1.2 Doubling and halving

Mathematics

Mathematics in the world around us

Educator section

Memorandum

Critical and developmental outcomes:

The learners must be able to:

1. identify and solve problems and make decisions using critical and creative thinking;

2. work effectively with others as members of a team, group, organisation and community;

3. organise and manage themselves and their activities responsibly and effectively;

4. collect, analyse, organise and critically evaluate information;

5. communicate effectively using visual, symbolic and/or language skills in various modes;

6. use science and technology effectively and critically, showing responsibility towards the environment and the health of others;

6. demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation;

7. reflect on and explore a variety of strategies to learn more effectively;

8. participate as responsible citizens in the life of local, national, and global communities;

9. be culturally and aesthetically sensitive across a range of social contexts;

10. explore education and career opportunities; and

develop entrepreneurial opportunities.

MODULE 1

• Integration of Themes: Friends
• Inclusively: Although we are all unique, we share many similarities; appearance, sport, education etc.
• Social Justice: Friends and their expected behaviour towards one another.
• A healthy environment: This is our responsibility – what can we do about keeping our environment healthy?

Educator’s page

Doubling

• Pick up 1 counter / block / bean in one hand.
• Pick up the same number in the other hand.
• How many?
• How many altogether?
• We can say 1 + 1 = 2
• What have we done?
• We have taken the same number in the other hand.
• We say WE HAVE DOUBLED ONE.
• One doubled is equal to 2.
• Follow the same steps with 2, 3, 4 and 5 so that learners understand the concept of doubling.
• Ask each one individually in order to assess whether he understands the term "double" and whether he can work out the doubles.
• How else can we double numbers besides using counters? Draw?
• Look around the room: Can you see any place where numbers are doubled?E.g. 4 windows on the left side and 4 windows on the right side.Lights?Body parts? - eyes, ears, hands, feet, fingers, toes.

Halving

Halving means sharing out equally between 2 people. Work on the mat, e.g.

• Take 2 countersShare them out between 2 childrenHow many will each get?What happens if we put the 2 counters together again? We will have 2. What is that called? Doubling.
• Take 4 counters.
• Follow steps as for 2
• Take 6
• Take 8
• Take 10

Leaner section

Content

Activity: doubling and halving [lo 1.10, lo 1.2, lo 1]

Doubling and Halving

Liz and Mike go for a walk.

They see all these doubles. They can halve them too.

Can you?

• Make sums with your doubles.

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• Doubling and halving

• I keep my things tidy.

• I have ______________________ pairs of socks.

• I have ______________________ socks altogether.

2 + 2 + 2 + 2 =____________________

2 taken 4 times is equal to ______________________

• I have ______________________ pairs of shoes.

• I have ______________________ shoes altogether.

2 + ___________ + ___________ = ___________

2 taken ___________ times is equal to ___________

• My shirts are stacked in 2's.

• I have ______________________ shirts altogether.

2 + 2 = ______________________

2 taken ______________________ times is equal to __________________

• I stack my toys

• Complete

3 boys wear _______________socks. 2 + 2 + 2 = _______________

5 girls have _______________eyes. 2 + 2 + 2 + 2 + 2 = _______________

1 mom has _______________ hands. 2 + 0 = . _______________

Pat and Ann have _______________ hands. 2 + 2 = _______________

Mike and Sisulu have _______________ shoes. 2 + 2 = _______________

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their 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 1.2: We know this when the learner counts forwards and backwards in:

1.2.1 ones from any number between 0 and 200;

1.2.2 tens from any multiple of 10 between 0 and 200;

1.2.3 fives from any multiple of 5 between 0 and 200;

1.2.4 twos from any multiple of 2 between 0 and 200;

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;