Mathematics
Advanced
50 mins
Teacher/Student led
+110 XP
What you need:
IWB/Projector/Large Screen

Location and Transformation Investigation

Design symmetrical patterns using flips and slides on a grid, record grid references before and after each move, and describe transformations so others can recreate them.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedI have a tile design on the grid. It was built by flipping and sliding one small shape, and it has a mirror line down the middle.

    Which moves do you think made it: flips, slides, or turns? And where on the grid do you think each piece sits?

    2 - Watch and Notice ~8 mins

    Two boards, and they belong together.

    First, a symmetrical design. Each shaded square on the left has a matching square the same distance on the other side of the mirror line. Symmetry tells you where the partner square is.

    Now three points on the co-ordinate grid. We read each one across first, then up, and write it as (across, up). A grid reference is how you name a square.

    Key point Today we need both at once. To flip a point across a mirror line you have to find where it lands, and then say its name so somebody else can find it too.

    3 - Find the Mirror Line ~6 mins

    Here is point A on the grid. This step is about the mirror line itself.

    First say A's grid reference out loud, across first, then up. Then find where a vertical mirror line could sit. Count how many squares A is from the line you choose, because that is the same number of squares it will land on the other side.

    Nobody is marked here. A pupil says the reference and the rest of the class agrees or corrects it out loud before we move on.

    Find the mirror line

    4 - Try It Together ~10 mins

    Our mirror line is the vertical line at 5 across, and you can see it on the grid.

    How a reflection works. Count the squares from the point to the mirror line. Count that same number of squares past the line on the other side. That is where the point lands. The up number never changes in a vertical mirror, only the across number does.

    We do these one at a time. Say the new reference aloud, across first, before the pupil at the board taps it in, and the class agrees before we start the next one:

    1. Reflect (2, 3) across the mirror line at 5 across.
    2. Slide (5, 1) three across and two up.
    3. Reflect (7, 4) across the mirror line and read its new reference.

    Reflect and slide, one at a time

    5 - Design Your Pattern in Your Copy ~4 mins

    COPYBOOK MOMENT

    Illustration for Design Your Pattern in Your CopyIn your maths copy on squared paper, design your own small symmetrical pattern on a grid. Draw a mirror line first, then shade one half and mirror it across the line.

    When your pattern is finished, label the grid reference of three of its squares, writing each one across first, then up.

    Pupil practice
    Module 8 · Symmetry, Location and Transformation Shape & Space
    Lesson 99 · Location and Transformation Investigation
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