VIEWS: 17 PAGES: 6 POSTED ON: 7/17/2011
Five daily lessons Unit 8 Properties of numbers and reasoning about numbers Year 4 This unit plan is designed to Spring term guide your teaching. Unit Objectives Year 4 You will need to adapt it to meet the needs of your class. Recognise negative numbers in context (e.g. on a number line, on a Page 14 temperature scale). Recognise and extend number sequences formed by counting from any Page 16 number in steps of constant size, extending beyond zero when counting Resources needed to teach this unit: back. Make and investigate a general statement about familiar numbers by finding Resource sheet 8.1 examples that satisfy it. Resource sheet 8.2 Explain methods and reasoning about numbers orally and in writing. Page 76 Resource sheet 8.3 Resource sheet 8.4 Resource sheet 8.5 Link Objectives Resource sheet 8.6 Resource sheet 8.7 Year 3 Year 5 Activity sheet 8.1 Order whole numbers to at least 1000 Order a given set of positive and negative OHT 8.1 and position them on a number line. integers (e.g. on a number line, on a temperature OHT 8.2 Describe and extend number scale). Large number cards, -5 to 5 sequences: count on or back in tens Recognise and extend number sequences formed Whiteboards or hundreds starting from any two- or by counting from any number in steps of constant Number fans three-digit number. size, extending beyond zero when counting back. Counting stick Investigate a general statement about For example: count in steps of 25 to 1000, and then Thermometer Interactive Teaching familiar numbers by finding examples back; count on or back in steps of 0.1, 0.2, 0.3… Program downloadable from website that satisfy it. Make and investigate a general statement about (www.standards.dfes.gov.uk) Explain methods and reasoning orally familiar numbers by finding examples that satisfy it. OHP calculator and, where appropriate, in writing. Explain a generalised relationship (formula) in Class set of calculators words. Thermometers Explain methods and reasoning. (Key objectives in bold) NNS Unit Plans Planning Day One Unit 8 Properties of numbers and reasoning Term: Spring Year Group: 4 sheet about numbers Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Questions Vocabulary Vocabulary Read and write Display Resource sheets 8.1 Recognise negative Discuss the activity and check the answers. whole numbers up to 8.5 in the following way: numbers in context e.g. Q Where would you see/use negative numbers? to 10 000 presented Using the interactive thermometer, ask children 8.3 in words and digits. 8.1 on a number line Introduce negative numbers through the context of temperature. Compare to look at the third thermometer on Activity 8.2 8.5 on a temperature scale. temperatures of different resources, central heating, a fridge, a freezer. sheet 8.1. Ask questions such as the following 8.4 Compare climates and discuss times of year when temperature was below for them to answer orally, demonstrate their zero. Look at a room and other thermometers together, pointing out the responses with the interactive thermometer. Say a number and point to negative values. the words on the display: Q What will the temperature be if it rises by 3oC? Draw a vertical number line on the board with zero marked in the middle e.g. ‘Three hundred and fifty- and 5 divisions above, 5 divisions below. Ask children to count on from Q What will it be if it drops by 2oC? six’; ‘Six thousand, nine zero as you point to the appropriate divisions above it on the line, then back hundred and one’. to zero. Point to the –1 position. Q What temperature is 3 degrees below zero or freezing point? Ask children to write the Q What does this mark represent? numbers in digits on their Q What temperature is 2 degrees above whiteboards. Establish it is a negative one and repeat for the other negative values. negative 6 degrees? Explain that numbers above zero are positive numbers, numbers below Write a number in digits on zero are negative numbers. Give examples of above and below freezing. the board, ask children to Write all the numbers (-5 to 5) alongside the line. Ask the class to count say the number and a back from 5 to –5, then up to 5. volunteer to point to the By the end of the lesson the children should words on the display. Write Draw a horizontal line: be able to: a number in digits and ask children to write the number in words on their Order a set of positive and negative whiteboards. 5 numbers; -5 Locate positive and negative numbers on a number line; Q Which whole numbers lie between –5 and 5? Use negative numbers in the context of temperature. In response to each suggestion, point along the line, asking children to tell you when to stop. (Refer to supplement of examples, section 6, VOCABULARY negative page 14.) positive Extend the line to –6 and 6. Ask the class to count back from 6 to the other above and below zero end of the line. Hand out cards –5 to 0 inclusive. Ask the children to come out and position themselves in order. Repeat with cards, from –5 to 5 using different children to order themselves. RESOURCES Give out Activity sheet 8.1. Ask children to complete the number lines. RESOURCES Thermometers Collect answers. Resource sheet 8.1 Activity sheet 8.1 Resource sheet 8.2 Large number cards –5 Discuss the four thermometers. Explain that each thermometer tells the Resource sheet 8.3 to 5 temperatures in degrees Celsius and 0oC is freezing point. Resource sheet 8.4 Thermometer Resource sheet 8.5 Interactive Teaching Ask children to fill in the missing temperatures. Whiteboards Program NNS Unit Plans Planning Day Two Unit 8 Properties of numbers and reasoning Term: Spring Year Group: 4 sheet about numbers Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Recognise negative Use a counting stick held Make and investigate a Draw a 3 x 3 grid on the board and Model how to start the process of Look again at the first grid. numbers in context. vertically to revise counting general statement about write in the numbers 1 to 9 as shown: investigation using a different set of between positive and familiar numbers by numbers, e.g. 6–14. Ask the children in pairs to discuss negative numbers. finding examples that the following: satisfy it. 1 2 3 Ask children to investigate this Use program ‘Thermometer’ statement using Resource sheet 8.6. Q Are any of the statements made or display OHT 8.1. Discuss true for all sets of numbers? the scale on the thermometer, 4 5 6 When children have investigated the identify zero and the value of statement and satisfied themselves Remind the children of the initial the intervals on the scale. that this is a general statement, ask: general statement. Point to a value and ask 7 8 9 children to write it on their ’Using the numbers 1, 1, 1, 2, 2, 2, 3, After a few minutes, choose pairs of whiteboards to show. Repeat 3, 3, can you fill in a grid where all the children to share their ideas with the for different values. rows, columns and diagonals total the class. Point out that 1-9 are consecutive same?’ numbers and show how they are Q What will this temperature arranged in the grid in order. be after a rise of 3 degrees, Ask the children to investigate this a fall of 4 degrees? statement using Resource sheet 8.6. By the end of the lesson the Ask children to total the middle row and the middle column, then each children should be able to: Demonstrate using the After the children have had a few tries Investigate a given statement by diagonal. thermometer to confirm the ask the following questions. finding and testing examples; children’s answers. Q What do you notice? Understand the term ‘general Q Will it work with 2 in the middle? 3 statement’. in the middle? Discuss and agree a statement and record it on the board, e.g. (Refer to supplement of examples, Q Where do the even numbers need section 6, page 80.) In this grid the middle row, the middle to be? column and each diagonal have a total of 15. When the majority of the class are convinced it can’t be done, ask: Q What other statements could you make? Q Can you explain why? VOCABULARY positive e.g. All the corner numbers are odd negative etc… above/below zero minus Tell the children you are going to give VOCABULARY them a general statement to total investigate. next, consecutive RESOURCES general statement Write on the board: OHT 8.1 Thermometer ’When nine consecutive numbers are Interactive Teaching arranged in order in a 3 x 3 grid, the Program RESOURCES middle row and column have the Counting stick Resource sheet 8.6 same total as each diagonal’. NNS Unit Plans Planning Day Three Unit 8 Properties of numbers and reasoning Term: Spring Year Group: 4 sheet about numbers Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Read and write Return to the display of Resource Make and Write 1 + 2 + 3 on the board. Discuss children’s findings numbers up to sheets 8.1 to 8.5. Point to a investigate a and agree statements for 10 000. number and ask children to read general statement Q What sort of numbers are these? each case. the number aloud as you point. about familiar Round three-digit Ask children to write the number in numbers by finding Ask children to find the total. Record it then write: Q Can you think of a numbers to the digit form on the board. examples that statement for the sum of nearest 10 or 100. satisfy it. 2+3+4= any odd number of Q What is 1000 more/100 less than 3+4+5= consecutive numbers? this? 4+5+6= 5+6+7= Discuss, allowing time for Q What do you get when you add children to collectively 200/subtract 1000/take away 50 Ask children to describe the list, copy the list and, record each total. Ask children to formulate the wording for the from this number? continue the pattern of calculations by three lines or more. statement, with your help if necessary. Ask children to say the answers Ask them to look at the totals. aloud and to point to the numbers Q What numbers could we on the display as they do so. Q Is there a pattern in the totals? Can you describe it? use to test the statement? Remind children about the rules for Q How might you explain it to someone? Collect answers and check rounding to the nearest 10, then the children’s calculations. the nearest 100. Establish that the totals are consecutive multiples of 3, starting at 6. Write on the board a three-digit Agree the general statement: ‘The sum of any three consecutive numbers is a multiple of By the end of the lesson the multiple of 10, e.g. 370. Ask 3’ and write it on the board. children should be able to: children to suggest numbers that Find examples that match when rounded to the nearest 10 Ask the children to find further examples to satisfy the statement. Encourage them to try a general statement; would give that number. Record larger numbers. Make and explain a them on the board. general statement. Discus results, ask for some examples and establish that the general statement appears to Repeat for a three-digit multiple of be true. (Refer to supplement of 100, asking children to give examples, section 6, page numbers that would make that Q Is it true for every set of three consecutive numbers? Can we see any relationships? 80.) number when rounded to the nearest 100. Q Is there a relationship between the totals and the numbers in each set? Provide other numbers for children Encourage children to offer reasons and explanations. Look at the adding of 1 to each to use number fans to show number to get the next three consecutive numbers and the property that the sum of three numbers that would round to them. consecutive numbers is 3 x the middle number. VOCABULARY nearest ten Q How many possible numbers are Q Can you use the rule to work out the sum of 29 + 30 + 31 without adding them together? nearest hundred there that would round to 460? round up round down Ask children to add groups of five consecutive numbers 1 + 2 + 3 + 4 + 5, 2 + 3 + 4 + 5 + 6 Q What about 300? VOCABULARY etc. and look for any patterns. Encourage them to make a general statement and test it by consecutive using other examples, e.g. 101 + 102 + 103 + 104 + 105. Collect answers and discuss multiple RESOURCES strategies. example Number fans pattern NNS Unit Plans Planning Day Four Unit 8 Properties of numbers and reasoning about Term: Spring Year Group: 4 sheet numbers Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Recall multiplication Play ‘Ping Pong’ for Make and Write a starting number on the board, e.g. 4. Identify the rule for the sequence x 4. Draw on the board: facts in the 3 and 4 x4 facts. The teacher investigate a times table. sets a rhythm with the general statement Write ‘the rule is + 3’. Statement children as shown about familiar 1st cross → 1 + (1 x 4) , … Begin to recall below, then gives a numbers by finding Discuss the rule and how to generate the 2nd cross → 1 + (2 x 4) multiplication facts number for children to examples that sequence using the rule. 3rd cross → 1 + (3 x 4) in the 6 times table. give the x 4 product satisfy it. Q Which table will generate within the rhythm set. Get children to recite the sequence formed, i.e. Test this sequence? Repeat the start number Recognise and 4, 7, 10, 13, 16, 19, 22. 10th cross → 1 + (10 x 4) twice to consolidate the extend number Write on the board: product. sequences. Q Is 34 in our sequence? In pairs get children to investigate and record in the same way, the number of posts needed 1 + ( ٱx ?) Teacher Children Continue counting to establish 34 is in the to make a fence. ping pong sequence. Test suggestions. ping pong ping pong Write 34 = 4 + ( ٱx 3). , , … Q What shape or symbol could 3 12 we use to generate a 3 12 Discuss this with the children and establish 10 sequence using the 6 times 7 28 goes in the box. Emphasise that you are Q Where have you seen a sequence like this table? 7 28 adding on a multiple of 3. before? 5 20 Give children two minutes to 5 20 Repeat for other sequences. Q Can we write each statement as work in pairs with 1 + ( ٱx 4)? whiteboards. Repeat for 3 x facts. Present this problem to the class: Introduce the 6 times Ask children to investigate the numbers of Collect ideas from the class table. Start in order 1 to Q How many squares will there be in the 10th posts used to build these huts: and discuss, e.g. 10, then randomly. cross? , , , … HOMEWORK – Practise six times Q What is the rule for the huts? table. What statement can we make? How do we test it? By the end of the lesson the children should be able to: Give children time to read the question and Investigate a problem by with the class work through the stages shown using the following skills: below. - recording - identifying a sequence Recording - making a general statement VOCABULARY - testing the statement. Cross Squares sequence VOCABULARY multiple 1 5 2 9 (Refer to supplement of multiply rule examples, section 6, pages 76 product predict 3 13 4 17 and 80.) NNS Unit Plans Planning Day Five Unit 8 Properties of numbers and Term: Spring Year Group: 4 sheet reasoning about numbers Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Recall Get the class to chant the 2 Make and Remind children of homework. ‘In the first table the sum of three numbers Discuss the activity, ask for multiplication facts times table, saying each investigate a in an L-shape always has factors 5 and 3.’ examples and record them on in 2, 3, 4 and 6 number statement twice. general statement Ask the class to count in 6s from zero to the board. times tables. about familiar 60. Show OHT 8.2 and ask class to Ask children to cover three numbers of their Repeat the chant this time numbers by finding count in 6s again. own using the L-shape, and sum them. Q If we extend the table to saying the 2 times table examples that numbers larger than 100, will followed by the 4 times table, satisfy it. Q How does OHT 8.2 help you with this Q Are your numbers multiples of 5 and our statement still work? i.e. counting? multiples of 3? Explain methods Use an example from the 1 x 2 = 2; 1x4=4 and reasoning. Establish that the last column in the table Collect responses and get the class to extended table and with the 2 x 2 = 4; 2x4=8 helps as these numbers are multiples of amend the statement, using calculators to children work through using the 3 x 2 = 6; 3 x 4 = 12… 6. confirm that the numbers are not always OHP calculator. multiples of 5. Highlight the doubling Q What can you say about the other Remind the children about their process. columns? ’The sum of three numbers in an L-shape is learning in this unit by asking always a multiple of 3.’ them the following question. Q What table could help us Establish that the 2nd, 4th and 6th learn our six times table? columns are multiples of 2, the 3rd and Ask children to find other examples that test Q Tell me three things you have 6th columns are multiples of 3. this. learnt in this unit? Get the class to chant the 3 times table, saying each Give out Resource sheet 8.7. Collect some examples to confirm the number statement twice. statement. Q What can you say about columns in the Repeat the chant but saying first and second table? Explain that you want the children to use the By the end of the lesson the the 3 times table, followed by second table and this time cover four children should be able to: the 6 times table, i.e. Identify the columns that have multiples numbers using a 2 x 2 square. Demonstrate Find examples that match a of 2, 4 and 5. Explain that you are going using: general statement; 1 x 3 = 3; 1x6=6 to use an L-shape to cover three numbers Explain methods and 2 x 3 = 6; 2 x 6 = 12 on the first table and then add these three 43 44 reasoning orally and record 3 x 3 = 9; 3 x 6 = 18… numbers. Demonstrate using the three work systematically. numbers: 48 49 Remind the children that the (Refer to supplement of numbers in the 6 times table 22 examples, section 6, pages 76 are double the numbers in the and add the numbers with the OHP and 80.) 3 times table. 26 27 calculator. 43 + 44 + 48 + 49 = Play ‘Ping Pong’ to practise 2, VOCABULARY Ask children to find sums of their own and With the OHP calculator show children 3, 4 and 6 times tables. Set a multiple make a statement they can test using how to find the sum of 22 + 26 + 27 = 75. rhythm then give numbers for factor examples of their own. children to respond with Q What do we know about this number? products as shown below: Collect children’s statements and gather Identify the number on the other two them into a common statement that children (x 3) Teacher Children RESOURCES can test with their own examples e.g. tables to establish that 75 has factors 5 ping pong OHT 8.2 and 3. Use the OHP calculator to confirm ping pong Resource sheet 8.7 ’In the second table the sum of four this. Make the statement: ping pong OHP calculator numbers in a 2 x 2 square always has a 5 15 Class set of factor of 4’. 9 27 calculators NNS Unit Plans