Primary 4 maths · Geometry · About 10 minutes
Complete symmetric figures on a grid
Compare corresponding points and distances, rather than just the overall outline.
Start the interactive lesson →Open practice activity
What you will learn
- Complete symmetric figures on a grid
Models used: number sentences, stories, diagrams.
Before you start
Fold it onto its partner
The dotted line is a mirror. This blue point is 3 squares to its left.
The dotted line is the fold. Matching points must be equally far from it.
The dotted line is a mirror. This blue point is 3 squares to its left.
Matching points lie the same perpendicular distance from the mirror, on opposite sides.
Left 3 units · right 1 units
The dotted line is the fold. Matching points must be equally far from it.
The orange point is too close. Move it until both points are equally far from the mirror.
Left 3 units · right 2 units
The dotted line is the fold. Matching points must be equally far from it.
Now both points are 3 squares away. Folding on the mirror line would make them meet.
Left 3 units · right 3 units
What did the picture help us see?
Now both points are 3 squares away. Folding on the mirror line would make them meet.
Worked example: A new example, together
A point is 5 grid squares to the left of a vertical mirror line. How many squares to its right is the reflected point?
Left 5 units · right 5 units
The dotted line is the fold. Matching points must be equally far from it.
Compare corresponding points and distances, rather than just the overall outline.
Reflection preserves distance at a right angle to the mirror line.
Left 5 units · right 5 units
The dotted line is the fold. Matching points must be equally far from it.
Move perpendicular to the mirror line.
Left 5 units · right 5 units
A point is 5 grid squares to the left of a vertical mirror line. How many squares to its right is the reflected point?
5 squares
The dotted line is the fold. Matching points must be equally far from it.
Move perpendicular to the mirror line.
Left 5 units · right 5 units
The dotted line is the fold. Matching points must be equally far from it.
Keep the same distance on the opposite side.
Left 5 units · right 5 units
The dotted line is the fold. Matching points must be equally far from it.
The reflected point is 5 squares to the right.
Left 5 units · right 5 units
The dotted line is the fold. Matching points must be equally far from it.
Check the result against the question we started with.
Both points are 5 units from the same mirror line.
We found 5 squares. Reflection preserves distance at a right angle to the mirror line.
Left 5 units · right 5 units
Common mistakes to discuss
- Copying across instead of reflecting. Each point of a reflection sits the same distance from the mirror line, on the opposite side.
Check your understanding
- Complete symmetric figures on a grid
- justify symmetry by matching points across a mirror
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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