Teaching pack · Year 7 Numberseegongsik /au
Mathematical modelling with rational numbers: a week of ready-to-teach maths
Five days of lessons for Year 7 Number. Print this pack and the week is prepared.
AC9M7N09
use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation
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: “The modelling cycle”, “A money problem as a model”, “Markup or discount, one model”, “Adding tax to a price”, “Which is the better buy?”.
seegongsik.com/au/y7/number/AC9M7N09
Aligned to Australian Curriculum V9 (AC9M7N09). 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 | The modelling cycle | Practise the idea with talk, board and worksheet | Board: The modelling cycle |
| 2 | A money problem as a model | Practise the idea with talk, board and worksheet | Board: A money problem as a model |
| 3 | Markup or discount, one model | Practise the idea with talk, board and worksheet | Board: Markup or discount, one model |
| 4 | Adding tax to a price | Practise the idea with talk, board and worksheet | Board: Adding tax to a price |
| 5 | Which is the better buy? | Practise the idea with talk, board and worksheet | Board: Which is the better buy? |
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 mathematical modelling with rational numbers. Ask: What did you practise today?
seegongsik.com/au/y7/number/AC9M7N09/pack
Day 1 · Teacher planDay 1 of 5
The modelling cycle
Children practise “The modelling cycle” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain the modelling cycle in Year 7 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 modelling cycle”,
- 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 modelling cycle”. 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 modelling cycle” on screen for the main block.
seegongsik.com/au/y7/number/AC9M7N09
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 modelling cycle.
Day 1 · Worksheet
The modelling cycle
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 money problem as a model
Children practise “A money problem as a model” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain a money problem as a model in Year 7 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 money problem as a model”,
- 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 money problem as a model”. 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 money problem as a model” on screen for the main block.
seegongsik.com/au/y7/number/AC9M7N09
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 money problem as a model.
Day 2 · Worksheet
A money problem as a model
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
Markup or discount, one model
Children practise “Markup or discount, one model” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain markup or discount, one model in Year 7 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 “Markup or discount, one model”,
- 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 “Markup or discount, one model”. 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 “Markup or discount, one model” on screen for the main block.
seegongsik.com/au/y7/number/AC9M7N09
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 markup or discount, one model.
Day 3 · Worksheet
Markup or discount, one model
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
Adding tax to a price
Children practise “Adding tax to a price” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain adding tax to a price in Year 7 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 “Adding tax to a price”,
- 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 “Adding tax to a price”. 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 “Adding tax to a price” on screen for the main block.
seegongsik.com/au/y7/number/AC9M7N09
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 adding tax to a price.
Day 4 · Worksheet
Adding tax to a price
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
Which is the better buy?
Children practise “Which is the better buy?” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain which is the better buy? in Year 7 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 “Which is the better buy?”,
- 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 “Which is the better buy?”. 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 “Which is the better buy?” on screen for the main block.
seegongsik.com/au/y7/number/AC9M7N09
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 which is the better buy?.
Day 5 · Worksheet
Which is the better buy?
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 Mathematical modelling with rational numbers
Cut out. Hold up a card and give an example.
The modelling cycle
Give an example.
A money problem as a model
Give an example.
Markup or discount, one model
Give an example.
Adding tax to a price
Give an example.
Which is the better buy?
Give an example.
Store in an envelope labelled AC9M7N09.
Mini-check · End of week
Show what you know: Mathematical modelling with rational numbers
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 (mathematical modelling with rational numbers) 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.