See the math move
Small tools that show what a number is doing. Drag a line and watch its slope, open an angle past a square corner, split a fraction bar, bend a shape until it becomes a square. Then try the same idea on paper.
Angles and shapes
Angle ExplorerOpen an angle past a square corner and watch its name change.acute, right, and obtuse angles
Quadrilateral ShapesDrag four corners into a square, rectangle, trapezoid or kite — and watch the angles always add to 360°.naming quadrilaterals and their 360° angle sum
Angles in a TrianglePick two corners of a triangle — the third is not yours to choose, and the three make 180°.two angles decide the third
Angles in Parallel LinesTurn a line across two parallel ones — eight angles, two numbers, and one pair locked together.corresponding and alternate angles need the lines to be parallel
Lines of SymmetryTurn a mirror across a shape until the reflection comes home. Most lines miss, and some shapes have no line at all.a fold that lands one half on the other — and a parallelogram has none
Slide, Turn, FlipSlide, turn or flip a shape on a grid — follow one corner's coordinates while every side and angle stays put.a move changes where a shape is, not what it is
What Stays The Same?Swing one arm and watch both angles run through every value they can take — the total sits there not moving, which is the whole of why knowing one tells you the other.two angles at a point move in opposite directions while their total refuses to change
Area and size
Pythagoras ExplorerPut a square on each side of a right triangle and see the two small ones fill the big one.why a² + b² = c²
Area & PerimeterCount the squares inside and trace the border — two different measurements of one rectangle.area is not the same as perimeter
Triangle AreaSlide the top corner sideways and watch the area stay exactly where it was.a triangle's area needs only base and height
Why Pi?Unroll a circle and lay its own width along it — three fit, and a bit, at every size.the way round is always 3.14 diameters
Inside and Outside a BoxResize a box and watch what it holds and what it takes to wrap — three boxes hold eight cubes and need three different skins.volume and surface area are two measurements that do not keep step
Fractions
Fraction BarSplit a bar and shade some — see the same amount as a fraction, a point, a decimal and a percent.equivalent fractions
Which Fraction is Bigger?Two bars the same length, one half already marked, and a button that cuts both into the same pieces without moving either amount.a bigger bottom number makes a smaller piece, not a bigger fraction
One Place, Several NamesPut a dot on a line from 0 to 1, then cut the line a different number of ways — the dot does not move, and that is all an equivalent fraction is.a fraction is a place on a number line, and the same place has several names
Numbers and proportion
Rounding on a LineSlide a number between two tens and watch the two distances — the shorter one is the answer, and halfway is an agreement.rounding is which mark the number is nearer
Jumps on a Number LineAdd and take away negative numbers as one jump — including 8 − (−3), the case no worksheet can print.the signs decide which way the jump faces
Percent of What?Put 20% on and take 20% off — the bars show why that does not bring you back to where you started.a percent is a share of whatever it is standing next to
The Point Never MovesMultiply and divide by ten on a place-value chart — the digits change columns and the point stays exactly where it was.multiplying by ten moves the digits, not the point
Which Numbers Make A Rectangle?Pull a block of squares wider and narrower — the widths that fill without a hole are the factors, and 15 turns out to make a perfectly good rectangle.a factor is a width that fills without a gap, and a prime has none but the line
Two Lines That Move TogetherOne slider through two number lines at once — 8 : 12 turns out to be the same place as 2 : 3, four steps along, with neither number ever gaining on the other.a ratio is what stays true while both quantities change, not a pair of numbers
Why Four Numbers?Pull the edges of a rectangle cut at each ten — the four patches are exactly the four numbers the written method has you find, and the big one is most of the answer.the numbers long multiplication makes you add are patches of one rectangle
Graphs and data
Slope ExplorerDrag two points and watch the line's steepness — rise, run, and the equation — change together.slope as rise over run
Mean and MedianSlide one number away from the rest — the balance point chases it, the middle one stays.one far-off value moves the mean and not the median
Throw It A Hundred TimesFlip a coin or roll a 4, 6 or 8-sided die as many times as you like — every face creeps toward its fair share, and ten throws is nowhere near enough to see it.a chance predicts the long run, not the next spin
Distance Between PointsMove two points on a grid and watch the triangle draw itself — one leg across, one up, and the line between them.the right triangle hiding between any two points
Everyday measures
Reading a RulerSlide a pencil along a ruler — the number at its end moves, and its length does not.the end number is the length only from zero
Coins and AmountsBuild fifty cents out of two coins or out of ten — the pile changes and the total does not.the same amount can be made of different coins
How Long From Then To Now?Drag the minute hand round a clock and watch the hour hand travel with it — then see the same interval laid out flat, with the o'clock you crossed marked on it.the hour hand moves the whole time, and that is where the hour is carried
29 tools. Each one ends at the worksheets for the same idea.