Teaching pack: Classifying triangles, quadrilaterals and polygons (Year 7)

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Teaching pack · Year 7 Spaceseegongsik /au

Classifying shapes: a week of ready-to-teach maths

Five lessons for Year 7 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet with practice and a stretch section, plus triangle and quadrilateral cards on a dot grid, a mini-check and every answer with its working.

AC9M7SP02

classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

Start here: five minutes to Monday

Skim the week at a glance on the next page.
Print the five days. Each day is two A4 sheets: a plan and a worksheet.
Print the two cut-out sheets at 100%: triangle cards (Day 1) and quadrilateral cards (Days 2 and 3), one set per pair.
Open the free interactive unit on the board. Every plan says which picture to show and which buttons to press.
Teach straight from the plan. Timings, talk prompts, misconceptions and worked answers are all on the one page.

The idea in plain words

A shape’s name is a promise about its properties. A triangle gets one name from its sides (equilateral, isosceles, scalene) and one from its angles (acute, right, obtuse). Quadrilaterals are named by parallel sides, equal sides, right angles and diagonals, and the names nest: every square is a rectangle and a rhombus, and every rectangle and rhombus is a parallelogram, but not the other way round. A polygon is regular only when all its sides and all its angles are equal. Classifying means checking properties, not judging by look.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 60 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point for two shorter sessions, and every worksheet ends with a stretch section for students who finish early.

How we name shapes

On the cards, the dots are 1 unit apart, so equal sides, parallel sides and right angles can be checked by counting along the grid. Give the most specific name first, then every other name that fits. In this pack a trapezium and a kite are shapes that are not parallelograms; some books define them more widely. Rulers and protractors are needed every day.

On the board

This pack is the printable half of a free interactive unit. The on-screen half has five interactive pictures (classifying triangles, the quadrilateral family, the angle sum of a polygon, regular versus irregular, and diagonals of quadrilaterals) plus a self-check quiz you can run as a class game on Day 5.

seegongsik.com/au/y7/space/AC9M7SP02

Aligned to the Australian Curriculum V9 (AC9M7SP02). This pack is original material from seegongsik, independently produced and not endorsed by ACARA. Curriculum content descriptors are (c) ACARA, licensed under CC BY 4.0. Free to print and use in class.

The week at a glance5 lessons

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

Day	Lesson	Students learn and do	On screen and on the desk
1	Triangles	Name triangles by their sides and by their angles, sort the triangle cards into a two-way table, and explain the empty boxes	Classifying triangles; triangle cards
2	Quadrilaterals	Check sides, angles and diagonals of the quadrilateral cards, and record which properties each kind always has	Diagonals tell quadrilaterals apart; quadrilateral cards
3	The quadrilateral family	Place the cards in a diagram of parallelograms, rectangles and rhombuses, and decide whether statements are always, sometimes or never true	The quadrilateral family
4	Polygons	Name polygons by their sides, decide whether each is regular and convex, and work out each angle of a regular polygon	Regular versus irregular; Angle sum of a polygon
5	Reasoning about shapes	Solve riddles, pick odd ones out with reasons, and decide which shapes can and cannot exist	Self-check quiz as a class game

How the week builds

Day 1 names triangles two ways; Days 2 and 3 classify quadrilaterals by their properties and fit the names into one family; Day 4 widens the view to polygons; and Day 5 reasons about which shapes can and cannot exist. It builds on angles and shapes in Year 6 and on angle sums (AC9M7M05), and it leads into sorting algorithms for shapes (AC9M7SP04) and to congruence and the properties of quadrilaterals in Year 8 (AC9M8SP01, AC9M8SP02).

Materials for the week (one trip)

From the classroom: pencils, rulers, protractors, scissors, glue, this pack printed at 100%.
Cut-out sheet 1, one set per pair: 12 triangle cards (Day 1).
Cut-out sheet 2, one set per pair: 12 quadrilateral cards (Days 2 and 3); keep them in an envelope between lessons.
Grid or dot paper for sketching (Days 4 and 5).

Words for the word wall

equilateral, isosceles, scalene, acute, right, obtuse, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, diagonal, parallel, perpendicular, polygon, regular, irregular, convex, concave, property

A note homeHome practice

Dear families

This week in maths, Year 7 is classifying triangles, quadrilaterals and other polygons by their sides and angles, and reasoning about how the names fit together, such as why every square is a rectangle but not every rectangle is a square.

Try this at home

Hunt for triangles and quadrilaterals around the house or on a walk, and name each as exactly as you can.
Look at a road sign, a tile or a window: is the shape regular? How could you check without a ruler?
Play “What am I?”: describe a shape by its properties, and the other person names it.
Ask: can a triangle have two right angles? Can a rectangle be a rhombus?

Shapes this week

Fill one row a day with a shape you found, where it was, and its most exact name.

Day	The shape	Where	Its name
Monday
Tuesday
Wednesday
Thursday
Friday

Printed from the free seegongsik Classifying shapes teaching pack · seegongsik.com/au/y7/space/AC9M7SP02/pack

Day 1 · Teacher planDay 1 of 5

Triangles

Every triangle gets two names: one from its sides (equilateral, isosceles, scalene) and one from its angles (acute, right, obtuse). Students name the triangle cards both ways, sort them into a two-way table, and explain why some boxes stay empty.

We are learning to

name a triangle by its sides and by its angles,
check sides and angles by counting on a grid or by measuring,
reason about which combinations of names can exist.

Success criteria

I can give any triangle both of its names.
I can explain why no triangle is both equilateral and right-angled.

You need

Triangle cards from cut-out sheet 1 (one set per pair, cut out before the lesson), rulers and protractors.

Lesson flow (about 60 minutes)

10 min	Two names Show the board (see the box). Ask: “The same triangle is in both rows. What two names could it have?”
30 min	Sort the cards Pairs name each card in Part A, then place the cards in the table in Part B.
20 min	The empty boxes Part C as a class; early finishers do Part D. Ask: “Could anyone draw a triangle for an empty box? What stops it?”

Two shorter sessions instead? Split after Part A; start the second with Part B.

On the board

Show “Classifying triangles”, which opens on “By sides”. Ask for each triangle’s name by its angles, then press “By angles” to check.

seegongsik.com/au/y7/space/AC9M7SP02

Watch for these ideas

Judging a right angle by eye on a tilted triangle, such as cards I and L. Check with the grid or a protractor.
Thinking an isosceles triangle must stand on its odd side and point up.
Calling a long, thin triangle obtuse without finding the angle over 90°.

Answers

Part A: A scalene acute, B isosceles right, C scalene obtuse, D isosceles acute, E scalene right, F equilateral acute, G isosceles obtuse, H scalene obtuse, I isosceles right, J scalene acute, K isosceles acute, L scalene right.
Part B: equilateral: acute F, right none, obtuse none; isosceles: acute D K, right B I, obtuse G; scalene: acute A J, right E L, obtuse C H.
Part C: equilateral right and equilateral obtuse stay empty for every triangle, not just these cards: the three equal angles of an equilateral triangle share 180°, so each is 60°.
Part D: drawings vary; check the equal sides by counting the same steps across and up on the grid.

Day 1 · Worksheet

Triangles

NameClassDate

A. Two names for each card

Card	By its sides	By its angles	How I checked
A
B
C
D
E
F
G
H
I
J
K
L

B. The two-way table

Write each card’s letter in the box that matches both of its names.

	acute	right	obtuse
equilateral
isosceles
scalene

C. The empty boxes

Which boxes are empty? Could you draw a triangle to go in each one? Explain.

D. Stretch

On dot paper, draw a right-angled isosceles triangle with no side along a grid line, and an isosceles triangle that is obtuse. Mark the equal sides on both.

Day 2 · Teacher planDay 2 of 5

Quadrilaterals

Quadrilaterals are told apart by equal sides, parallel sides, right angles and diagonals. Students name the cards with a reason, and record which properties each kind always has.

We are learning to

check the sides, angles and diagonals of a quadrilateral,
name a quadrilateral and give the property that proves it,
record which properties each kind of quadrilateral always has.

Success criteria

I can name each card and prove it with a property.
I can say what a rhombus always has and what it does not always have.

You need

Quadrilateral cards from cut-out sheet 2 (one set per pair, cut out before the lesson), rulers and protractors.

Lesson flow (about 60 minutes)

10 min	Diagonals Show the board (see the box). Ask: “Which two of these shapes have diagonals that cross at right angles? What else do they share?”
30 min	Check the cards Pairs name every card in Part A, writing the property that proves each name.
20 min	Always or not always Parts B and C; early finishers do Part D. Ask: “A rectangle can have all sides equal. Why is the answer still “not always”?”

Two shorter sessions instead? Split after Part A; start the second with Part B.

On the board

Show “Diagonals tell quadrilaterals apart”, which opens on the square. Press “rectangle”, then “rhombus”, then “parallelogram”, asking each time whether the diagonals will be equal and square on.

seegongsik.com/au/y7/space/AC9M7SP02

Watch for these ideas

Judging parallel sides by eye. Two sides are parallel when they take the same steps across and up on the grid.
Calling a tilted square a rhombus or a diamond. Check for a right angle.
Thinking a square is not a rectangle. It has every property a rectangle needs.

Answers

Part A: A parallelogram, B square, C kite, D rectangle, E rhombus, F trapezium, G concave quadrilateral, H square, I rhombus, J irregular quadrilateral, K rectangle, L trapezium; a proof is the property that sets the kind apart (Part B).
Part B (Y yes, N not always, in the table’s column order): square Y Y Y Y Y; rectangle N Y Y Y N; rhombus Y Y N N Y; parallelogram N Y N N N; kite N N N N Y; trapezium N N N N N.
Part C: (1) and (2) both: four right angles and equal diagonals.
Part D: for example (0, 0), (1, 2), (4, 0), (1, −2), a kite: its diagonals are both 4 long and square on, but do not cut each other in half.

Day 2 · Worksheet

Quadrilaterals

NameClassDate

A. Name the cards

Card	Most exact name	The property that proves it
A
B
C
D
E
F
G
H
I
J
K
L

B. Always?

Write yes if every shape of that kind has the property, or not always.

	All sides equal	Both pairs of opposite sides parallel	Four right angles	Diagonals equal	Diagonals cross at right angles
square
rectangle
rhombus
parallelogram
kite
trapezium

C. Compare

What does a square always have that a rhombus does not always have? ______________________
What does a rectangle always have that a parallelogram does not always have? ______________________

D. Stretch

On dot paper, draw a quadrilateral whose diagonals are equal and cross at right angles, but which is not a square. What is it?

Day 3 · Teacher planDay 3 of 5

The quadrilateral family

The names nest: a square is a rectangle and a rhombus, and both are parallelograms. Students place the cards in a diagram of the family, and decide whether statements are always, sometimes or never true.

We are learning to

place quadrilaterals in a diagram that shows how their names nest,
decide whether a statement about shapes is always, sometimes or never true,
back the decision with a reason or an example.

Success criteria

I can show where squares, rectangles and rhombuses sit among the parallelograms.
I can back a “sometimes” answer with one example where it is true and one where it is not.

You need

The quadrilateral cards from Day 2 and the worksheet.

Lesson flow (about 60 minutes)

10 min	Boxes inside boxes Show the board (see the box). Ask: “A square lights all four boxes. Why does a parallelogram light only two?”
25 min	Place the cards Pairs lay the cards on the diagram in Part A, write the letters in, then do Part B.
25 min	Always, sometimes, never Part C, pairs first and then as a class; early finishers do Part D. Ask: “What do you need to show that a statement is “sometimes” true?”

Two shorter sessions instead? Split after Part B; start the second with Part C.

On the board

Show “The quadrilateral family”, which opens on the square. Press “rectangle”, then “parallelogram”, then “quadrilateral”; before each press, ask which boxes will light up.

seegongsik.com/au/y7/space/AC9M7SP02

Watch for these ideas

Thinking a square cannot be a rectangle because it has a name of its own.
Putting the squares in the rectangles only. They belong where the rectangles and rhombuses overlap.
Backing “sometimes” with one example. It needs one case where it is true and one where it is not.

Answers

Part A: both rectangles and rhombuses (squares) B, H; rectangles only D, K; rhombuses only E, I; other parallelograms A; outside the parallelograms C, F, G, J, L.
Part B: B quadrilateral, parallelogram, rectangle, rhombus, square; D quadrilateral, parallelogram, rectangle; E quadrilateral, parallelogram, rhombus; F quadrilateral.
Part C: (1) always: four right angles, two pairs of parallel sides; (2) sometimes: when its sides are equal; (3) sometimes: when it is a square; (4) always: opposite sides parallel; (5) never: they would use up all 180°; (6) sometimes: when it is a rectangle; (7) sometimes: when its angles are 45°, 45°, 90°; (8) never: equilateral angles are all 60°.
Part D: statements vary; each “sometimes” needs a case for and a case against.

Day 3 · Worksheet

The quadrilateral family

NameClassDate

A. Place the cards

Write each card’s letter in the part of the diagram where it belongs.

B. Every name that fits

From quadrilateral, parallelogram, rectangle, rhombus and square, write every name that fits the card.

Card B: ________________________________________________

Card D: ________________________________________________

Card E: ________________________________________________

Card F: ________________________________________________

C. Always, sometimes or never?

Statement	Always, sometimes or never	Reason or example
A square is a rectangle.
A rectangle is a square.
A rhombus has four right angles.
A rhombus is a parallelogram.
A triangle has two right angles.
A parallelogram has equal diagonals.
A right-angled triangle is isosceles.
An obtuse triangle is equilateral.

D. Stretch

Write three statements of your own about shapes: one always true, one sometimes true and one never true.

Day 4 · Teacher planDay 4 of 5

Polygons

A polygon is regular only when all its sides and all its angles are equal, and convex when every angle is under 180°. Students classify polygons, find the angles of regular polygons, and reason about which can exist.

We are learning to

name polygons by their number of sides,
decide whether a polygon is regular, and whether it is convex,
work out each interior angle of a regular polygon.

Success criteria

I can explain why a rhombus is not a regular polygon.
I can find each angle of a regular polygon from its number of sides.

You need

The worksheet, rulers, protractors, and dot or grid paper.

Lesson flow (about 60 minutes)

10 min	Regular or not Show the board (see the box). Ask: “A rhombus has four equal sides. Why is it not a regular quadrilateral?”
30 min	Classify Students complete Parts A and B, measuring where the drawing does not settle it.
20 min	Can it exist? Part C as a class; early finishers do Part D. Ask: “Why must the number of sides come out as a whole number?”

Two shorter sessions instead? Split after Part A; start the second with Part B.

On the board

Show “Regular versus irregular”, which opens on a regular quadrilateral. Press “show irregular”, then “pentagon”, then “show regular”; before each press, ask what will stay the same and what will change.

seegongsik.com/au/y7/space/AC9M7SP02

Watch for these ideas

Taking equal sides alone as regular, as with a rhombus, or equal angles alone, as with a rectangle.
Not counting a concave polygon’s sides as a polygon of that name: the L-shape is a hexagon.
Using 180 ÷ n for each angle, not (n − 2) × 180 ÷ n.

Answers

Part A (convex unless marked): (1) pentagon, regular; (2) quadrilateral, not regular (sides equal, angles not); (3) hexagon, not regular (sides not all equal), concave; (4) hexagon, regular; (5) quadrilateral, not regular (angles equal, sides not); (6) pentagon, not regular (sides not all equal); (7) octagon, regular.
Part B (sides: sum, each angle): 5: 540°, 108°; 6: 720°, 120°; 8: 1080°, 135°; 10: 1440°, 144°; 12: 1800°, 150°.
Part C: (1) 180 − 150 = 30° at each turn, and 360 ÷ 30 = 12 sides, a regular dodecagon; (2) no: 360 ÷ 80 = 4.5, not a whole number of sides.
Part D: for example (0, 0), (2, 1), (3, 3), (2, 5), (0, 4), (−1, 2): sides all √5, angles not equal.

Day 4 · Worksheet

Polygons

NameClassDate

A. Classify

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Shape	Name by sides	Regular?	Convex?	Reason
(1)
(2)
(3)
(4)
(5)
(6)
(7)

B. Angles of regular polygons

Number of sides	5	6	8	10	12
Sum of the angles
Each angle

C. Can it exist?

Each angle of a regular polygon is 150°. How many sides does it have? ____________
Could a regular polygon have angles of 100°? Explain. ______________________

D. Stretch

On dot paper, draw a hexagon whose six sides are all equal but which is not regular. How do you know it is not regular?

Day 5 · Teacher planDay 5 of 5

Reasoning about shapes

Knowing the properties lets students reason: name a shape from a description, pick an odd one out with a reason, and decide which shapes cannot exist and why. Then the quiz.

We are learning to

name a shape from a list of its properties,
explain why some combinations of properties are impossible.

Success criteria

I can name a shape from its properties and justify the name.
I can explain why a shape cannot exist, using angles or parallel sides.

You need

The worksheet, dot or grid paper, and the unit’s self-check quiz on the board.

Lesson flow (about 60 minutes)

10 min	What am I? Describe a shape one property at a time; pairs name it as soon as they are sure. Ask: “Which property finally settled it, and why?”
30 min	Problems Students work through problems 1 to 6; 7 and 8 are the stretch.
20 min	Class quiz game Run the self-check quiz as a class game (see the box), then wrap up.

Two shorter sessions instead? Split after problem 3; start the second with problem 4.

On the board

Scroll to “Quick self-check” at the foot of the unit. Read each question aloud, give pairs half a minute to agree, then press the class’s choice; the box shows at once whether it is right, and a choice cannot be changed once pressed.

seegongsik.com/au/y7/space/AC9M7SP02

Watch for these ideas

Naming from the look of a drawing instead of from its properties.
Giving an odd one out without the property that makes it odd.
Deciding a shape is impossible without a reason: angle sums and parallel sides settle most cases.

Answers with working

(a) a rhombus that is not a square; (b) a trapezium; (c) a right-angled isosceles triangle; (d) a regular hexagon.
the kite, the only one that is not a parallelogram (another choice is fine with a property to back it).
no: a right angle and an angle over 90° already add to more than 180°.
no: the two angles along each of the other two sides add to 180°, so a right angle always comes with a second one.
a parallelogram: both pairs of opposite sides are parallel, the sides are 4 and √10, and there is no right angle.
no: four right angles make a rectangle, and only a rectangle with equal sides is a square.
yes, such as (0, 0), (4, 0), (4, 2), (2, 4), (0, 2): right angles at the bottom two corners and the top.
five, in an L-shaped hexagon, which is concave; a convex hexagon has at most three.

Day 5 · Worksheet

Reasoning about shapes

NameClassDate

Give a reason with every answer.

Problems (7 and 8 are the stretch)

What am I?
(a) I have four equal sides, and my diagonals are not equal. ____________________
(b) I have exactly one pair of parallel sides. ____________________
(c) I am a triangle with a right angle and two equal sides. ____________________
(d) I have six equal sides and six equal angles. ____________________
Which is the odd one out: square, rectangle, rhombus, kite? Why?
Can a triangle be both right-angled and obtuse? Explain.
Can a trapezium have exactly one right angle? Explain.
A quadrilateral has corners at (0, 0), (4, 0), (5, 3), (1, 3). Plot it on grid paper and name it, with a reason.
Ben says that a shape with four right angles must be a square. Is Ben right? Explain.
Stretch. Can a pentagon have exactly three right angles? Sketch one on dot paper or explain why not.
Stretch. What is the greatest number of right angles a hexagon can have? Sketch it.

Cut-out sheet 1 of 2Triangle cards

Triangle cards

Day 1. Cut out the 12 cards. The dots are 1 unit apart; count along the grid, or measure with a ruler and a protractor.

Cut-out sheet 2 of 2Quadrilateral cards

Quadrilateral cards

Days 2 and 3. Cut out the 12 cards. Check sides, angles and diagonals by counting along the grid, or with a ruler and a protractor.

Mini-check · End of the weekSpace

What we know: Classifying shapes

NameClassDate

Work on your own. Give a reason with every answer; the dots are 1 unit apart.

Name this triangle by its sides and by its angles.
____________________
Can a triangle be both equilateral and obtuse? Explain. ______________________
Give this quadrilateral its most exact name, and a property that proves it.
____________________
Which of these always has equal diagonals: rhombus, rectangle, parallelogram or kite? ____________

Always, sometimes or never: a parallelogram is a rectangle. ______________________
Always, sometimes or never: a square is a rhombus. ______________________
Each angle of a regular polygon is 140°. How many sides does it have? ____________
Is a rhombus with a right angle a regular polygon? Explain.

How did this week feel? Circle one: I can teach it · I am getting there · I need more help

Mini-check · Answers and markingFor the teacher

Answers and marking guide

Answers with working

Scalene and right-angled: the sides are √5, √20 and 5, all different, and 5 + 20 = 25, so the angle at (1, 2) is a right angle.
No: each angle of an equilateral triangle is 60°, so none can be over 90°.
A square, tilted: four equal sides of √10 and a right angle at every corner.
The rectangle. A square has them too, as a special rectangle; a rhombus, parallelogram and kite do not always.
Sometimes: only when its angles are right angles.
Always: a square has four equal sides.
180 − 140 = 40° at each turn, and 360 ÷ 40 = 9 sides: a regular nonagon.
Yes: a rhombus with a right angle is a square, with all sides equal and all angles 90°.

A quick three-level guide

Idea	Working towards	At standard	Beyond
Triangles (Q1, Q2)	names a triangle one way only	gives both names and checks the right angle	explains which combinations cannot exist
Quadrilaterals (Q3, Q4)	names by the look of the shape	names by properties, with a proof	uses diagonals to tell kinds apart
Relationships (Q5, Q6)	treats each name as separate	says always, sometimes or never with a reason	gives a case for and against a "sometimes"
Polygons (Q7, Q8)	thinks equal sides make a polygon regular	checks sides and angles, and finds each angle	works back from an angle to the number of sides

Eight questions, four ideas. A student at standard names triangles both ways, names quadrilaterals from their properties, places them in the family with reasons, and tells regular polygons from irregular ones.

Weekly recordClass checklist

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

Name	Triangles	Quads	Family	Polygons	Reasoning

The five columns are the five days: triangles, quadrilaterals, the quadrilateral family, polygons, and reasoning about shapes.