Place Value and Decimals 1 – Objectives Explore the Place Value of large numbers by ordering and comparing on a number line. Key Stage 3 objective: Order decimals and use the number line as a model for ordering of the real numbers. You will need: Mini whiteboards or students’ exercise books. © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Mastered it? Compare the size of numbers Which of these symbols belong in each box? >, < or = 34210 3420 70131 71310 94210 53420 Students record on mini whiteboards or in the back of exercise books. Answers: 34210>3420 70131<71310 94210>53420 a=3420 d=34210 g=53420 j=70131 k=71310 n=94210 Which letters on the number line represent the 6 numbers above? © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Mastered it? What is the value of it? Write down: a family member’s age the number of pets you own the number of days in your birthday month this year __________________________________ Look at the digits you have written down. What is the largest number you can create with these digits? Where is the number on this number line? Who in the class has created the largest number? Students record on mini whiteboards or in the back of exercise books. Example A family members age:15 Number of pets you own: 3 The number of days in your birthday month, this year: 30 15,3,30 largest number 53310 © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Objectives Explore the Place Value of large numbers by ordering and comparing on a number line. If students have demonstrated good understanding, finish here. Otherwise continue to the direct teaching section. © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Direct Teaching So, how do we place 32,500 on this number line? 30,000 31,000 32,000 33,000 34,000 35,000 36,000 37,000 38,000 39,000 40,000 32,500 is halfway between 32,000 and 33,000 Then, let’s ‘zoom in’ to this section of the number line Students record on mini whiteboards or in back of books. It’s more than 30,000 and less than 40,000 First, let’s think about which 10,000s it sits between… © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Direct Teaching When placing numbers in order, how do we decide which is bigger? 56,139 46,139 This one has more 10,000s. 56,139 Use the 5 digits in this number to make the smallest and largest possible numbers. Use the animations to work through the teaching input. Model use of appropriate Place Value language during teaching and discussion. 1 3 9 smallest 5 6 9 6 1 largest 5 3 © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Direct Teaching 1. Read the numbers shown by the green arrows. 2. What number is labelled by the blue arrow? a b c d Model use of appropriate Place Value language during teaching and discussion. Students could discuss in pairs, showing responses on whiteboards as necessary. Watch out for students who have difficulty writing numbers where zero is used as a place holder, e.g. the first purple arrow (ca. 10,070). Answers: greens: ‘ten thousand’, ‘eleven thousand’; blue = 10,550; purple a ≈ 10,070, b ≈ 10,250, c ≈ 10,710, d ≈ 10,980 3. What numbers might be shown by the four purple arrows? © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Individual Practice 8 6 Use these 5 digit cards to make a number that will go between the green arrows. 4 3 9 7 5 2 1 Use these 5 digit cards to make a number that will go between the blue arrows. Encourage students to explore a range of possibilities for each set of numbers. For example, the first group could begin with the 6 or the 8. Answers: green arrows: any 5-digit number beginning with 6 or 8, e.g. 60,483 or 83,640 blue arrows: any 5-digit number beginning with the 2, e.g. 29,715 or 21,579 © Hamilton Trust Keeping Up Term 1 Week 1 Day 2

PV and Decimals 1 – Individual Practice Choose a set of numbers to mark as accurately as possible on your 0 - 100,000 number line. 44,000 12,000 78,000 49,900 67,500 43,800 12,300 76,850 49,950 67,450 Encourage students to work as accurately as possible, recognising that working to the nearest ‘one’ is impractical at this scale. NB The red set will be easier to place. Answers: Use animation to reveal. © Hamilton Trust Keeping Up Term 1 Week 1 Day 2