Mental

Question 1

What is partitioning

Answer 1

Split number into component parts before calculating

Question 2

What is stepping stones or bridging

Answer 2

Use number bonds of 10,100 1000 etc
Land on murliple of 10 or 100 to mean that the next jump is more straight forward.
73+48
73+7=80 +1+40

Question 3

What is compensating?

Answer 3

Adding/subtracting a whole number to make the sum easier - then adding/subtracting back on the additional number after. Eg .73+48
73+50-2

Question 4

Doubles and near doubles?

Answer 4

23+24 - double 23 and add 1

Question 5

Double and halving?

Answer 5

X4 double and double again..
Eg 16*4
=double 16=32 x2 = 64

Question 6

Friendly numbers?

Answer 6

Make the sum easier by changing one of the numbers to have the same ending eg 742-146, make it 742-142 then subtract another 4 after .. can use an empty number line to explain

Question 7

What does cardinal aspects of number mean

Answer 7

A number being a description of a set of things (3 sisters)

Question 8

How can cardinal aspect of number be taught to young child?

Answer 8

Matching 3 sets of things with 3 other sets of things. Eg matching 3 spoons to 3 cups. Learner recognises there is something the same about the 2 sets - they identify an equivalence. That three-ness of 3 is the concept as 3 as a cardinal number

Question 9

What is the ordinal aspect of a number?

Answer 9

Numbers as a means of ordering. Eg. I’m 3 and you are 6. On my next birthday I’ll be 4. These numbers are no referring to sets of things. Tells which order things are.

Question 10

What’s a good way of teaching ordinal aspects of numbers?

Answer 10

When we represent numbers as locations on a number strip. Or points on a number line.

Question 11

What is nominal aspect of numbers?

Answer 11

Where a numeral is used a label or name without any ordering being implied. Eg the number 4 bus.

Question 12

What’s the difference between a natural number and an integer?

Answer 12

A natural number is a whole number . Integers are all numbers including negative and positive integers.

Question 13

What are rational numbers

Answer 13

Those that include fractions and decimal numbers. Named so because a fraction is a ratio.

Question 14

What is the augmentation structure of addition and what materials and language should be used?

Answer 14

It is where you start with one number (1.67) and add on 12 for example. Use a number line. “Start at” “and count on” “increase by” “go up by”

Question 15

Name 4 categories of Situations where subtraction would be the best sum to do? Give an example for each

Answer 15

1. The partitioning structure
2. The reduction structure
3. The comparison structure
4. The inverse of addition structure
5. A quantity is partitioned off in some way and we must work out what is left. Eg 17 marbles, remove 5, how many left?
6. Reduction structure- use of a number line, a quantity is reduced by some amount, what is the reduced value?
   “Start at x and count back y”
7. Comparison structure- making a comparison between 2 groups “what is the difference? How many more?” Materials- number line, or number blocks in groups.
8. Inverse addition- “what must be added to x” or “how many more x are neeeed ?” Or this toy costs 90p but I only have 50p, how much more do I need?”

Question 16

What’s wrong with introducing chimney sums too early?

Answer 16

Too early introduction to algorithms - prevents full grasp of number understanding- more fully understood with concrete materials, and mental strategies first. Also children tend to think of the digits in the number they are adding as being seperate numbers to each other.

Question 17

What is stable order principle

Answer 17

Counting a set of blocks in the correct order

Question 18

What is to one to one principle ?

Answer 18

Number of numbers spoken matches the objects to be counted - so if there are 4 toys and even if 1.3 .4.5 at rebar the child says as they count them, although not counted correctly they have a number for each object