YDM-CCP teacher resources


Introduction

The YuMi Deadly Centre (YDC) is a research centre within the Faculty of Education at QUT. Its aim is to enhance the teaching and learning of mathematics so that students have improved employment and life chances. YDC collaborates with primary and secondary schools and TAFEs to conduct mathematics projects to support them in the teaching of mathematics. YDC can tailor such a project for your school or cluster.

YuMi Deadly Mathematics is the mathematics pedagogic framework developed by the YDC to be the basis of its mathematics projects. It was developed as a result of a grant from the Queensland Department of Education and Training. It was originally designed for Aboriginal and Torres Strait Islander and low SES students but has since been found to be excellent for all students. It is based on an understanding of sequencing, connections and big ideas and involves using a cycle of teaching strategies to plan and teach mathematics lessons and units.

The Reality-Abstraction-Mathematics-Reflection cycle

The Reality Abstraction Mathematics Reflection cycle diagram

The Reality-Abstraction-Mathematics-Reflection cycle (or RAMR cycle) is the teaching cycle at the heart of YuMi Deadly Mathematics. It advocates using the four components in the figure on right as a cycle for planning and teaching mathematics. It proposes:

  • working from reality and local culture (prior experience and everyday kinaesthetic activities)
  • abstracting mathematics ideas from everyday instances to mathematical forms through an active pedagogy (kinaesthetic, physical, virtual, pictorial, language and symbolic representations, i.e. body → hand → mind)
  • consolidating the new ideas as mathematics through practice and connections
  • reflecting these ideas back to reality through a focus on applications, problem solving, flexibility, reversing and generalising.

A more detailed description of the four components of the RAMR cycle is in the table below.

Reality

  • Local knowledge:
    Identify local student cultural-environmental knowledge and interests that can be used to introduce the idea.
  • Prior experience:
    Ensure existing knowledge prerequisite to the idea is known.
  • Kinaesthetic:
    Construct kinaesthetic activities, based on local context, that introduce the idea.

Abstraction

  • Representation:
    Develop a sequence of representational activities (physical to virtual to pictorial materials to language to symbols) that develop meaning for the mathematical idea.
  • Body-hand-mind:
    Develop two-way connections between reality, representational activities, and mental models through body → hand → mind activities.
  • Creativity:
    Allow opportunities to create own representations, including language and symbols.

Mathematics

  • Language/symbols:
    Enable students to appropriate and understand the formal language and symbols for the mathematical idea.
  • Practice:
    Facilitate students' practice to become familiar with all aspects of the idea.
  • Connections:
    Construct activities to connect the idea to other mathematical ideas.

Reflection

  • Validation:
    Facilitate reflection of the new idea in terms of reality to enable students to validate and justify their new knowledge.
  • Applications/problems:
    Set problems that apply the idea back to reality.
  • Extension:
    Organise activities so that students can extend the idea (use reflective strategies – flexibility, reversing, generalising, and changing parameters).

 

Planning and teaching of mathematics

The process of planning and teaching mathematics is based around the RAMR cycle. By breaking instruction down into the four parts and taking account of the pedagogical approaches described above, the cycle can lead to a structured instructional sequence for teaching a mathematics idea. The innovative aspect of RAMR is that the first two components of the cycle (reality and abstraction) develop the mathematics idea while the second two components (mathematics and reflection) reconnect it to the world and extend it. For example, whole-number place value built around the pattern of threes where hundreds-tens-ones applies to ones, thousands, millions, and so on, can be easily extended to metrics by considering the ones to be millimetres, the thousands to be metres and the millions to be kilometres.

The teacher resources (lesson plans)

The teacher resources for Prep to Year 9 have been developed to provide models that support aspects of the Australian Curriculum content descriptors and cross-curriculum priorities (embedding Aboriginal and Torres Strait Islander histories and culture).

The teacher resources may be used as lesson plans and follow the RAMR framework which is designed to develop the proficiencies – understanding, fluency, problem solving, and reasoning – to assist students to work mathematically. The resources have been written using the RAMR cycle headings.

The username and password to download these resources is provided in the Review section of the YDM Professional Learning Online Blackboard site for YDC project participants.  Once you have obtained the username and password, use the following steps to download the resources:

  • Click on the title of the teacher resource.
  • Enter the provided username and password into the authentication popup.
  • On the user agreement page, tick the acceptance checkbox and click on the download button.
  • Save the document to your computer.

Prep

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

Bits and pieces
Students will partition and add small collections to represent addition as combining parts of a whole by modelling and sharing in practical situations.

Let's go hunting
Students will describe addition and represent addition experiences by comparing, ordering and making correspondences between collections and explaining their reasoning, initially to 20.

Partners
Students will match numerals to quantities, connect number names, numerals and quantities, including zero, initially up to 10 and then beyond.

Pattern hunt
Students will copy, describe and continue simple repeating patterns. They will sort and classify familiar objects and explain the basis for these classifications and also copy, continue and create patterns with objects and artwork.

Spot the number
Students will recognise amounts to five without counting, subitising small collections of objects to determine how many.

Measurement and Geometry

Guess where?
Students will describe the location of objects by indicating positions to describe and identify position and movement using the everyday language of location.

How long does it take?
Students will describe, compare and order the duration of events in their investigation of a day's duration and the sequence in the phases of a day.

My drink bottle
Students will compare the spaces within containers to compare capacity and use direct and indirect comparison to decide which holds more and explain reasoning in everyday language.

Sensational shape hunt
Students will compare shapes by sorting, describing and naming familiar two-dimensional shapes and three-dimensional objects in the environment.

For members only.

Year 1

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

Big steps in growing
Students will skip count in tens, identify the numbers in the counting pattern and use skip counting by tens to count a collection. They will develop confidence with number sequences to and from 100 by ones from any starting point. Students will skip count by twos, fives and tens starting from zero.

Pattern pursuit
Students will identify, describe and create repeating patterns by investigating and describing number patterns formed by skip counting and patterns with objects.

Put them together
Students will rearrange the parts of an addition situation to show the commutative principle, using appropriate thinking strategies to solve simple addition problems. They will record addition problems with numerals and symbols.

The teen game
Students will use standard place-value partitioning to represent 'teen' numbers. They will recognise, model, read, write and order numbers to at least 100 and locate these numbers on a number line.

When I'm a teenager
Students will identify, represent and order 'teen' numbers. They will recognise, model, read, write and order numbers to at least 100 and locate these numbers on a number line.

Measurement and Geometry

Dare to compare
Students will identify and explore the attribute of length by measuring and comparing the lengths and capacities of pairs of objects using uniform informal units.

My special time
Students will tell time to the hour and half-hour and match analog and digital time representations.

Statistics and Probability

Deadly data
Students will select a suitable question for gathering data then collect simple data and record responses using a simple data display to represent, read and interpret data.

What's the chance?
Students will explore and describe the likelihood of an event occurring using the chance terms 'possible' and 'impossible'. They will identify outcomes of familiar events involving chance and describe them using everyday language such as 'will happen', 'won't happen' or 'might happen'.

For members only.

Year 2

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

The animals went in two by two
Students will recall the twos counting sequence and use skip counting by twos to count a collection. They will investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences.

Patterns
Students will recall the fives and tens counting sequence and use skip counting by fives and tens to count a collection. They will investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences. They will also describe patterns with numbers and identify missing elements.

How many clumps?
Students will represent multiplication and division and connect division and multiplication using part-part-whole terms. They will recognise and represent multiplication as repeated addition, groups and arrays and recognise and represent division as grouping into equal sets and solve simple problems using these representations.

Measurement and Geometry

Clever calendars
Students will use calendars for a variety of purposes, explain that calendars can look different, that Aboriginal peoples and Torres Strait Islander peoples may recognise different seasons and explore examples of calendars for Indigenous people. They will name and order months and seasons and use a calendar to identify the date and determine the number of days in each month.

Which is the longest?
Students will measure the length of selected objects using informal units and order objects from shortest to longest. They will compare and order several shapes and objects based on length using appropriate uniform informal units.

Out and about
Students will interpret simple maps and identify the relative positions of key features.

Shape search
Students will identify a variety of four-sided shapes and describe the features of square, rectangle, rhombus and kite. They will describe and draw two-dimensional shapes, with and without digital technologies.

Tracking triangles
Students will identify a variety of three-sided shapes and describe the features of all triangles. They will describe and draw two-dimensional shapes, with and without digital technologies

Statistics and Probability

Favourites
Students will collect simple data from questions asked and display simple data in a picture graph or column graph. They will identify a question of interest based on one categorical variable, collect data relevant to the question, check and classify data and create displays of data using lists, tables and picture graphs and interpret them.

Today's traffic tale
Students will collect simple data from opportunities to observe events and display it in a picture graph after identifying a question of interest based on one categorical variable. They will gather data relevant to the question, check and classify data and create displays of data using lists, tables and picture graphs and interpret them.

For members only.

Year 3

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

Hundreds and thousands
Students will compare three-digit numbers, describing them as 'bigger than' and 'smaller than' and order a series of three-digit numbers on an empty number line, showing relative position. They will recognise, model, represent and order numbers to at least 10 000 and apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems.

School Challenge
Students will represent four-digit numbers to 2000 with materials and read, write and compare three-digit and four-digit numbers. They will recognise, model, represent and order numbers to at least 10 000 and apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems.

Flying high
Students will partition four-digit numbers into place-value parts. They will recognise, model, represent and order numbers to at least 10 000 and apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems.

Wholes and parts
Students will describe fractions as equal-sized parts of a whole and represent halves, fourths and eighths of a whole shape or object. They will model and represent unit fractions including half, quarter, third, fifth and their multiples to a complete whole.

Cutting it up
Students will represent fractions using linear materials and recognise key equivalent fractions and share collections equally to solve simple problems (halves, quarters and eighths). They will model and represent unit fractions including half, quarter, third, fifth, eighth and their multiples to a complete whole.

Measurement and Geometry

Angle it
Students will describe angles as the amount of turn between two lines and locate angles in the real world. They will identify angles as measures of turn and compare angle sizes in everyday situations.

Fill it up
Students will establish a mental image of one litre and measure the capacity of familiar everyday containers using litres. They will measure, order and compare objects using standard metric units of length, mass and capacity.

Statistics and Probability

Come in spinner
Students will recognise and describe variations in results and conduct a simple experiment with spinners. They will conduct chance experiments, identify and describe possible outcomes and recognise variation in results.

Lucky dip
Students will describe everyday chance events and conduct chance experiments. They will collect, organise, and display data and interpret and compare data displays.

For members only.

Year 4

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

Act it out
Students will revise and extend fluency of recall of the 10× facts, solve multiplication and division problems and describe and continue patterns created from multiplication

How many quads?
Students will revise and extend fluency of recall of the 4× facts, solve multiplication and division problems and describe and continue patterns created from multiplication.

Left overs
Students will investigate the relative position of numbers by modelling fractional numbers between whole numbers, represent linear models of fractions along number lines and use these models to count by quarters, halves and thirds, including with mixed numerals, and solve simple fraction addition problems.

Spending the Lotto millions!
Students will apply standard and non-standard partitioning to seven-digit numbers. They will apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems. They will recognise that the place-value system can be extended to tenths and hundredths and make connections between fractions and decimal notation.

Tuckshop orders
Students will make calculations with money and solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies.

Walking the rope
Students will develop an understanding of the proportion and relationships between fractions in the third, sixth and ninth family. They will represent fractions using linear models and symbols and form a generalisation about fractions equivalent to one whole.

Measurement and Geometry

How long is a foot?
Students will measure and compare objects using an informal measurement instrument for length and measure lengths and distances using scaled instruments.

Make your own ruler
Students will measure and compare lengths using an informal instrument and then identify formal and metric units of length. They will use scaled instruments to measure and compare lengths.

My town
Students will use everyday language to give directions, follow directions to locate positions on maps and draw plans from a bird's-eye view. They will use simple scales, legends and directions to interpret information contained in basic maps.

Symmetry hunt
Students will investigate flip, slide and turn symmetry, identify symmetry in the environment and understand some objects have more than one line of symmetry. They will create symmetrical patterns, pictures and shapes with and without digital technologies.

For members only.

Year 5

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

Bright budgeting
Students will make calculations with money amounts, make financial decisions and create simple financial plans.

Crack the code
Students will create number patterns involving adding and subtracting whole numbers and fractions.

Pizza for lunch
Students will recognise and model fractions flexibly using materials and diagrams to perform addition or subtraction of fractions with like denominators.

Measurement and Geometry

Packaging
Students will use the features and properties of three-dimensional (3D) objects to identify and create nets of 3D objects. They will connect 3D objects with their nets and other two-dimensional representations.

Patrolling the perimeter
Students will measure the dimensions of rectangles (including squares) in the environment then estimate and measure the perimeters of rectangles (including squares) using metric units. They will calculate the perimeter of rectangles using familiar metric units.

Skateboard skills
Students will identify the components and properties of angles, identify right angles and compare angles, classifying them in relation to right angles.

Supersize it
Students will transform and enlarge shapes using a grid. They will describe translations, reflections and rotations of two-dimensional shapes, apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original.

Statistics and Probability

Chances are
Students will calculate the sum of probabilities for a chance experiment and compare frequency predictions with actual data. They will list outcomes of chance experiments involving equally likely outcomes, represent probabilities of those outcomes using fractions and recognise that probabilities range from 0 to 1.

For members only.

Year 6

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

An equal share
Students will compare and order proper and improper fractions and mixed numbers with related denominators on a number line.

Smart shopping
Students will compare and evaluate two shopping options. They will find a simple fraction of a quantity where the result is a whole number, and add and subtract decimals, with and without digital technologies. They will Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies.

Ups and downs
Students will investigate everyday situations that use integers and will locate and represent positive and negative whole numbers on a number line.

Measurement and Geometry

Angle strength
Students will calculate unknown angles using angle relationships. They will investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles and use results to find unknown angles.

Change course
Students will identify transformations, and rotational and line symmetry, in regular and irregular polygons, and use transformations and symmetry to make a tessellating shape. They will investigate combinations of translations, reflections and rotations, with and without the use of digital technologies.

Convert me
Students will explore measurement prefixes and convert between units of measurement. They will convert between common metric units of length, mass and capacity.

Fencing the yard
Students will review and calculate perimeters and areas of rectangles and solve problems involving the comparison of lengths and areas using appropriate units.

Statistics and Probability

Loaded dice
Students will conduct chance experiments, record data into a frequency table and represent data using a column graph. They will conduct chance experiments with both small and large numbers of trials using appropriate digital technologies.

For members only.

Year 7

To download the teacher resource, click on the title of the teacher resource listed below:

Number and Algebra

Form one family
Students will add and subtract fractions with related denominators. They will solve problems involving addition and subtraction of fractions with related denominators.

How much is this part?
Students will multiply proper, improper and mixed fractions.

What's the link?
Students will create algebraic expressions to describe number sequences and evaluate them by substituting a given value for each variable.

What's the overlap?
Students will multiply a decimal by a whole number and by a decimal. They will solve problems involving decimal multiplication using efficient strategies.

Measurement and Geometry

Allied shapes
Students will calculate the area of triangles and parallelograms using formulas. They will establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving.

Angle connections
Students will use angle relationships to find the value of corresponding, alternate and co-interior angles.

Statistics and Probability

Give it your best shot
Students will calculate the mean, median and mode for sets of data and select the appropriate measure of centre.

What are the odds?
Students will calculate the probability for single-step events using sample spaces and construct sample spaces for single-step experiments with equally likely outcomes. They will calculate the probabilities for events.

For members only.

Year 8

The teacher resources will be available soon

Number and Algebra

Between the waterholes
Students will represent, order, compare, add and subtract integers using efficient mental and written strategies and appropriate digital technologies.

Common connections
Students will apply the distributive law to factorise algebraic expressions with numerical factors. They will sketch linear functions using the x- and y-intercepts.

Maths magic
Students will create linear mathematical models to solve a problem.

Best buys
Students will represent and interpret rates expressed in words and table form.

Measurement and Geometry

How many layers?
Students will develop the general formula for the volume of a prism.

Transfigure the shape
Students will calculate perimeter and area of kites, rhombuses and trapeziums.

Statistics and Probability

How fair is this?
Students will explore the effect of bias and outliers on summary statistics (mean, median, mode, range).

One word changes it all
Students will review and use the probability formula for simple ‘and’, ‘or’ and ‘not’ events and also describe events using ‘and’, ‘or’ and ‘not’ language.

For members only.

Year 9

The teacher resources will be available soon

Number and Algebra

How does my garden grow?
Students will explore the rule for calculating the gradient.

Exponential change
Students will investigate patterns of numbers arising for the power of ten for positive and negative exponents. They will also write numbers in scientific notation and convert them to standard decimal form and vice versa.

Measurement and Geometry

Different cans
Students will calculate the volume of right prisms and cylinders.

Statistics and Probability

Family tree
Students will construct frequency tables and histograms. They will then describe the distribution of data and locate the mean, median and range on histogram displays.

For members only.

Training in YuMi Deadly Maths

Training in YuMi Deadly Maths will enable your school to utilise a pedagogy that will enhance student learning outcomes in mathematics. Schools with strong practice in YuMi Deadly Maths can be contacted or visited to see YuMi Deadly Maths in action. For further information, contact:

YuMi Deadly Centre, 07 3138 0035, ydc@qut.edu.au
Ms Gillian Farrington, 07 3138 0062, gh.farrington@qut.edu.au.

Contacts

QUT YuMi Deadly Centre

Phone: +61 07 3138 0035
Fax: +61 07 3138 3985
Email: ydc@qut.edu.au

School of Curriculum
Faculty of Education
Queensland University of Technology
Kelvin Grove Campus
S Block, Victoria Park Road
Kelvin Grove, QLD 4059
Australia