Teaching pack · Year 9 Spaceseegongsik /au
Why Trig Ratios Stay Constant: Similarity: a week of ready-to-teach maths
Five days of lessons for Year 9 Space. Print this pack and the week is prepared.
AC9M9SP01
recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity
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: “Same angle, three sizes”, “Similar means proportional sides”, “The ratio is unchanged”, “Why k cancels”, “Naming sine, cosine, tangent”.
seegongsik.com/au/y9/space/AC9M9SP01
Aligned to Australian Curriculum V9 (AC9M9SP01). 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 | Same angle, three sizes | Practise the idea with talk, board and worksheet | Board: Same angle, three sizes |
| 2 | Similar means proportional sides | Practise the idea with talk, board and worksheet | Board: Similar means proportional sides |
| 3 | The ratio is unchanged | Practise the idea with talk, board and worksheet | Board: The ratio is unchanged |
| 4 | Why k cancels | Practise the idea with talk, board and worksheet | Board: Why k cancels |
| 5 | Naming sine, cosine, tangent | Practise the idea with talk, board and worksheet | Board: Naming sine, cosine, tangent |
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 why trig ratios stay constant: similarity. Ask: What did you practise today?
seegongsik.com/au/y9/space/AC9M9SP01/pack
Day 1 · Teacher planDay 1 of 5
Same angle, three sizes
Children practise “Same angle, three sizes” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain same angle, three sizes 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 “Same angle, three sizes”,
- 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 “Same angle, three sizes”. 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 “Same angle, three sizes” on screen for the main block.
seegongsik.com/au/y9/space/AC9M9SP01
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 same angle, three sizes.
Day 1 · Worksheet
Same angle, three sizes
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
Similar means proportional sides
Children practise “Similar means proportional sides” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain similar means proportional 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 “Similar means proportional 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 “Similar means proportional 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 “Similar means proportional sides” on screen for the main block.
seegongsik.com/au/y9/space/AC9M9SP01
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 means proportional sides.
Day 2 · Worksheet
Similar means proportional 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 3 · Teacher planDay 3 of 5
The ratio is unchanged
Children practise “The ratio is unchanged” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain the ratio is unchanged 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 “The ratio is unchanged”,
- 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 “The ratio is unchanged”. 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 “The ratio is unchanged” on screen for the main block.
seegongsik.com/au/y9/space/AC9M9SP01
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 the ratio is unchanged.
Day 3 · Worksheet
The ratio is unchanged
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
Why k cancels
Children practise “Why k cancels” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain why k cancels 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 “Why k cancels”,
- 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 “Why k cancels”. 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 “Why k cancels” on screen for the main block.
seegongsik.com/au/y9/space/AC9M9SP01
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 why k cancels.
Day 4 · Worksheet
Why k cancels
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
Naming sine, cosine, tangent
Children practise “Naming sine, cosine, tangent” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain naming sine, cosine, tangent 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 sine, cosine, tangent”,
- 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 sine, cosine, tangent”. 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 sine, cosine, tangent” on screen for the main block.
seegongsik.com/au/y9/space/AC9M9SP01
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 sine, cosine, tangent.
Day 5 · Worksheet
Naming sine, cosine, tangent
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 Why Trig Ratios Stay Constant: Similarity
Cut out. Hold up a card and give an example.
Same angle, three sizes
Give an example.
Similar means proportional sides
Give an example.
The ratio is unchanged
Give an example.
Why k cancels
Give an example.
Naming sine, cosine, tangent
Give an example.
Store in an envelope labelled AC9M9SP01.
Mini-check · End of week
Show what you know: Why Trig Ratios Stay Constant: Similarity
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 (why trig ratios stay constant: similarity) 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.