Level 4 learning programme example
- The learning programme examples are 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 1 – Geometrical focus
The focus for this term is to place a geometrical lens over the teaching and learning of mathematics and statistics.
Ideas for teaching and learning activities
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Activity: Culturally locating our students in the class
- Mapping and orienteering:
- Field trips – link to geography
- Geocaching
- Trigonometry – trig points on hills
- Landscaping – link with technology
- Mapping and orienteering – link with health and PE
- Navigation
- Satellite and astronomy – link with science and physics
- Matariki – link with languages, especially Māori
- Waka ama
- The Pacific
- GPS trails around the school
- 2D and 3D shapes – links with technology and visual arts:
- Transformational geometry:
- Interactive websites
- Geometric patterns in different cultures – from a geometric and algebraic sense
- Kōwhaiwhai
- Islamic art
- Siapo
- Escher
- Penrose tiles
- Mosaics
- Friezes
- Describing linear patterns:
- Perimeter fences, areas and volumes, for example, stacking sugar cubes
- Tukutuku patterns
- Kaleidoscopes
- Telescopes and microscopes – link with science and physics
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
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.
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Term 2 – Statistical focus
The focus for this term is to place a statistical lens over the teaching and learning of mathematics and statistics.
Ideas for teaching and learning activities
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CensusAtSchool activities – Level 4/5:
- Rumbling tummy
- Chocolicious
- Armspans
- Speedster
- Which average?
- Scatter it
- Time flies
- The case of the missing cake
- Bear hugs 1, Bear hugs 2, Bear hugs 3
- Nosey parker 1, Nosey parker 2
- Are you getting enough zzz?
- 8 glasses per day
- Who wants to be a millionaire?
- Big foot
- A tall tale
- Tell it like it is!
- Masterpiece 1, Masterpiece 2, Masterpiece 3
- Posing summary investigative questions
- Using data cards
- Analysis tools
- Cleaning data
Suggested achievement objectives
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.
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Term 3 – Graphical focus
- Patterns:
- Growth and patterns in nature
- Triangular numbers, square numbers, pentagonal numbers
- Multiple representations, tables, graphs, equations
- Using experiment and data from other learning areas:
- Time related data
- Temperature related data
- Linear relationship data, for example, springs and weights
- Links to Technology, Science, Social Science
- Graphs tell stories:
- 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.
- Links to literacy, numeracy, concepts of gradient, interpreting graphs, focus on features of graphs, relationships.
Suggested achievement objectives
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.
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Links
Resources
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Lovitt, C., & Clarke, D. (1992). MCTP professional development package: Activity bank volume 1. Carlton, Victoria: Curriculum Corporation.
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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.
- US26623 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
In addition, complementary achievement standards may be offered if students are working at a suitable level. Some of the following maybe appropriate:
- AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
- AS91030 Mathematics and statistics 1.5 Apply measurement in solving problems – 3 credits; Internal
- AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems – 2 credits; Internal
- AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
- AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle – 3 credits; Internal
Last updated September 9, 2018
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