Friday
Friday: Patterns Everywhere
Rocket holds a sheet of wrapping paper up to the light. "The same leaf, over and over. Slides."
"And the tiles by the sink," Raven says. "Each one is the one beside it, flipped. What do you notice about the letters b and d?"
"A flip!" Rocket says. "And p is b turned a half turn. The alphabet is full of moves."
Nova hovers over the floor grid, her light flicking from tile to tile. "Your floor pattern is a sequence of moves," she says.
"Slide, flip, slide, flip," Rocket says, laying L-tiles in a row. "They fit without gaps."
Raven checks the corners. "Congruent tiles, every one." Nova hums. "Review today. Tomorrow you lay the floor."
Moves in everyday places
| Where | Move | Why |
|---|---|---|
| a repeating wallpaper pattern | translation | the same shape slides along the wall |
| the letters b and d | reflection | one is the mirror image of the other |
| the letters b and q | rotation | a half turn takes one to the other |
| a row of floor tiles | translation and reflection | each tile slides or flips onto the next |
| a spinning pinwheel | rotation | every blade turns about the center pin |
Every one of these keeps the shape the same size with the same angles. That is why the tiles fit and the pattern repeats.
The week in five lines
- Translation slides: (x + a, y + b). Reflection flips: (x, -y) across the x-axis, (-x, y) across the y-axis.
- Rotation turns: a quarter turn counterclockwise about the origin is (-y, x). A half turn is (-x, -y).
- Every move keeps lengths, angles and parallel sides the same.
- The image is congruent to the original.
- Two figures are congruent when a sequence of moves lands one on the other.
- Read the question.
- Tap your answer.
Which move takes the gold figure to the blue figure?
Which move takes the gold figure to the blue figure?
Which move takes the gold figure to the blue figure?- Read the question.
- Tap your answer.
| Week review | True or false? |
|---|---|
| A translation keeps every length the same. | ? |
| A reflection across the x-axis changes the sign of y. | ? |
| A rotation changes the angles of a shape. | ? |
| Two congruent tiles cover the same area. | ? |
| A slide can turn the L to face the other way. | ? |
- ?We wrote a coordinate rule for each move.
- ?We read Raven's tile log and used two moves in a row to show congruence.
- ?We measured the L-tile before and after each move in Build Lab, and nothing changed but position.
- ?We named three moves: slide, flip and turn, and found where corners land.
Write two letters that are flips of each other, and two that are turns.
Slides, flips and turns are everywhere. Tomorrow is Build Day: the clubhouse floor gets its pattern.