Changing and fixed amounts
Identify quantities that can change and quantities that stay the same within a stated real-life situation and time period, and explain why: on one school bus trip the number of seats stays the same while the number of passengers changes from stop to stop. 'Stays the same' describes that situation and time, not something that can never change
Lesson
Set out your lesson
“Changing and fixed amounts means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Ruler, cup, or clock as fits the topic
- Paper for recording
Extra for the adult
Worked example. Measure a pencil as about 15 cm and write the unit with the number.
Optional challenge. For Changing and fixed amounts, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Changing and fixed amounts, not mastery.
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Teaching approaches
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1 approach
Changing and fixed amounts means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Ruler, cup, or clock as fits the topic; Paper for recording. Adult measures one example and records the unit. Child makes three measurements or time/money readings and records each with units. Done: three recordings with correct units. Stop after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceChanging and fixed amounts practice
Practice key ideas from Changing and fixed amounts.
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Counting Squares
Before you open · source notes
Counting Squares supports changing and fixed amounts. Not every worksheet pack.
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Before you openAsk the learner to explain one step of “Counting Squares” in their own words.
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Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Counting Squares.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
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Check understanding
- Sort cards for one stated situation (e.g. a school bus trip: seats on the bus, passengers on board, wheels, stops still to go) into 'changes' and 'stays the same'
- Explain why one quantity changes and another stays the same in that situation (e.g. 'people get on and off at stops, but the seats are fixed to the bus')
- Name one quantity that changes during their school day (e.g. children in the room) and one that stays the same during that day (e.g. desks), and say what could change the second one at another time
“On a bus ride, can your child tell you which numbers change along the way (like how many passengers are on board) and which stay the same for that trip (like how many seats there are) — and explain why?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 6–7
Standards