Angles in Parallel Lines

After I introduce angles in parallel lines to my class and discuss the correct reasoning. I want to show them lots of different examples and non examples so they are confident in recognising alternate, co-interior, corresponding and opposite angles, whilst still noticing basic angle facts.

After we have spent time doing this I want to look at these questions

Surds

I have been thinking about some further connections between area and surds. I started this thinking a few years back after a discussion with https://twitter.com/Arithmaticks

I wanted to look at some shapes where the lengths were roots

I have also been trying to connect surds and prime factor decomposition. Especially since we’re looking for square number factors that are easily identified once the number is in prime factor form.

Quadratic Graphs

I’m teaching year 11 foundation classes this year and we are looking at quadratic graphs and we’ve previously looked at sequences. We have discussed some of the things they will need to be able to do well to be able to plot the graphs and I want them to see connections with the equations and the graphs such as translations of graphs. We did a lot of discussion about the difference between linear and quadratic sequences and then we looked at plotting linear graphs and the links between the sequence, the y-co-ordinate and the same with quadratic sequences. We also reviewed what we knew about negative numbers, order of operations and substitution.

Angles on a Straight line

I want to make sure I don’t rush the “angles on a straight line” fact and ensure I cover questions where students have to reason as well as find missing angles. I also want to give students exposure to questions where more than one point is marked on a line and students have to find missing angles around those points.

Laws of Arithmetic

I love playing countdown with my classes every now and then. Generally I give students longer than they would get in the real game and encourage them to think about different ways to get close to a number using fewer numbers so they can then hit the target number by using the remaining numbers.

EG: if they have a target of 836 and they have the numbers: 8, 50, 2, 4, 3, 1

Rather than finding 8 times 50 times 2 then trying to make 36 from 1, 3, 4

See if they can find 836 by doing 8 times (50 times 2 add 4) this way we reach 832

Students thought this was clever but they weren’t comfortable doing it in practice so I thought I’d give them a different task. I slimmed down the numbers and added more targets. I want to see how many they can make.

Linear Graphs

I have been working through linear sequences and the next topic is graphs. It was perfect next step and it allows students to see the sequence increases on a graph. I have often used Boat Hire when first looking at graphs. It’s a fantastic lesson taken from a sequences of lesson featured in ICCAMS Students make sense of the information, rather than plotting an arbitrary equation. Two options of hiring a boat are posed; one is a lower hourly cost but higher initial cost and the other boat company is the opposite way round (higher hourly cost, lower initial cost) Students look at the situation where two choices are posed and are invited to decide which is better. There isn’t a definitive answer because the “better” options is dependant on how many hours you hire the boat for. so this lends itself well to plotting the information on a graph.

The group I’m teaching linear graphs at the moment is in year 11 and we’ve just looked at linear sequences, looked at Boat Hire and now seem comfortable with plotting equations. My next step is for the class to spot parallel and perpendicular lines and what that means for the gradient. I want them to see what happens to the line when the gradient is a larger value and also link it back to linear sequences.

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.