Symmetry Worksheets

Symmetry means that one half of a shape is the mirror image of the other half. The four PDFs on this page give children a colored half on a grid and ask them to color the matching half on the other side of the dashed line, and every sheet has an answer key. They follow standard 4.G.A.3 of the Common Core standards for grade 4 geometry, and the notes below explain mirror lines, rotational symmetry and the symmetry of letters.

Mirror, mirror

A shape is symmetrical if you can fold it along a line and both halves match. On these grids, the left half is colored and children color the right half as its mirror image. The trick: count squares out from the dashed line. A square one step left of the line needs a partner one step right of it.

Symmetry worksheets: what is in the set

There are 4 symmetry worksheets on this page, and every one has an answer key except for any cut-out games. Each set has four grids, and the left half is colored, so children color the right half as its mirror image.

Symmetry: what it means and how to test it

A shape has symmetry if it can be changed in some way and still look exactly the same. The simplest kind is line symmetry: fold the shape along a line, and if both halves match exactly, the line is a mirror line. Wikipedia’s article on symmetry explains that there are other kinds, such as turning a shape around a point. This table shows the three cases that children meet in primary school:

The worksheets on this page use line symmetry only. A small mirror is the best test, since children can put it on the dashed line and see whether the reflection matches the other half of the picture.

Line of symmetry worksheets: counting the lines

Line of symmetry worksheets ask for a shape’s lines of symmetry, and the answer depends on the shape. A regular polygon with n sides has n mirror lines, and the same number of turns that match, which is called the order of rotational symmetry. The smallest turn is 360° divided by n. This table shows five regular shapes and the circle:

Other shapes have fewer lines. This table shows seven shapes that are not regular, and compares their lines with their order of rotation:

The parallelogram is the one that surprises children. It looks symmetrical, but it has no mirror line. It does have rotational symmetry, since a half turn takes it onto itself. The 2D shapes page has all the quadrilaterals.

Mirror image worksheets: reflecting on a grid

The mirror image worksheets use a grid with a dashed line down the middle. Each colored square on the left has a partner on the right at the same distance from the line. If a square is 2 steps to the left of the line, its mirror image is 2 steps to the right, in the same row. This table shows the rule for a grid that is 10 squares wide, with columns numbered from 0:

The rule is that a square in column c is matched by a square in column 9 − c, in the same row. Children do not need the rule, since they count the squares, but it shows how reflection can be written as arithmetic. The same idea comes back in grade 6 with coordinates, in the graphing worksheets.

Complete the symmetrical picture: step by step

To complete the symmetrical picture on a worksheet, children can follow the same five steps every time. Writing them on a card helps children who rush:

1. Find the dashed line, the mirror line.
2. Pick a colored square next to the line and find its row.
3. Count how many squares it is from the line.
4. Count the same number on the other side of the line, in the same row, and color that square.
5. Do the same for every colored square, row by row, and check with a mirror.

It is easier to go row by row from the top, and to color a whole row before moving down. A child who colors from the middle outward is more likely to lose their place.

Symmetry grade 4: the 4.G.A.3 standard

For symmetry grade 4, the standard is 4.G.A.3. It asks children to recognize a line of symmetry as a line across a figure so that the figure can be folded along it into matching parts, to identify figures that have line symmetry, and to draw the lines. The standard has two parts: recognizing a mirror line, and drawing one. The worksheets on this page practice the first part, and a good follow-up is to give children a shape and ask them to draw all its lines. The Common Core standards for grade 4 geometry list the other grade 4 geometry standards, and the angles page covers the next one, 4.G.A.1.

Symmetry in letters and words

The letters of the alphabet are a good way to find mirror lines. The result depends a little on the font, but in a simple capital-letter font the sorting is as follows:

Letters with a horizontal mirror line make a famous trick. A word written only with those letters, such as BOOK, COOK, DICE, CODE, HIDE, ECHO, can be read in a mirror that is held under the line of text, because every letter reflects onto itself. Words made of letters with a vertical mirror line, such as MOM, WOW, TOT, AHA, look the same in a mirror beside them if the word also reads the same backwards. Children can try to find more of both kinds.

Symmetry in nature and design

Symmetry is everywhere, and children can look for it in nature, in flags and in signs. This table gives eight examples, with the number of mirror lines:

A butterfly has one line, and a snowflake has six. Folding paper and cutting a shape gives the same result: fold a sheet once and cut half a heart, and the unfolded heart has one mirror line. Fold it twice and the cut shape has two lines, and so on. The fractions worksheets use the same idea when they cut a shape into halves.

Common mistakes with symmetry

The most common mistake is to see a diagonal as a mirror line in a rectangle. This table shows five mistakes, what went wrong and the fix:

Symmetry word problems

Symmetry questions come up in art, signs and letters. Ask children to draw the shape and the lines, and to check with a fold:

Games and activities for mirror reflection

Children learn mirror reflection best when they play with it. These games use things that are found at home or in a classroom:

• Paper cutting: fold a sheet of paper, cut a shape from the folded edge, and unfold it
• Mirror writing: write a word with a mirror next to it, and see what changes
• Ink blots: put paint on one half of a folded sheet, press, and open it to see the symmetrical pattern
• Pattern blocks: build a symmetrical design on one side of a line, and ask a friend to complete the other side
• Symmetry hunt: look for symmetrical objects in the room: a chair, a book, a door
• Geoboard reflections: make a shape on one side of a rubber band and its reflection on the other

Extra support and extra challenge with mirror reflection

For children who need more support: start with a folded paper and a small mirror, and use simple pictures with few squares. Count the squares from the line with a finger. Color one row at a time, and check each row with the mirror. Do the first set only, with the answer key, before moving on.

For children who need more challenge: ask for the mirror lines of a regular hexagon, for a shape with exactly two lines, and for a design that has both line and rotational symmetry. A grid with a diagonal mirror line is also a good challenge.

How to tell that a child is ready to move on from mirror reflection

1. The child finds a mirror line by folding.
2. The child colors the mirror image of a picture on a grid.
3. The child counts the mirror lines in a square and a rectangle.
4. The child says when a shape has no mirror line.

When all four are true, move on to the angles page.

A 20-minute lesson on mirror reflection

A short lesson is the best way to introduce mirror reflection. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where mirror reflection fits across the grades

No skill stands alone. This table shows what children learn before and after mirror reflection, with the standard that goes with each step:

This page is part of the geometry sequence. The whole sequence is on the geometry worksheets page.

Helping at home with mirror reflection

Parents do not need to be experts to help with mirror reflection. These suggestions work well, and each takes only a few minutes:

• Fold a napkin in half and look for symmetry in the pattern.
• Look for mirror lines in leaves, flowers and flags.
• Use a small mirror on a picture to check the answer.
• Ask the child to draw half a butterfly and to complete it.
• Praise the child who counts squares from the line.

How to check progress in mirror reflection

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for mirror reflection

Most children need about a week of short sessions for mirror reflection. This plan follows the order of the worksheets on this page:

When the plan is complete, move on to the angles page. The whole sequence is on the geometry worksheets page.