Place Value and Decimals 1 – Objectives Explore the Place Value (PV) chart from thousands to hundredths; Carry out PV addition and subtraction. Key Stage 3 objective: Understand and use place value for integers of any size. You will need: Mini whiteboards or students’ exercise books. © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

PV and Decimals 1 – Mastered it? 1. What is the value of 7 in each of these numbers? 270 7345 6.7 9.17 714.68 2. Write the numbers above in words. Read the numbers aloud for the benefit of any students for whom reading English is an issue. Two hundred and seventy Seven thousand three hundred and forty five Six point seven OR six and seven tenths Nine point one seven OR nine and seventeen hundredths Seven hundred and fourteen point six eight OR seven hundred and fourteen and sixty eight hundredths Students record on mini whiteboards or in back of exercise books. Answers: a) 70, b) 7000, c) 0.7, d) 0.07, e) 700 © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

PV and Decimals 1 – Mastered it? Complete the addition pyramid What happens if you change the position of numbers in the bottom row of the pyramid? Create a number pyramid with a top number 5679. Students record on mini whiteboards or in the back of exercise books. Answers: Middle two numbers 1347 and 1992 Top number 3339 © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

PV and Decimals 1 – Objectives Explore the Place Value (PV) chart from thousands to hundredths; Carry out PV addition and subtraction. If students have demonstrated good understanding, finish here. Otherwise continue to the direct teaching section. © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

PV and Decimals 1 – Direct Teaching What about ‘sixty three point zero nine’? So, where does the number ‘thirty four point six eight’ sit on the place value grid? Make one up for a friend using these place value columns… 10s 1s 0.1s tenths 0.01s hundredths . Students could draw their own PV grids and record on mini whiteboards or in back of books. 3 4 6 8 6 3 0 9 © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

PV and Decimals 1 – Direct Teaching hundredths tenths ones tens hundreds thousands The place value chart is a useful reminder of the value of each digit in a number… Watch out for students who are unsure what each digit represents in a number; they may need more time using PV charts or using PV cards to make numbers. So, this number reads: ‘Five thousand, six hundred and thirty nine’ 5,639 Where did all the zeros go? © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

5,619 PV and Decimals 1 – Direct Teaching 5619 + 3000 8619 What do you need to add to this number to turn the 5 into an 8? 5,619 5619 + 3000 8619 What is the Place Value of the 3? NB Changing the 9 into an 8 will require subtraction, not addition… Answers: 5619 + 3000 = 8619, then, in any order… +200, +70, -1, e.g. 8619 + 200 = 8819, 8819 + 70 = 8889, 8889 – 1 = 8888 Now let’s change the other digits into 8s using three separate Place Value calculations. © Hamilton Trust Keeping Up Term 1 Week 1 Day 1

PV and Decimals 1 – Individual Practice Have a go at the calculations in each box: Choose 3 numbers from this box. Write PV calculations to change all their digits into 9s. 8,793 6,864 5,839 6,264 3,225 4,850 3,675 2,703 The second box is slightly harder as it requires subtraction, rather than addition. Answers: 6264 + 3735 = 9999, 3225 + 6774, 2703 + 7296, 5039 + 4960, 4146 + 5853 8793 – 6571 = 2222, 6864 – 4642, 5839 – 3617, 4850 – 2628, 3675 - 1453 Choose 3 numbers from this box. Write PV calculations to change all their digits into 2s. 5,039 4,146 © Hamilton Trust Keeping Up Term 1 Week 1 Day 1