Creating a 2D Shape Unit
It was great to work on a 2D shape unit with the teachers at Morphett Vale East Primary School this week. I am particularly impressed by the way they have moved well beyond a reliance on worksheets.
We did not begin by looking at the Australian Curriculum. Yes, we did come to it after sharing our initial ideas, to ensure we were on track.
It is my belief that a Shape Unit, no matter what the age, should not start with nouns (names of shapes, etc) and adjectives (properties etc). This will inevitably lead to teaching only those things and likely ending up with boring worksheet pages that have students colouring the triangles green or mindlessly and pointlessly filling in a properties shape table.
OMG, I did that when I was at school a hundred years ago!
We started with action verbs that relate 2D shape to what we do in the real world.
As a sewer (pronounce that sower, please), I fold, cut, join, manipulate and transform shapes to create garments. Graphic designers visualize how to place shapes in a design for best effect. Landscape gardeners reduce trees, shrubs, garden beds into their simplest forms as they design.
The following list of verbs that we created is not definitive but is a starting point to get the cogs whirring.
- visualize (most important)
- fold, join, cut, take apart, put back together, draw, (diagram or plan)
- rotate, flip, turn, slide, stretch,
- predict, prove, justify, check, experiment, describe, explain
None of the above are likely to happen on a worksheet. Students have to be hands-on, doing stuff for the active verbs to become reality.
Leading on from my last blog, is our play with a simple square piece of paper.
A warning here; have extra pieces available because many students have had limited experience with folding and cutting (not just the littlies).
For all ages , Step 1 is to fold the square askew similar to the one shown below.
Depending on skill level and development, students are asked questions such as:
- “How many shapes will you see when you open it up?”
- “Will the shapes be identical, congruent, symmetrical?”
- “Do you expect to see any 3, 4, 5 sided figures?”
- “Can you draw the shapes before you open up and have a peek?”
Step 2 is to fold through the fold and fold again so that they now have something that looks a bit like this:
Questions like the previous ones are asked again, before opening up the piece of paper to check.
Many students do not have the vocabulary to talk about and name the shapes that they see. This is a great opportunity to introduce terms such as polygons, quadrilaterals, irregular shapes, regular shapes and, as happened yesterday, heptagon or octagon.
It is surprising how many students, even in the upper grades, think that an irregular shape is ‘not a shape’ or that cannot recognize and name an irregular shape such as this.
What to do with the piece of paper (all grades)
Cut along the folds, shuffle up the pieces and turn some over. Challenge the students with: “Now put the shape back together.”
Some students actually say it can’t be put back together because … “it’s different now.”
Some students do not think about finding those corners that were the right angles that made the square. Some students will be really quick, and some will struggle because they do not visualise flips and turns. Some do not think about flipping a piece over even though they have seen some being flipped.
It’s also fun to use the pieces to make something that looks a bit like a house or a boat by visualising, rotating, turning and joining pieces.
It’s even more fun to combine with a friend and repeat the steps. Throughout this phase, using the language of shape, properties and transformations is of the essence. For instance:
- “This triangle looks like a roof.”
- “If we flip this over and rotate it, it will make a garage on the side.”
- “Now we’ve joined these two pieces we have a pentagon that looks like a house.”
For older students
Let’s investigate and conjecture. Students can explore:
- What shapes can be made with 2/3/4 folds (predict, reason, test and make conjectures such as “It won’t be possible to make 4 completely different shapes.” Or “The only fold that will lead to symmetry is an accurate fold in half first.”
- Which angles are most common when they unfold, e. g. right angles, acute angles, obtuse angles, even reflex angles.
- The sum of the internal angles and whether that will always be the same.
- Whether they can fold so that when they open up their square they will see, adjacent/opposite/vertically opposite or complementary angles.
- What new shapes can be found by joining the cut-up pieces along different edges. We found 11 sides to be quite common and enjoyed playing with the word hendecagon, an 11-sided figure.
We tracked back from this activity and found every one of the verbs had been applied. We also checked against the Australian Curriculum and found that we had ‘excelled’!
No doubt you can think of other ideas – we ran out of time.
Want to learn more with us? Building Multiplicative Thinking, Early Subtraction and other digital products are available on our website.