COMO WEST MATHS
INSERVICE 3-6
Overview
What does Mathematics look like in the classroom?
Daily counting – Fast maths
Focus unit and differentiated lessons incl. maths
mentals
How to help at home
Working mathematically / Problem solving
Questioning and mathematical language
Mental strategies
School A-Z website / Mathletics
Helping kids feel good about maths
Activities to do at home
Daily counting – Fast maths
A maths warm up is a five to ten minute activity that gets the students ready
for their lesson.
We use a variety of warm ups:
• Fast Maths sheets – levelled from 1 to 100
• Each student works at their own level
Auditory – teacher call out the maths questions and student writes answers
These could be quick facts for example:
5x4, 20/5, 125–26, 84 + 19
Innovative Technology
• YouTube clips
• Internet games
What is the purpose of a maths warm up?
Studies indicate that by using maths warm ups:
• they get students’ attention,
• they focus students on maths, and the game/activity puts students in a
positive frame of mind prior to starting the math lesson.
• Increase speed in the maths operations (x, +, -, /)
• Increase confidence
Warm up can also encourage creative thinking:
an example:
The teacher might write on the interactive whiteboard:
The answer is 17 – what is the question?
Students brainstorm to think of all possible questions:
16 + 1
8½+8½
15.2 + 1.8
Displaying a picture of a stadium packed with people
What question could we ask, even if we don’t know how to answer it yet?
Possible questions include:
How many people are at the stadium?
How much did people spend on tickets?
How many hot dogs were sold at this game?
Maths warm ups are to get each students mind firing ready
for the lesson ahead.
Como West Mathematics Program,
Focus Units and Differentiated Lessons.
• This year it became mandatory for all N.S.W. schools to teach
using the new Mathematics K-10 Syllabus.
• In Semester 1, 2014 our school began developing a new
Mathematics program that aligned itself with the incoming
Mathematics K-10 Syllabus as well as suiting the needs of our
staff and students.
• In Semester 2, 2014 our school implemented the draft
program and refined it ready to use for the start of 2015.
Focus Units
• Each strand of Mathematics: Number and Algebra, Measurement
and Geometry and Statistics and Probability are covered in a yearly
scope and sequence and are programed into focus units
• Focus units run for 3 weeks and include an aspect of Number and
Algebra as well as an aspect of either Measurement and Geometry
or Statistics and Probability
• During the 3 weeks the teacher will timetable in their lessons
around these aspects. For example: Term 1 Weeks 1-3 focus unit is
whole number, time and angles
• Once the focus unit has been taught the child is assessed on their
learning
Differentiated Mathematics
Lessons
• The new K-10 Mathematics syllabus is designed for students
to keep achieving and moving along the Mathematics
continuum
• Once children have mastered the concept they move along
the continuum
• By the end of Year 4 children should be competent with all
stage 2 outcomes taught and ready for stage 3 content
• Similarly, by the end of Year 6 children should be competent
with all of stage 3 outcomes taught and ready for stage 4
content.
BUT….
• Children master content when they have a full understanding
of what they have learnt. As we know, some children can
grasp content quickly, while other students need more time
and practice to grasp the content
• In Mathematics, it is important for children to master the
concept before he/she can move forward
• In all mathematics lessons, what we teach has to be
meaningful for every student in the class
• By differentiating lessons we can cater for every student in our
class from where they are progressing on the continuum.
Working Mathematically
Problem Solving
What are students doing when they’re
Working Mathematically?
Working Mathematically is the thinking and doing of
mathematics. It is an essential part of the learning process.
Working Mathematically provides students with the
opportunity to engage in genuine mathematical activity and
develop the skills to become flexible and creative users of
mathematics
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COMMUNICATING
Describe, represent and explain mathematical
situations, concepts, methods and solutions to
problems.
Using appropriate mathematical language and
terminology
Representing ideas in tables, diagrams, graphs,
symbols, notation and conventions.
Reporting in oral, written or graphical forms
PROBLEM SOLVING
Formulate and solve problems
Design investigations and plan approaches
Apply strategies to seek solutions
Verify that answers are reasonable
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REASONING
Explaining their thinking
Deduce and justify strategies used and conclusions
reached
Adapting what is known to the unknown
Transferring learning from one context to another
Proving that something is true or false
Explaining choices
UNDERSTANDING
Make connections between related concepts
Represent concepts in different ways
Identify commonalities and differences between
aspects of content
Describe their learning mathematically
Interpret mathematical information
FLUENCY
Choosing appropriate procedures
Carrying out appropriate procedures flexible,
accurately, efficiently and appropriately
Recall factual knowledge and concepts readily
Problem Solving
Reciprocal Numeracy Explained
• DESCRIPTION
Reciprocal numeracy is a collaborative problem solving strategy used to support student’s in comprehending text.
• PURPOSE
To improve student’s understanding and unpacking of mathematics word problems.
A major problem students have when problem solving is at the ‘transformation stage’ ie. Selecting an appropriate
strategy.
• HOW IT WORKS
The teacher and the students take it in turns to lead discussion and raise questions about the word problem. The
teacher models through ‘think loud’ a series of steps students follow to solve and unpack word problems.
The follow prompts are provided to students as visual prompt cards or on a prompt page as a scaffold to support
students internalising the process.
The prompts and specific metalanguage are explicitly modelled and taught.
A student wishing to solve a written mathematics problem typically has to work through the following steps:
Reciprocal Numeracy
Step 1
Step 2
CLARIFY
READ
Read the question carefully.
Circle any clunks (words).
Clarify the clunks (words) you don’t
understand or can’t read.
Try
• Rereading the question
• Looking up the word in a
dictionary
• Maths glossary
• Asking for help
Reciprocal Numeracy
Step 3
Step 4
FIND OUT
RESTATE
What information in the question
is/is not important to find the
answer?
Restate the question in your own
words.
Underline the important
information in the question.
Reciprocal Numeracy
Step 5
WORK IT OUT
Select the most appropriate strategy.
Use the strategy to work out the
answer.
Now work it out using a different
strategy.
Record your strategies - show your
working out to the solution.
Record down the answer.
Strategies:
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Add/Subtract/Multiply/Divide
Draw a diagram, table or graph
Draw a picture
Look for a pattern
Guess and check
Act it out or use objects
Work backwards
Make a model
Brainstorm
Use simpler numbers
Create a tree diagram
Reciprocal Numeracy
Step 6
CHECK IT
Reread the question
Ask yourself have I answered the
question?
• Step 7
REPORT BACK
Substantive conversation through
reflection.
Share strategies used.
Does the answer make sense?
Can you check the calculation.
More then one way to solve a
problem.
Questioning and Mathematical Language
count forwards
combines with
joins
how many more
all together
counting on
combine
plus
add
total
double
addition
round to.
sum
increase
group
number of groups
array
multiply
double
product
multiple
factor
count backwards
take away
minus
the difference between
less than
subtract
subtraction
round to.
decrease
share
sharing
shared between
shared equally
divide
halve
quotient
Mental Strategies
School A to Z
• School A to Z has been produced by the NSW Department of
Education
• For parents who are keen to support their child's learning and
gain a better understanding for the work being done in the
classroom.
• Practical homework help for school subjects and tips on
learning,
• Includes articles and resources that provide more information
about how you can assist your child at home.
• Website http://www.schoolatoz.nsw.edu.au
Mathletics
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Engaging for students - Rewards and certificates
Levelled and extension activities
Can be used to reinforce concepts taught at school
Students instantly know if they are on the right track and can
work through the curriculum at their own pace.
• Yearly subscription already paid for. App available
Maths - Making Kids Feel Good
• Helping kids feel good about maths
• Talk positively about maths so your child also values it
• Everyone has a mathematical ego and this ego really determines a child’s mathematical success
• Kids who hear their parents say ‘I was terrible at maths at school’ has a real effect
• Making maths fun
• Another way you can make kids feel good about maths and build that mathematical ego is through
games
• Maths is a subject that really lends itself to games and we try to incorporate these games in our daily
teaching. We do this through (Mathletics, games on our interactive whiteboard and so on)
• You can do this at home as well using dice in board games:
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reading the face on a die without counting the dots
Adding two dice together
Working on what you need to roll to get to where you want
• It’s important to make sure you get them to explain how they got the answer and to think aloud
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How did you get that answer? What strategy did you use?
Research has shown that when kids think about the strategies they use in maths it can really contribute to their
understanding
• Another really effective way of allowing your child to feel comfortable with maths is pointing it
out in everyday life
• Cooking in the kitchen (measurement of ingredients in recipes)
• Operating the microwave (numbers and counting backwards)
• Finding a certain house number down the street (counting by 2s)
Activities to do at home