ways

4500 m = ? km

350 g = ? kg

Which is more: 1.7 L or 1650 mL?

Measuring and Drawing Angles up to 360°

The small angle between two arms is 95°. What is the reflex angle?

The clockwise angle from arm A to arm B is 210°. What is the counterclockwise angle from A to B?

To draw a 290° angle with a 180° protractor, which angle do you draw first?

Complementary, Supplementary and Opposite Angles

What is the complement of 64°?

What is the supplement of 64°?

Two straight lines cross. One angle is 38°. Find the other three.

Interior and Exterior Angles of Polygons

A triangle has angles of 57° and 78°. Find the third angle.

A quadrilateral has angles of 70°, 110° and 95°. Find the fourth.

An interior angle of a triangle is 48°. What is the exterior angle at that vertex?

Quick review of angle facts, drawn to true size: complementary angles add to 90°, supplementary angles add to 180°, opposite angles are equal, and a triangle's angles add to 180°.

Area of Rhombuses, Kites and Trapezoids

A kite has diagonals of 14 cm and 9 cm. Find its area.

A trapezoid has parallel sides of 7 m and 11 m and a height of 6 m. Find its area.

A rhombus has diagonals of 10 cm and 10 cm. What is its area? What special rhombus is it?

Area of Composite Polygons

An L-shape is 9 m by 7 m overall with a 4 m by 3 m corner missing. Find its area.

A shape is a 6 cm by 5 cm rectangle with a triangle on top (base 6 cm, height 4 cm). Find its area.

A polygon has vertices at (0, 0), (4, 0), (4, 4), (2, 6), (0, 4). Find its area.

Nets of Prisms and Pyramids

How many faces does a hexagonal pyramid have?

A net has 2 pentagons and 5 rectangles. What does it make?

Can a cube net contain a 2-by-2 block of squares?

Surface Area of Prisms and Pyramids

Find the surface area of a box 7 cm by 4 cm by 2 cm.

Find the surface area of a cube with 6 cm edges.

A square-based pyramid has a 5 cm by 5 cm base and triangle faces with a height of 8 cm. Find its surface area.

Just for fun

Why did the protractor bring snacks to the unit review?

It wanted to make sure every angle was covered!

How to use this review

Do one section at a time. Cover the answer, try the question on paper (sketch a grid or a shape whenever it helps!), then check. Put a star beside any question you got wrong. When you finish, go back to the lesson with the most stars and redo its "More practice" questions. Mistakes show you exactly what to practise next, and fixing them is how you get stronger.

Check your understanding

Quiz

Which quadrilateral has diagonals that are equal, perpendicular and bisect each other?

What is the order of rotational symmetry of a rectangle that is not a square?

A top view with numbers has just one row: 3, 1, 2. How many cubes are in the structure?

Which point is in quadrant II?

Rotate (2, 6) 90° clockwise around the origin.

820 cm = ? m

The small angle between two arms is 130°. What is the reflex angle?

Three angles of a quadrilateral are 80°, 100° and 90°. What is the fourth?

A trapezoid has parallel sides of 4 cm and 10 cm and a height of 5 cm. What is its area?

10.

What is the surface area of a box that is 3 cm by 2 cm by 2 cm?

For parents and teachers

How to use the results: Look at which questions caused trouble and revisit that lesson.

Mixed up which quadrilaterals have which diagonal properties → Quadrilaterals: Sides, Angles and Diagonals.
Thought a rectangle's diagonals are lines of symmetry, or forgot the full turn when finding the order → Line Symmetry and Rotational Symmetry.
Put the stacks in the wrong place, or mixed up left and right in the side view → Building 3D Objects from Top, Front and Side Views.
Went the wrong way for a negative coordinate, or miscounted across zero → The Cartesian Plane: All Four Quadrants.
Changed the wrong sign in a reflection, or turned the wrong way → Reflections and Rotations in Four Quadrants.
Applied both steps to the original shape, or undid steps in the wrong order → Combining Transformations and Predicting Results.
Multiplied instead of dividing when going to a larger unit → Metric Units: Measuring and Converting Both Ways.
Gave the small angle instead of the reflex angle → Measuring and Drawing Angles up to 360°.
Mixed up 90° and 180° totals → Complementary, Supplementary and Opposite Angles.
Used 180° for a quadrilateral, or confused interior and exterior angles → Interior and Exterior Angles of Polygons.
Used a slanted side as the height, or forgot to divide by 2 → Area of Rhombuses, Kites and Trapezoids.
Missed a piece or a missing length in a composite shape → Area of Composite Polygons.
Miscounted faces, or chose an arrangement that can't fold → Nets of Prisms and Pyramids.
Missed or double-counted faces when finding surface area → Surface Area of Prisms and Pyramids.

Social-emotional learning (A1) was woven through the unit: checking work with a second strategy, organizing multi-step problems, explaining reasoning and learning from mistakes. Celebrate the effort as well as the answers.