Students Starting at Level 4 Working on Level 4/5 in Year 11

Students starting at level 4 working on level 4/5 in year 11

·  The following learning programme example is divided into three terms of work. Each term has an overarching mathematical and statistical focus to support the learning.

·  Possible teaching and learning activities are given, from which teachers could select activities that best meet the needs of the students in their class/school. In addition teachers could select teaching and learning activities that they currently use, or source others that would meet student needs and address the focus.

·  Each term has a list of possible achievement objectives to select from, the choice of which will depend on the teaching and learning activities selected.

·  The intent is to be more holistic in the selection of achievement objects to allow for natural connections between and within strands.

·  Some achievement objectives could be summatively assessed directly through achievement or unit standards; others could be assessed through in-class formative or summative assessment. Not all achievement objectives need to be assessed.

Term One – Geometrical focus

The focus for this term is to place a geometrical lens over the teaching and learning of mathematics and statistics.

Term Two – Statistical focus

The focus for this term is to place a statistical lens over the teaching and learning of mathematics and statistics.

Term Three – Graphical focus

The focus for this term is to place a graphical lens over the teaching and learning of mathematics and statistics.

*means that there is a web link listed at the end

#means that there is a book reference at the end

Ideas for teaching and learning activities / Suggested achievement objectives – selected from below depending on the teaching and learning activities chosen /
Term One – Geometrical focus
·  Culturally locating our students in the class*
·  Mapping and orienteering
o  Field trips – link to Geography
o  Geocaching
o  Trigonometry – trig points on hills
o  Landscaping – link with technology
o  Mapping and orienteering – link with Health and PE
o  Navigation
o  Satellite and Astronomy – link with Science and Physics
o  Matariki – link with Languages, especially Maori
o  Waka ama
o  The Pacific
o  GPS trails around the school
·  2D and 3D shapes – links with Technology and Visual Arts
o  Modelling
o  Scale diagrams
·  Transformational geometry
o  Interactive websites
o  Geometric patterns in different cultures – from a geometric and algebraic sense
§  Kowhaiwhai*
§  Islamic art*
§  Siapo
§  Mosaics
§  Friezes
§  Escher
§  Penrose tiles*
o  Describing linear patterns:
§  Perimeter fences, areas and volumes, for example, stacking sugar cubes
§  Tukutuku patterns*
o  Kaleidoscopes
o  Telescopes and microscopes – link with Science and Physics / Number strategies and knowledge
NA4-1 Use a range of multiplicative strategies when operating on whole numbers.
NA4-2 Understand addition and subtraction of fractions, decimals, and integers.
Patterns and relationships
NA4-8 Generalise properties of multiplication and division with whole numbers.
NA4-9 Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
Shape
GM4-5 Identify classes of two- and three-dimensional shapes by their geometric properties.
GM5-5 Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
GM5-6 Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.
Position and orientation
GM4-7 Communicate and interpret locations and directions, using compass directions, distances, and grid references.
GM5-7 Construct and describe simple loci.
GM5-8 Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
Transformation
GM4-8 Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
GM5-9 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
GM5-10 Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.
Measurement
GM4-1 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
GM4-2 Convert between metric units, using whole numbers and commonly used decimals.
GM4-4 Interpret and use scales, timetables, and charts.
Geometrical focus continued
·  MCTP Professional Development Package: Activity Bank#
o  Danger distance (#1, p100)
o  Volume of a room (#1, p151)
o  Platonic Solids (#1, p203)
o  Regular polygons (#1, p232)
o  Mental Map (#2, p340)
o  Estimation (#2, p 411)
o  How many people can stand in your classroom? (#2, p445)
Term Two – Statistical focus
·  CensusAtSchool activities* – Level 4/5:
o  Rumbling tummy
o  Chocolicious
o  Armspans
o  Speedster
o  Which average?
o  Scatter it
o  Time flies
o  The case of the missing cake
o  Bear Hugs 1, Bear Hugs 2, Bear Hugs 3
o  Nosey Parker 1, Nosey Parker 2
o  Are you getting enough zzz?
o  8 glasses per day
o  Who wants to be a millionaire?
o  Big foot
o  A tall tale
o  Tell it like it is!
o  Masterpiece 1, Masterpiece 2, Masterpiece 3
o  Posing summary investigative questions
o  Using data cards
o  Analysis tools
o  Cleaning data / Number strategies and knowledge
NA4-1 Use a range of multiplicative strategies when operating on whole numbers.
NA4-2 Understand addition and subtraction of fractions, decimals, and integers.
NA4-4 Apply simple linear proportions, including ordering fractions.
Measurement
GM4-1 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
GM4-2 Convert between metric units, using whole numbers and commonly used decimals.
GM4-4 Interpret and use scales, timetables, and charts.
Statistical investigation
S4-1 Plan and conduct investigations using the statistical enquiry cycle:
A determining appropriate variables and data collection methods
B gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends
C comparing distributions visually
D communicating findings, using appropriate displays.
S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
A determining appropriate variables and measures
B considering sources of variation
C gathering and cleaning data
D using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets
E comparing sample distributions visually, using measures of centre, spread, and proportion
F presenting a report of findings.
Statistical literacy
S4-2 Evaluate statements made by others about the findings of statistical investigations and probability activities.
S5-2 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
Probability
S4-3 Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.
S5-3 Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.
S5-4 Calculate probabilities, using fractions, percentages, and ratios.
Term Three – Graphical focus
·  Patterns
o  Growth and patterns in nature
o  Triangular numbers, square numbers, pentagonal numbers
o  Multiple representations, tables, graphs, equations
·  Using experiment and data from other learning areas
o  Time related data
o  Temperature related data
o  Linear relationship data, for example, springs and weights
o  Links to Technology, Science, Social Science
·  Graphs tell stories
o  A picture tells a thousand words; write the thousand words for the graph as a class, five groups of five – 200 words per group. Be descriptive, one page per group, one paragraph each.
o  Links to literacy, numeracy, concepts of gradient, interpreting graphs, focus on features of graphs, relationships. /

Number strategies and knowledge

NA4-1 Use a range of multiplicative strategies when operating on whole numbers.
NA4-2 Understand addition and subtraction of fractions, decimals, and integers.
NA4-3 Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-4 Apply simple linear proportions, including ordering fractions.
NA4-5 Know the equivalent decimal and percentage forms for everyday fractions.
NA4-6 Know the relative size and place value structure of positive and negative integers and decimals to three places.
NA5-1 Reason with linear proportions.
NA5-2 Use prime numbers, common factors and multiples, and powers (including square roots).
NA5-3 Understand operations on fractions, decimals, percentages, and integers.
NA5-4 Use rates and ratios.
NA5-5 Know commonly used fraction, decimal, and percentage conversions.
NA5-6 Know and apply standard form, significant figures, rounding, and decimal place value.

Equations and expressions

NA4-7 Form and solve simple linear equations.
NA5-7 Form and solve linear and simple quadratic equations.

Patterns and relationships

NA4-8 Generalise properties of multiplication and division with whole numbers.
NA4-9 Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
NA5-8 Generalise the properties of operations with fractional numbers and integers.
NA5-9 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.

*WEB Links

·  Culturally locating our students in the class NEEDS LINK WHEN ESTABLISHED

·  Tukutuku patterns – on NZMaths http://www.nzmaths.co.nz/node/394

·  Penrose tiles –

o  Wikipedia http://en.wikipedia.org/wiki/Penrose_tiling;

o  Wolfram mathworld http://mathworld.wolfram.com/PenroseTiles.html;

·  Kowhaiwhai –

o  at the Auckland Museum http://www.aucklandmuseum.com/site_resources/library/Education/Teachers_Guide/Teacher_Resources_Library/Maori_Education_Kits/Maori_02Kowhaiwhai_1_.pdf;

o  on NZMaths http://www.nzmaths.co.nz/resource/k-whaiwhai;

·  Islamic art – Pattern in Islamic Art http://www.patterninislamicart.com/

·  CensusAtSchool - http://www.censusatschool.org.nz/classroom-activities/

#Book resources

#1 Lovitt, C., & Clarke, D. (1992). MCTP Professional Development Package: Activity Bank Volume 1. Carlton, Victoria: Curriculum Corporation

#2 Lovitt, C., & Clarke, D. (1992). MCTP Professional Development Package: Activity Bank Volume 2. Carlton, Victoria: Curriculum Corporation

possible assessment PROGRAMME

Most likely these students will be working with the three numeracy unit standards.

US 26623 Use number to solve problems 4 credits Internal

US26627 Use measurement to solve problems 3 credits Internal

US26626 Interpret statistical information for a purpose 3 credits Internal

For information on numeracy unit standards: http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/ncea-rules-and-procedures/secondary-schools-supporting-information/literacy-numeracy-2011/unit-standards/#note1

In addition complementary achievement standards may be offered if students were working at a suitable level some of the following maybe appropriate:

1.1 Apply numeric reasoning in solving problems 4 credits Internal

1.5 Apply measurement in solving problems 3 credits Internal

1.9 Apply transformation geometry in solving problems 2 credits Internal

1.10 Investigate a given multivariate data set using the statistical enquiry cycle 4 credits Internal

1.11 Investigate bivariate numerical data using the statistical enquiry cycle 3 credits Internal

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