Teaching pack · Year 9 Algebraseegongsik /au
Gradient, Midpoint and Distance: a week of ready-to-teach maths
Five days of lessons for Year 9 Algebra. Print this pack and the week is prepared.
AC9M9A03
find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane
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: “Two points, two differences”, “Gradient as rise over run”, “Midpoint by averaging”, “Distance is the hypotenuse”, “An irrational distance”.
seegongsik.com/au/y9/algebra/AC9M9A03
Aligned to Australian Curriculum V9 (AC9M9A03). 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 | Two points, two differences | Practise the idea with talk, board and worksheet | Board: Two points, two differences |
| 2 | Gradient as rise over run | Practise the idea with talk, board and worksheet | Board: Gradient as rise over run |
| 3 | Midpoint by averaging | Practise the idea with talk, board and worksheet | Board: Midpoint by averaging |
| 4 | Distance is the hypotenuse | Practise the idea with talk, board and worksheet | Board: Distance is the hypotenuse |
| 5 | An irrational distance | Practise the idea with talk, board and worksheet | Board: An irrational distance |
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 gradient, midpoint and distance. Ask: What did you practise today?
seegongsik.com/au/y9/algebra/AC9M9A03/pack
Day 1 · Teacher planDay 1 of 5
Two points, two differences
Children practise “Two points, two differences” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain two points, two differences 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 “Two points, two differences”,
- 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 “Two points, two differences”. 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 “Two points, two differences” on screen for the main block.
seegongsik.com/au/y9/algebra/AC9M9A03
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 two points, two differences.
Day 1 · Worksheet
Two points, two differences
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
Gradient as rise over run
Children practise “Gradient as rise over run” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain gradient as rise over run 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 “Gradient as rise over run”,
- 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 “Gradient as rise over run”. 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 “Gradient as rise over run” on screen for the main block.
seegongsik.com/au/y9/algebra/AC9M9A03
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 gradient as rise over run.
Day 2 · Worksheet
Gradient as rise over run
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
Midpoint by averaging
Children practise “Midpoint by averaging” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain midpoint by averaging 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 “Midpoint by averaging”,
- 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 “Midpoint by averaging”. 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 “Midpoint by averaging” on screen for the main block.
seegongsik.com/au/y9/algebra/AC9M9A03
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 midpoint by averaging.
Day 3 · Worksheet
Midpoint by averaging
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
Distance is the hypotenuse
Children practise “Distance is the hypotenuse” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain distance is the 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 “Distance is 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 “Distance is 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 “Distance is the hypotenuse” on screen for the main block.
seegongsik.com/au/y9/algebra/AC9M9A03
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 distance is the hypotenuse.
Day 4 · Worksheet
Distance is 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 5 · Teacher planDay 5 of 5
An irrational distance
Children practise “An irrational distance” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain an irrational distance 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 distance”,
- 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 distance”. 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 distance” on screen for the main block.
seegongsik.com/au/y9/algebra/AC9M9A03
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 distance.
Day 5 · Worksheet
An irrational distance
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 Gradient, Midpoint and Distance
Cut out. Hold up a card and give an example.
Two points, two differences
Give an example.
Gradient as rise over run
Give an example.
Midpoint by averaging
Give an example.
Distance is the hypotenuse
Give an example.
An irrational distance
Give an example.
Store in an envelope labelled AC9M9A03.
Mini-check · End of week
Show what you know: Gradient, Midpoint and Distance
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 (gradient, midpoint and distance) 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.