Number Unit 22号单元.doc

Number Level 2: Number patterns and relationshipsCurriculum focusNumbers, counting and numerationAt this level students develop their ability to count forwards and backwards to 1000 and skip-count to 100. They use various materials to represent groups of 10 and to develop the concept of place-value leading to reading, writing, renaming and ordering numbers up to three digits.They are introduced to the concept of fractions, recognising simple fractional parts of both objects and collections of objects.They use a four-function calculator to explore counting sequences and to consolidate place-value concepts.Key descriptors: count forwards and backwards, skip-count, base 10, place-value, fraction, counting sequences.Mental computation and estimationAt this level students explore the part-whole relationships of numbers less than 20 using materials to support their recall of addition and subtraction facts where necessary. They develop and use strategies of counting-on, counting-back and making up to 10 together with knowledge of doubles and the commutative and associative properties of addition to obtain facts not automatically recalled. They develop estimation strategies for counting and for checking computations with larger numbers.Key descriptors: part-whole relationship, addition and subtraction facts; mental computation strategies, commutative property, associative property, estimation strategies, checking.Computation and applying numberAt this level students develop their ability to use known facts, base 10 materials and diagrams to model trading and regrouping and to assist them in using number sentences to record answers to addition and subtraction algorithms problems.They use informal written methods based on place-value leading to the development of written algorithms for addition and subtraction of whole numbers to 99.They represent, create, model and solve whole-number problems, including those involving all forms of the operations of addition and subtraction and the grouping and sharing interpretations of multiplication and division. These problems may be generated by stories, real situations and pictures involving collections of objects, money and informal units of measurement.Key descriptors: base 10 materials, trading, regrouping, addition and subtraction algorithms, grouping, sharing, multiplication, division.Number patterns and relationshipsAt this level students represent, identify, extend and devise whole number patterns using materials, automatic recall and a calculator. Counting sequences appropriate to this level may involve addition, subtraction, doubling and halving including use of the constant function facility of a calculator.They construct and complete simple statements of equality involving whole numbers, addition or subtraction and use patterns to generate further addition and subtraction equations from a given equation.Key descriptors: whole number patterns, constant addition facility, doubling and halving, equations.Mathematical reasoningAt this level, students consider and check the reasonableness and truth of mathematical statements which occur in space, number, measurement, and chance and data activities appropriate to this level. The emphases are on activity involving the use of materials, and in measurement, on the use of informal units.Key descriptors: check, reasonableness, materials, informal units.Strategies for investigationAt this level, students express mathematical ideas in space, number, measurement and data. They consider and answer questions, including questions that are posed by the students which arise in everyday situations and stories, and test the validity of the answers to these questions.Key descriptors: mathematical idea, question, pose, everyday situation, story, test, validity.Unit overviewIn this unit students will engage in activities that involve: representing and describing simple number patterns exploring patterns in numbers and predicting elements recognising, copying, devising and continuing simple repeating sequences of numbers exploring the functions and operations of a calculator through informal activities using the calculator to explore number patterns exploring and using the patterns and relationships in addition and subtraction equations.Links to other KLAsLinks to Course Advice unitsprevious/next levelMathematics Level 1: Number patterns and relationshipsNumber Level 3: Number patterns and relationshipsConceptual and mathematical languageabove, addition, all over, behind, below, beginning, between, beside, calculator, checking, continue, copy, count forwards and backwards, different, display, division, doubling, end, equations, estimation fraction, grouping, halving, in a line, in front of, last, match, middle, missing, multiplication, next, next to, numbers, order, patterns, place-value, regroup, repeat, size, same, shapes, sharing, skip-count, story, trading, What comes next?, whole number, under, zero.Student learning activitiesTeaching notesAssessment ideasEXPLORE SPATIAL AND NUMERICAL PATTERNS: Books and chooksRecognise patterns in the whole number system. MANUP201Represent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudent use a variety of counting books, number rhymes and chants to explore number patterns and methods of counting.Materials required Counting books, such as:One Woolly Wombat, by Rod Trinca & Kerry ArgentOne Dragons Dream, by Peter PaveyThe Hilton Hen House, by Jo Hinchcliffe.ActivityUse a variety of counting books, number rhymes and chants to explore number patterns and methods of counting. Read the stories, acting them out where appropriate. Focus on the illustrations and numbers to draw out the pattern. Devise strategies for counting the items and recording number sentences. Students share their strategies for counting the total number of items.Teacher reference resourcesOne Woolly Wombat, Rod Trinca & Kerry ArgentOne Dragons Dream, Peter PaveyThe Hilton Hen House, Jo HinchcliffeAssessment adviceChoose individual students to explain to the rest of the class their strategies for counting the items and deciding on the pattern. Record these strategies on the class list.Student learning activitiesTeaching notesAssessment ideasEXPLORE SPATIAL AND NUMERICAL PATTERNS: The mystery missing elementRecognise patterns in the whole number system. MANUP201Represent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudents identify the missing shape in a pattern, and describe the pattern.Materials required Geometric shapes Construction materials Calculators.ActivityCreate a pattern of shapes on the floor, deliberately leaving out a shape, for instance: circle, square, triangle, circle, square, triangle, circle, triangle. Ask students to identify the missing shape and describe the pattern. On completing the pattern, discuss students choice of the missing element. Encourage them to continue the pattern and deliberately leave out a shape, which the class has to identify. (This activity could be adapted for colour and number patterns.) Students repeat the activity in pairs, using construction materials or a calculator.Teacher reference resourcesThe assessment activity has been adapted from, Profiling Mathematics: Tasks for Assessing Learning, Level 2, pp. 5455Young Australia Maths, Teachers Resource Book, Level 1, pp. 125127, Keep the Pattern Going, Collect the Pattern card games.Teaching adviceBingo cards and boards can be designed to reflect pattern sequences, such as:Assessment adviceHave students look carefully at the pattern:Ask: How many pieces will you need to continue it?The students should answer: I think I will need. pieces, then. pieces.Ask them to make a pattern using their own choice of materials, then to draw it.Have them check and record the number of pieces used:I needed. pieces, then. pieces.Have them do the same with this pattern:Ask them to make their own patterns that increase and then give them to others to continue.Student learning activitiesTeaching notesAssessment ideasREPRESENT, CREATE, MODEL AND SOLVE PROBLEMS: Pattern cardsRepresent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudents create patterns using their own choice of materials, then explain their pattern to a classmate.Materials required Blocks, counters or shapes.ActivityHave students create patterns using their own choice of materials, then explain their pattern to a classmate. They need to explain whether it is a repeating pattern and what this means. Once the pattern is confirmed, each student records it accurately on a card (ensuring that the repeating element is shown at least three times). These cards can be used for other students to copy and continue the patterns.Teacher reference resourcesM3 Mathematics: Making Patterns, pp. 1825, Making simple patterns covers using formal and informal materials; pp. 8687, Identifying patterns has students using 10 x 10 grid and writing their names repeatedly to fill the squares. What patterns do you see? Change the size of the grid (6 x 6) and repeat. How has the pattern changed? Why?Rigby Maths 2000, Teachers Resource Book 1, pp. 6068, covers finding, copying, extending, creating and filling in patterns.Macmillan Mathematics, Teachers Resource Book, Level 1, pp. 283284, Something is Missing uses shapes and people.Profiling Mathematics: Tasks for Assessing Learning, Level 2, pp. 3839, Continue the Pattern includes several shape patterns for students to continue and write about.Talking Maths, pp. 2425, Floor Tiles. Students create floor tile patterns using seven colours.Maths Share Activities at home for primary school children and families, Lower level, Card L92, Too Many Socks has students sorting, matching and counting socks, creating and drawing sock patterns.Teaching adviceIt is useful for students creating a pattern to record what they began with, then compare it with the finished pattern, reflecting on how the pattern developed.Assessment AdviceAs students create patterns, note the types of patterns they make, using shape, colour, size and number. Elicit information by asking questions, such as: What can you tell me about your pattern? What makes it a pattern? What will come next?Record students comments as anecdotal records or as part of an annotated class list.Student learning activitiesTeaching notesAssessment ideasRECOGNISE, CREATE AND DESCRIBE NUMBER PATTERNS: Pattern: skipping rhymesRecognise patterns in the whole number system. MANUP201Represent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudents skip with ropes, using the patterns in traditional rhymes.Materials required A book of rhymes, such as Far Out Brussel Sprout by J. Factor Skipping ropes.ActivityStudents skip with ropes using the patterns in traditional rhymes (Two, four, six, eight, Mary at the cottage gate) and new rhymes like those in Far Out Brussel Sprout. These rhymes include elements of number. Ask students questions, such as: What is the pattern you are skipping? (Have them share and justify their patterns). How could you record the pattern for others to use? (Have them share and record their ideas).Students write their own rhymes, creating the skipping patterns to use with them.Share these with others.Teacher reference resourcesFar Out Brussel Sprout by J. Factor.Young Australia Maths, Teachers Resource Book, Level 1, pp. 125127, Keep the Pattern Going, Collect the Pattern card games.Books You Can Count On, pp. 7880, lists books featuring counting, classifying, computation, pattern and order, with brief descriptions of storylines and how they can be used for classroom counting activities.Assessment adviceStudents draw a pattern in a sequence in their maths journals. They write about the rule involved, using their own words.Student learning activitiesTeaching notesAssessment ideasRECOGNISE, CREATE AND DESCRIBE NUMBER PATTERNS: Patterns on the calculatorRecognise patterns in the whole number system. MANUP201Represent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudents work in pairs with a calculator, exploring and sharing patterns.Materials required Calculators (one per pair of students)ActivityCalculators are useful when exploring patterns. Students work in pairs with a calculator, exploring and sharing its functions. Draw a large outline of a calculator on the board and write a number pattern for the students to copy (2 3 3 2 3 3 2). One student copies the pattern onto the calculator, then the other checks the pattern to see if it matches. Ask: What will the next number be? The pattern can be continued on paper. Students swap roles to explore a new number pattern. Partners create patterns for each other to copy.ExtensionStudents use manipulatives to create a physical representation of each pattern. Do they see the individual numbers as quantities (two tiles, three tiles, three tiles, two tiles.) or just symbols (red, blue, blue, red.)?Use number pattern cards in a game. The first to key in the pattern on a calculator wins.Teacher reference resourcesThis activity has been adapted fromMacmillan Mathematics, Teachers Resource Book, Level 1, p. 284.Thinkin Things, Edmark, attributes, spatial relationships, critical thinking and memory skills. Assessment adviceWorking in small groups, students discuss their understandings about patterns. Ask: What is a pattern? How do you know you are looking at a pattern? What ways do you identify the parts of a pattern?Each group can share some of their discussion with the class.Note any misconceptions they may have.Student learning activitiesTeaching notesAssessment ideasRECOGNISE, CREATE AND DESCRIBE NUMBER PATTERNS: Pattern gamesRecognise patterns in the whole number system. MANUP201Represent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudents use a variety of games to develop experience in identifying and explaining rules for continuing a sequence.Materials required Games such as:Pattern dominoes (commercial or home-made), sequenced to make patternsBingo boards and cards can be made that reflect pattern sequences (using shapes, stickers, or wrapping paper designs)Pattern cards can be made for students to use with manipulatives.ActivityA variety of games can be used to develop discussion and experience in identifying and explaining the rules for continuing a sequence.Teacher reference resourcesM3 Mathematics: Making Patterns, pp. 3841, Using numbers to describe patterns. Analyse patterns numerically and assign numbers.Macmillan Mathematics, Teachers Resource Book, Level 1, pp. 281282 Playing with Patterns, Activity Cards. Level 1, Number, Card 31 Square numbers, Card 33, Toothpick puzzles.Assessment adviceStudents reflect on the games by answering the following questions: Is the game fair? If you could change the game in one way, what would you change? What were we practising and looking at when we played this game?Note the knowledge of pattern shown, especially of common elements.Student learning activitiesTeaching notesAssessment ideasRECOGNISE, CREATE AND DESCRIBE NUMBER PATTERNS: Spaceships and peopleRecognise patterns in the whole number system. MANUP201Represent, identify, extend and devise whole number patterns. MANUP202Check the truth of number statements and conjectures as well as the consistency of number patterns arising from operations carried out with materials and informal written methods. MARSR201Focus of the activityStudents use concrete materials to count by twos.Materials required Play-dough Small plastic teddies in two colours (or alternative plastic figures).ActivityStudents make play-dough spaceships carrying a given number of occupants (two plastic teddiesone red and one blue). Ask: How many people are there in all the spaceships in the room? and How can we organise a way to count them? The answer might be: Count blue teddies as a visual cue to skip counting (two, four, six, eight, ten). Create and count patterns with two as the unit (pairs of shoes / socks / gloves / eyes / ears). Explain how the pattern works. Ask: What happens if