The Concept of Equals

This is always a favourite lesson of mine. I love listening and observing students inquire into and displaying their understanding of what equals means.

A formative assessment from the previous lesson told me that most students has misconceptions about the meaning of equals.

"It means total"

"It is the answer"

"It's the amount"

One student said, "it means the same". I followed on with this.

I read the wonderful book, Equal Shmequal by Virginia Kroll

At one point in the story at little turtle asks, "What does equals mean?"

I stopped their and then asked them to show me their understanding of, what it "means"?

I got out scales, fraction prices, cubes, corks, clocks, dominoes and white boards to see if students could make the connection that equals can be used not just in an equation.

After giving students a chance to show me their thinking many started to gain an understanding that equals means the same as.

I then did a number talk using this equation:

1+1+1= 2+1

I asked them to prove it and reflect on why it was true or false.

Here are some of their reflections

Lessons like this prove to me the value of inquiry maths and inquiry in general. In the past I would have just assumed that this concept was known. Students understanding in maths is much more important than simply solving problems and so much more fun as well.

Fractions and Play

I found myself planning another pizza fraction problem when it dawned on me that kids don't just eat pizza. Fractions play a part in many different aspects of our lives. So instead of coming up with another pizza or biscuit sharing activity, I decided to bring in water with cups and bottles, different fake foods, paper, lego, and blocks and let the kids explore.

I asked my students to show me their understanding of 'a whole'.

I wanted them to show me different examples of 'a whole'. e.g A whole piece of paper, a whole bunch of bananas, a whole cup of water.

I also asked them to show me how different parts can make a whole. 1/2 + 1/2 = 1 whole, 5 bananas make the whole bunch, 5 cups of water fill the whole water bottle etc.

I basically wanted them to show me their understanding of the central idea.

Fractions are a ways of representing whole-part relationships.

Students playing with making different fraction amounts.

Cutting up a whole piece of paper into different parts.

Creating a whole soccer team, two whole teams, half of the field, talking about half time.

Students playing with creating a whole box of bagels, making a whole ham burger, a whole much of bananas.

What fraction of the food is meat?

Creating different fraction amount with cups of water. 

This student was showing me that 1/2 + 1/2 = 1 whole. She then asked what if we use 'x' (multiplication)? This really intrigued her and she went to ask another student.  He shrugged! I wrote this on the board to reflect on in our next lesson. A hard concept to understand (I must admit I had to google it!), but it reinforces what can happen when you let kids inquire and explore in maths.

Using Key Concepts at Inquiry Stations

Using key concepts to drive my stations or areas or rotations (whatever you call them) was a great way to let kids explore shapes through different lens.

I don't know why, but I don't do this as nearly enough as I should. Using key concepts makes me think about things differently and allows me to come up with ideas that I normally wouldn't have thought of.

FORM: What shapes can you make from other shapes? What will that look like?

Students discovered that you can make a trapezoid using 3 triangles and you can then combine 2 trapezoids to make a hexagon!

REFLECTION: We had already explored properties of triangles. I used this station and the concept of reflection to get kids to think about what they have learnt.




CHANGE: Student had to change shapes using an original shape or by combining other shapes.




FUNCTION: How can I find a shape that has all these properties?