Adding and subtracting (age 9+)
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
Share and support
Teaching Table
Set out your lesson
Track several additions and subtractions in a five-digit context. Keep a labeled intermediate total and justify each method.
Ask the learner to plan a start of 100 items, 30 received and 20 used (110 remain). Then use the preceding two-step and large-column lessons as needed. Ask why a target minus the amount already collected gives the shortfall. Do not infer readiness from source availability.
Check readiness directly. Prerequisite availability is not attainment.
Start with the readiness check. Use Show, then Guided, then a fresh Try. These linked lessons may need several short sessions; do not impose a speed target. Read the active sheet on screen and answer on plain paper or by typing. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt. Record any hints, scribing or calculation help. Oral explanations are allowed but do not show independent reading or handwriting. Use as much space and time as needed; pause or split the lesson. Keep this adult guide and all keys private. Share only the active learner sheet. Before Try, put Show, Guided work and notes aside. Keep the fresh Try givens available. Give no answer or target method during the first attempt. If help is needed, give it and mark the attempt supported. Review the key after the attempt. Record the actual response and help; do not invent success or infer mastery from one attempt. These are fictional paper or oral mathematics tasks. No personal information, public sharing, purchase, physical experiment or real measurement is required.
Record the actual response and assistance. These tasks do not establish mastery.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
Teaching limits and safe use
These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.
The canonical bottle situation is modeled. Fresh tasks are fictional balances, not financial guidance or real transactions. They provide bounded multi-step practice, not fluency certification.
Record the actual response and assistance. These tasks do not establish mastery.
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Track several additions and subtractions in a five-digit context. Keep a labeled intermediate total and justify each method.
Track several additions and subtractions in a five-digit context. Keep a labeled intermediate total and justify each method.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
External links for extra practice. They do not replace Gakuva’s teaching approach.
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Check understanding
- A school collects 12,450 bottles in Week 1 and 8,372 in Week 2; their target is 25,000 — how many more do they need?
- Choose between mental and written methods for each step and explain why
- Solve a three-step problem involving addition and subtraction of five-digit numbers
“If your child is given a multi-step problem — like planning a budget where money is added and spent in several steps — can they decide which operations to use at each stage and explain their thinking?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 9–10