Numbers, Operations, and Relationships PDF

Numbers, operations and Relationships Numbers, operations and relationships focuses on the: development of number sense for learners. This includes the meaning of different kinds of numbers, the relationships between different kinds of numbers, the relative size of different numbe...

Numbers, operations and Relationships Numbers, operations and relationships focuses on the: development of number sense for learners. This includes the meaning of different kinds of numbers, the relationships between different kinds of numbers, the relative size of different numbers, and representation of numbers in lots of different ways.  Place value of the digits By place value we mean the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 517 389 is 7 Thousands or 7 000. However, the place value of 7 in 715 389 is 7 Hundred thousands or 700 000.  Expanded notation Digits in a number can be represented using expanded notation (breaking down the number). For example, the number 517 389 can be represented using expanded notation,e.g. 500 000+ 10 000+ 7000+ 300+ 80+ 9  Activity What is the correct number of the following expanded notations: a) 30+4+ 2000+ 500+ 60 000 b) 2+2+ 40+30+ 800+ 6000+ 70 000  Answers a) 62 534 b) 76 874  Counting in ascending order(arranging from the smallest to the largest)and descending order(from the largest to the smallest) Arrange these numbers in ascending order: 34 289, 34 288, 34 287, 34 286, 34 285, 34 284 How to teach ascending/descending order 1. You look at the value of each digit if they are the same in each number, e.g. Ten thousand, Thousands, Hundreds and Tens are the same. 2. You look at the values of each digit if they are different/changing, e.g. ones/units are different/changing 3. Arrange the digits that are changing/different from the smallest to the largest, e.g. 4,5,6,7,8 and 9. 4. Write the full number, e.g. 34 284, 34 285, 34 286,34 287, etc 5. In descending order, you will start with the bigger number,e.g.34 289, 34 288.  Activity Write down 5 steps that you can follow using the following numbers: 556, 554, 555, 557, 559, 558.  Answer 1. You look at the value of each digit if they are the same in each number, e.g. Hundreds and Tens are the same. 2. You look at the values of each digit if they are different/changing, e.g. ones/units are different/changing. 3. Arrange the digits that are changing/different from the smallest to the largest, e.g. 4,5,6,7,8 and 9. 4. Write the full number, e.g. 554, 555, 556, 557, 558, 559. 5. In descending order, you will start with the bigger number, e.g. 559, 558, 557, 556, 555, and 554.  Describing numbers in word form Numbers can be represented or written in words. For example, 399 can be stated as Three hundred and ninety-nine. 587 256 in the word form is Five hundred and eighty- seven thousand, two hundred and fifty- six.  Comparing numbers Comparing numbers is the process of identifying the number that is greater than, smaller than, or equal to another number. There are signs that we use to compare the numbers: Greater than/ smaller than ()NB- The sign opens on to the side of the greater number) , e.g. 567> 555  Use of basic operations There are four basic operations in mathematics: 1. Addition- We use this operation when we want to find out the total of the two or more numbers; e.g. 5+3= 8( The total of five and three is eight) 5+3+2= 10 ( The total of five, three and two is Ten).  basic operations-continued Subtraction- is used to find the difference between two numbers, e.g. 10-5=5 ( The difference between ten and five is five)  basic operations-continued Multiplication helps us to find the total number of items quickly, e.g. 3+3+3+3+3+3= 18 can be written using multiplication(6x3 or 3x6).NB-The order of how you place the numbers does not change the product, e.g 6x3=18 and 3x6= 18.  basic operations-continued Division helps us to separate or divide the number of objects into equal size groups. To divide, we need to know the total number of objects or to know the total number of groups ( groups of dogs) Total number of dogs is 15 and the total number of children is 5. If we divide the number of dogs equally to each child, each child will get 3. (15÷5=3).