Mathematics · Numbers and calculation
Everyday calculations: start with the quantity
Read the roles of numbers, compare decimals, and interpret equal groups and remainders before choosing an expression.
HITOIKI LEARNING · TOPICS
A small guide to your next discovery
Think about quantities, shapes and the world around you. Each guide brings together an idea, a way to reason about it and examples you can check at your own pace.
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Within each subject, guides follow a learning order. Use the prerequisite and next-guide links to build on what you know.
Mathematics
Numbers and calculation
Mathematics · Fractions and ratios
Fractions and ratios: name the whole
Work from equal pieces to equivalent fractions and proportional shares, keeping the reference whole explicit.
Geometry
Mathematics · Geometry
Geometry: read the conditions of the shape
Connect angle, length and area questions to stated geometric properties, including the perpendicular height that a base requires.
Data
Mathematics · Data summaries
Reading data: mean, median and range
Choose a summary by its definition: a shared total for the mean, an ordered position for the median, or an endpoint difference for the range.
Mathematics · Probability
Probability: list the outcomes before counting
Use the stated fairness and independence conditions to count equally likely outcomes and interpret at least one.
Units and measurement
Mathematics · Units and measurement
Changing units while keeping the quantity
Convert length, volume and area by tracking what one unit represents, including the two dimensions of a square unit.
Expressions and relationships
Mathematics · Expressions and relationships
Expressions: give the unknown a role
Read an equality, a cost expression and a proportional rule by naming what the unknown represents and checking the stated relationship.
Graphs and coordinates
Mathematics · Graphs and coordinates
Graphs and coordinates: read what each axis means
Connect an initial value, a horizontal distance section and an ordered coordinate pair to their stated axes and quantities.
Counting and intervals
Mathematics · Counting and intervals
Counting objects: groups, gaps and endpoints
Distinguish full groups from enough groups, and count positions on an open path separately from positions around a closed loop.
Probability conditions
Mathematics · Probability conditions
Probability conditions: does the next draw change?
Read replacement, distinguishable results and independence before choosing the outcome model for a probability calculation.
Science
Everyday science
Science · Everyday phenomena
Everyday science: objects, effects and conditions
Use familiar devices and temperature observations to distinguish what happens, what causes it, and the conditions of a measurement.
Forces and tools
Science · Motion and forces
Motion and forces: description before cause
Separate distance, time and changes in motion, then identify the net force relevant to the stated object.
Living things
Science · Biology
Living things: connect structures and functions
Read plant, animal and ecology questions by separating the organism, its structures, its functions and its connections to other organisms.
Weather
Science · Weather and observation
Weather observations: read the quantity and the unit
Interpret rainfall as a depth, convert a stated depth and area into volume, and connect thunderstorm phenomena with cumulonimbus clouds.
Matter
Science · Matter and substances
Matter: separate state from composition
Distinguish the shape and volume of a state of matter from the elemental composition of a pure substance.
Properties of sound
Science · Properties of sound
Sound: separate pitch, intensity and transmission
Ask what carries the vibration, which quantity relates to pitch, and which controlled change increases sound intensity.
Electricity and measurement
Science · Electricity and measurement
Electricity: a path through, or a comparison across?
Connect a metal conductor, a series ammeter and a parallel voltmeter to the different quantities the examples describe.
Counting atomic particles
Science · Atoms and particles
Atomic counts: identity, mass number and charge
Choose which particles to count when an example asks for atomic number, mass number or electrical neutrality.
Cell structures
Science · Cell structures
Cell structures: name the cell before the part
Read the basic cellular unit, a plant cell wall and the nucleus’s genetic-information role with the cell type kept explicit.
The Solar System and light
Science · The Solar System and light
The Solar System: object type, orbit and light
Distinguish what kind of object the Sun is, which planet orbits nearest to it, and why the Moon appears bright.
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