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Five daily lessons Unit 6 Division, decimals and problem solving Year 6 This Unit Plan is designed to Summer term guide your teaching. Unit Objectives You will need to adapt it to Year 6 meet the needs of your class. Derive quickly division facts corresponding to Page 59 multiplication tables up to 10 x 10. Order a mixed set of numbers with up to three decimal Page 29 Resources needed to teach this unit: places. Solve a problem by extracting and interpreting Pages 115, 117 information presented in tables, graphs and charts. Resource sheet 6.1 Resource sheet 6.2 Resource sheet 6.3 Link Objectives Resource sheet 6.4 Resource sheet 6.5 Year 5 Year 7 OHT 6.1 OHT 6.2 Know by heart all multiplication facts up to Consolidate the rapid recall of number Self-assessment sheet 6.1 10 x 10. facts, including multiplication facts to Self-assessment sheet 6.2 Order a set of numbers with the same number 10 x 10, and quickly derive associated Whiteboards of decimal places. division facts. Calculators Solve a problem by representing and Compare and order decimals in different interpreting data in tables, charts, graphs and contexts. diagrams. Given a problem that can be addressed by statistical methods, suggest possible answers. (Key objectives in bold) Interpret diagrams and graphs. NNS Unit Plans Planning Day One Unit 6 Division, decimals, and problem solving Term: Summer Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Derive facts Write 7 x 8 = 56 on the Solve a problem by On the board, present the table below: Discuss strategies. Write on the board: corresponding to board. Ask the children to extracting and multiplication facts. state facts which can be interpreting information Input Output Q Is this a harder problem, why? Input Output derived from this fact. presented in tables. 2 and 3 4 1, 2 and 3 1 Record their suggestions, 7 and 4 1 Establish there are fewer pairs and no 2, 3 and 4 5 e.g. 0 and 5 10 zeros. 1, 0 and 2 2 1 and 6 11 56 ÷ 8 = 7 4 and 8 12 Q If I tell you that 0 and 7 give an output Ask the children to solve the 5.6 ÷ 8 = 0.7 of 21 does this help? problem. 56 ÷ 0.8 = 70 Explain that the output number can be 5.6 ÷ 0.8 = 7 made using the two input numbers. Encourage the children to use this piece Q What strategy did you use with a 70 x 8 = 560 (Explain that the same operations have of information to see that the second three number input? 70 x 80 = 5600 been used on each pair of numbers in number is multiplied by 3. 7 x 16 = 112 the table.) Collect responses and compare 14 x 4 = 56 Q What other pair of numbers would help strategies. Confirm the rule is 28 x 2 = 56 Q What operations have been carried out you? multiply the first number by the 0.7 x 80 = 56 on the two input numbers to get the third number then subtract the 0.7 x 8 = 5.6 output? Agree that a pair with the second number second number. 0.7 x 0.8 = 0.56 zero would help. Collect answers and discuss strategies. HOMEWORK – Ask the children to Prompt the children to Q If 0 and 0 gives 0 does this help? solve the two tables below: identify, extend and explain Q Which pairs of input numbers gave you particular pattern of facts. most help? Why? Agree it does not and invite the children Input Output to select another pair with a zero, e.g. 1 1, 3 6 Ask the children in pairs to Encourage the children to explain which and 0 gives 2. Confirm the rule is double 4, –1 11 use 6 x 9 = 54 and derive pairs they used to establish a rule and the first number and add triple the second 1, –2 1 as many related facts as which they used to test it. Confirm rule number. Highlight the strategies the 2, –2 8 they can in two minutes. is double second number and subtract children used and draw out the Collect examples to first number. usefulness of the zeros. Input Output identify patterns. 2, 2, 2 6 Write: Set the children to work in pairs producing 1, 5, 0 5 Repeat using another input/output tables of their own. 2, 3, 1 5 multiplication fact with the Input Output Encourage them to have outputs that are 2, 0, 5 10 children recording only 2 and 5 19 negative numbers. Bring pairs together to division facts. 1 and 4 14 solve one another’s problems. Collect (Answer: (3 x x) + (1 x y) = 6 and 4 and 3 17 examples and share with the whole class. (0 x x) + (1 x y) + (2 x z) = 6) Q What operations are used to get the output? Where x is the first number, y the second and z the third. Allow the children a short time to work in VOCABULARY pairs to find the rule. ASSESSMENT – Explain to the input children that during the week they will output be completing ‘My Mathematics’ self- operation assessment sheets they will take to their secondary school. NNS Unit Plans Planning Day Two Unit 6 Division, decimals, and problem solving Term: Summer Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Derive quickly Write 9 x 4 = 36 on Solve a problem by Show OHT 6.1. Collect responses and write the predictions Return to Table 5. division facts the board. Ask the extracting and on the board. Get the children to choose corresponding to children to state interpreting Establish that it contains 36 numbers with one six numbers and find their total from each Q What is the largest number in the multiplication facts. division facts information decimal place. Point to the last column. of the two tables. table? derived from this presented in tables. fact. Record these Q In order, which are the 2 smallest numbers Q Was our prediction correct? Why? Collect the children’s responses. facts, prompt the Order a mixed set of in this column? use of patterns to numbers with up to Agree that the totals were 20 and that the Q How did you scan the table to find your extend the range of three decimal Agree they are 17.7 and 17.9 and write them numbers on Tables 1 and 2 have been answer? facts. places. on the board. divided by 10 to give the numbers on Tables 3 and 4. Discuss the different strategies the Repeat, starting Undertake column Q What numbers lie between 17.7 and 17.9? children used. with other addition of numbers Ask the children to look at Tables 5 and 6. multiplication facts. involving decimals. Collect answers and record the numbers, in Q What is a systematic way of finding the The children work the correct order, between 17.7 and 17.9. Q Can you predict the totals for these two smallest number in the table? in pairs and record tables? answers on Explain to the children that you are going to Collect responses and agree that finding whiteboards. choose six numbers and sum them. Once Collect and record predictions encouraging the smallest number in the first row and you choose a number, you cannot choose the children to justify their predictions. Get comparing this with numbers in Identify some any other number in that row or column. the children to test these predictions. subsequent rows one at a time, is a patterns used and Choose 56.9 say, circle it, cross out the other Agree that the totals are 2 and 2000 systematic method. ask the children to numbers in the row and column containing respectively. Explain to the children that explain them. 56.9. Repeat, e.g. choose 24.4 from the they are going to try to find the answer to remaining numbers. Continue crossing out this question. ASSESSMENT – the relevant numbers until you have six Give out ‘My Mathematics’ Self- numbers left. Get children to add the six Q What is it about the way the numbers are assessment sheet 6.1. Explain that the numbers up. arranged that results in the same totals? sheet is to help the children to identify what mathematics they have been able Q What is the total of these six numbers? Ask the children to identify any patterns in to do during the week. There will be the tables. some time each lesson for them to Collect answers and agree the answer is 200. complete the sheet. Q Are there any connections between Give out Resource sheet 6.1. Tell the numbers in the different rows or Ask the children to work out the first children to use Table 1 and choose six columns? cloud question on the sheet. Say that numbers of their own, using the same you want them to write in the middle process, and add these six numbers up. Encourage the children to use Table 6 and loop, division facts corresponding to 3 x Collect answers and confirm the answers are to work from the numbers in the first row 8. When they have done this, they all 200. to see how the numbers in the other rows should show their work to a friend. are connected. Collect the children’s Some of the children may need help. Get the children to repeat the exercise in observations. Table 2. Agree the total is still 200. Tell the children that they should tick the Q If we add together the first row and adjust box to say if they required any help. RESOURCES Look at Tables 3 and 4. the total in the same way that the rows OHT 6.1 are connected, what number do we get? Give the children a few minutes to Self-assessment Q Can you predict the total for these tables? complete this task and ask them to put RESOURCES sheet 6.1 Build on this to establish how the table was this sheet away ready for their next Whiteboards Resource sheet 6.1 constructed. mathematics lesson. NNS Unit Plans Planning Day Three Unit 6 Division, decimals, and problem solving Term: Summer Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Vocabulary Vocabulary Focus Questions Derive division facts Get the class to Solve a problem by Show the first table on OHT 6.2. Explain that it is Return to the homework corresponding to recite the 8 and 9 extracting and the results of a school sports day. Q How can we use this method to find the points for set on day 1. Ask the multiplication facts. times tables. interpreting first place? children to explain their Repeat. information Q How many events took place? solutions to the two presented in tables. Collect responses and using the Yellow team’s problems. Recite the 8 times Establish that there are 26 first, second and third results work through; table again but this Explain methods places. Yellow team; (10 x F) + (10 x 1) = 60 so Make links between the time stop at a and reasoning. 10 x F = 50 and F = 5. homework and this lesson. particular Q How many points did each team collect? Emphasise that in each multiplication fact. Give out Resource sheet 6.2. Discuss the three case they are finding in the Agree that it depends on the points awarded for tables. Explain that the school was trying out new operation used in this Ask a child to write first, second and third places. Say that there are 3 points systems. Tables 1 and 2 still result in the lesson the points to a related division points for first place, 2 for second and 1 for third same overall order of the four teams. However, multiply the first, second on the board. Ask place. after some complaints, the Blue team was and third places by. another child to reinstated in two events as the winners, and Emphasise that the write another Get the children to work out the points for each another point system was used. This time the number zero is particularly related division and team and record these on the OHT. order of the teams has changed. helpful as multiplying zero so on. Continue by anything still gives zero. until six division Show the second table on OHT 6.2. Compare the Q Can you find the different three point systems facts have been total points in the two tables. used? recorded. Get the ASSESSMENT – rest of the class to Q Why are the totals different? Collect the answers to Table 1. Discuss the Ask the children to confirm the facts strategies the children used. complete the next ‘cloud’ are correct and, in Agree the awarding of points for places is different. question on the ‘My pairs, to use each Say third place is still awarded 1 point. Q How do the positioned results of the Green and Mathematics’ Self- of the six facts to the Red teams differ? assessment sheet 6.1. derive another fact. Q What is the new point-awarding system? Agree that they only differ in their number of Get each child to discuss it Collect some Ask the children to work in pairs to find the new second places. Ask the children to explain how with a friend as before and responses quickly point system. Collect answers and discuss the they might use this information, and to continue tick the appropriate box. and record these children’s strategies. Remind the children that they working on Tables 1 and 2. Help those children who on the board. know third place was awarded one point. need it. Discuss how the children used the Green and Red Repeat stopping at Q What information did you use to find the points teams’ results to find the points for second place. Give the children a few other facts within for second place? Encourage the children to support their minutes to complete the the 8 and 9 times explanations and reasoning using the symbols task and put the sheet tables until the Establish that the Blue team had no first places. introduced earlier, e.g. Green team – Red team; 2 away carefully for the next board is full of On the board write down the statement; x S = 10 so S = 5. lesson. division facts. Blue team; (10 x S) + (10 x 1) = 40. Collect responses to Tables 2 and 3. Remind the Q What does this statement mean? children of the importance of reading carefully the RESOURCES information contained in the tables. Encourage OHT 6.2 Establish that S stands for the number of points for them to invent and use their own symbolism. Resource sheet 6.2 second place and the Blue team had 10 second Compare the different methods the children used. Self-assessment places and 10 third places. With the class deduce sheet 6.1 that this means; 10 x S = 30 so S = 3 points. NNS Unit Plans Planning Day Four Unit 6 Division, decimals, and problem Term: Summer Year Group: 6 sheet solving Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Vocabulary Vocabulary Questions Order a mixed set Write on the board: 2.407. To solve a problem Give out Resource sheet 6.3. Explain that the first half of the sheet sets Stop the class. of numbers with up by extracting and out costs of holidays. Give the children time to read the sheet and to three decimal Q How do we decide whether 2.217 is bigger or interpreting discuss the information contained in the table. Q How are you recording your places. smaller than 2.407? information costings? presented in tables. Q What does it cost to fly to Villa Dream from the East Midlands? Explain methods Collect reasons and discuss the values of the Discuss alternatives and share and reasoning. different digits. Write the two numbers on the Confirm the children can read the information and interpret the strategies. Tell the children to put board with a large gap between the numbers. supplements. their work away carefully as they will continue with the task in the next Q Where should I write 2 and 2.5? Q What will it cost for a ten-year-old child to stay 7 nights in the Grand lesson. Hotel? Establish where these numbers should be recorded and write on the board as: Confirm the children understand the reductions that apply for children ASSESSMENT – under 15. Continue to probe the children’s use and understanding of Ask the children to complete the last 2 A 2.217 B 2.407 C 2.5 D 2.8 E the table. two ‘cloud’ questions on the ‘My Mathematics’ Self-assessment sheet Where A, B, C, D and E are the intervals Explain that the second table on the sheet identifies the local facilities. 6.1, discuss them with a friend and between the numbers. The children might tick the appropriate box. Help any find it helpful if all the numbers had three Q Which accommodation has access to a swimming pool? children who need it. Give the decimal places, e.g. 2 = 2.000; 2.3 = 2.300. children a few minutes to complete Ensure the children can interpret the table correctly. the table. Q Where should I record 2.3? Give out Resource sheet 6.4. Explain that the sheet sets out the Discuss the work with the children The children show their answers using holiday requirements of four families. Give the children time to read the then ask them to put their sheets whiteboards. Discuss why 2.3 is in the set of four requirements. away for next lesson. interval B between 2.217 and 2.407. Repeat using numbers with one, two and three Q Which families enjoy shopping? decimal places. Ensure the children can identify the different holiday requirements of Write the digits 3, 7, 2, 5 on the board. each family. Q Using these four digits, what numbers can Explain to the children that they are to use the information on Resource you make that fit in the interval B? sheet 6.3 to select and cost appropriate holidays for the families. They are to present their findings as short portfolios for each family. Collect answers and establish that 2.375 and 2.357 fit in the intervals. Q What should go in these portfolios? Q Using these four digits, can you make Discuss the children’s ideas and record these on the board. Ensure the numbers that fit in any other intervals? costings include travel and accommodation costs. Ensure that the facilities are also included. Remind children that two of the families Discuss possibilities and establish numbers in have identified budgets and would not be likely to exceed these by interval D only are possible. Give the children much. Explain to the children that they are acting as travel agents who another four digits, e.g. 9, 2, 1, 2 to use. RESOURCES want to sell their holidays so they might want to emphasise key points. Resource sheet 6.3 Discuss how the children might do this. Repeat using another starting decimal Resource sheet 6.4 RESOURCES number, e.g. 7.016. Self-assessment Set the children to work in pairs constructing their holiday portfolios. Whiteboards sheet 6.1 NNS Unit Plans Planning Day Five Unit 6 Division, decimals, and problem solving Term: Year Group: 6 sheet Summer Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/Focus Questions Vocabulary Vocabulary Consolidate Write the following grid on the board: To solve a problem Remind the children about the holiday Collect in the calculators and give out Resource sheet 6.5. Say that this mental skills. by extracting and requirements they were costing and the represents some of the items the families bought before they went on First Second interpreting portfolios they were preparing in the holiday. Number Result Operation Operation information previous lesson. Set the children to presented in tables continue to work in pairs on their planning Q The Ahmeds bought two pairs of sunglasses and a bottle of suntan 4 60 and charts. and costing portfolios. lotion; how much did they spend? As the children complete their portfolios, Collect answers and pose a question about each family. Explain that the children are to identify organise them into groups of four to read two operations that convert 4 into 60. one another’s portfolios and to compare Ask the children to compare the way the information is set out on Resource Say that one operation must be x or ÷, the costings etc. Ask them to decide sheet 6.5 with the tables on the other Resource sheets 6.3 and 6.4. the other + or –. Write three examples whether the portfolios they are reading: on the board: Q When does a table help you; when is a table unnecessary? – give detailed costings for travel and – 1, x 20; x 50, – 120; + 116, ÷ 2. accommodation; Collect responses and discuss the relative merits of the tables and the – identify the facilities that are available; chart. Q Do these three examples work? – are accurate; – meet the budgets of the two families; Collect answers and establish that – sell the holidays to the families. ASSESSMENT – x 50, – 120 gives 80 not 60. Give out ‘My Mathematics’ Self-assessment sheet 6.2. After the children have read one another’s Ask the children for other examples for portfolios, discuss with the class the Allow time for the children to read and complete the three input–output class to check. Change the rules about different holidays that have been offered to tables on the sheet and describe their strategies. the operations and change the the families and the costings involved. As numbers. Use decimals, make the a class, agree on which holidays they think Discuss the solutions to the problems with the class. result negative, have a result smaller meet the requirements of the different than the start number. families and confirm the costs of the Explain that the table on the bottom half of the sheet is for the children to holidays. summarise how well they have been able to answer each question. Ask the children to look at the statements in the left-hand column. The questions alongside each statement are intended to remind the children what each statement means. Ask the children to look back on their work to help them fill in the table. Encourage the children to complete each statement by putting a tick in one box. Ask the children to complete the target statement by choosing one of the three areas of mathematics where they think they need to improve. For those children who where able to answer all the questions without RESOURCES help, discuss the learning objectives for Year 7 shown on the front page of Calculators the unit. Resource sheet 6.5 Get the children to stick ‘My Mathematics’ Self-assessment sheets 1 and 2 Self-assessment in their books under their work. sheet 6.2 NNS Unit Plans

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posted: | 3/20/2010 |

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