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# Counting

Module by: Siyavula Uploaders. E-mail the author

## Counting

### Begin to solve problems in context

NUMBERS, OPERATIONS AND RELATIONSHIPS

• Numbers are wonderful. We need them every day in our lives. Welcome to the wonderful world of numbers, figures and symbols. We hope to travel with you on the journey of exploration in the world of numbers, so let’s start.

1. COUNTING IN THE EVERYDAY WORLD

• In the Foundation Phase you learnt to count to at least 1 000. See how well you can complete the following exercise:
• Each day airlines need to work with many numbers. Imagine you are a member of a ground crew and you are counting paper coffee mugs for the passengers on an aircraft.

1.1 You are counting them in 2s and have reached 592. Write down the next five numbers:

1.2 Now you decide it is quicker to count them in 5s. You reach 980. Write down the next five numbers:

1.3 You are still counting paper cups for the aircraft but now you decide to count them in tens. You have reached 660. Write down the next five numbers:

1.4 Now you are in a hurry! You count them in 25s. You reach 725. Write down the next five numbers:

1.5 You have enough paper cups for a month! Count them in 50s from 800 to one thousand and fifty and write down these numbers:

1.6 The plane is about to take off! Now you are really in a hurry! Count them in hundreds from 0 to 1 100 and write down the last five numbers:

1.7 The distance from Cape Town to Johannesburg is one thousand, four hundred and two kilometres. Write this distance in numbers:

Now we know you can count to 1 000. Can you make your calculator count in 2s without pressing  2 each time?

Press 2  = = = =

Some calculators need the command: 2   = = = = or

2  K = = = =

2.2 Make your calculator start at 1 004 and count on in 2s

Clear your calculator. Now press 1 004 + 2 = = = =

Some calculators need: 2 + + 1 004 = = = =

2.3 How will you make your calculator “count backwards”?

Clear your calculator. Begin with 7 190 and count backwards in 2s.

Some calculators need: 2 - - 7 910

Always remember to clear your calculator before you begin. Now you are ready to begin the “Group Work”.

You should do the next few exercises for five minutes each day for the rest of the first term at least, until you find them really easy. Numbers may be changed.

3. COUNTING FORWARDS AND BACKWARDS (Oral group work):

Now that you have learnt how to make your calculator count backwards and forwards in intervals, check that you can still do so too, aloud. You may work in groups. Only one learner in each group will be using a calculator. Your educator will explain how to play this game, so listen carefully.

3.1 Count on in 2’s from 186 to 204. Count backwards in 2s from 208 to 194.

3.2 Count on in 3’s from 0 to 36. Count backwards in 3s from 36 to 0.

3.3 Count on in 5’s from 375 to 425. Count backwards in 5s from 545 to 485.

3.4 Count on in 10’s from 950 to 1 020. Count backwards in 10s from 950 to 840.

3.5 Count on in 25’s from 625 to 1 000. Count backwards in 25s from 975 to 675.

3.6 Count on in 50’s from 550 to 1 050. Count backwards in 50s from 750 to 350.

3.7 Count in hundreds from 400 to 1 100. Count backwards in 100s from 1 000 to 0.

4. COUNTING FORWARDS AND BACKWARDS (Individually):

5. COUNTING WITH LARGER NUMBERS (Oral individual work):

• Remember to use your calculator as an investigative (learning) tool if necessary:

5.1 Count on in 2s from 9 980 to 10 000. Count backwards in 2s from 5 010 to 4 990.

5.2 Count on in 3s from 8 982 to 9 000. Count backwards in 3s from 1 836 to 1 800.

5.3 Count on in 5s from 4 870 to 5 015. Count backwards in 5s from 9 125 to 8 980.

5.4 Count on in 10s from 8 960 to 9 020. Count backwards in 10s from 5 100 to 4 980.

5.5 Count on in 25s from 7 625 to 7 750. Count backwards in 25s from 10 000 to 9 875.

5.6 Count on in 50s from 8 250 to 8 500. Count backwards in 50s from 9 750 to 9 500.

5.7 Count on in hundreds from 5 400 to 6 000. Count backwards in 100s from 7 000 to 6 000

HANDS ON! WRITTEN WORK. Now use your calculator as an investigative tool and complete the written work:

## Assessment

LEARNING OUTCOME 1: Numbers, Operations and Relationships

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: 1.1 The learner is able to count forwards and backwards in a variety of intervals (including 2s; 3s; 5s; 10s; 25s; 50s and 100s) between 0 and 10 000;

Assessment Standard 1.10: The learner is able to use a range of techniques to perform written and mental calculations with whole numbers including:

• building up and breaking down numbers;
• rounding off and compensating;
• doubling and halving;
• using a number-line;
• using a calculator.

Assessment Standard 1.9: The learner is able to perform mental calculations involving: addition and subtraction:

Assessment Standard 1.6: The learner is able toperform mental calculations involving: addition and subtraction:

## Memorandum

COUNTING IN THE EVERYDAY WORLD

• 594; 596; 598; 600; 602
• 985; 990; 995; 1 000; 1 005
• 670; 680; 690; 700; 710
• 750; 775; 800; 825; 850
• 800; 850; 900; 950; 1 000; 1 050
• 700; 800; 900; 1 000; 1 100
• 1 402 km
• COUNTING WITH A CALCULATOR

3. COUNTING FORWARDS AND BACKWARDS

3.1 186; 188; 190; 192; 194; 196; 198; 200; 202; 204

206; 204; 202; 200; 198; 196; 194;

3.2 0; 3; 6; 9; 12; 15; 18; 21; 24; 27; 30; 33; 36

36; 33; 30; 27; 24; 21; 18; 15; 12; 9; 6; 3; 0

3.3 375; 380; 385; 390; 395; 400; 405; 410; 415; 420; 425

545; 540; 535; 530; 525; 520; 515; 510; 505; 500; 495; 490; 485;

3.4 950; 960; 970; 980; 990; 1 000; 1 010; 1 020

950; 940; 930; 920; 910; 900; 890; 880; 870; 860; 850; 840

3.5 625; 650; 675; 700; 725; 750; 775; 800; 825; 850; 875 900; 925; 950; 975; 1 000

975; 950; 925; 900; 875; 850; 825; 700; 775; 750; 725; 600; 675

3.6 500; 550; 600; 650; 700; 750; 800; 850; 900; 950;

1 000; 1 050

750; 700; 650; 600; 550; 500; 450; 400; 350

3.7 400; 500; 600; 700; 800; 900; 1 000; 1 100

1 000; 900; 800; 700; 600; 500; 400; 300; 200; 100; 0

4. COUNTING: (practice)

5. COUNTING WITH LARGER NUMBERS (Oral individual work; control with a calculator if necessary.)

5.9 980; 9 982; 9 984; 9 986; 9 988; 9 990; 9 992; 9 994; 9 996; 9 998; 10 000

5 010; 5 008; 5 006; 5 004; 5 002; 5 000; 4 998; 4 996; 4 994; 4 992; 4 990

5.2 8 982; 8 985; 8 988; 8 991; 8 994; 8 997

5.2 (cont.) 1 836; 1 833; 1830; … 1 800

5.3 4 870; 4 875; 4 880l; … 5 015

9 125; 9 120; 9115; … 8 980

5.4 8 960; 8 970; 8 980; … 9 020

5 100; 5 090; 5080; … 4 980

5.5 7 625; 7650; 7675; … 7 750

10 000; 9 975; 9 950; … 9 870

5.6 8 250; 8 300; 8 350; … 8 500

9 750; 9 700; 9 650; … 9 500

• 5 400; 5 500; 5 600; …6 000

7 000; 6 900; 6 800; …6 000

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