The School Direct (Salaried Route) Mathematics Portfolio ...login.myeportfolio.tv/Login/PortfolioFolders/School... · School Direct Salaried Maths Portfolio 2016 The School Direct

School Direct Salaried Maths Portfolio 2016

The School Direct (Salaried Route) Mathematics Portfolio 2016-17

The purpose of this portfolio is to support you in your development to become an effective teacher of

mathematics. It collects together in one place materials which are used, or are completed, over the

course of your training in order to enable you to discuss elements of your development with your

teacher mentor and visiting tutor.

Most importantly, it is designed to enable you to answer the question: “What have I learned over my

training and how has this helped me develop my teaching of mathematics to support pupil

progress over time?”

The evidence in this portfolio will support you to meet Teachers’ Standard 3. You may draw on

elements of this portfolio when completing your evidence bundles (which you will compile in order to

demonstrate you have met the Teachers’ Standards: mathematics teaching is Teachers’ Standard 3,

sub-heading e)

Contents: Please organise your Mathematics Portfolio into the following sections

Section 1: On-going development

1.1 Maths Action Plan: You will need to write sharply focussed targets to develop

your maths subject knowledge. These targets must be achievable in a short space of time (1-2 weeks) and, when achieved, replaced with new targets. At any one time, you should not have more than 3 tightly written targets. As appropriate, targets might need to be transferred to the Weekly Mentor Meeting form.

Section 2: Auditing and developing your subject knowledge for teaching mathematics

2.1

Preparatory task 1: orientation reading Notes on – how would you characterise your experience of learning maths and how has your view of maths as a subject been affected by your own school experience?

2.2 Preparatory task 2: maths subject knowledge audit You will have completed a mental maths ‘test’ and identified gaps in your subject knowledge. File the audit here.

2.3

Preparatory task 3: maths diagnostic audit You will have examined your subject knowledge by working through 6 questions, supporting you to ‘deconstruct ’your knowledge to examine not just what you know, but how you know it. File your work here.

2.4

SK1 (subject knowledge per se) tasks In your first few weeks, you will need to complete additional tasks to help you to develop your maths subject knowledge and identify areas that you need to work on. Full details are attached to this document. Include this in your Individual Training Plan. File the work in this section. - Mental maths ‘50 questions’ - True/false and Always/Sometimes/Never - KS2 SATs papers

2.5 Supplementary work, such as Haylock chapters, which evidences what you have done to develop your subject knowledge and complete your targets.


Section 3: UH sessions related to teaching mathematics

3.1 Powerpoint slides plus notes from the teaching sessions on campus.

Section 4: School-led experience of the teaching of mathematics

4.1 Term 1 focus: Fluency with numbers/Arithmetic

Early in term 1 you will particularly need to focus on the teaching of number work/arithmetic, which includes number labels, counting, fractions and decimals, calculation and times tables. This work will help you to think about supporting children to become ‘fluent’. You will need to file evidence for each of the following:

Observe the teaching of number work/arithmetic and make notes (to

file here).

With the help of your mentor, identify a child in the class and observe him/her during a lesson on number work/arithmetic (note their attitude, the resources they used, or could have, what they found

easy/hard, how they engaged with their learning etc). Discuss with your mentor the next steps for that child.

(With support) Plan a lesson which explicitly addresses the next steps for the identified child. Think carefully about the developmental

needs, learning objective(s) and the success criteria. The lesson could be for a group or for the whole class. (There are example lesson plans in your

documentation.) File the lesson plan here.

Teach the planned lesson and evaluate the impact on the child’s development/learning. Did they meet the outcomes/success criteria?

How do you know? Discuss your findings with your mentor. How will

this learning contribute to progress over time?

As appropriate, set subject knowledge targets for your own future development (to add to the action plan in section 1.1).

4.2 Lesson observation form for teaching of number/arithmetic: Term 1

You will need to be formally observed by your mentor teaching a whole class lesson on some aspect of number/arithmetic. This may be the lesson in section 4.1 if that was planned for the whole class. Please file here the lesson plan (unless it is in section 4.1), your evaluation of the lesson and a copy of the LOF.

Complete the right-hand box to show your grade.

Grade for this

lesson:


4.3 Term 2/3 focus: Problem solving and reasoning

During term 2 or 3 you will particularly need to focus on supporting children to develop skills in problem solving and reasoning. These are essential elements of learning which support conceptual understanding rather than simply following procedures. They require children to:

Be challenged through well-chosen higher order thinking questions which

- require careful articulation of ideas and - enable pupils to reassess their understanding and, therefore,

move their learning forward

Be encouraged to discuss mathematical problems in order to build confidence, resilience and perseverance (and that discussion should be pupil-pupil as well as pupil-adult)

See the connections in maths and, for example, be able to use their existing skills to solve problems which are unfamiliar and non-routine

See errors and misconceptions as part of the process of learning

Choose and use resources and representations, including their own mark-making, that help them to make sense of mathematical concepts and explain and share their ideas

Plan for a sequence of structured learning opportunities/sequence of lessons which develop children’s skills in problem solving and reasoning, clearly indicating, in your lesson plans, how you are incorporating ideas highlighted above. Are the

lesson objectives clear and progressive? Do they address the skills being developed (rather than the activities undertaken?) Will the children know what ‘success’ will look like and how they will demonstrate their learning?

File the lesson plans, or an outline/overview of the lessons, in this section.

Implement/teach this planned sequence. One of these lessons will need to be formally observed by your mentor (or Visiting Tutor). It should be at the later part of the sequence so that impact on pupil progress can be assessed.

Assess the impact of this sequence on the children’s development/learning. Did they meet the learning outcomes? How do you know? What sources of evidence show this? How will this support progress over time?

Evaluate the sequence: note your strengths and any areas that you need to address. Use this to set developmental targets.

4.5 Lesson Observation Form for teaching of problem solving and reasoning: You will need to be formally observed by your mentor teaching a whole class lesson from the sequence. Please file the lesson plan and your evaluation of the lesson and a copy of the LOF.

Complete the right-hand box to show your grade.

Grade for this

lesson:


Additional SK1 (subject knowledge per se) audits

Section 2.4 of your maths portfolio details three SK1 audits that you need to carry out before

placement 1. Below you will find details of these:

Mental maths ‘50 questions’:

Complete the questions below and then mark them – the answer sheet is included in this

pack.

True/false and Always/Sometimes/Never

Complete the questions and mark them (answers are included). There are follow up

questions for you to complete.

KS2 SATs papers

You need to complete a set of (end of) KS2 papers from a recent SAT test. There are

three papers (Paper 1: Arithmetic, Paper 2: Reasoning, Paper 3: Reasoning). These have

recently changed, so you can use the 2016 tests if you can access them, or the sample

tests from:

https://www.gov.uk/government/publications/2016-key-stage-2-mathematics-sample-test-

materials-mark-schemes-and-test-administration-instructions

In order to maximise your learning from this exercise, you should consider:

1. Can I do the questions myself (and get the right answer)?

2. Did I do it in a way that primary school children might approach it?

3. Are there other ways of doing it?

4. How could pictures or resources enable me to show someone else how I did it?

https://www.gov.uk/government/publications/2016-key-stage-2-mathematics-sample-test-materials-mark-schemes-and-test-administration-instructions

https://www.gov.uk/government/publications/2016-key-stage-2-mathematics-sample-test-materials-mark-schemes-and-test-administration-instructions


SK1 – Mental Maths Skills

The following questions should be carried out mentally.

No calculators are allowed. Pencil and paper can be used for

jottings. Avoid using standard written methods – the emphasis here

is on mental methods.

NAME:

What is 15% of 200? Give three different ways of working out the

answer to 15% of 120.

What is 120% of 15?

Find a way of explaining why 15% of 120 is the

same as 120% of 15 (this could involve pictures

which ‘prove’ rather than ‘show’ the

equivalency)?


What is 100

33 as a percentage? As a decimal?

To find 5

2 as a percentage and

28

21

(efficiently) as a percentage uses two different

methods. Explain these.

(a) What is 18% as a decimal?

(b) What is 140% as a decimal?

(c) What is 6.5% as a decimal?

What is 5

1 of 45?

Explain why this helps in finding 5

3 of 45.

In a class of thirty-five pupils, four out of seven

are girls. How many boys are there in the

class?

(a) What is 0.7 as a fraction?

(b) What is 55% as a fraction in its simplest form?


Give two different mental strategies to find

29 x 40.

What is 3.4 x 11? 240 x 1.5 has the same answer as 24 x 15.

Give three other (similar) calculations which also

have the same answer as 240 x 1.5.

(a) How many hours are there in 3½ days?

(b) How many weeks are there in 3½ years?

(c) How many minutes are there in 3½

hours?

(d) How many decades are there in 85 years?

(e) How many seconds are there in 1 hour?

Complete by putting in =, > or <:

(a) 8417 mm 84.17 m

(b) 23.1 cm 0.231 m

(c) 7 m 0.07 km

(d) 11 inches 32 cm

(e) 10 miles 15 km

Choose the best estimate for each statement:

(a) A glass holds (30 ml, 300 ml, 3000 ml) of orange juice

(b) An ice cream scoop has a capacity of (8 ml, 8 cl, 8 l).

(c) Marsha is 10. She has a mass of about (0.4 kg, 4 kg, 40 kg).

(d) A paperback book has a mass of about (0.001 kg, 0.01 kg, 0.1 kg).

What is the mean (average) of 17, 13 and 12? Three numbers have a mean (average) of 8.

What is the sum of the three numbers (that is,

what total do you get of you add the three

numbers together)?

Three numbers have a mean of 10. The biggest of

the three numbers is double the size of one of the

other numbers. What could the three numbers

be?


(a) What is the remainder when 42 is divided by 10?

(b) What is the remainder when 276 is divided by 5?

(c) What is the remainder when 3 337 is divided by 3?

What are the possible remainders when a

number is divided by 5?

A number is divisible by 6 and has a remainder of 4

when it is divided by 5. What could the number

be

(a) if it has two digits?

(b) if it has three digits?

The 40 tins of tuna in a box weigh 10 kg.

What does each tin weigh in grams?

What will the date be four weeks after

October 15th?

A cyclist travels 6 metres every second. How

many kilometres will she cycle in 10 minutes?

You now need to mark your own work using the answer sheet provided.

You will end up with a score out of 50.

Record your score here.

__________________ out of 50


Having completed this exercise, think about how confident you are in your own subject knowledge (that is, what you can do, not your

confidence to teach). Tick one box.

1. Excellent

2. Good 3. Satisfactory 4. Weak

Now think about areas you need to work on. Use this exercise to update your Action Plan.

Put this audit into your Maths Portfolio.


SK1 – Mental Maths Skills ANSWERS

When you mark your work, you will arrive at a score out of 50.

What is 15% of 200? 1 mark

Answer: 30

Give three different ways of working out the

answer to 15% of 120. 3 marks – 1 mark for each

Possibilities include:

10% of 120 plus 5% of 120

Or: half of 30% of 120

Or: 15% of 100 plus 15% of 20

Or: 15% of 12, then multiply answer by 10

Or: 15x120, then divide by 100

Or: 15x12, then divide by 10 etc

What is 120% of 15? 1 mark

Explain why 120% of 15 is the same as 15% of

120?

1 mark

Answer: 18

Possible explanation: In both cases the

calculation involves multiplying 15 by 120 and

dividing the answer by 100.

What is 100

33 as a percentage? As a decimal?

2 marks

Answers: 33% and 0.33

To find 5

2 as a percentage and

28

21 as a

percentage uses two different methods. Explain

these. 2 marks

The first uses equivalent fractions/decimals,

whereas the second uses cancelling.

(d) What is 18% as a decimal? 1 mark Answer: 0.18

(e) What is 140% as a decimal? 1 mark Answer: 1.4

(f) What is 6.5% as a decimal? 1 mark Answer: 0.065


Change 5

2 to an equivalent fraction

100

40

which is equivalent to 40%. Or, convert to an

equivalent decimal, 0.4.

Cancel 28

21 first to

4

3 and recognise

this

as 75%.

What is 5

1 of 45? 1 mark

Answer: 9

Explain why this helps in finding 5

3 of 45.

1 mark

Answer: 5

3 is 3 lots of

5

1 so you can find

5

3 of 45 as 3x9.

In a class of thirty-five pupils, four out of seven

are girls. How many boys are there in the class?

1 mark

Answer: 15

[Three out of seven are boys.

7

3 of 35 = 3 x (

7

1 of 35) = 3 x 5 = 15 ]

(c) What is 0.7 as a fraction? 1 mark

Answer: 10

7

(d) What is 55% as a fraction in its simplest form? 1 mark

Answer: 20

11


Give two different mental strategies to find

29 x 40. 2marks

Possibilities include

29 x 4 x 10

Or 20 x 40 plus 9 x 40

Or 30 x 40 then subtract 40

Or 29 x 20 then double etc

What is 3.4 x 11? 1 mark

Answer: 37.4

[Possibly, the most efficient mental method is

3.4x10 plus 3.4x1]

240 x 1.5 has the same answer as 24 x 15.

Give three other (similar) calculations which

also have the same answer. 3 marks

Possibilities include:

2 400 x 0.15 2.4 x 150

24 000 x 0.015 0.24 x 1 500

240 000 x 0.0015 0.024 x 15 000 etc

(f) How many hours are there in 3½ days? Answer: 84 1 mark

(g) How many weeks are there in 3½ years? Answer: 182 1 mark

(h) How many minutes are there in 3½ hours? Answer: 210 1 mark

(i) How many decades are there in 85 years? Answer: 8.5 1 mark

(j) How many seconds are there in 1 hour? Answer: 3 600 (60x60) 1 mark

Complete by putting in =, > or <:

5 marks

(f) 8417 mm < 84.17 m

(g) 23.1 cm = 0.231 m

(h) 7 m < 0.07 km

(i) 11 inches < 32 cm

(j) 10 miles > 15 km

Choose the best estimate for each statement:

4 marks

(e) A glass holds (30 ml, 300 ml, 3000 ml) of orange juice

(f) An ice cream scoop has a capacity of (8 ml, 8 cl, 8 l).

(g) Marsha is 10. She has a mass of about (0.4 kg, 4 kg, 40 kg).

(h) A paperback book has a mass of about (0.001 kg, 0.01 kg, 0.1 kg).


What is the mean (average) of 17, 13 and 12?

1 mark

Answer: 14

[To find the mean of three numbers, add them

together and divide the result by 3.]

Three numbers have a mean (average) of 8.

What is the sum of the three numbers?

1 mark

Answer: 24

[To calculate the mean, you first find the sum

and then divide by 3. If sum÷3 = 8 then

sum = 3x8.]

Three numbers have a mean of 10. The

biggest of the three numbers is double the size

of one of the other numbers. What could the

three numbers be?

1 mark

Possible answers include:

0, 10, 20: 1.5, 9.5, 19: 7, 9, 14:

1, 2, 27: 4.4, 8.8, 16.8 etc

[You know the sum of the three numbers is 30

– this is useful when trying out possibilities]

(d) What is the remainder when 42 is divided by 10? Answer: 2 1 mark

(e) What is the remainder when 276 is divided by 5? Answer: 1 1 mark

(f) What is the remainder when 3 337 is divided by 3? Answer: 1 1 mark

[Note: you did not need to perform any

divisions in order to answer these. For

example, you should recognise that 3 336 is

What are the possible remainders when a

number is divided by 5?

1 mark

Answer: 0, 1, 2, 3 or 4

[Make sure you don’t forget the 0!]

A number is divisible by 6 and has a remainder

of 4 when it is divided by 5. What could the

number be

(c) if it has two digits? 1 mark Possible answers: 24, 54 or 84

(d) if it has three digits? 1 mark Possible answers include:

144, 174, 204, 234 etc


divisible by 3 (we don’t care what the answer is,

though) so there will be a remainder of 1.]

The 40 tins of tuna in a box weigh 10 kg.

What does each tin weigh in grams? 1 mark

Answer: 250g

[10 000 ÷ 40 = 1000 ÷ 4. One way of dividing by

4 is to halve and halve again – this is a quick

mental strategy here.]

What will the date be four weeks after October

15th? 1 mark

Answer: 12th November

A cyclist travels 6 metres every second. How

many kilometres will she cycle in 10 minutes?

1 mark

Answer: 3.6 km

[6 m every second equates to 360 m every

minute, so 3 600 m in 10 minutes.]


SK1 audit – True/false and Always/sometimes/never

As you work through these questions, consider the pedagogical benefits of questions of this type.

Although they may be classed as ‘closed’ questions, they require higher order thinking and therefore give

opportunities to challenge children’s thinking and develop their reasoning skills.

Part 1: Questions 1-12 are statements which are either true or false: read the statement and circle either T or F. [In Part 4 there are follow up questions in order to help you assess your knowledge and understanding further.]

1.

A circle has one side

T / F

2.

There are 100 cm in 1 m and so there are 100 cm2 in 1 m2

T / F

3.

When you draw a bar graph, there must be a space between the bars.

T / F

4.

A fraction means a number less than 1.

T / F

5.

The only 2 numbers that add to make zero are zero and zero.

T / F

6.

A ratio of 1:2 is equivalent to the fraction 3

1.

T / F

7.

There are 360 seconds in an hour.

T / F

8.

5 is a multiple of 15.

T / F

9.

A rectangle has only got 2 lines of symmetry.

T / F

10.

347 ÷ 5 is equivalent to 5

347

T / F

11.

The digital time 11:10 is ten minutes past 11.

T / F


12.

If you roll two fair dice and add the numbers, the most likely total you will get is 7.

T / F

Part 2: Questions 13-20 are statements which are either always true, sometimes true or never true: read the statement and circle either A (always), S (sometimes) or N (never). [In Part 4 there are follow up questions to complete in order to help you assess your knowledge and understanding further.]

13.

When you multiply two numbers, the answer is bigger.

A / S / N

14.

A 2D shape with four equal sides is a square.

A / S / N

15.

Triangles have acute internal angles.

A / S / N

16.

Any parallelogram can be cut into two pieces which fit together to make a rectangle.

A / S / N

17.

Prime numbers are odd.

A / S / N

18.

A pentagon has 5 equal sides.

A / S / N

19.

If you arrange the digits 1, 2, 3, and 4 to make a 4 digit number, that 4 digit number is divisible by 3.

A / S / N

20.

A spinner has three colours, red, green and blue. The probability it

lands on red is 3

1.

A / S / N

Part 3: Now mark your answers using the answer grid at the end. Put your score here: / 20


Part 4: Follow up questions The following questions revisit the ideas of the questions covered. Refer back to the previous questions 1-20 if it helps, and now complete these.

1. What is a ‘side’? Do 3D shapes have ‘sides’?

2. What does the prefix ‘cent’ mean? Relate this to centimetre, centilitre etc. Gives examples to show this. What does the prefix ‘kilo’ mean? Relate this to kilogram, kilometre etc.

3. What is the difference between ‘continuous’ and ‘discrete’ data? Can you give examples?

4. How do you change fraction to its decimal equivalent? Use an example to work through this.

5. How would you use a number line to demonstrate adding 5 and -4?

6. Draw a picture to demonstrate the equivalence.

7. How many hours are there in a week?

8. What is the difference between a factor and a multiple?

9. A rectangle is one example of a “quadrilateral” – a 2D closed shape with four sides. How many other quadrilaterals can you name?


10 Without doing the full division, how can you work out what the remainder is when 347 is divided by 5?

11. Why might a child think that 11:10 is eleven minutes past 10?

12. What is the least likely total when you roll two fair dice and add the numbers?

13. Give an example of two numbers which multiply to give an answer which is the same as one of the starting numbers.

14. Is a square a rectangle?

15. Is it possible to draw a triangle with two obtuse angles?

16. How do you find the area of a parallelogram?

17. Explain why 1 is NOT a prime number.

18. What is the difference between ‘regular’ and ‘irregular’ polygons?[A polygon is a closed 2D shape with straight sides, such as a square, a triangle, a pentagon, a parallelogram etc]


19. What is the trick for testing whether a number is divisible by 3?

20. Draw two different spinners (for qu 20) where this IS a true statement.

Answers

1. F 8. F 15. S 2. F 9. T 16. A 3. F 10. T 17. S 4. F 11. T 18. S 5. F 12. T 19. N 6. T 13. S 20. S 7. F 14. S

Documents

The School Direct (Salaried Route) Mathematics Portfolio ...login.myeportfolio.tv/Login/PortfolioFolders/School... · School Direct Salaried Maths Portfolio 2016 The School Direct