1. Chapter 4 Number: Counting; place value; fractions, decimals and percentages

2. Chapter Summary
This chapter will support you in understanding how children learn to count
It will offer activities to develop pupils understanding of place value
It will offer activities which allow pupils to make connections between fractions, decimals and percentages

3. Counting
The one-to-one principle: a child who understands this principle knows that we only count each object once
The stable order principle: a child who understands this principle knows that the order of number names always stays the same
The cardinal principle: a child who understands this principle knows that the number they attach to the last object gives the number in the count
The abstraction principle: a child who understands this principle knows that we can count anything. The objects do not all need to be the same
The order irrelevance principle: a child who understands this principle knows that we can count objects in any arrangment and still get the same number

4. Place value
The column that a digit is placed in determines its value

5. Portfolio Task Write ½ in the centre of a piece of paper
Create a web diagram with as many different representations of ½ as you can think of.

6. .
Ratio and Proportion
Ratio describes part to part relationships. There are 2 red beads for every blue bead. The beads are in the ration 2:1
Proportion describes part to whole relationships. 2/3 of the beads are red.

7. Multiplying and dividing by 10
Write a single digit in the middle of the page.
Multiply this number by 10 and write this number above the original number. Repeat working up the page until you have 5 numbers.
Now divide your original number by 10. Write the new number underneath your original number. Repeat working down the page
What patterns do you notice?

8. Fractions as equal areas
How many different ways can you shade a sqaure to represent ½
Repeat this for 1/3 and 1/4

9. Chocolate Fractions
Place three chairs at the front of the class. Place one bar of chocolate on one chair, two bars on the next and three bars on the next. Ask ten pupils to take it in turns to stand behind one chair making their choice of chair one after the other.
When all the pupils are standing behind the chairs they can divide the chocolate on the chair equally between the children at that chair.
This activity leads to a great deal of discussion about fractions as equal areas.

10. Observing counting and understanding number
Watch the first five minutes of ‘Decimals forever’ on the companion website:
How would you organise you classroom for this activity?
Which fractions would you choose?
How would you differentiate the activity?