E. Spatial Sense · Spatial Sense: Angles, Triangles, Transformations and Area

Spatial Sense: Angles, Triangles, Transformations and Area: Unit Review

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

Learning goals

I can compare, measure, draw and estimate angles.
I can classify and construct triangles, and identify congruent shapes.
I can draw views of objects, use coordinate grids with scales, and translate, reflect and rotate shapes.
I can choose and convert metric units, find areas of parallelograms and triangles, and compare area and perimeter.

Words to know

degree (°)
The unit for measuring angles. A right angle is 90° and a straight angle is 180°.

protractor
A tool for measuring and drawing angles.

congruent
Same size and same shape.

rotation
A turn around a fixed point.

convert
To change a measurement to a different unit without changing its size.

height
The distance from a base to the opposite side or vertex, measured at a right angle to the base.

Let's review!

In this unit you became an angle measurer, a triangle builder, a transformation expert and an area problem-solver. You compared and measured angles with wedges and protractors, sorted and constructed triangles, checked congruent shapes, drew top, front and side views, used coordinate grids with different scales, translated, reflected and rotated shapes, chose and converted metric units, found the area of parallelograms and triangles, and saw that the same area can have different perimeters.

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

The three transformations. A translation keeps the shape facing the same way, a reflection makes a mirror image, and a rotation turns it around a point. The image is always congruent to the original.

Area formulas from this unit, all with base 6 and height 3. The height (dashed) always makes a right angle with the base. A triangle is half of the matching parallelogram.

Comparing Angles: Matching and Angle Units

Angle A measures 3 wedges and angle B measures 5 wedges (same wedge size). Which is bigger?

Using wedges that are 1/8 of a circle, how many wedges make a straight angle?

Two angles open the same amount, but one has much longer arms. Which angle is bigger?

Protractors: Measuring Angles in Degrees

How many degrees is a right angle?

An angle's arm crosses where the scales say 40 and 140. The angle is wider than a square corner. What is it?

Is a 91° angle acute, right or obtuse?

Drawing Angles and Estimating with Benchmarks

An angle is a little smaller than a right angle. Give a good estimate.

What is the angle between the hands of a clock at 4:00?

When you draw an angle, where do you put the protractor's centre mark, and where does the baseline go?

Triangles: Sorting by Sides and Angles

A triangle has angles 60°, 60° and 60°. Give both names.

Two angles of a triangle are 35° and 45°. Find the third angle. Name the triangle by its angles.

A triangle has sides 6 cm, 6 cm and 4 cm. Name it by its sides.

Constructing Triangles from Sides and Angles

Can sides of 2 cm, 5 cm and 9 cm make a triangle?

You draw a 7 cm side with angles of 50° and 40° at its ends. What is the third angle? What kind of triangle is it?

Two sides of a triangle are 5 cm and 8 cm, with a 60° angle between them. Describe how to construct it.

Congruent Triangles, Rectangles and Parallelograms

Is a 5 cm × 3 cm rectangle congruent to a 3 cm × 5 cm rectangle?

Two parallelograms both have sides of 6 cm and 4 cm. One has angles of 60° and 120°, and the other is a rectangle. Are they congruent?

Triangle X has sides 4, 5, 6 cm. Triangle Y has sides 6, 4, 5 cm. Are they congruent?

Top, Front and Side Views

What is the top view of a cone standing on its base?

Four cubes are stacked in a tower. What is the front view?

Three cubes sit flat on a table: 2 side by side in front, and 1 behind the left one. Describe the top view and the front view.

Coordinate Grids with Different Scales

On a grid that counts by 10s, a point is 4 spaces across and 2 spaces up. What are its coordinates?

Describe the translation from (15, 30) to (45, 10).

On a grid that counts by 10s, a point is halfway between the 20 line and the 30 line across. What is its x-number?

Translations and Reflections on a Grid

Translate (5, 2) 4 units left and 5 units up.

Reflect (1, 4) in the mirror line x = 3.

Reflect (2, 7) in the mirror line y = 5.

Rotations: Quarter Turns and Half Turns

Rotate (6, 2) 90° clockwise around (4, 2).

Rotate (5, 8) 180° around (5, 5).

Rotate (5, 7) 90° counterclockwise around (5, 5).

Choosing Metric Units: Estimating and Measuring

Which unit would you use for the mass of a dog: g or kg?

About how much area does your fingernail cover?

A shape on a 1 cm grid covers 7 full squares and 6 half squares. What is its area?

Converting Metric Units: Bigger Units to Smaller Units

8 km = ? m

4.5 L = ? mL

A 2 m ribbon is cut into 40 cm pieces. How many pieces?

Area of a Parallelogram

A parallelogram has a base of 9 cm and a height of 7 cm. What is its area?

A parallelogram has a base of 12 m, a height of 4 m and a slanted side of 5 m. What is its area?

A parallelogram has an area of 56 cm² and a base of 8 cm. What is its height?

Area of a Triangle

A triangle has a base of 10 cm and a height of 7 cm. What is its area?

A right triangle has sides of 9 m and 4 m next to the right angle. What is its area?

A triangle has an area of 30 cm² and a base of 6 cm. What is its height?

Same Area, Different Perimeters

List the whole-number rectangles with an area of 18 and their perimeters.

A garden must have an area of 49 m². Which whole-number rectangle uses the least fence? How much fence?

A 2 × 8 rectangle and a 4 × 4 square both have an area of 16. Compare their perimeters.

Just for fun

Riddle: What do you call a parrot that has flown away?

A polygon (Polly gone)!

How to use this review

Do one section at a time. Cover the answer, try the question on paper (draw a sketch for geometry questions!), 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.

Check your understanding

Quiz

An angle's arm crosses where the scales say 70 and 110. The angle is narrower than a square corner. What is it?

Two angles of a triangle are 90° and 30°. What is the third angle?

A triangle has a base of 8 cm and a height of 9 cm. What is its area?

Which sides can make a triangle?

Which pair of shapes is congruent?

What is the top view of a soup can standing up?

Describe the translation from (10, 40) to (30, 15).

Rotate (7, 3) 90° clockwise around (4, 3).

3.2 km = ? m

10.

Which rectangle with an area of 16 has the smallest perimeter?

For parents and teachers

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

Mixed up which angle is bigger, or counted wedges unevenly → Comparing Angles: Matching and Angle Units.
Read the wrong protractor scale → Protractors: Measuring Angles in Degrees.
Estimates far from measures, or drawing errors → Drawing Angles and Estimating with Benchmarks.
Wrong triangle names or missing angles → Triangles: Sorting by Sides and Angles.
Unsure whether a triangle is possible, or how to construct one → Constructing Triangles from Sides and Angles.
Thought same-area or same-angle shapes were congruent → Congruent Triangles, Rectangles and Parallelograms.
Drew views in 3D or missed hidden cubes → Top, Front and Side Views.
Counted squares instead of reading the scale, or mixed up the order in (x, y) → Coordinate Grids with Different Scales.
Copied a shape across a mirror line without flipping it → Translations and Reflections on a Grid.
Turned the wrong way or lost the centre → Rotations: Quarter Turns and Half Turns.
Chose an unsuitable unit or miscounted half squares → Choosing Metric Units: Estimating and Measuring.
Divided instead of multiplied when converting → Converting Metric Units: Bigger Units to Smaller Units.
Used the slanted side instead of the height → Area of a Parallelogram.
Forgot to divide by 2 → Area of a Triangle.
Mixed up area and perimeter → Same Area, Different Perimeters.

Social-emotional learning (A1) was woven through the unit: celebrate persistence, careful checking and learning from mistakes.