At this primary school in Maidenhead I started off as a TA in a Year 5/6 class. On the first day whilst talking to the classroom teacher (Miss N), we realised we
came from similar part of Wiltshire and even had a friend in common. They
worked with each other and I used to live 5 doors down.
A lot of things happened in my 7-8 ish months, but I learnt
so much about working in a primary school environment. I held a drama club, was
given a group of children to keep occupied during lunchtimes, organised an
external Athletic Competition, created and assisted in making classroom
displays and quite often took a more active role in PE Lessons.
Rather than break each day/week into; I did this and I did
that, I am instead going to give my observations in their own subjects. I will
start with maths first.
Maths
There were 2 mixed classes and this meant Maths was also
split into two ability groups. I worked with the higher group and expected
SAT’s grades were 4A-5A with some even achieving Level 6. The class was further
divided into year groups. There were 3 sets of 4 year 5’s sat together and 6
sets of 4 year 6’s. This meant that although the teaching was the same, at
various points across the lesson, Miss N could address part of the class without
having to disrupt everyone.
Differentiated
Work was normally differentiated 3 ways. Bronze, Silver, and
Gold, with Platinum added for the Gifted and Talented. Quite often I noticed a
lot of students attempting a harder task without getting to grips with what
they were learning and this either resulted in frustration or realisation that
they should have started on something less challenging and progress afterwards.
Boys/Girls Only Classroom learning
Once a week all of the boys from both years work in one
classroom and same for the girls. This was done for a number of reasons
including; lower ability can learn from higher ability, different dynamics of
students working together, boys and girls often work better in separate rooms,
and also it was usually fun experimental tasks or maths challenges to complete.
Maths lessons covered whilst I was in this class
Now although its not going to be in a Math’s SAT’s paper
anytime soon, Sudoko is great for
problem solving and I observed two boys working on a beginner puzzle to start
with. Great choice especially as one of the boys rushed and struggled at first
but quickly realised his mistake (although he sometimes added same numbers in a
box). The other boy needed a bit of explaining at first but got straight to
work.
Another topic was symmetry
and one of the boys is very meticulous with his presentation. He showed the
names of the shapes and also how many sides each had. The I Can was: Make
a shape that has a line of symmetry.
Symmetry progressed
in further lessons, to include the I Can:
Translate, rotate and reflect a shape. I Can: Rewrite the co-ordinates of a
translated shape, I Can: Write co-ordinates of my translated shape. I
sat with a group of year 6’s and helped them to accurately rotate a shape, understand the
order of rotational symmetry and also find the order
of rotational symmetry for many different shapes.
3D shapes was an
interesting lesson because not only did we look at the obvious choices (cube
and sphere), the class explored many other shapes including; cone, cuboids,
triangular-based pyramid, square-based pyramid, and prism. I Can: Accurately draw
a range of 3D shapes, I
Can: Identify properties of 3D shapes.
From top left to
bottom right: Cube, Cuboid, Prism, Triangular-based pyramid, Square-based
pyramid, Cone, Cylinder and Sphere.
This time I
worked with Year 5’s plus a Year 6. Firstly they drew as many 3D shapes as they
could think of and after Miss N asked the class what properties were in some of
them. For example a Cube has; 6 faces (sides),
8 vertices (corners) and 12 edges.
Secondly each
pair were given a sheet of sugar paper and 2 sheets- one with 8 3D shapes and
the other their descriptions. Their job was to work out which matched and stick
them together. Although three of the group worked it out quickly, one needed
some advice working it out. The Year 6 had previously covered this before so
was able to assist the others with matching up.
The next day
I worked with the same group and this progressed onto looking at which net
makes a cube. A sheet of different nets (what a 3D shape would look if it were
opened out). I Can: Identify which nets
would make a cube. I Can: Identify 3D shapes using different nets.
Area and Perimeter
was a tough lesson I thought and some of the Year 6’s struggled with some
of the more complex shapes.
After working with the year 5’s, I found they couldn't differentiate between a full shape and one with part missing/taken away. The
question asked them to work out the area of the rest of the shape but first
they had to work out a) the whole shape area, b) the
missing piece area and c) minus one from the
other. I think when it is covered again in the future; it will start to
make a lot more sense.
Factors and Multiples
followed the following week and the Year 5’s were asked to use a Venn
Diagram to sort out the multiples of 2 and 5, then 3 and 4 and finally Odd
number and/or 3. I Can: Recognise the factors and multiples of a number.
The
group I worked with took to the task comfortably and one of them only one wrote
down too quickly which resulted in getting a few wrong.
That week the class moved on towards probability and the likely-hood of something happening. The first
part was a fun exercise with sentences such as ‘I will come to school tomorrow,
or I am always in bed by 9o’clock’, and the class had to answer with a choice
of Certain, Likely, Unlikely or Impossible.
Investigating probability further, the Year 5’s matched
statements with a fraction and
worked in teams to achieve the answer. Similar to the 3D shapes, this used two
separate sheets of paper except was stuck down in their exercise books.
With fractions in mind, the next lesson was to understand
the difference between ratio and proportion. I Can:
Simplify ratios, and I Can: Solve ratio problems.
Miss N brought the whole class to the carpet space and used the
Smart board to teach how to work out ratio and proportion. In a survey there
were 6 red cars and 10
blue cars = 6/10 or 3/5 as a simplified fraction. So for every 3 red cars there are 5
blue cars.
Equivalent
ratios and simplest form
If you are making orange squash
and you mix one part orange to four parts water, then the ratio of orange to
water will be 1:4 (1 to 4).
If you use 1 litre of orange, you
will use 4 litres of water (1:4).
If you use 2 litres of orange,
you will use 8 litres of water (2:8).
If you use 10 litres of orange,
you will use 40 litres of water (10:40).
These ratios are all equivalent
1:4 = 2:8 = 10:40
1:4 = 2:8 = 10:40
Both sides of the ratio can be
multiplied or divided by the same number to give an equivalent ratio.
One of my favourite lessons was looking at Averages and Mean, Mode, Median and Range. The class were given playing cards,
asked to choose 10 and work out the different averages of those selected. J, Q
and K all counted as 10.
For example: 5, 8,
5, J, Q, 5, 6, 2, 9 and 7 were those chosen.
In order this was 2, 5, 5, 5, 6, 7, 8, 9, J, Q
or 2, 5, 5, 5, 6, 7, 8, 9, 10, 10 in numerical terms.
or 2, 5, 5, 5, 6, 7, 8, 9, 10, 10 in numerical terms.
Mode is the number that appears the most = 5
Median is the middle value (the number in the
middle). If there are two numbers in the middle, look at the median for those
two. The median of 6 and 7 is 6.5.
Mean is the total of the numbers divided by how many numbers
there are.
2+5+5+5+6+7+8+9+10+10 = 67
67 divided by 10 = 6.7
Range is the smallest number subtracted from the largest
number. 10-8 = 2
This lesson progressed
nicely into a maths project called ‘If the World
Were a Village’. It looked at a fictional village with a population of 100 people. The edition of the book
used written only a few years ago when the population was 6.7 billion people. So each person in the village represented 67 million people with a ration 1:67,000,000.
I assisted one
of the year 6 boys and he came up with an idea to use a pie chart to represent
the water usage and cleanliness. The results were amazing especially as quite a
lot of the village had no running water in their homes.
Religious stats:
For example, 61
people would be from Asia, 13 from Africa, 12 from Europe, 8 from South and
Central America, 5 from Canada and the US, and 1 from Oceania. The book
continues with this analogy, to explore themes of language, age, religion,
school, food, money and electricity,. It highlights key development ideas in a
simple way and is great basis for maths handling.
I Can: Interpret statistics to
create a chart or graph
Religious stats:
33 would be Christians
21 Muslims
15 Hindu
6 Buddhists
11 Would believe in
other religion
14 Would be without any
religion or atheist
Language stats:
15 Would speak Chinese,
Mandarin
7 English
6 Hindi
6 Spanish
5 Russian
4 Arabic
3 Bengali
3 Portuguese
The others would speak
Indonesian, Japanese, German, French or some other language
Other notable stats:
20 are
malnourished
1 is dying
of starvation, while 15 are overweight
Of the
wealth in this village, 6 people own 59% (all from the United States), 74
people 39%, and 20 people share the remaining 2%
Of the
energy of this village, 20 people consume 80%, and 80 people consume 20%
20 have no
clean, safe water to drink
56 have access to sanitation
56 have access to sanitation
15 adults
are illiterate
1 has a university degree
7 have
computers
It was an
incredible amount of information and the class handled it extremely well. Some
were shocked at the lack of resources and amenities the rest of the world has
and others couldn't imagine what life would be like without running water or
electricity. All of the best displays were presented in the school corridor and
it was nicely decorated with photocopies of pages from the book and the stats
provided.
With two year groups being taught in the same class, work has to often be differentiated and this was highlighted well in a percentages lesson.
Change 48% to a decimal. 48 divide by 100 = 0.48
Change 0.48 to a percentage. 0.48 multiplied by 100 = 48%
Graphs and Charts were
covered a lot during this topic and these included Bar and picture graphs, as well
as pie and tally charts.
With two year groups being taught in the same class, work has to often be differentiated and this was highlighted well in a percentages lesson.
Year 6 I Can: Consolidate different
methods to calculating percentages
Year 5 I Can: Find equivalent
fractions, decimals or percentages
The explanations above shows the same result but by going about it in 3 different ways. This is good because not everyone is comfortable with all of them and also some can be quicker to different people.
Below is how to change both; a percentage to a decimal and also a decimal to a percentage The explanations above shows the same result but by going about it in 3 different ways. This is good because not everyone is comfortable with all of them and also some can be quicker to different people.
Change 48% to a decimal. 48 divide by 100 = 0.48
Change 0.48 to a percentage. 0.48 multiplied by 100 = 48%
A more in depth lesson on fractions followed with I Can: Compare and order fractions. This was a lesson involving some differentiated worksheets for the class to choose from.
One had a
list of fractions for example; 3/5, 4/8, 1/2,
5/10 and the task was to
re-order them by size. Beforehand EN explained that in order to compare
fractions you need to change them so they have the same denominator –please see
diagram below.
So using the fractions above I would need to find the same (or common) denominator, which in this case is 40. Whatever we do to the bottom number, we also do to the top number.
So using the fractions above I would need to find the same (or common) denominator, which in this case is 40. Whatever we do to the bottom number, we also do to the top number.
3/5 = 24/40. This is because 5x8= 40
and 3x8 =24
4/8 = 20/40. This is because 8x5= 40
and 4x5 =20
½= 20/40. This is because 2 x 20 = 40 and 1 x 20 = 20
5/10 = 20/40. This is because 10x4= 40
and 5x4 =20
As you can see a lot of them represent
a 20/40, which is a half. I would now
order the same ones out in smallest denominator order, purely for aesthetic
reasons.
½, 4/8, 5/10 and finally 3/5
One way the class created fractions was by picking out dominoes that were handed out and laying them vertically. Rather than using the standard 1-6 digits, Miss N added extra ones with numbers up to 9. The principle of the lesson was then the same as above.
The next day (and after
the class had got to grips with ordering fractions), they went on to look
at I Can: Convert between mixed number and improper
fractions.
As you can see, with any improper or mixed fraction it is quite simple to convert between the two.
There are many that mean the same
thing as division or are linked to it. They include;
Interpreting data was something I did with the lower ability class and this included the I Can: Interpret data on a Venn diagram, and
I Can: gather data and present on a Carrol diagram.
These were great ways to lay out data; whilst both looking completely different, similar information can be
displayed on each.
Finally and a bit more
of a challenge, the class learnt how to plot using all four quadrants.
One way the class created fractions was by picking out dominoes that were handed out and laying them vertically. Rather than using the standard 1-6 digits, Miss N added extra ones with numbers up to 9. The principle of the lesson was then the same as above.
As you can see, with any improper or mixed fraction it is quite simple to convert between the two.
Short Division (bus-stop method), which was hard for
some of the year 6’s to grasp previously, was looked at by approaching it using
dice. I Can: Consolidate my short division
method.
Take 3 dice
and use 1st one as the number to
divide by and the 2nd & 3rd numbers to create a
2digit number to divide from. Roll all three and make up the division as stated above. Should the
numbers be too easy, change them around. There
will at some times be remainders and this is how the short division method helps.
6 / 66 was the highest number possible
to make whilst 1 / 11 was the smallest number made.
Below are
examples I found on TES, which uses more than no’s 1-6.
Divisible by
Factor
Halve
Left over
Remainder
Share
When using division in
calculations, always ensure the number you started with gets smaller. Numbers
can’t always be divided exactly and occasionally there are remainders or numbers left over.
The example on the right is a more complex way of doing the same sum however this time instead of putting remainder 2, the 2 has been turned into a decimal number and made smaller into .4
With protractors being used in the SAT’s
papers in May, Miss N decided to do go through measuring angles. A protractor is
usually 180 degrees and split into 180 lines. 0, 10, 20 through to 180 are printed although 1,
2, 3, 4, 5 through to 179
are also indicated but numbers not printed.
As before
with division, multiplication is also a big focus in SAT’s. Miss N showed the class
various methods with the I Can: Use a
suitable method to solve multiplication problems.
If however
you are multiplying by a number over 10 for example 13 x 38, use the same
method as to the right except break it down into two parts.
38 x 3 and 38 x 10 and add the two parts up together
38 x 3 = 114
38 x 10 = 380
114 + 380 = 494
Rounding up or down to the nearest 1, 10, 100 or 1,000, was a quick end to one of the
lessons because although it was easy for most of the class, some just needed it
to be reinforced.
Always remember if the number you want to round off is a 1, 2, 3 or 4, you go down,
however if the number is a 5, 6, 7, 8 or 9, you
go up.
What is 23,745 to
the nearest thousand?
First, look
at the digit in the thousands place.
It is a 3. This
means the number lies between 23,000 and 24,000. Next we look at the digit to the right of the 3, which is a
7. That means 23,745 is closer to 24,000.
23,745 to the nearest thousand is 24,000
23,745 to the nearest hundred is 23,700
23,745 to the nearest hundred is 23,700
These were great ways to lay out data; whilst both looking completely different, similar information can be
displayed on each.
One of the last
Math’s lessons I did, before being asked to work 1-1 with a year 4 boy, was
based on converting between metric and
imperial units of measure. These lessons were brilliant because some of the
imperial units I had never heard of before or if I had done, I didn't know who to use them properly. Miss N asked the class if they knew any of the metric or imperial
measurements and what they stood for, then she asked if any knew how they
linked together.
Metric length measurements
Length is measured in
millimetres (mm), centimetres (cm), metres
(m) or kilometres (km). These are known as metric units of length.
1 cm = 10 mm
1 m = 100 cm
1 km = 1000 m
Imperial length measurements
Miles, feet and inches are old units of length. These are
known as imperial units of length but are not now commonly used in
maths.
There are 12 inches in a foot.
An inch is roughly equal to 2.5
centimetres.
A foot is roughly equal to 30
centimetres.
A mile is roughly equal to 1.5
kilometres.
Metric units of mass
Mass is measured in grams (g), kilograms (kg)
and tonnes. These are known as metric units of
mass.
1 kg = 1000 g
1 tonne = 1000 kg
Imperial units of mass
Ounces and pounds are old units of mass.
These are known as imperial units but are not
now commonly used in maths.
There are 16 ounces in a pound.
An ounce is roughly equal to
25 grams.
A pound (454g) is equal to just under half a kilogram (500 g).
Metric units of capacity
Capacity is measured in millilitres (ml) and litres (l).
1 l = 1000 ml
Imperial units of capacity
Pints and gallons are old units of capacity (imperial units).
There are 8 pints in a
gallon.
A pint is equal to just over half a litre.
A gallon is roughly equal to 4.5 litres.
Miss N handed out some
worksheets covering all of the different units of measure and some even
included extra measurements such as;
Length: decimetre (one tenth of a metre), furlong (1/8 mile), hand (4in), league
(3miles)
Capacity: quart (2pints),
Mass: dram (1/16 of an ounce)
Algebra was one of the final lessons I observed whilst in the class and I could
see that it was less daunting for them, than it was for me in secondary school
when I learnt it. Again the students
were quick to respond to questions from Miss N, and she pointed out that it will
feature in the SAT’s.
Algebraic terms and expressions
In algebra, letters are
used when numbers are not known.
Algebraic terms, like 2s or 8y, leave the multiplication signs out. Rather
than '2 × s', write 2s, rather than '8 × y'
write 8y.
A string of numbers and
letters joined together by mathematical operations such as + and - is called an
algebraic expression.
Like terms
Algebraic terms that
have the same letter are called like terms. Only like terms can be added or subtracted.
Example
So 9b, -7b and 13b are like terms, but 6t, 5x and -11z are not like terms.
When like terms are added and subtracted, it is called
simplifying.
Adding and subtracting
like terms
The Khan family and the
Norman family visit the zoo together - there are
8 children and 7 adults
in the group. Because there are more than 10
people, the families can
take advantage of a special offer - 1 child can be admitted free of charge.
As before let's use g for
the cost of child admission, and k for the cost of adult admission.
Cost for the Khan family = 3g +
3k
Cost for the Norman family = 5g + 4k
Offer = - g
Total cost = 3g + 3k + 5g + 4k - g
Simplified = 3g + 5g - g + 3k + 4k = 7g + 7k
X and y coordinates was came next, and this looked at axis.
All graphs have an x-axis
and a y-axis. Here is a diagram of a typical set of axes.
The point (0,0) is called the origin.
The horizontal axis is the x-axis.
The vertical axis is the y-axis.
One way to remember
which axis is which is 'x is a cross so
the x axis is across'.
Coordinates are also written alphabetically - so x comes before y (x, y). One way to remember is 'you go along the hallway before you go up the stairs'.
Coordinates
Coordinates are written
as two numbers, separated by a comma and contained within round brackets. For
example, (2, 3), (5, 7) and (4, 4)
The first number refers to the x coordinate.
The second number refers to the y coordinate.
Plotting coordinates
When describing
coordinates, always count from the origin.
For example, to describe
the position of point A, start at the origin and move two squares in the horizontal (x) direction.
Then move three squares in the vertical (y) direction.
The coordinates of point
A are therefore (2, 3).
Finally and a bit more
of a challenge, the class learnt how to plot using all four quadrants.
Extending the x and y
axes beyond the origin reveals the negative scales. The
areas of the graph between axes are called quadrants. So now we have four quadrants in total.
Coordinates in these
quadrants are still described in terms of x and y. But now we can have negative
values for x, y or both.
The coordinates of A are (-2, 3).
The coordinates of B are (-3, -4).
SAT’s papers
In March and the second week after Spring Half Term, Miss N and Miss G The Year 5 teacher decided to start giving the Year 6’s mock papers. They began in the mid 00's, and over the next few weeks progressed to
the 2013 tests. They were the Level 3-5 papers and each breakdown of marks gave
which sub-level each student had achieved.
Each day after the test, the class went through the 1 and
2 mark questions themselves using a different coloured pen to mark it. This
gives the students ownership and the ability to correct their-own mistakes.
Honesty is key, and I walked about the class ensuring no-one attempted to
change the answer before marking. Results varied but that was to be expected
given the diverse ability of the students.
I think that introducing the papers (which gradually get
harder) to the students, they quickly overcome any exam fears and are know what
equipment to use and where to sit before the real thing.
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