To represent, recognise and compare numbers

Content

Activity: To represent, recognise and compare numbers [LO 1.3]

To be able to calculate correctly [LO 1.8]

To improve mental arithmetic skills [LO 1.9] 1. If you know your tables very well it is easy to multiply and divide, especially with greater numbers. Work with a friend. See how quickly you can catch the correct fishes that go with the multiplication tables, by colouring them in. 1.1 8× table - green 1.2 9× table - blue 1.3 12× table - yellow

2. Now let us see whether you can improve your mental arithmetic skills! Work on your own and complete the following mental arithmetic test as quickly and accurately as possible! (Note: in Mathematics brackets mean “do that bit first”). 2.1 14 + 9 + 4 = _________________ 2.2 Halve 137: _________________ 2.3 30 × _________________ = 3000 2.4 (42 ÷ _________________) + 9 = 16 2.5 567 _________________ 23 = 590 2.6 9 × 6 = _________________ 2.7 _________________ × 8 = 56 2.8 _________________ - 15 = 285 2.9 80 + 65 + 155 = _________________ 2.10 1 003 - 19 = _________________ 2.11 72 ÷ 9 = _________________ 2.12 (5 × 6) + 13 = _________________ 2.13 108 ÷ _________________ = 8 2.14 _________________ ÷ 12 = 6 2.15 Double 67: _________________ 2.16 (5 × _________________) - 9 = 11 2.17 11 × 12 = _________________ 2.18 _________________ ÷ 7 = 12 2.19 Round off to the nearest 100: 3 550 _________________ 2.20 Round off to the nearest 1 000: 7 299_________________ Colour in: My previous mental arithmetic mark was: BETTER WORSE THE SAME

3. In this activity it is important to look at the value and place value of every digit. Work with a friend and see whether you can answer the following questions: 3.1 Which number is 1 more than 9 999? _________________________________ 3.2 Which number is 10 more than 9 990?________________________________ 3.3 Which number is 100 more than 9 900?_______________________________ 3.4 Which number is 1 000 more than 9 000?______________________________ 3.5 The number 10 000 is 10 more than __________________________________ 4 Let's see if you were right! TEN THOUSANDS DO YOU REMEMBER? 10 units = 10 × 1 = 10 10 tens = 10 × 10 = 100 10 hundreds = 10 × 100 = 1 000 4. Complete the following: 10 thousands = 10 × ......................... = ......................... In the notation column it looks like this: × 10 × 10 × 10 × 10 Ten thousands Thousands Hundreds Tens Units TT T H T U 10 000 1 000 100 10 1 10 × 10 × 10 × 10 10 × 10 × 10 10 × 10 10 × 1 1 × 1 ÷ 10 10 ÷ 10 ÷ 10

DID YOU KNOW? We read 43 685 as: forty three thousand, six hundred and eighty five 5. In our everyday lives it is also important to be able to say numbers correctly in words, because it will help us to compare numbers with one another. Write the following numbers in words: 5.1 23 918 _________________________________________________________ 5.2 47 007 _________________________________________________________ 6. A number line can also help you represent numbers more easily. You can "see" where they lie on the number line and compare them more easily. Study the number line below: 6.1 Which numbers are, omitted at A, B, C, D and E?

A: __________________________________________________________________ B: __________________________________________________________________ C: __________________________________________________________________ D: __________________________________________________________________ E: __________________________________________________________________ 6.2 Now take turns with a friend to show where the following numbers will be on the number line. Use an arrow: a) 8 979 b) 11 003 c) 12 250 d) 14 997 e) 16 016 7. It is important to calculate answers correctly. To do this, we must decide what to do. Decide how you are going to calculate the answer of each question. Then fill in the missing numbers. Then compare your work with that of a friend. 7.1 10 000 = ___________________________________________ thousands 7.2 10 000 = ___________________________________________ hundreds 7.3 10 000 = ___________________________________________ tens 7.4 6 × 10 × 10 × 10 × 10 = ______________________________________ 7.5 500 × ________________________________________________ = 50 000 7.6 3 000 × _______________________________________________ = 30 000 7.7 26 567 is 10 000 less than _________________________________________ 7.8 ________________________________________ is 10 000 more than 6 824 7.9 _________________________________________is 50 000 less than 53 612 7.10 15 000 lies exactly halfway between _______________________ and 20 000 LET’S REVISE! DO YOU STILL REMEMBER? If you are asked to round off 627 to the nearest 10, it simply is a different way of asking: Is 627 nearer to 630 or to 620? Let us have another look at the number line:

627 is nearer to 630. If we therefore round 627 off to the nearest 10, the answer will be 630. NOTE THIS: If the number is exactly halfway between two numbers, e.g. 625, we round it off to the higher number. The answer will therefore be 630. LET’S REVISE MORE

CHALLENGE Are you able to complete the following?

1. Rounding off can help you to estimate answers quickly. In this way you can determine what an answer should be approximately. Use your existing knowledge of rounding off and complete: Round off to the nearest 100: 1.1 a) 624 ___________________ b) 896 ___________________ c) 450 ___________________ d) 1 239 ___________________ Round off to the nearest 1 000: 1.2 a) 3 429 ___________________ b) 8 140 ___________________ c) 25 712 ___________________ d) 56 500 ___________________ 1.3 True or False? a) 249 rounded to the nearest 100, is 200 ____________________________ b) 587 rounded to the nearest 100, is 600_____________________________ c) 11 450 rounded to the nearest 1 000, is 11 000_______________________ d) 23 811 rounded to the nearest 1 000, is 24 000_______________________ NUMBER CORRECT CODE 1 – 4 1 5 – 8 2 9 – 12 3 13 – 15 4

PLAY THIS GAME Work with a friend. Use playing cards from which the 10, Jack, Queen, King, Ace and Joker have been removed. Player A chooses any five cards and places them face up, e.g. 5 ; 7 ; 1 ; 2 ; 1 Player B now has to arrange the cards to obtain the highest possible number, e.g. 75 321. Write it down. Then player B arranges the cards to obtain the lowest number possible, e.g. 12 357. Write it down. Next, player B calculates the difference between the 2 numbers with the help of a pocket calculator. Take turns to use all the cards in this way and compare your answers. Do you detect any pattern?

TIME FOR SELF-ASSESSMENT ONCE MORE At this stage we would like to know how YOU feel about the work we have done thus far. Be honest and colour in the right block! I know the 8×, 9× and 12× tables to 12 × …. And have seen the patterns in each ______ ______ ______ I understand the meaning of ten thousands ______ ______ ______ I am able to read numbers from a number line ______ ______ ______ I am able to round off to the nearest 100 and use rounding off to estimate and to solve problems ______ ______ ______ I am able to round off correctly to the nearest 1 000 and use rounding off to estimate and to solve problems ______ ______ ______