Teaching pack · Year 10 Spaceseegongsik /au
Deductive Proof: Reasoning from Theorems, Not Measuring: a week of ready-to-teach maths
Five days of lessons for Year 10 Space. Print this pack and the week is prepared.
AC9M10SP01
apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems
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: “Measuring shows one case; proving covers all”, “A proof is a chain of justified steps”, “Worked proof: vertically opposite angles”, “Using a theorem to solve a spatial problem”, “One gap breaks the whole proof”.
seegongsik.com/au/y10/space/AC9M10SP01
Aligned to Australian Curriculum V9 (AC9M10SP01). 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 | Measuring shows one case; proving covers all | Practise the idea with talk, board and worksheet | Board: Measuring shows one case; proving covers all |
| 2 | A proof is a chain of justified steps | Practise the idea with talk, board and worksheet | Board: A proof is a chain of justified steps |
| 3 | Worked proof: vertically opposite angles | Practise the idea with talk, board and worksheet | Board: Worked proof: vertically opposite angles |
| 4 | Using a theorem to solve a spatial problem | Practise the idea with talk, board and worksheet | Board: Using a theorem to solve a spatial problem |
| 5 | One gap breaks the whole proof | Practise the idea with talk, board and worksheet | Board: One gap breaks the whole proof |
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 deductive proof: reasoning from theorems, not measuring. Ask: What did you practise today?
seegongsik.com/au/y10/space/AC9M10SP01/pack
Day 1 · Teacher planDay 1 of 5
Measuring shows one case; proving covers all
Children practise “Measuring shows one case; proving covers all” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain measuring shows one case; proving covers all 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 “Measuring shows one case; proving covers all”,
- 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 “Measuring shows one case; proving covers all”. 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 “Measuring shows one case; proving covers all” on screen for the main block.
seegongsik.com/au/y10/space/AC9M10SP01
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 measuring shows one case; proving covers all.
Day 1 · Worksheet
Measuring shows one case; proving covers all
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
A proof is a chain of justified steps
Children practise “A proof is a chain of justified steps” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain a proof is a chain of justified steps 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 “A proof is a chain of justified steps”,
- 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 “A proof is a chain of justified steps”. 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 “A proof is a chain of justified steps” on screen for the main block.
seegongsik.com/au/y10/space/AC9M10SP01
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 a proof is a chain of justified steps.
Day 2 · Worksheet
A proof is a chain of justified steps
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
Worked proof: vertically opposite angles
Children practise “Worked proof: vertically opposite angles” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain worked proof: vertically opposite angles 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 “Worked proof: vertically opposite angles”,
- 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 “Worked proof: vertically opposite angles”. 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 “Worked proof: vertically opposite angles” on screen for the main block.
seegongsik.com/au/y10/space/AC9M10SP01
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 worked proof: vertically opposite angles.
Day 3 · Worksheet
Worked proof: vertically opposite angles
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
Using a theorem to solve a spatial problem
Children practise “Using a theorem to solve a spatial problem” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain using a theorem to solve a spatial problem 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 “Using a theorem to solve a spatial problem”,
- 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 “Using a theorem to solve a spatial problem”. 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 “Using a theorem to solve a spatial problem” on screen for the main block.
seegongsik.com/au/y10/space/AC9M10SP01
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 using a theorem to solve a spatial problem.
Day 4 · Worksheet
Using a theorem to solve a spatial problem
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
One gap breaks the whole proof
Children practise “One gap breaks the whole proof” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain one gap breaks the whole proof 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 “One gap breaks the whole proof”,
- 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 “One gap breaks the whole proof”. 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 “One gap breaks the whole proof” on screen for the main block.
seegongsik.com/au/y10/space/AC9M10SP01
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 one gap breaks the whole proof.
Day 5 · Worksheet
One gap breaks the whole proof
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 Deductive Proof: Reasoning from Theorems, Not Measuring
Cut out. Hold up a card and give an example.
Measuring shows one case; proving covers all
Give an example.
A proof is a chain of justified steps
Give an example.
Worked proof: vertically opposite angles
Give an example.
Using a theorem to solve a spatial problem
Give an example.
One gap breaks the whole proof
Give an example.
Store in an envelope labelled AC9M10SP01.
Mini-check · End of week
Show what you know: Deductive Proof: Reasoning from Theorems, Not Measuring
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 (deductive proof: reasoning from theorems, not measuring) 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.