Teaching pack · Year 10 Numberseegongsik /au
Approximation versus Exact: How Rounding Errors Grow: a week of ready-to-teach maths
Five days of lessons for Year 10 Number. Print this pack and the week is prepared.
AC9M10N01
recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations
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: “Round once, or keep it exact”, “The error compounds step by step”, “Exact forms hit the point; rounded ones miss”, “More digits shrink the error, but never to zero”, “Keep the surd, or round too soon”.
seegongsik.com/au/y10/number/AC9M10N01
Aligned to Australian Curriculum V9 (AC9M10N01). 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 | Round once, or keep it exact | Practise the idea with talk, board and worksheet | Board: Round once, or keep it exact |
| 2 | The error compounds step by step | Practise the idea with talk, board and worksheet | Board: The error compounds step by step |
| 3 | Exact forms hit the point; rounded ones miss | Practise the idea with talk, board and worksheet | Board: Exact forms hit the point; rounded ones miss |
| 4 | More digits shrink the error, but never to zero | Practise the idea with talk, board and worksheet | Board: More digits shrink the error, but never to zero |
| 5 | Keep the surd, or round too soon | Practise the idea with talk, board and worksheet | Board: Keep the surd, or round too soon |
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 approximation versus exact: how rounding errors grow. Ask: What did you practise today?
seegongsik.com/au/y10/number/AC9M10N01/pack
Day 1 · Teacher planDay 1 of 5
Round once, or keep it exact
Children practise “Round once, or keep it exact” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain round once, or keep it exact 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 “Round once, or keep it exact”,
- 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 “Round once, or keep it exact”. 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 “Round once, or keep it exact” on screen for the main block.
seegongsik.com/au/y10/number/AC9M10N01
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 round once, or keep it exact.
Day 1 · Worksheet
Round once, or keep it exact
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
The error compounds step by step
Children practise “The error compounds step by step” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain the error compounds step by step 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 error compounds step by step”,
- 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 error compounds step by step”. 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 error compounds step by step” on screen for the main block.
seegongsik.com/au/y10/number/AC9M10N01
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 error compounds step by step.
Day 2 · Worksheet
The error compounds step by step
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
Exact forms hit the point; rounded ones miss
Children practise “Exact forms hit the point; rounded ones miss” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain exact forms hit the point; rounded ones miss 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 “Exact forms hit the point; rounded ones miss”,
- 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 “Exact forms hit the point; rounded ones miss”. 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 “Exact forms hit the point; rounded ones miss” on screen for the main block.
seegongsik.com/au/y10/number/AC9M10N01
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 exact forms hit the point; rounded ones miss.
Day 3 · Worksheet
Exact forms hit the point; rounded ones miss
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
More digits shrink the error, but never to zero
Children practise “More digits shrink the error, but never to zero” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain more digits shrink the error, but never to zero 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 “More digits shrink the error, but never to zero”,
- 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 “More digits shrink the error, but never to zero”. 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 “More digits shrink the error, but never to zero” on screen for the main block.
seegongsik.com/au/y10/number/AC9M10N01
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 more digits shrink the error, but never to zero.
Day 4 · Worksheet
More digits shrink the error, but never to zero
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
Keep the surd, or round too soon
Children practise “Keep the surd, or round too soon” with talk, the board picture, and a short worksheet. About 40 minutes.
We are learning to
- explain keep the surd, or round too soon 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 “Keep the surd, or round too soon”,
- 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 “Keep the surd, or round too soon”. 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 “Keep the surd, or round too soon” on screen for the main block.
seegongsik.com/au/y10/number/AC9M10N01
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 keep the surd, or round too soon.
Day 5 · Worksheet
Keep the surd, or round too soon
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 Approximation versus Exact: How Rounding Errors Grow
Cut out. Hold up a card and give an example.
Round once, or keep it exact
Give an example.
The error compounds step by step
Give an example.
Exact forms hit the point; rounded ones miss
Give an example.
More digits shrink the error, but never to zero
Give an example.
Keep the surd, or round too soon
Give an example.
Store in an envelope labelled AC9M10N01.
Mini-check · End of week
Show what you know: Approximation versus Exact: How Rounding Errors Grow
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 (approximation versus exact: how rounding errors grow) 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.