3.6 Fractions with squares

• Colour the circles that have been cut in half. The halves must be the same size.

• Complete these number lines.

• Mark halfway between 0 and 10 with an X.

• Mark halfway between 10 and 20 with an X.

• Mark halfway between 20 and 30 with an X.

Rounding off numbers

• Look!

The truck has travelled past the halfway mark X as far as 8.

• The car has not yet reached the halfway mark X at 5.
• To round off the distance that the truck travelled to the nearest multiple of 10 , we can say 8 can be rounded off to 10.

It is nearer to 10 than to 0 .

In the same way numbers 5, 6, 7 and 9 can be rounded off to the nearest multiple of 10, which is 10.

But numbers 4, 3, 2, 1 cannot be rounded off to 10 because they are less than halfway to the next multiple of 10.

They are nearer to 0 than to 10.

• To round off these numbers;

14 becomes 1 0

16 becomes 20

18 becomes ________________________

11 becomes ________________________

12 becomes ________________________

15 becomes ________________________

17 becomes ________________________

19 becomes ________________________

7 becomes ________________________

6 becomes ________________________

8 becomes ________________________

9 becomes ________________________

• My alarm clock rang at half past six.
• The long hand was on the six and the short hand halfway between the six and the seven.

The long hand had travelled halfway around the clock, from 12 to 6.

• 

  Complete the times on these clocks.

Fractions with shapes

• Take a square piece of paper.
• Fold it in half.
• Fold it in half again.

• Open the paper and cut along the folds.
• How many pieces are there? _______________________pieces.
• Each part is called “one quarter,” which means one of 4 parts .

• Colour in one quarter.

• How many quarters will be equal to one half?
• Colour in the quarters to show one half.

• _______________________ quarters make one half.
• _______________________ quarters make one whole.

• Look!
• Shapes that are divided into 4 equal parts have been divided into quarters .
• Colour in one quarter in each of these shapes.

• Colour in 2 quarters.

• 2 quarters are equal to _______________________
• 4 quarters are equal to _______________________

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.7: We know this when the learner solves and explains solutions to practical problems that involve equal sharing and grouping and that lead to solutions that also include unitary fractions (eg. ¼);

Assessment Standard 1.10: We know this when the learner uses the following techniques:

1.10.1 building up and breaking down numbers;

1.10.2 doubling and halving;

1.10.3 using concrete apparatus (e.g. counters);

1.10.4 number-lines.

Learning Outcome 4: The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assessment Standard 4.1: We know this when the learner reads analogue and digital clock time in hours and minutes.