Connecting Representations
Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)
Share and support
Teaching Table
Set out your lesson
Make a story, a model and an equation say the same thing.
Comfort with the particular task and communication mode; optional oral/scribed work is recorded separately.
Check the learner can access these words/materials and prerequisite ideas; historical authorship is not readiness or mastery. If not, demonstrate briefly or revisit the named prerequisite.
Use tokens or circles drawn on paper and the supplied part-whole frame. No printer: view only the active learner card on screen, or an adult copies its exact prompts onto plain paper without answers. Oral pointing/dictation is an access option; record it as adapted/supported and do not claim handwriting from it. Keep adult keys/scripts separate; supply only the current stage.
Use fictional cases and invented identifiers; never record personal conflicts, health, bank details or family spending. Adult prompts/keys are private companion files, never learner links.
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.
One addition and one subtraction context; fresh transfer within a narrow range.
Use fictional cases and invented identifiers; never record personal conflicts, health, bank details or family spending. Adult prompts/keys are private companion files, never learner links.
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Make a story, a model and an equation say the same thing.
Make a story, a model and an equation say the same thing.
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
Reviewed external links that reinforce this concept. They do not replace Gakuva’s teaching approach.
No reviewed resources for this concept yet.
The teaching approach above still stands. Curated practice links will appear here as the shelf fills.
Check understanding
- Write a number sentence (e.g. 14 + 5 = 19) to match a word problem and explain the connection
- Draw a bar model or part-whole diagram to represent a problem, then solve using the diagram
- Translate between a concrete model and a symbolic equation, describing what each number represents
“When your child solves a word problem, can they draw a diagram or write a number sentence to show their thinking — and then explain how the picture and the numbers match the real situation?”
Curriculum record
- Type
- Meta
- Subject
- Mathematics
- Domain
- Mathematical Thinking
- Age range
- Ages 6–7