Maths Year 6 Weekly Plan: Autumn Week 2: Decimals and written addition Objectives: Understand place value in numbers with 3 decimal places; Divide by 10,100 and 1000 to give answers with 3 decimal places; Multiply numbers with 3 decimal places by 10, Tuesday Monday 100 and 1000; Position 3-place decimal numbers on a number line and begin to round to the nearest whole, 0.1 or 0.01; Compare numbers with 3 decimal places; Solve problems involving number; Add 2 or 3 amounts of money using column addition; Add 2 or 3 numbers with two decimal places in a measures context, e.g. metres; Use rounding to check answers. Starters Whole class teaching Guided group and independent paired/indiv practice activities Plenary Place nos with 2dp on a line Understand place value in numbers with three decimal places Most children/Harder I’m thinking of Chn play in pairs. They Display a place value chart showing 1s, 0.1s, 0.01s and 0.001s Chn complete place value number sentences, e.g. 1 + 0.5 + a number. I shuffle a pack of 0–9 cards (see resources). Point to the line of 0.001s and remind chn that □ = 1.583 (see resources). add 0.005 to it and sketch a 0–1 line for these are 1/1000s. Ring a number on each line and ask chn to and get 0.245. GUIDED: Y6 Easier them both to use. The 1st write the total on their w/bs. Repeat, but this time missing out What was my Draw a place value grid on the f/c with column headings: child takes 4 cards and uses the 0.1s or 0.01s. Point out how we use zero as a place holder to 100s, 10s, 1s, 0.1s, 0.01s and 0.001s. Write the number 3.45 number? Write them in order to make a pair show that there are no 1s, 0.1s or 0.01s but not to show there the addition. in it. What happens to each digit when we divide by 10? of numbers to mark on the are no 0.001s if there are no decimal places afterwards, e.g. we I’m thinking of Each digit moves one place to the right. Ask a child to write line, e.g. 0.36 and 0.47. The write 3.45 not 3.450. What happens to the digits as each number in the new number, i.e. 0.345. Chn work in pairs to write a a number. I other child takes the next is multiplied by 10? 100? 1000? And when nos are divided by 10? add 0.1 to it place value addition for this, i.e. 0.3 + 0.04 + 0.005. Write two cards and tries to make a 10? 1000? Display a place value grid showing 1s, 0.1s, 0.01s and and get 6.196. 25.6 in the grid. This time we are going to divide by 100. number in between. If 0.001s (see resources). Write 2 in the grid. What will happen if we What happens this time? Ask a child to write the number in What was it? successful they win that divide 2 by 100? Agree that the 2 will move 2 places to the right What addition the grid and all chn to write the PV addition. Repeat for round; if not the 1st child and write zeros to show there are no 1s or 0.01s. The 2 is 1/100 can you write? 245.6 ÷ 100 and 780.6 ÷ 100. Chn then think of their own does. Swap and repeat on a of its previous value, so it is now worth 2/100. Repeat for 2 ÷ Rpt. numbers between 100 and 1000 to divide by 100. This prenew line. 1000. Ask chn to multiply 0.02 by 10 and divide 0.02 by 10. teaching should help them with Tuesday’s lesson. Count in steps of 0.01 Multiply and divide by 10, 100 and 1000 Whole class practice Ask several and 0.1 through Give four chn number cards, e.g. 1, 2, 3 and 4, Task 1: Chn work out the outputs, for × 10, ÷ 10, × 100, ÷ 100, × 1000 and ÷ 1000 pairs to share multiples of 0.1 and 1 and ask them to stand on either side of a large function machines (see resources). some of their Count round the class in decimal point on the f/c to show 1.234. Ask them Task 2: Chn work in pairs to take it in turns to choose a machine, then secretly inputs and steps of 0.01 from 4.85 to multiply their number by 10 and move think of an input, work out the output and tell their partner the output. The outputs. The to at least 5.15 and accordingly. Do the class agree? × 10 again, then partner guesses the input. If correct, they both record the corresponding rest of the back. Count in steps of ÷ 100, × 100, then ÷ 1000. Repeat with 4 new chn number sentence. Answers should have no more than 3 decimal places. class guess 0.1 from 2.34 to at least showing 4567, ÷ 1000, × 10, × 100, ÷ 100, × 10 Easier: Chn just do Task 1, and work in pairs using a place value grid (see day 1 which function 4.44 and back. etc. Occasionally pause and ask questions such resources) and digit cards to help. machine was as: what is the 7 worth now? And if we ÷ by GUIDED: Medium used. 1000? And if we × by 10? Sit with different groups to do Task 2. © Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. MATHS Y6 Week 2 Autumn Friday Thursday Wednesday Maths Year 6 Weekly Plan: Autumn Week 2: Decimals and written addition Starters Whole class teaching Guided group and independent paired/indiv practice activities Plenary Round nos with 2dp to Place numbers with 3 decimal places on lines; round to the nearest 0.01, 0.1 Most children/Harder Ask chn to nearest 1 and 0.1 or 1; Compare 2 numbers Chn place numbers with 3 decimal places on lines, think of a Play Dartboard rounding at Show chn a 0–0.1 landmarked line (see resources). Challenge them to think of then solve ‘Who am I?’ puzzles (see resources). number http://www.topmarks.co.uk a number with 3 decimal places that lies between 0.01 and 0.02. Ask two chn GUIDED: Y6 Easier between 3 /Flash.aspx?f=DartboardRo to write their nos on the line. Ask them to explain how they did this. Are they Write nos 5.289, 5.974, 5.278 and 5.419 on cards. and 4 with 3 undingv2. Choose TU.t(h) – closer to 0.01 or 0.02? Rpt for nos between 0.07 and 0.08 and round each to decimal Chn put them in order from smallest or greatest. nearest whole. Chn round the nearest 0.01, asking pairs of chn to compare their nos. Show the 0–1 places. They Sketch a line from 5 to 6, marking on 0.1s. each number to the nearest landmarked line. Ask chn to think of numbers between 0.4 and 0.5 with 3 work as a Together mark and label where each number whole. Next ask chn to decimal places. Ask two to place them on the line; the rest of the class say group to put belongs on the line. Does this match their ordered round the nos with 2dp to whether they round to 0.4 or 0.5. Repeat with a 4–5 empty line, asking chn to list? Ask chn to make up four new numbers them in the nearest tenth. place nos between 4 and 5. Class say whether they round to 4 or 5. order. between 5 and 6 and repeat. Pairs of nos with Add 2 or 3 amounts of money using column addition; Use rounding to check answers Whole class practice Ask chn to work in 1dp and a total Show chn three DVDs, with price labels £10.49, £14.79 and £12.25. Ask chn to round to the Chn practise using column addition to pairs to write an of 10 nearest pound in order to give an estimate of the total cost. Show chn how to use compact add two then three amounts of money; addition of three Play ‘ping pong’. addition to find the total cost. Remind them that we always leave a line below the numbers they do as many questions as they can, amounts (Easier You call out a we are adding so we have room to write any digits we have to add in. So 9p, 9p and 5p is starting at question 5 (see resources). group could add to number with one 23p, so we write 3 under the pennies and 2 in the 10p column to stand for 20p. Do this. Now Easier: Chn start at question 1 adding amounts) that decimal place, we have 40p, 70p, 20p and 20p, making £1.50 all together, so we write 5 under the 10p mostly two amounts. they think will e.g. 3.6. Chn say column, and 1 in the pound column, waiting to be added to the other pounds. Finish the Harder: Chn start at question 9 and add have an answer the complement addition and compare the answer with chn’s estimate. Add the £10s to complete the three amounts. between £50 and to 10, e.g. 6.4. addition. Ask chn to use compact addition to find the total cost of three DVDs costing £15.79, GUIDED: Medium £60. They swap Occasionally say £8.69 and £12.45 after estimating the total. But just before you do, what do you think will be Work with chn to support them in with another pair ‘ping’ to which important about laying this addition out? Agree that it is important to align the decimal adding three amounts, encouraging to check. No zeros they reply ‘pong’. points. Take feedback and agree the answer. them to estimate first. allowed! Complements to the Add 2 or 3 numbers with 2 decimal places in a measures Most children/Easier A scientist has added next whole context, e.g. metres; Use rounding to check answers Chn practising adding pairs of distances, with one ‘carry’ then two a pair of distances Write the following Say that a group of scientists are investigating how far ‘carries’ (see resources). They then answer a question requiring from the following, numbers on the board snails crawl in a day. Sally the snail crawled 10.57 metres them to round each answer. but can’t remember in a 3 × 4 grid: 3.79, in the morning and 8.36 metres after lunch. Ask chn to which they were! GUIDED: Harder 2.64, 8.45, 7.25, 9.58, round each distance to the nearest metre to estimate the Say that Selina Snail crawled 9.34m in the morning, 6.45m in the Write 12.46m, 9.78m, 3.96, 6.85, 8.78, 5.37, total. Show how to set this out as a column addition, 10.24m and 11.67m afternoon, and 4.78m in the evening. Ask chn to round each 8.51, 4.43, 7.05. Chn pointing out how you are aligning the decimal points. Talk distance to the nearest metre to estimate the total, then work on the board. She only copy the grid but write through adding the centimetres, e.g. 7cm and 6cm gives needed the answer to together to find the total. What is this distance to the nearest how much more is 13cm, then write 1 under the 10s of cm. Repeat for the nearest metre, metre? And nearest 10cm? Challenge chn to work in pairs to use needed to make the Sidney Snail who has crawled 12.34m, then 10.86m. and thus as 24m. the digits 1 to 9 to write additions of three numbers, each with 2 next whole, e.g. Carefully talk through adding 30cm and 80cm to give 1m Which two numbers decimal places. They can only use each digit once in each sum. writing 0.21 in the first and 10cm. Point out how this is very similar to adding do you think she They find the highest total possible, the least and then the closest space. amounts of money. added? that they can to 10m. © Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. MATHS Y6 Week 2 Autumn Maths Year 6 Weekly Plan: Autumn Week 2: Decimals and written addition Resources 0–9 cards Monday: 10s, 0.1s, 0.01s, 0.001s place value chart (see resources) Monday: 100s, 10s, 0.1s, 0.01s, 0.001s place value grid (see resources) Monday: Activity sheet of place value additions and subtractions (see resources) Large digit cards Tuesday: Activity sheet of function machines (see resources) Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx?f=DartboardRoundingv2 Wednesday: Landmarked lines (see resources) Wednesday: ‘Who am I?’ activity sheet (see resources) Three DVDs, with price labels £10.49, £14.79 and £12.25 Thursday: Whole class practice (see resources) Friday: Adding distances activity sheet (see resources) Abacus Year 6 Textbook 1 Abacus Textbook Pages for Alternative/Additional Practice Day Tuesday Wednesday Friday Group Easier/Most children Harder Easier Harder Easier/Most children Harder Page Textbook 1, page 6 Textbook 1, page 7 Textbook 1, page 8 Textbook 1, page 10 Textbook 1, page 20 Textbook 1, page 21 The links to the websites and the contents of the web pages associated with such links specified on this list (hereafter collectively referred to as the ‘Links’) have been checked by Hamilton Trust (being the operating name of the registered charity, William Rowan Hamilton Trust) and to the best of Hamilton Trust’s knowledge, are correct and accurate at the time of publication. Notwithstanding the foregoing or any other terms and conditions on the Hamilton Trust website, you acknowledge that Hamilton Trust has no control over such Links and indeed, the owners of such Links may have removed such Links, changed such Links and/or contents associated with such Links. Therefore, it is your sole responsibility to verify any of the Links which you wish you use. Hamilton Trust excludes all responsibility and liability for any loss or damage arising from the use of any Links. Scroll down for Outcomes © Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. MATHS Y6 Week 2 Autumn Maths Year 6 Weekly Plan: Autumn Week 2: Decimals and written addition Outcomes Monday Tuesday 1. Understand the effect of multiplying and dividing by 10, 100 and 1000. 2. Understand place value in numbers with 3 decimal places. 3. Solve place value addition and subtractions. 1. Understand the effect of multiplying and dividing by 10, 100 and 1000. 2. Understand place value in numbers with 3 decimal places. Outcomes for most children Wednesday 1. Place numbers with 3 decimal places on landmarked and empty number lines. 2. Use knowledge of decimals to solve puzzles. Thursday Friday 1. Use column addition to add three amounts of money, e.g. £45.78 + £25.79 + £24.85. 1. Use column addition to add three distances, e.g. 9.34m + 6.45m + 4.78m. 2. Use rounding to estimate totals. Default (outcomes for children not on statements but not able to reach the outcomes for most children) 1. Use PV grids to multiply and divide by 10, 100 and 1000. 2. Begin to understand place value in numbers with 3 decimal places. 3. Write place value additions. 1. Use PV grids to multiply and divide by 10, 100 and 1000. 2. Understand place value in numbers with 3 decimal places. 1. Place numbers with 3 decimal places on landmarked lines. 2. Use this to help order numbers with 3 decimal places. 1. Use column addition to add any pair of amounts of money, e.g. £45.78 + £25.79. 1. Use column addition to add pairs of distances, e.g. 10.34m + 11.75m with one or two ‘carries’. Only record names of children who struggled or exceeded these outcomes © Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. MATHS Y6 Week 2 Autumn