Teaching pack · Year 9 Measurementseegongsik /au
Pythagoras and Trigonometry in Right-Angled Triangles: a week of ready-to-teach maths
Five days of lessons for Year 9 Measurement. Print this pack and the week is prepared.
AC9M9M03
solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles
Start here: five minutes to Monday
- Skim the week at a glance.
- Print the five days (plan + worksheet each).
- Cut out the card sheet once.
- Open the free interactive unit on your board.
- Teach from the plan.
On the board
On-screen pictures: “Naming the sides”, “Angles add to 180, the acute pair to 90”, “Similar triangles and scale factor”, “Pythagoras: squares on the sides”, “An irrational hypotenuse”.
seegongsik.com/au/y9/measurement/AC9M9M03
Aligned to Australian Curriculum V9 (AC9M9M03). Original material from seegongsik. Descriptors (c) ACARA, CC BY 4.0.
The week at a glance5 lessons
The week at a glance
One lesson a day. Run them in order where you can.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Naming the sides | Practise the idea with talk, board and worksheet | Board: Naming the sides |
| 2 | Angles add to 180, the acute pair to 90 | Practise the idea with talk, board and worksheet | Board: Angles add to 180, the acute pair to 90 |
| 3 | Similar triangles and scale factor | Practise the idea with talk, board and worksheet | Board: Similar triangles and scale factor |
| 4 | Pythagoras: squares on the sides | Practise the idea with talk, board and worksheet | Board: Pythagoras: squares on the sides |
| 5 | An irrational hypotenuse | Practise the idea with talk, board and worksheet | Board: An irrational hypotenuse |
Materials
- This pack printed.
- Pencils and the board or projector.
- Optional counters or rulers if a day plan names them.
A note home
This week in maths we work on pythagoras and trigonometry in right-angled triangles. Ask: What did you practise today?
seegongsik.com/au/y9/measurement/AC9M9M03/pack
Day 1 · Teacher planDay 1 of 5
Naming the sides
Children practise “Naming the sides” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain naming the sides in Year 9 words,
- use the board picture to check thinking,
- record an example on paper.
Success criteria
- I can show one example of today’s idea.
- I can say the idea in a short sentence.
You need
- interactive unit open on “Naming the sides”,
- worksheet (next sheet), one per child,
Lesson flow (about 40 minutes)
| 5 min | Warm-up Ask: “What might help us today?” |
| 10 min | On the board Open “Naming the sides”. Ask: “What changed on the screen?” |
| 15 min | Worksheet Children complete the day sheet. |
| 10 min | Share Ask: “In one sentence, what was today’s idea?” |
On the board
Leave “Naming the sides” on screen for the main block.
seegongsik.com/au/y9/measurement/AC9M9M03
Watch for
- Skipping the board -- bring them back to the picture.
- Correct answer with no explanation -- ask how do you know?
Answers and look-fors
- Meeting the idea sounds like a clear sentence about naming the sides.
Day 1 · Worksheet
Naming the sides
NameClassDate
Use the board picture. Show your thinking.
1. Draw or write one example from the board.
2. What is the main idea in your words?
3. Make a second example of your own.
I know I am right because
I can teach this idea to a partner:Yes □ No □
Day 2 · Teacher planDay 2 of 5
Angles add to 180, the acute pair to 90
Children practise “Angles add to 180, the acute pair to 90” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain angles add to 180, the acute pair to 90 in Year 9 words,
- use the board picture to check thinking,
- record an example on paper.
Success criteria
- I can show one example of today’s idea.
- I can say the idea in a short sentence.
You need
- interactive unit open on “Angles add to 180, the acute pair to 90”,
- worksheet (next sheet), one per child,
Lesson flow (about 40 minutes)
| 5 min | Warm-up Ask: “What might help us today?” |
| 10 min | On the board Open “Angles add to 180, the acute pair to 90”. Ask: “What changed on the screen?” |
| 15 min | Worksheet Children complete the day sheet. |
| 10 min | Share Ask: “In one sentence, what was today’s idea?” |
On the board
Leave “Angles add to 180, the acute pair to 90” on screen for the main block.
seegongsik.com/au/y9/measurement/AC9M9M03
Watch for
- Skipping the board -- bring them back to the picture.
- Correct answer with no explanation -- ask how do you know?
Answers and look-fors
- Meeting the idea sounds like a clear sentence about angles add to 180, the acute pair to 90.
Day 2 · Worksheet
Angles add to 180, the acute pair to 90
NameClassDate
Use the board picture. Show your thinking.
1. Draw or write one example from the board.
2. What is the main idea in your words?
3. Make a second example of your own.
I know I am right because
I can teach this idea to a partner:Yes □ No □
Day 3 · Teacher planDay 3 of 5
Similar triangles and scale factor
Children practise “Similar triangles and scale factor” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain similar triangles and scale factor in Year 9 words,
- use the board picture to check thinking,
- record an example on paper.
Success criteria
- I can show one example of today’s idea.
- I can say the idea in a short sentence.
You need
- interactive unit open on “Similar triangles and scale factor”,
- worksheet (next sheet), one per child,
Lesson flow (about 40 minutes)
| 5 min | Warm-up Ask: “What might help us today?” |
| 10 min | On the board Open “Similar triangles and scale factor”. Ask: “What changed on the screen?” |
| 15 min | Worksheet Children complete the day sheet. |
| 10 min | Share Ask: “In one sentence, what was today’s idea?” |
On the board
Leave “Similar triangles and scale factor” on screen for the main block.
seegongsik.com/au/y9/measurement/AC9M9M03
Watch for
- Skipping the board -- bring them back to the picture.
- Correct answer with no explanation -- ask how do you know?
Answers and look-fors
- Meeting the idea sounds like a clear sentence about similar triangles and scale factor.
Day 3 · Worksheet
Similar triangles and scale factor
NameClassDate
Use the board picture. Show your thinking.
1. Draw or write one example from the board.
2. What is the main idea in your words?
3. Make a second example of your own.
I know I am right because
I can teach this idea to a partner:Yes □ No □
Day 4 · Teacher planDay 4 of 5
Pythagoras: squares on the sides
Children practise “Pythagoras: squares on the sides” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain pythagoras: squares on the sides in Year 9 words,
- use the board picture to check thinking,
- record an example on paper.
Success criteria
- I can show one example of today’s idea.
- I can say the idea in a short sentence.
You need
- interactive unit open on “Pythagoras: squares on the sides”,
- worksheet (next sheet), one per child,
Lesson flow (about 40 minutes)
| 5 min | Warm-up Ask: “What might help us today?” |
| 10 min | On the board Open “Pythagoras: squares on the sides”. Ask: “What changed on the screen?” |
| 15 min | Worksheet Children complete the day sheet. |
| 10 min | Share Ask: “In one sentence, what was today’s idea?” |
On the board
Leave “Pythagoras: squares on the sides” on screen for the main block.
seegongsik.com/au/y9/measurement/AC9M9M03
Watch for
- Skipping the board -- bring them back to the picture.
- Correct answer with no explanation -- ask how do you know?
Answers and look-fors
- Meeting the idea sounds like a clear sentence about pythagoras: squares on the sides.
Day 4 · Worksheet
Pythagoras: squares on the sides
NameClassDate
Use the board picture. Show your thinking.
1. Draw or write one example from the board.
2. What is the main idea in your words?
3. Make a second example of your own.
I know I am right because
I can teach this idea to a partner:Yes □ No □
Day 5 · Teacher planDay 5 of 5
An irrational hypotenuse
Children practise “An irrational hypotenuse” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain an irrational hypotenuse in Year 9 words,
- use the board picture to check thinking,
- record an example on paper.
Success criteria
- I can show one example of today’s idea.
- I can say the idea in a short sentence.
You need
- interactive unit open on “An irrational hypotenuse”,
- worksheet (next sheet), one per child,
Lesson flow (about 40 minutes)
| 5 min | Warm-up Ask: “What might help us today?” |
| 10 min | On the board Open “An irrational hypotenuse”. Ask: “What changed on the screen?” |
| 15 min | Worksheet Children complete the day sheet. |
| 10 min | Share Ask: “In one sentence, what was today’s idea?” |
On the board
Leave “An irrational hypotenuse” on screen for the main block.
seegongsik.com/au/y9/measurement/AC9M9M03
Watch for
- Skipping the board -- bring them back to the picture.
- Correct answer with no explanation -- ask how do you know?
Answers and look-fors
- Meeting the idea sounds like a clear sentence about an irrational hypotenuse.
Day 5 · Worksheet
An irrational hypotenuse
NameClassDate
Use the board picture. Show your thinking.
1. Draw or write one example from the board.
2. What is the main idea in your words?
3. Make a second example of your own.
I know I am right because
I can teach this idea to a partner:Yes □ No □
Cut-out cardsReuse all week
Talk cards for Pythagoras and Trigonometry in Right-Angled Triangles
Cut out. Hold up a card and give an example.
Naming the sides
Give an example.
Angles add to 180, the acute pair to 90
Give an example.
Similar triangles and scale factor
Give an example.
Pythagoras: squares on the sides
Give an example.
An irrational hypotenuse
Give an example.
Store in an envelope labelled AC9M9M03.
Mini-check · End of week
Show what you know: Pythagoras and Trigonometry in Right-Angled Triangles
NameClassDate
Work on your own. Use pictures or numbers.
1. Draw or write the big idea of this week.
2. Give one clear example.
3. Give a second different example.
4. What mistake should we watch for?
I can explain this idea to a partner:Yes □ No □
Mini-check · AnswersTeacher
Answers and look-fors
- Item 1 names the unit idea (pythagoras and trigonometry in right-angled triangles) in child words.
- Items 2-3: two different correct examples.
- Item 4: a real muddle for this topic.
Use day-plan look-fors across the week.