Investigating Quadrilaterals

This week’s maths lessons were built around one central theme: investigating quadrilaterals.

Rather than introducing shapes through diagrams and definitions, I wanted the girls to discover the shapes themselves through living maths and hands on maths activities.

They have technically covered many of these concepts before. However, I’ve noticed something important: simply seeing diagrams and being told facts doesn’t always lead to real understanding.

My girls need to touch, build, explore, and manipulate maths in order for it to truly make sense.

So our week was filled with shapes, marshmallows, magnets, play dough, and even tray bakes!

Our Maths Goals for the Week

Our objectives for the week were to:

• Discover the names and shapes of quadrilaterals
• Recognise quadrilaterals as both mathematical shapes and real-life objects
• Sort, classify, and represent data using a collection of quadrilaterals
• Understand the difference between 2D and 3D shapes
• Learn the terms cube, cuboid, and square-based pyramid
• Discover the properties of cube nets
• Design and build their own cube from a net

While the list looks ambitious, the beauty of investigating quadrilaterals is that many concepts naturally overlap and connect.

Investigating Quadrilaterals: Investigating 2D Quadrilaterals

We began with an open-ended exploration of two-dimensional shapes.

I gathered a variety of shapes in different sizes and forms and simply placed them on the table.

Before saying anything, I let the girls examine them carefully.

Then I asked:

“How could you classify these shapes?”

Because they have done classification work in science, they immediately understood the concept.

They began grouping shapes according to criteria they created themselves.

This simple exercise encouraged them to truly observe the properties of shapes, rather than simply recognising them by name.

Discovering Mathematical Language

After grouping the shapes, I asked the girls to name each category they had created.

The purpose was to help them see that mathematical vocabulary is often logical, frequently drawing from Latin or Greek roots.

We looked at the structure of words such as:

• triangle
• rectangle
• polygon

Once we gathered all the quadrilaterals together, I asked them a fun question:

“If you could name these shapes, what would you call them?”

Their answer?

“Cuatrangles.”

They explained their reasoning perfectly:

• Cuatr- from their Spanish knowledge of the number four (cuatro)
• -angles because the shapes have four angles

I was quite impressed with their reasoning!

Things became slightly less sensible when they started inventing names for the individual shapes but the creativity was wonderful.

Finally, I introduced the actual mathematical names using matching cards.

The girls repeated the matching activity each day to reinforce the terminology.

Building Shapes with Food

Each day I told a short mathematical story.

The girls were given toothpicks and marshmallows and asked to build the shape described in the story.

If they could correctly name the quadrilateral, they could eat it.

I would like to note an important educational observation:

The brain works significantly better when food is involved.

Naturally, their older brother T11 insisted on participating whenever marshmallows were present!

Elastic Band Geometry

Another favourite activity involved elastic bands and a pin board.

The girls stretched elastic bands to create different quadrilaterals.

One child would build a shape while the other guessed which quadrilateral it was.

They continued until they had created every quadrilateral we had studied.

This activity was fantastic for reinforcing:

• angles
• side lengths
• visual recognition

Sorting and Graphing Quadrilaterals

Next, I gave the girls a bag filled with quadrilaterals.

Their task was to:

1. Sort the shapes
2. Count each type
3. Display their findings using a pictograph

We created the graph directly on the table using the shapes themselves.

This informal approach helped remove the pressure that sometimes comes with graphing while showing them how simple data representation can be.

Play Dough Geometry

We then moved on to play dough modelling.

The girls created squares and rectangles first.

From these, they discovered how other quadrilaterals could form through simple manipulation.

For example:

• A rhombus looked like a squashed square
• A trapezium resembled a square with a tilted top
• A parallelogram resembled a squashed rectangle
• A deltoid could be created by adjusting the sides of a square

While not perfectly mathematical explanations, these hands-on discoveries helped the shapes stick in their memory.

Mathematical Language in Everyday Life

To show how mathematical language appears outside maths lessons, we explored the names of certain muscles in the human body:

• trapezium
• rhomboid
• deltoid

The girls investigated where these muscles were located and created hypotheses about why they were given those names.

Using mathematical vocabulary in everyday conversations is something I am actively encouraging in our home.

Many exam questions are missed not because children lack understanding—but because they don’t recognise the vocabulary used.

As a result, I have now become something of a self-proclaimed mathematical bore.

Investigating Quadrilaterals: Moving Into 3D Shapes

Next we shifted our focus to 3D shapes with quadrilateral bases.

Using a set of geometric models, the girls sorted the shapes and selected those with quadrilateral bases.

I asked them to describe the difference between 2D and 3D shapes.

They correctly identified:

• 2D shapes have length and width
• 3D shapes have length, width, and depth

Investigating Quadrilaterals: Building 3D Shapes

We continued exploring shapes using:

• play dough
• magnetic construction pieces

First the girls built 2D shapes, then expanded their creations into 3D structures.

This naturally led to the creation of cubes, cuboids, and pyramids.

Investigating Quadrilaterals: Investigating Cube Nets

One of the most fascinating parts of the week involved cube nets.

I gave the girls squared paper and challenged them:

“Can you design a net that folds into a cube?”

At first, I thought this would be extremely difficult.

Instead, they began dismantling their magnetic cube models to understand how the faces connected.

From this investigation they discovered an important rule:

A cube has six square faces.

Therefore, any cube net must contain six squares.

Investigating Quadrilaterals: The Rules They Discovered

After experimenting, the girls developed several hypotheses:

• No more than four squares in a row
• The net must include a length of four squares
• The remaining two squares must appear on opposite sides
• Extra squares can appear in different positions along the row of four

They discovered six cube nets.

There are actually eleven possible cube nets, but I chose not to tell them this yet.

Next week they will continue investigating and revising their rules.

This mirrors the process used by real mathematicians:

1. Observe
2. Form hypotheses
3. Test them
4. Revise them

At this stage, there is no fear of being wrong, only excitement about discovering something new.

Investigating Quadrilaterals: Designing and Building a Cube

The following day the girls transferred their discoveries to paper.

They:

1. Selected one of their cube nets
2. Drew it on squared paper using rulers
3. Added flaps for folding
4. Cut and assembled their cube

They marked flap placements with “F” on the template before constructing the final model.

Investigating Quadrilaterals: The Most Delicious Maths Lesson Ever

Our final activity might have been the girls’ favourite.

We made rice crispy, marshmallow, and toffee tray bakes.

Once the mixture cooled, I asked them to:

• cut out different quadrilaterals
• name each one
• describe its properties

Only then could they eat it.

I have never seen children so enthusiastic about maths.

The quadrilateral tray bakes were eventually shared with the whole family, though not without considerable excitement first!

Investigating Quadrilaterals: Investigating Parallel and Intersecting Lines

During the tray bake activity the girls repeatedly used the phrase parallel lines.

This led to an interesting question:

The deltoid has no parallel lines so what are those lines called?

We explored this on the whiteboard by extending the sides of a deltoid.

The girls observed that when extended, the lines eventually meet.

From this we concluded:

Two straight lines in a 2D plane will either be:

• parallel, or
• intersecting

They even proposed a simple way to prove lines are parallel:

Extend the lines and see if they ever meet.

We left the idea of skew lines in 3D for another day.

Reflection Questions for Homeschool Parents

1. Do your children learn maths best visually, verbally, or physically?
2. How could investigating quadrilaterals deepen their understanding of shapes?
3. Do you emphasise mathematical vocabulary in everyday conversation?
4. How often do your maths lessons allow room for discovery and hypothesis?
5. Could food-based maths activities increase engagement in your homeschool?

Hands-On Maths Activities to Try

1. Shape Sorting

Provide a collection of shapes and ask children to classify them using their own criteria.

2. Marshmallow Geometry

Use marshmallows and toothpicks to build quadrilaterals.

Correctly named shapes can be eaten!

3. Elastic Band Geoboard

Create quadrilaterals using elastic bands on a geoboard.

Have children identify each shape.

4. Play Dough Transformations

Start with a square and reshape it into different quadrilaterals.

Discuss how the properties change.

5. Cube Net Investigation

Challenge children to find all the cube nets.

Encourage them to write rules and test their theories.

Final Thoughts on Investigating Quadrilaterals

This week of investigating quadrilaterals was filled with exploration, creativity, and discovery.

The girls spent over an hour and a half each day doing maths and not once did I hear a complaint.

When maths becomes hands-on, exploratory, and meaningful, children stop seeing it as a subject to complete and start seeing it as something fascinating to uncover.

And that, to me, is the true beauty of living maths.

For all of my living hands-on maths posts, click here