# Equivalent Expressions

Today my class looked at solving equations. I decided that we needed to review solving equations and substitution in order to work through simultaneous equations. However, when we looked at the equation:

7 – 2x = 9

The issue students had with this question was that they wanted to add 7 to balance the equation because they believed that the sign was part of the 7. We had to stop and look at what 7 – 2x meant and how it also meant – 2x+7.

They weren’t convinced initially and they are an excellent class to teach. They share their ideas continuously and aren’t afraid of getting things wrong. I felt like each time I uncovered an issue, I was faced with another. We spent time looking at equivalent calculations than solving equations.

The class are in year 10 and they are a set 2 of 4, yet they seemed surprised that – 4 + 5 = 5 – 4

So for the next lesson we will be looking at the following questions

# Divisibility

I was playing SET with my family (the object of the game is to get 3 cards for a set and the person with the most cards at the end win)

At the end of the game, we counted our cards and I said to one person “you have miscounted” They looked puzzled but checked and was surprised to learn that I was correct. I thought it would make an interesting question in class. I changed the original numbers. I then thought it might make a good starting point for a discussion on divisibility of 3. I then started thinking of other questions that relied on the divisibility of 3.

# Ratio

Colleagues in my dept have been looking at Ratio with year 10 and in particular, questions involving ratio that change when one quantity is shifted.

EG:

Ali and Bo share money in the ratio 7 : 5. Ali gives £24 to Bo and the ratio of their amounts is now 1 : 2. How much did they each have to start with?

I was thinking about how it can be linked to fractions that are shaded. When we want to compare fractions we can create common denominators and when we want to compare ratios we scale the ratios so they have the same number of parts… 3 : 2 has 2 parts and 7 : 8 has 15 parts. If we multiply 3 : 2 by 3 then we have a ratio 9 : 6.

# Area (Equal – Pythagorean Triples)

I have been looking at Pythagoras with year 11 and also looking at Pythagoras in context questions. When we looked at question with a Pythagorean triple, I drew an square with length 5cm with a square of length 4cm cut away, next to it I drew a square with length 3cm. We discussed why the two shapes equalled. This left me thinking about other shapes with equal areas.

# Vectors

Starting out with Vectors with one of my year 11 classes. I thought I’d start with co-ordinates and looking at the distance between them. Then discuss vectors and how they differ from co-ordinates.

# Tessellation

I have used geometer sketch pad for a number of years to create tessellations. I made this about 10 years ago and I still use it now

# Lowest Common Multiple

Lowest Common Multiple

I have been looking at questions that involve multiples and LCM

I will add more when I get a chance to add the ones I’ve been compiling.    # Squares

I have been looking over this old image I made back in 2016. I wanted to look at different ways of viewing square numbers. The image at the top right is one of my favourite and I first saw it on the nrich website: https://nrich.maths.org/2275 Squares

It led me to think about the difference of two consecutive squares and the questions below. # Area and Perimeter of 2D Shapes

I have been playing around with some ideas and questions on Area and Perimeter. I was looking at the changes to the perimeter when I doubled the length of one side and then looked at how it affected the area when a rectangle was enlarged. There is quite a difference in the difficulty of each question. Whilst I was looking at some of these ideas in Geogebra I thought about the idea of moving one vertex of a triangle, whilst maintaining the same area and what the possibilities were. I thought it might make an interesting question when looking at the area of a triangle. I usually start looking at the area of a triangle by using a prompt like the one below. I find it fascinating that moving one vertex of a triangle along the line parallel to the line joining the other two vertices always results in the same area.      Area and Perimeter of shape problems

Perimeter and Area of Irregular Shapes 