Pictograms

I have never been a fan of pictograms and felt they were an inferior way of displaying data. Students took too long drawing images and it seemed to me that a bar chart was a much neater way to display data. It wasn’t until I marked the November Resit exam that it suddenly dawned on me the potential that Pictograms had. Students could solve questions using proportional reasoning and there were some neat ways to solve the answers. On the question I marked, students had to find out the total frequency, given the key was 8 pictures. Some students tried to work out each row individually but others found out how Many shapes there were and multiplied by 8. I saw such a range of successful and less successful methods to solve the problem. From that question i made the following resource

Bearings

I like using a hexagon when looking at bearings (without or without isometric paper) plus its a topic that we teach alongside angle reasoning so students have just looked at angles in a polygon. I spend time looking at bearings that can be calculated using angles  found on parallel lines and I also look at angles that can be measured using a protractor. The purpose of this lesson is to get students correctly using the north line and clockwise to find the correct path. Heres the ppt: BearingsScreen Shot 2019-11-06 at 21.36.17

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Algebraic Fractions

I am teaching the topic: Algebraic Fractions for the first time in years. I didn’t like how I taught it before so I spent some time rethinking how I teach it. I thought that if students understand adding and subtracting fractions then the can generalise it. So I will send some time going over adding and subtracting fractions first.Screen Shot 2019-10-04 at 20.39.27

The move on to fractions involving letter notation.

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I also want students to see that the final simplified algebraic expression can be substituted and still works.

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I plan to then give the following questions:

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Mixed Attainment – Shape

We are teaching mixed attainment year 7 for the entire year (we used to teach for a half term and then set them) Its been an interesting experience. I have felt more settled because I know my class wont be swapped part way through a year and have to learn new routines and expectations. I also have to keep reminding myself that there will be pupils in the class who might struggle and because I have 24 pupils and not 8, I have to keep reminding myself that this isn’t a set 2 or 3 but a mixed attainment group. Things I have learnt so far:

Students who have prior attainment that would lead you to believe they would struggle have really excelled.

Students who have prior attainment that would lead you to believe that they can work at a faster pace have tried to prove they have the understanding but when given some questions to test their understanding they have struggled.

My first topic was Shape… Area, Perimeter, Volume and Surface Area. These were taught over many lessons but I’ve written about them below like it was a continuous lesson.

I started with discussing Perimeter and how we could measure the distance moved by the robot around a grid. They then discussed what they noticed. Everyone coped well with finding the perimeter and they discussed why the perimeters were equal.

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I didn’t want to have tiered questioning but rather have questions that all students could access but form a discussion point about how they answered the questions. I hoped to ask questions that could be answered in a variety of ways but students would learn from each other. Generally this has been the case. Students could all find the perimeter and area of the shapes above but some started to notice links and patterns and set about proving why they were linked. er2

After Perimeter we looked at Area over several lessons. We started with area of a Rectangles and compound shapes and then looked at Triangles, then looked Kites and Prallelograms, and finished with Trapezium. After spending a lesson looking at Area of Rectangles we looked at compound Area. We use the same question but split in different ways.

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When we looked at triangles we spent some time discussing the fraction shaded in each diagrams. Students came up to the front of the class and showed how they got a quarter in each image.

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After looking at the fractions of the images above we looked at the ones below. Students identified that areas and how they were able to find them using half of the rectangle or by moving shapes around.

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Then after the area of the triangle we looked at other 2D shapes in this manner.

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We were able to find the area of 2D shapes from the area of a rectangle and some students expressed this as a formula and some as a fraction of a rectangle. When we looked at the Trapezium we looked at moving pieces so it formed a rectangle. We discovered that the rectangle formed, always had a length that was the midpoint of the two parallel sides. Some students knew the formula for the area of the trapezium but liked to see how it was derived. Students came to the board to calculate questions and it was nice to see their interpretation of how to find the area.

After we had spent time on the 2D shapes we moved to 3D and looked at Volume. Students used centimetre cubes to find the volume of prisms. We shared answers and discussed multiple methods. We discovered that cuboids had 3 different approaches. you could find the number of cubes from any one of its 3 unique cross-sections and then count the ‘layers’ of the cross-section. This helped the move to cuboids-without-cubes-to-count a lot easier. Students were keen to show me that they could still find the volume in several ways but sometimes there was an ‘easier’ way. EG: Find 25 times 4 then times 7  rather than finding 7 times 25 first.

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We then had a lesson that I knew was going to be shortened so we used sticks and had a go at building 3D shapes – in particular prisms. I thought that we could use this to see the number of faces and see the cross section of the prisms we built. The next step is Surface Area and I’m looking forward to looking at nets of prisms.

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Dividing and Multiplying Decimals

I think some students look at questions involving decimals with fear. It sometimes feels that they haven’t realised that the rules of multiplication of whole numbers are the same when dealing with decimals.

With division, it surprises me when students can deal with a fraction that has a decimal because they can create an equivalent fraction that has whole numbers but if its written with an obelus they start working with long division.

Anyway, heres a few questions i’m using in class to practice multiplying and dividing decimals.

Dividing Decimals

Multiplying Decimals

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