imagery for decimals

Thinking 101 2014 [email protected]

Imagery for Decimals


Area ModelsNumberline ModelsUse the correct vocabulary

Compare Compare Compare


One 1


One tenth of the one is coloured red.


How many tenths should fit in the one?


One whole is the same as ten tenths

Thinking 101 2014 [email protected] €

1010=1


€

1100

= 0.01


How many hundredths in one tenth?In one whole?


Ten hundredths in one tenth

€

10100

= 0.10

€

10100

=110

€

0.10 = 0.1


one thousandth

€

11000

= 0.001


How many thousandths in one hundredth?


ten thousandths in one hundredth

€

101000

=1100


How many thousandths in one tenth?

€

1001000

=110


ten tenths

One hundred hundredths

One thousand thousandths

€

1010=100100

=10001000


€

1010=100100

=10001000


onethousand thousandths


one thousandthis inside onehundredth is inside one tenth is inside 1


0 1 2 3

OneOne tenthOne thousandth


0 1 2 3

Where are the tenths? The hundredths?

Where is 0.7? Where is 0.07?Where is 2.7?Where is 2.07?


0 1 2 3

0.07 0.7 2.07 2.7


Play on a numberline:

three tenths, thirty tenths

6 hundredths, 60 hundredths

14 tenths, 140 hundredths

63 hundredths, 6 tenths


Area Models are based on place value

1 This is one


1 x 10 = 10

Multiply 1 x 10

1

10


Multiply 10 x 10

Why did we move to area?


Linear model: 100 x 1

I cannot show it here.


Multiply 100 x 10

Why do we move to volume?


A linear model 100 x 10

I cannot show it here.


If you work your way backwards, divide by 10 to undo.

1000 ÷ 10 = 100

Do you understand division:Sharing out equally so give out tens till they are all goneFill ten groups equally or as equally as possible.


If you work your way backwards, divide by 10 to undo.

100 ÷ 10 = 10

Do you understand division:Sharing out equally so give out tens till they are all goneFill ten groups equally or as equally as possible.


10 ÷ 10 = 1 You cannot share out tens till they are all gone so you have to think about filling or making ten equal groups... There will be one in each


1 ÷ 10 You cannot share out tens till they are all gone so you have to think about making ten equal groups... There will be one tenth of the whole in each.


1 ÷ 10 = Decimals have their own notation. 0.1

€

110


Blow it up so you can see inside


€

110

€

110

€

110

€

110

€

110

€

110

€

110

€

110

€

110

€

110

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1


€

110

€

110

€

110

€

110

€

110

€

110

€

110

€

110

€

110

€

110

You can describe 1 as ten tenths

€

1010=1.0


Compare or 0.1 to 1 and to 10

€

110

€

110

0.1


Compare or 0.1 to 1 to 10 on a numberline

€

110

0 1 2 3

0.1


Compare to 1 to 10on a numberline

€

110

0 5 10 15

1

imagery for decimals

Documents