Teacher Notes

Symbols I do: my turn to talk. This is the explanation section of our lesson where you are required to listen. We do: this is where we discuss or work on the concepts together. You do: your turn to be involved. You may be working in a group or on an activity individually.

What is Place Value? Whenever we work with numbers, we work with place value. The two ideas go together like ice cream and chocolate sauce, movies and popcorn, weekends and sleep-ins! But… What is place value? Why is it important? How does it help numbers to make sense? Share your ideas of what place value is and how it works.

Each digit in its place gives a number its overall value. Defining Place Value Numbers are made from digits - 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. When we create numbers using these digits, every digit has a place. Each place within a number has a value. Each digit in its place gives a number its overall value.

Place Value in Base 10 Our numbers use a place value system based on groups of ten. This means that each place value column is ten times larger than the column before. Ten Thousands Thousands Hundreds Tens Ones/Units 10 x 1 thousand 10 x 1 hundred 10 x 1 ten 10 x 1 unit

Applying Place Value to Numbers How do we place each digit correctly when writing a number? Saying the number aloud can help us to do this. e.g. 43 722 (forty-three thousand, one hundred and thirty-two) Ten Thousands Thousands Hundreds Tens Ones/Units 4 3 1 2 4 x 10 000 3 x 1000 1 x 100 3 x 10 2 x 10

Zero as a Place Holder What if a number has no hundreds? No tens? No units? We use a zero as a ‘place holder’ in the number to show this. e.g. 36 099 (thirty-six thousand and ninety-nine) Ten Thousands Thousands Hundreds Tens Ones/Units 3 6 9 3 x 10 000 6 x 1000 0 x 100 9 x 10 9 x 1

From Words to Numbers - Activity Say each number aloud, then add it to the place value chart. T. Th Th H T O/U sixteen thousand, four hundred and twenty-one fifty-three thousand, two hundred and three ninety thousand and seventy-four eighty-nine thousand, one hundred and six thirty-one thousand, nine hundred and twenty-one

From Words to Numbers - Activity Say each number aloud, then add it to the place value chart. T. Th Th H T O/U 1 6 4 2 5 3 9 7 8 sixteen thousand, four hundred and twenty-one fifty-three thousand, two hundred and three ninety thousand and seventy-four eighty-nine thousand, one hundred and six thirty-one thousand, nine hundred and twenty-one

Place Value – Independent Task To revise place value to the tens of thousands, complete the Wendy’s Place Value Wall Worksheet. If you have time, choose five numbers from Wendy’s wall to write in words in your workbook.

What is Partitioning? When working with numbers, especially larger numbers, it can be very helpful to break the number down into smaller parts. Breaking a number down using place value can help us to see each smaller part that the larger number is made from. The process of breaking a number into smaller parts is called partitioning.

Using a Numeral Expander A numeral expander is a helpful tool to use when partitioning numbers by place value. An open numeral expander can show the place value of each digit in the larger number. The numeral expander shows that the number 28 246 has 2 tens of thousands, 8 thousands, 2 hundreds, 4 tens and 6 ones. 2 8 4 6 ten thousands thousands hundreds tens ones

Using a Numeral Expander A numeral expander is designed to bend and fold. This makes it possible to explore the value of the number as a whole (not just the place value of each digit). Here are some examples: 2 8 4 6 ones 2 8 4 6 tens ones 2 8 4 6 thousands tens ones How else could you show the value of 28 246?

Exploring Partitioning - Activity As a class, use a numeral expander to explore all the possible ways to express the value of the number shown below. Record your explorations around the number on the next slide. 9 3 6 7 1 ten thousands thousands hundreds tens ones

Exploring Partitioning - Activity 9 3 6 7 1 ten thousands thousands hundreds tens ones

Partitioning - Independent Task Use the Numeral Expander - Tens of Thousands to explore a 5-digit number of your choice. In your workbook, record all the different ways that you can express the value of your number.

What is Expanded Notation? We have learned that larger numbers can be broken into smaller parts through the process of partitioning. Another method we can use to identify the value of each digit in a number is to write the number in expanded form. The process of writing a number to show the value of each digit is called expanded form or expanded notation.

Using Expanded Notation Here is an example of writing a number in its expanded form. T. Th Th H T O/U 5 4 2 3 1 10 000 1000 100 10 54 231 can be broken in to: 5 tens of thousands 4 thousands 2 hundreds 3 tens 1 ones/units 54 231 = 50 000 + 4000 + 200 + 30 + 1

Using Expanded Notation - Activity Working together as a class, use the Place Value Cards – 10 000, 1000, 100, 10, 1 to model each number from the table. Use these to help you write each number in expanded notation. T. Th Th H T O/U 4 5 8 9 6 3 7 2 1

Using Expanded Notation - Answers T. Th Th H T O/U 4 5 8 9 6 3 7 2 1 = 40 000 + 5000 + 800 + 9 = 60 000 + 3000 + 300 + 70 + 2 = 90 000 + 6000 + 40 + 4 = 20 000 + 2000 + 600 + 50 = 10 000 + 3000 + 800 + 6

Expanded Notation - Independent Task Play a game of Expanded Notation Dominoes with a group of your classmates. As an extra challenge, time yourselves to see how long it takes to match up all the dominoes.

What is Rounding? Sometimes, we just want numbers to be easy and simple! One method of simplifying numbers is rounding. Rounding a number makes the number easier to work with, but keeps the value of the number close to what it originally was. Simplifying a number to make it easier to work with is called rounding.

Rounding Down to the Nearest 10 Find the tens column. Circle the digit. Look at the digit in the units place. Underline it. If the digit in the units place is a 1, 2, 3 or 4, the number will be rounded down. The digit in the tens place will stay the same and the digit in the units place will change to a 0. 63 60

Rounding Up to the Nearest 10 Find the tens column. Circle the digit. Look at the digit in the units place. Underline it. If the digit in the units place is a 5, 6, 7, 8 or 9, the number will be rounded up. The digit in the tens place will increase by 1 and the digit in the units place will change to a 0. 67 70

Rounding Down to the Nearest 100 Find the hundreds column. Circle the digit. Look at the digit in the tens place. Underline it. If the digit in the tens place is a 1, 2, 3 or 4, the number will be rounded down. The digit in the hundreds place will stay the same and the tens and units digits will change to a 0. 213 200

Rounding Up to the Nearest 100 Find the hundreds column. Circle the digit. Look at the digit in the tens place. Underline it. If the digit in the tens place is a 5, 6, 7, 8 or 9, the number will be rounded up. The digit in the hundreds place will increase by one and the tens and units digits will change to a 0. 276 300

Rounding to 100 - Activity Should these numbers round up or down to the nearest 100? Move the birds so they are sitting in the correct nests. 2147 2153 2092 2218 2176 2100 2200

Did the birds find their nests? Rounding to 100 - Answers Did the birds find their nests? 2218 2147 2092 2153 2176 2100 2200

Rounding Numbers – Independent Task In pairs, play a game of Race Up the Rounding Ladder. Once you have finished, try choosing some random number cards to round to the nearest 10, 100 or 1000.

Place Value in Base 10 - Revision As we have learned, our numbers use a place value system based on groups of ten. Each place value column is ten times larger than the column before. 1 10 100 1000 10 000 Look at the numbers in the box. Can you see a pattern?

Making Numbers Larger As we move from the ones column into the tens column, a zero is added. This shows that the number is ten times larger – it has been multiplied by 10. The same thing happens as we keep moving to the left through the columns - the pattern never ends! Ten Thousands Thousands Hundreds Tens Ones/Units 10 000 1000 100 10 1 x 10 x 10 x 10 x 10

Making Numbers Smaller As we move from the ten thousands column into the thousands column, a zero is removed. This shows that the number is ten times smaller – it has been divided by 10. The same thing happens as we move to the right through the columns. Ten Thousands Thousands Hundreds Tens Ones/Units 10 000 1000 100 10 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10

Multiplying and Dividing Multiples of 10 There is a simple shortcut you can use when multiplying and dividing numbers by 10 or 100. To multiply a number by 10, add one zero. To multiply a number by 100, add two zeros. To divide a number by 10, remove one zero. To divide a number by 100, remove two zeros.

Multiplying and Dividing by 10 Work together as a class to complete the table below. x 10 ÷ 10 3790 7040 16 460 67 210 55 800

Multiplying and Dividing by 10 - Answers Work together as a class to complete the table below. X 10 ÷ 10 3790 37 900 379 7040 70 400 704 16 460 164 600 1646 67 210 672 100 6721 55 800 558 000 5580

Multiplying and Dividing - Independent Task In small groups, play the Multiply It and Divide It! Board Game. As an extra challenge, time yourselves to see how long it takes to answer each question.