He rārangi kupu e pā ana ki ēnei peka o roto i te wānanga pāngarau.
A vocabulary list relationg to these aspects of mathematical understanding.
latitude (takenga mai: aho – line; pae – horizontal)
longitude (takenga mai: aho - line; pou [poutū] - vertical)
direction, bearing, orientation, directed toward (kupu kē atu: anga, aro ~nga)
orientation
geometry
transformation geometry
invariant property (takenga mai: āhuatanga – property; pūmau – fixed, constant, permanent)
direct route (kupu kē atu: ahunga ā-manu)
scale (takenga mai: arawhata – ladder)
ratio scale
line scale
statement scale
orienteering (takenga mai: awhe – go, travel; ara – path; rau - hundred, many)
approximate
perpendicular, at right angles (takenga mai: hāngai – across, at right angles, astride)
hangarite Tūingoa, Tūmahi Poro, Tūāhua
symmetrical, symmetry (takenga mai: hanga – shape; rite – alike, corresponding)
rotational symmetry
line symmetry, reflective symmetry
diagonal
irregular, asymmetric (takenga mai: hikuwaru – crooked, asymmetrical)
hoahoa ~ina Tūingoa, Tūmahi Whiti
diagram (takenga mai: hoahoa – plan of a house)
floor plan
scale drawing, scale diagram
isometric diagram
locus (takenga mai: huanui – path, pathway)
horizontal (kupu kē atu: pae, whakapae)
huri ~hia ~hanga Tūingoa, Tūmahi Whiti
rotate, rotation, turn
half-turn (180˚)
quarter-turn (90˚)
inverse rotation
overlap
isometric (takenga mai: ine – measure; rite - alike, corresponding)
compass (direction)
clock, o'clock (takenga mai: He kupu mino.) (kupu kē atu: matawā)
analogue clock
kauhuri ~a ~nga Tūingoa, Tūmahi Poro
flip (kupu kē atu: huripoki)
inverse
anticlockwise
angle
whole angle, full turn (360˚)
angle of elevation
angle of depression
corner (kupu kē atu: akitu)
globe (takenga mai: mahere - map; ao - world; porotaka - round [shape])
scale map
road map
interactive map
object (before transformation) (takenga mai: mātā [mātāniho] – print or mark of teeth; oroko – for the first time)
matapae ~hia Tūingoa, Tūmahi Whiti
predict, prediction
image (takenga mai: mātā [mātāniho] – print or mark of teeth; tuhi – draw, write) (kupu kē atu: otinga)
rotated image (kupu kē atu: otinga hurihanga)
translated image (kupu kē atu: otinga nekehanga)
reflected image, mirror image (kupu kē atu: otinga whakaatanga)
space, spatial
neke ~hia ~hanga Tūingoa, Tūmahi Whiti
translate, translation, move (kupu kē atu: nuku)
equal, congruent (tohu: =)
similar (shape)
answer, product, quotient, result, solution (takenga mai: oti – finished, completed) (kupu kē atu: hua)
proportional relationship (tohu: 
) (takenga mai: pānga - relationship; pā - relate to, to be connected with; riterite - be alike, regular)
peg board (takenga mai: board, surface; kōputaputa – pitted, full of holes)
co-ordinate plane
geoboard (takenga mai: papa – board; tīrau – peg, stick)
grid paper
vector
vertical (kupu kē atu: pou, poupou)
centre (kupu kē atu: pokapū)
centre of rotation
centre of enlargement
invariant, fixed, constant
pūtahi ~tanga Tūingoa, Tūmahi Poro
intersect, intersection (takenga mai: pūtahi – join, meet)
degree (angle and temperature) (tohu: º) (takenga mai: putu - lie one upon another) (kupu kē atu: tākiri [kupu mino])
midpoint (of a line segment) (takenga mai: pū [pūwāhi] – point; waenga – the middle, midst)
collinear points
north (kupu kē atu: tokerau)
perpendicular line
line of symmetry
vertical line
concurrent lines, intersecting lines
mirror line (kupu kē atu: paeata)
parallel line
below, bottom, under
west (kupu kē atu: uru)
resource, learning materials
digital resource (takenga mai: rauemi – resource; mati – digit; hiko [tāhiko] – electronic)
transformation sequence
strategy (takenga mai: rau [rauhanga] – cunning, resourceful; taki – lead, bring along)
east (kupu kē atu: waho)
north-east
south-east
similar (in proportion)
regular (shape) (kupu kē atu: ōrite)
length, long
rōpinepine Tūingoa, Tūmahi Poro
tesselate, tessellation, tiling, mosiac (takenga mai: rōpine – place close together)
inside
south (kupu kē atu: tonga)
compass (for drawing circles) (takenga mai: tā –to draw; porowhita – circle) (kupu kē atu: taputapu tuhi porowhita)
apparatus, device, equipment, instrument, tool
close (near) (kupu kē atu: pātata)
order of symmetry
opposite (kupu kē atu: anganui)
concrete model (takenga mai: ōkiko - physical; ō - pertaining to; kiko - body, substance)
mathematical model
co-ordinate, position (takenga mai: taunga – resting place, anchorage) (kupu kē atu: takotoranga)
polar coordinates (takenga mai: taunga – position; ahu – direction; roa – length)
Cartesian coordinates (takenga mai: taunga – position; tukutuku – grid)
scale factor for enlargement (takenga mai: tau – number; rahi – size) (kupu kē atu: tau whakarahi)
distant, distance (kupu kē atu: mamao)
altitude, height, high, tall (kupu kē atu: tāroaroa [of a person], tiketike)
limit of accuracy (takenga mai: tepe – boundary, limit; tika – correct)
accurate, correct, valid (kupu kē atu: tōtika)
method, technique, convention, meaning
tirohanga (mai i te taha) matau Tūingoa
right side view
tirohanga (mai i te taha) mauī Tūingoa
left side view
front view
tirohanga (mai i) muri Tūingoa
rear view
tirohanga (mai i) raro Tūingoa
bottom view
tirohanga (mai i) runga Tūmahi Whiti
plan view (kupu kē atu: tirohanga ā-manu, hoahoa ā-manu)
north (kupu kē atu: raki)
south (kupu kē atu: runga)
zoom (takenga mai: topa - to soar, swoop,)
axis (takenga mai: tuaka – midrib of a leaf)
axis of symmetry
grid
isometric grid
identity (takenga mai: tūmau – fixed, constant)
west (kupu kē atu: rātō)
north-west
south-west
east (kupu kē atu: rāwhiti)
representation
whakaata ~tia ~nga Tūingoa, Tūmahi Whiti, Tūāhua
reflect, reflection, mirror
glide reflection
to plan or map
forward
backward
whakarahi ~a ~nga Tūingoa, Tūmahi Whiti, Tūāhua
enlarge, enlargement (kupu kē atu: whakanui ~a)
parallel (takenga mai: whakarara – mark in parallel lines)
extend, lengthen
clockwise (kupu kē atu: ā-karaka)