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.
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
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)
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”
I was looking at a question similar to the one below
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?
Correct one Piece of Information
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.
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
Order of Operations
I have used an ‘insert the brackets’ type question before but find students can sometimes just wait for the answer to just jump out at them rather than trying to fit in brackets to make the answer work (even if its on a trial an error basis). I like using the same expression so students are more inclined to try a few ideas. After using a similar question to the one below, one of my year 7 class said he had found some answers that weren’t in the cloud so i thought it might be nicer to give them an expression and ask them to find as many different answers as they could by inserting brackets.
I have been looking at Rotational Symmetry with year 7 and I was surprised at how much my high attaining students struggled with describing the symmetry of a given shape.
I created a task where students had to colour blue and red squares so that the rotational symmetry was either order 4 or 2. Students started with the grid of 3 by 3 and they completed that task but we talked about why some were possible and other weren’t and how you could know. Also, we discussed that if we had a solution for 2 squares then 7 was possible and the same for 3/6 and 4/5.
Today during a year 10 lesson, students were faced with a calculation: 81 – 45 during a worded problem. They reached the answer 36. One student was waiting for the other students to reach their answer and he said “All of the numbers are in the 9 times table”
We stopped to look at why that was and we came to the conclusion that if you had 9 nines and you subtract 5 nines then you are left with 4 nines. Students explored which calculations this worked for and they summarised that two numbers that are in the same times table had a difference that was also in that times table.
I then went home thinking about generalisations and how this isn’t always apparent
I want students to notice that when you subtract multiples of the same number then the difference is also a multiple of that number.
I then hope to move onto 3 and 3 squared and how you cannot simplify this.
I think the slide below is a little complicated but i want students to compare the two ideas.