Year Planner. Years 3/4

Year Planner              Years 3 & 4                 Terms 1-4

Each term revisits concepts and teaching and learning takes individual students to higher level of understanding. 

Individual student growth documented against VELS Progression Points for each topic each term.

 

Addition

 

Strategies include

Counting forwards on 100’s Chart, Open Number Lines, Partial Sums addition, Counting on Addition using Place Value  (Jump strategy).

 

Subtraction

 

Strategies include Counting Backwards on 100’s Chart, Open Number Lines, Counting Up or Counting Back to find difference,

Counting Up using Place Value.

Multiplication

 

Strategies include Making Arrays, Multiplication as Repeated Addition. Partial Products Multiplication and the Area Model for Multiplication (box method).

 

Division

 

Strategies include division as sharing, what to do with left overs, sharing one place value at a time (left to right).

Inverse of multiplication (2x?=6).

Fractions

 

Making explicit links to division and multiplication.

(½ of 6 is 3, 6÷2=3, 2x3=6, 3+3=6, 6-3-3=0).

Denominator is number of groups shared between. Numerator number of groups selected. (Group is the whole & One is the whole).

Shape

 

Location

Chance

Data

Measurement.

Decimals & Percent

Recognise and describe polygons

students sort lines, shapes and solids according to key features.

Recognise and describe the directions of lines as vertical, horizontal or diagonal.

They use grid references (for example, B5 on a street directory) to specify location 

and compass bearings to describe directions.

Locate and identify places on maps and diagrams.

They give travel directions and describe positions using simple compass directions (for example, N for North) and grid references on a street directory.

Investigate natural variability in chance events and order them from least likely to most likely.

Compare the likelihood of everyday events (for example, the chances of rain and snow).

They describe the fairness of events in qualitative terms (likely, unlikely)

Conduct experiments and collect data to construct simple frequency 

graphs.

They use simple two-way tables (karnaugh maps) to sort non-numerical data.

Measure the attributes of everyday objects and events using formal (for example, metres and centimetres) and informal units(for example, pencil lengths).

Recognise and name common three-dimensional shapes such as spheres, prisms and pyramid.

Identify edges, vertices and faces.

Use nets to create three-dimensional shapes and explore them by counting edges, faces and vertices

They use local and larger-scale maps to locate places and describe suitable routes between them.

Plan and conduct chance experiments (for example, using colours on a spinner) and display the results of these experiments.

Interpret timetables and calendars in relation to familiar events.

Tell the time using analogue and digital clocks and relate familiar activities to the calendar

Visualise and draw simple solids as they appear from different positions.

Use two-dimensional nets, cross-sections and simple projections to represent simple three-dimensional shapes.

 

 

Recognise different types of data: non-numerical (categories), separate numbers (discrete)  or points on an unbroken number line (continuous).

Explore the concept of angle as turn (for example, using clock hands) and as parts of shapes and objects (for example, at the vertices of polygons).

Recognise angles are the result of rotation of lines with a common end-point

Investigate simple transformations (reflections, slides and turns) to create  tessellations and designs.

Follow instructions to produce simple tessellations (for example, with triangles, rectangles, hexagons) and puzzles such as tangrams.

 

 

Use a column or bar graph to display the results of an experiment (for example, the frequencies of possible categories).

 

·         Contexts include Whole Number, Length, Time, Mass, Volume, Money.

·         Money used to develop concepts of Decimals within Operations.

·         All strategies emphasise use of Place Value components.

·         Teachers need to make explicit the links between the four operations and Fractions.

·         All activities emphasise the use of Number in student relevant authentic open contexts.

·         Differentiation built into every lesson extending understanding for all students.

 

 

 

 

 

 

Warm Up Activities emphasise the following throughout the year.

Patterns (Counting and Shape), Probability games, Automatic recall of simple number facts (Doubling, adding two one digit numbers, compliments of ten, odd and even, etc), Matching Analogue, Digital and Written time.

 

Problem Solving activities aligned to topics under investigation presented to students weekly to further develop Proficiency Strands of Australian Curriculum (Understanding, Fluency, Problem Solving & Reasoning). Resources include Exemplars, Pictures/Numbers/Words.com)

 

Literacy emphasised for each topic. Students to become fluent in vocabulary of each topic.

 

Written Share/Reflections of developed understandings are standard practice and completed at the end of every lesson.

 

All lessons to explicitly identify to students the Learning Intentions for each lesson.

 

Mathematics - Level 3

Learning focus

As students work towards the achievement of Level 3 standards in Mathematics, they recognise and explore patterns in numbers and shape. They increasingly use mathematical terms and symbols to describe computations, measurements and characteristics of objects.

In Number, students use structured materials to explore place value and order of numbers to tens of thousands. They skip count to create number patterns. They use materials to develop concepts of decimals to hundredths. They use suitable fraction material to develop concepts of equivalent fraction and to compare fraction sizes. They apply number skills to everyday contexts such as shopping. They extend addition and subtraction computations to three digit numbers. They learn to multiply and divide by single digit numbers.

In Space, students sort lines, shapes and solids according to key features. They use nets to create three-dimensional shapes and explore them by counting edges, faces and vertices. They visualise and draw simple solids as they appear from different positions. They investigate simple transformations (reflections, slides and turns) to create tessellations and designs. They explore the concept of angle as turn (for example, using clock hands) and as parts of shapes and objects (for example, at the vertices of polygons). They use grid references (for example, A5 on a street directory) to specify location and compass bearings to describe directions. They use local and larger-scale maps to locate places and describe suitable routes between them.

In Measurement, chance and data, students measure the attributes of everyday objects and events using formal (for example, metres and centimetres) and informal units(for example, pencil lengths). Students tell the time using analogue and digital clocks and relate familiar activities to the calendar. Students investigate natural variability in chance events and order them from least likely to most likely. Students conduct experiments and collect data to construct simple frequency graphs. They use simple two-way tables (karnaugh maps) to sort non-numerical data.

In Structure, students use structured material (in tens, hundreds and thousands) to develop ideas about multiplication by replication and division by sharing. They recognise the possibility of remainders when dividing. They learn to use number properties to support computations (for example, they use the commutative and associative properties for adding or multiplying three numbers in any order or combination). They investigate the distributive property to develop methods of multiplication and division by single digit whole numbers. They learn to use and describe simple algorithms for computations. They use simple rules to generate number patterns (for example, ‘the next term in the sequence is two more than the previous term’). They create and complete number sentences using whole numbers, decimals and fractions.

When Working mathematically, students use mathematical symbols (for example, brackets, division and inequality, the words and, or and not). Students develop and test ideas (conjectures) across the content of mathematical experience. For example:

  • in Number, the size and type of numbers resulting from computations
  • in Space, the effects of transformations of shapes
  • in Measurement, chance and data, the outcomes of random experiments and inferences from collected samples.

Students learn to recognise practical applications of mathematics in daily life, including shopping, travel and time of day. They identify the mathematical nature of problems for investigation. They choose and use learned facts, procedures and strategies to find solutions. They use a range of tools for mathematical work, including calculators, computer drawing packages and measuring tools.

National Statements of Learning

This learning focus statement, with the following elaboration, incorporates the Year 3 National Statement of Learning for Mathematics.

Elaboration:

They recognise angles … as parts of shapes and objects …

Standards

Number

At Level 3, students use place value (as the idea that ‘ten of these is one of those’) to determine the size and order of whole numbers to tens of thousands, and decimals to hundredths. They round numbers up and down to the nearest unit, ten, hundred, or thousand. They develop fraction notation and compare simple common fractions such as 3/4 > 2/3 using physical models. They skip count forwards and backwards, from various starting points using multiples of 2, 3, 4, 5, 10 and 100.

They estimate the results of computations and recognise whether these are likely to be over-estimates or under-estimates. They compute with numbers up to 30 using all four operations. They provide automatic recall of multiplication facts up to 10 × 10.

They devise and use written methods for:

  • whole number problems of addition and subtraction involving numbers up to 999
  • multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten (for example, 5 × 100, 5 × 70 )
  • division by a single-digit divisor (based on inverse relations in multiplication tables).

They devise and use algorithms for the addition and subtraction of numbers to two decimal places, including situations involving money. They add and subtract simple common fractions with the assistance of physical models.

Space

At Level 3, students recognise and describe the directions of lines as vertical, horizontal or diagonal. They recognise angles are the result of rotation of lines with a common end-point. They recognise and describe polygons. They recognise and name common three-dimensional shapes such as spheres, prisms and pyramids. They identify edges, vertices and faces. They use two-dimensional nets, cross-sections and simple projections to represent simple three-dimensional shapes. They follow instructions to produce simple tessellations (for example, with triangles, rectangles, hexagons) and puzzles such as tangrams. They locate and identify places on maps and diagrams. They give travel directions and describe positions using simple compass directions (for example, N for North) and grid references on a street directory.

Measurement, chance and data

At Level 3, students estimate and measure length, area, volume, capacity, mass and time using appropriate instruments. They recognise and use different units of measurement including informal (for example, paces), formal (for example, centimetres) and standard metric measures (for example, metre) in appropriate contexts. They read linear scales (for example, tape measures) and circular scales (for example, bathroom scales) in measurement contexts. They read digital time displays and analogue clock times at five-minute intervals. They interpret timetables and calendars in relation to familiar events. They compare the likelihood of everyday events (for example, the chances of rain and snow). They describe the fairness of events in qualitative terms. They plan and conduct chance experiments (for example, using colours on a spinner) and display the results of these experiments. They recognise different types of data: non-numerical (categories), separate numbers (discrete), or points on an unbroken number line (continuous).They use a column or bar graph to display the results of an experiment (for example, the frequencies of possible categories).

Structure

At Level 3, students recognise that the sharing of a collection into equal-sized parts (division) frequently leaves a remainder. They investigate sequences of decimal numbers generated using multiplication or division by 10. They understand the meaning of the ‘=’ in mathematical statements and technology displays (for example, to indicate either the result of a computation or equivalence). They use number properties in combination to facilitate computations (for example, 7 + 10 + 13 = 10 + 7 + 13 = 10 + 20). They multiply using the distributive property of multiplication over addition (for example, 13 × 5 = (10 + 3) × 5 = 10 × 5 + 3 × 5). They list all possible outcomes of a simple chance event. They use lists, venn diagrams and grids to show the possible combinations of two attributes. They recognise samples as subsets of the population under consideration (for example, pets owned by class members as a subset of pets owned by all children). They construct number sentences with missing numbers and solve them.

Working mathematically

At Level 3, students apply number skills to everyday contexts such as shopping, with appropriate rounding to the nearest five cents. They recognise the mathematical structure of problems and use appropriate strategies (for example, recognition of sameness, difference and repetition) to find solutions.

Students test the truth of mathematical statements and generalisations. For example, in:

  • number (which shapes can be easily used to show fractions)
  • computations (whether products will be odd or even, the patterns of remainders from division)
  • number patterns (the patterns of ones digits of multiples, terminating or repeating decimals resulting from division)
  • shape properties (which shapes have symmetry, which solids can be stacked)
  • transformations (the effects of slides, reflections and turns on a shape)
  • measurement (the relationship between size and capacity of a container).

Students use calculators to explore number patterns and check the accuracy of estimations. They use a variety of computer software to create diagrams, shapes, tessellations and to organise and present data.

 

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