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.

er

img_3068

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.

Screen Shot 2019-10-01 at 20.16.39

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.

Screen Shot 2019-10-01 at 20.10.17

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.

Screen Shot 2019-10-01 at 20.10.26Screen Shot 2019-10-01 at 20.11.11

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

Screen Shot 2019-10-01 at 20.11.20

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.

Screen Shot 2019-10-01 at 20.12.40Screen Shot 2019-10-01 at 20.12.54

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.

EFe2VkWWkAA94xGEFe2VkUX4AEtIdk

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

image.png

image.png

Unlock the Box

I have been using these boxes for year 6 transition afternoons and they have been very successful. Students work together in groups to solve the clues to open the padlocks. Some students have a system and work through methodically. Some just sitting trying out combinations – usually getting frustrated.

The boxes are from The Works and cost £35 for 10

The hasp and lock are £1.29 from the Range

The padlocks are 2 for £1 from Poundland

I have included the tasks I have used but as the combinations can be changed, I intend to alter these.

I have also varied what goes into the box, prizes include; chocolate, certificates, more problems to solve,

Unlock The Box

Probability (A Game)

My year 8 class had spend time discussing ‘odds’ in gambling and we talked about the recent match between Spurs and Liverpool. I said the odds for Spurs to win meant that if I placed a £10 bet and Spurs won then I would receive £20 plus my £10 bet. I thought it might be a good idea to simulate a similar situation without the money.  I showed them a bag of 12 counters and 6 were red, 3 blue, 2 green and 1 yellow. Students would choose where to place 4 marks in their grid (like the one below)

Screen Shot 2018-02-27 at 17.33.09

if i pulled out a counter and they had a tally in the matching box they got those points per mark. So for example if they put a tally in each box and I pulled out a Green counter they would get 6 points but if they put two marks in green then they’d receive 12 points (2 lots of 6)

The person with the highest score after 12 tries won. We also talked about how many of each colour we would expect after 12 attempts.

I asked students to minus 48 from their score and see if it was a negative or positive. Can you think why?

They really enjoyed the task and we then had some great discussions about theory and practical and why how some students chose to place their tallies. Students used language such as ‘I put 2 in red because theres a 50:50 chance it will be red but i also placed one in yellow because although its a 1 in 12 chance but if it does come up then i’ll get 12 points.’

Once we were finished the wining students with the highest points score came up (they had 120 points) and they were allowed to place their 120 marks on the grid. I said i’d only be drawing out one counter. One boy put all points into Red straight away and the girl split hers over Yellow, Green, and Blue. I enjoyed listening to the students comments towards the two winners. I heard things like “don’t put any in Red. He put all his in Red so unless you put all yours in Red you won’t win” “It doesn’t matter how many you put in the other colours” “You have the same chance with your colours as Red”

Then I pulled out a RED counter … cue the whoops and shouts.

The girl said “I had 120 points, i should have just stopped there because now I have nothing”

 

Correcting one piece of information

I was looking at a question similar to the one below

Screen Shot 2019-05-22 at 10.27.59

I started thinking about the responses that my class had given;

Some found that Ades amount couldn’t be £15 (£10 × 1.5  = £15 and then £10 and £15 didn’t make £35)

Some used the fact ‘1.5 times more’ to show that amounts were £14 and £21

Some used the fact that if Bella had £10 and Ade had £10 × 1.5 = £15 then the total was incorrect. I started thinking about what pupils would do to ‘fix’ the error. What if the total amount was wrong? What if the ‘1.5’ was wrong? What if Bella’s amount was wrong?

Screen Shot 2019-05-22 at 10.28.07

Correct one Piece of Information

Halfway Fractions

Year 11 have been looking at a variety of Paper 1 (non calculator) questions ahead of their exam on Tuesday. One question seemed to be challenging for the students in my class. They were given a number line from 0 to 2 marked at every quarter and they were to find the FRACTION that was halfway between two given fractions. Here is a sample of the answers year 11 gave. This is a foundation class but targets of 4s and 5s.

IMG_4342IMG_4341IMG_4340IMG_4339

Most if not all of the students converted the fractions to decimals and then subtracted the two decimals but then struggled to halve 0.75.

I spent some time with a small group of students and we looked at splitting the scale further and in doing so the students spotted an easier way to find the half way point. What I found interesting was that students didn’t see that the halfway fraction between 1/2 and 1  1/4 was the same as the halfway fraction between 3/4 and 1.

It made me think about finding the numbers in the middle of these pairs of numbers

8 and 10

7 and 11

5 and 13

1.5 and 16.5

I made the following for the next lesson and I wonder if students can make the connections between the 3 questions

Screen Shot 2019-05-16 at 22.50.11

 

decimals-fractions.pptx