1. Place Value, Addition and Subtraction
SCITT Day 2
Place Value, Addition and Subtraction

2. Session objectives (We will):
consider the importance of ‘Place Value’ in the teaching of Number;
review a range of models and images that can be used to develop understanding;
to review the National Curriculum approach to addition and subtraction using mental methods, informal jottings, written methods and calculators;
review aspects of measures – estimation, measuring and reading scales.

3. Associated issues for teaching
Review all aspects of your own mental methods of calculation for addition and subtraction
Explore the rationale behind the delaying of vertical methods of recording
Review a range of Oral and Mental Starters and how to engage learners.
Consider simple resources and the role of practical work in the classroom.

4. Have you used the website www.ncetm.org.uk since the last session?
Feedback
Have you used the website since the last session?

5. Mental Oral Starter
Boxes 100 =
& Squashy Boxes!

6. Mental and Oral Starters
What are they for?
How can they be used?
What have you seen?
What makes a ‘good’ MOS?
What do you need to consider if planning a mental/ oral starter?

7. Leinhardt et al (1991)
“…the use of multiple representations in general is an important part of teachers’ knowledge of mathematics and they can play an important role in the explanation of mathematical ideas.”

8. The teacher’s classic mistake…
Without thinking we assume that children see what we see.
And yet…
children work with what they see, as they build their very own, unique concept images.

9. Number Track Games Race to the Moon A two player game!
You need two counters.
Set your number line with START at the ‘bottom’ and 10 at the ‘top’.
(Put 10 on a post-it)
Who can reach number 10 first?
Roll dice and move upwards.

10. Number Track Games ‘Adds’ vs ‘Takes’ Number track marked 0 – 10
The ‘ball’ starts on 5.
One player is ‘adding’, the other ‘taking away’.
Who can score a goal? (by reaching 0 or 10 or ‘beyond’!)

11. Number lines 3 (or 4) in a line
One number line (0-100) between 2 or 3 players (marked in divisions, age-appropriate)
Player 1 turns over 2 digit cards and make a two-digit number.
Place that number where it ‘lives’ on the number line and write their initial above it.
Player 2 ….
Play continues until one player has 3 places on the line with no other players placed in between.

12. Other number lines… How could these games work on these number lines:
3 x table line?
50-60?
Fractions (0, ½ ,1, 1½…)?
Decimals (0, 0.1, 0.2,…)?
Negative Nos (-5 to 5)?

13. 1-100 Place a counter over numbers that have significance for you
“Hide the number”
1 number
A cross (+ or x)
5 random numbers

14. Define…
‘Place Value’
(with examples)

15. National Curriculum 2014
What are the end of year expectations for Number & Place Value across the school? (Track from Y1 to Y6) What other strands of mathematics require an understanding of Place Value? (Implicit or explicit)

16. NC2014 Look at your year group…
What models and images would you use to support learners?
[Numicon/ straws/ Dienes/ exchange boards / coins/ PV cards/ number lines/ 0-99 square]

17. What concepts are involved here?
Make 50
Exchange Boards
What concepts are involved here? H T U
Now ‘Make 0’
Use of Base 10 equipment v Counters/ digits?

18. Progression in Calculation
Counting
Early stages of mental calculation and learning number facts
Working with larger numbers and informal jottings
Non-standard expanded written methods
Standard written methods
Is this clear in NC2014?
Where do you fit in with this progression?

19. Before ANY calculation:
THINK…!
Before ANY calculation:
Approximate,
calculate,
check it mate!
Three decisions…
“Can I use a…”
mental method?
written method?
calculator?

20. This document offers an overview of progression and ideas for practising different mental calculation strategies.
Four operations
+ - x ÷

21. Ian Thompson
“One of the reasons why teachers should discuss children’s mental strategies in the classroom and get them to try out each other’s methods is to legitimate the use of personal (as opposed to ‘school approved’) strategies. Teachers need to be aware of the range of available methods, not so they can formally teach them, but to enable them to support children who are developing proficiency with a particular strategy…also to ensure that children do not receive advice that confuses rather than clarifies.”

22. Consider
When vertical methods are first introduced learners need to see them alongside related mental methods.
It is important that the children have a good understanding of place value and partitioning using concrete resources and visual images to support calculations.
The expanded method enables children to see what happens to numbers in the standard written method.

23. Explore…
= – 38 =
= – 486 =
Work these out ‘mentally’ or with a written method on your own, then share your methods with your table.
Please feel free to record in any way you find useful.
(In carrying out the calculation or in explaining to others.)

24. Calculator digits

25. Calculators Main roles A calculating aid A learning aid
An aid for generating mathematics

26. A calculator Confusions… Type in 1212121212 Read the number you get…
Confusing?
Limitations…
10 ÷ 3 =
Now take the answer and multiply it by 3…
Using the ‘Function Machine’ Type in: = 0 Now press = = = = = =… what is happening? What other functions can you get the machine to do? Memory – in/ out Use the MR and M+ buttons to calculate: ( ) x 3 =

28. Measuring Instruments
What range of measuring instruments are there?
Similarities?
Differences?
What aspects of measure? Units?
Length
Time
Weight ….

29. Reading Scales
Reading Scales is just applying knowledge of number lines…?
Isn’t it?
Create a step-by-step set of instructions for children to be able to read scales accurately…using one of the following examples

31. What is the length of the key in mm?
Which jug holds the most?
How much more? Explain how you worked it out.

32. Task 2: Hand in Day 4
Work with a group of children on a task involving calculation (examples from relevant year group expectations).
What different calculation strategies/ methods are they familiar with?
Discuss with pupils different models & images they utilise to explain HOW they did the calculations? (With KS2 children you might be able to explore alternative methods and discuss ‘efficiency’.)

33. Task 2: WILF OUTCOMES
be aware of the range of calculations that children might do mentally and/or with paper and pencil recording
listen to children’s explanations/ reasoning
annotate children’s work to show their thinking
consider next steps (including other models and images you could/would introduce)
show an awareness of any errors/ misconceptions and how they may be addressed

34. Did we?
consider the importance of ‘Place Value’ in the teaching of Number?
review a range of models and images that can be used to develop understanding?
to review the National Curriculum approach to addition and subtraction using mental methods, informal jottings, written methods and calculators?
review aspects of measures – estimation, measuring and reading scales.