Teaching pack · Year 10 Measurementseegongsik /au
Pythagoras and Trigonometry: a week of ready-to-teach maths
Five days of lessons for Year 10 Measurement. Print this pack and the week is prepared.
AC9M10M03
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression
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: “Pythagoras: squares on the sides”, “Finding the hypotenuse”, “The three trigonometric ratios”, “Solving for an unknown side”, “Solving for an unknown angle”.
seegongsik.com/au/y10/measurement/AC9M10M03
Aligned to Australian Curriculum V9 (AC9M10M03). 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 | Pythagoras: squares on the sides | Practise the idea with talk, board and worksheet | Board: Pythagoras: squares on the sides |
| 2 | Finding the hypotenuse | Practise the idea with talk, board and worksheet | Board: Finding the hypotenuse |
| 3 | The three trigonometric ratios | Practise the idea with talk, board and worksheet | Board: The three trigonometric ratios |
| 4 | Solving for an unknown side | Practise the idea with talk, board and worksheet | Board: Solving for an unknown side |
| 5 | Solving for an unknown angle | Practise the idea with talk, board and worksheet | Board: Solving for an unknown angle |
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. Ask: What did you practise today?
seegongsik.com/au/y10/measurement/AC9M10M03/pack
Day 1 · Teacher planDay 1 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 10 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/y10/measurement/AC9M10M03
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 1 · 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 2 · Teacher planDay 2 of 5
Finding the hypotenuse
Children practise “Finding the hypotenuse” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain finding the hypotenuse in Year 10 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 “Finding the 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 “Finding the 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 “Finding the hypotenuse” on screen for the main block.
seegongsik.com/au/y10/measurement/AC9M10M03
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 finding the hypotenuse.
Day 2 · Worksheet
Finding the 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 □
Day 3 · Teacher planDay 3 of 5
The three trigonometric ratios
Children practise “The three trigonometric ratios” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain the three trigonometric ratios in Year 10 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 three trigonometric ratios”,
- 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 three trigonometric ratios”. 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 three trigonometric ratios” on screen for the main block.
seegongsik.com/au/y10/measurement/AC9M10M03
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 three trigonometric ratios.
Day 3 · Worksheet
The three trigonometric ratios
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
Solving for an unknown side
Children practise “Solving for an unknown side” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain solving for an unknown side in Year 10 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 “Solving for an unknown side”,
- 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 “Solving for an unknown side”. 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 “Solving for an unknown side” on screen for the main block.
seegongsik.com/au/y10/measurement/AC9M10M03
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 solving for an unknown side.
Day 4 · Worksheet
Solving for an unknown side
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
Solving for an unknown angle
Children practise “Solving for an unknown angle” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain solving for an unknown angle in Year 10 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 “Solving for an unknown angle”,
- 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 “Solving for an unknown angle”. 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 “Solving for an unknown angle” on screen for the main block.
seegongsik.com/au/y10/measurement/AC9M10M03
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 solving for an unknown angle.
Day 5 · Worksheet
Solving for an unknown angle
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
Cut out. Hold up a card and give an example.
Pythagoras: squares on the sides
Give an example.
Finding the hypotenuse
Give an example.
The three trigonometric ratios
Give an example.
Solving for an unknown side
Give an example.
Solving for an unknown angle
Give an example.
Store in an envelope labelled AC9M10M03.
Mini-check · End of week
Show what you know: Pythagoras and Trigonometry
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 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.