# Articles

Below are a series of helpful articles.
Select the category of interest to reveal all the articles within that area.

Assessment

#### Assessment: getting everything done

By Tierney Kennedy  How do we get everything done? Good assessment takes time.  It is important to make sure that your grading decisions are not made on the basis of only one or two measures, but on the clear progress of a student over time.  Sometimes this requirement can make it tricky to... READ MORE

We have included here some assessment samples to download, with the aim of coming to a joint understanding of what the criteria mean and how to assign a grade.  Remember to download the June 2013 edition of The Insightful Classroom newsletter to use the initial sample assessment and the flow ... READ MORE

These tasks are designed to take 5-10 minutes to complete with each class. They will give you a very quick idea of how successful your current approaches are at dealing with the major student misconceptions about number.  Please take 5 minutes to ask the questions to your class.  Make sure that y... READ MORE

#### Assessing for Understanding rather than Fluency

In classrooms around the country gifted mathematics students are hiding in support maths.  They have been overlooked by our current Fluency assessment - left back, seeming to struggle and falling behind. Here are some simple questions that I use as a very quick diagnostic tool for students working in different grades: Prep:  C... READ MORE

Australian Curriculum

#### Introducing two-digit numbers

It can be tricky for a lot of students to see the need for bundling.  Often students in early primary (and sometimes later than that) will have an understanding of one to one correspondence for relatively large numbers without also developing the concept of "tens".  Here is a fun task t... READ MORE

#### The missing link from Place Value: Relative Size

Place value is one of the Big Ideas in number identified by Dr Dianne Siemon during the National Middle Years project as pivotal for later mathematical development. Students who are missing place value concepts in middle primary school are in significant danger of failing high school mathematics. We often ask students... READ MORE

#### Critical number concepts >>> The first three years

Download the PDF of this article here:  Critical number concepts - the first three years Check out a video for my Top 5 Diagnostic Tasks in Lower Primary here Watch our free full-length recorded webinar on Key number concepts for F-3 here.

It would be lovely if we had time to teach every ... READ MORE

#### Open Number Lines

Open number lines can be one of the best teaching tools ever.  Here are a few of our favourite ideas for how to use them: Use the line for base 10 numbers...  Start at 0, end at 1000 - ask students where 10 and 100 go. Use the line for i... READ MORE

#### Improving student reasoning

Sometimes kids who are seemingly brilliant at maths have a great deal of trouble showing or explaining how they solved a problem.  Try these suggestions: Try asking these questions instead of "How did you get your answer?" What operations did you use? With which numbers? What did you do first? Then what did ... READ MORE

#### What do the proficiency strands mean?

Fluency in the Australian Curriculum refers to building students’ content, basic skills, speed and accuracy in routine questions. Routine questions are those that students have been shown how to solve, whether these involve a single step, multiple steps, remembering a formula, or applying a formula to solve a simple situation.  Most questions fou... READ MORE

#### What is an insightful problem?

Problem-Solving in the AC refers to having students attempt never-before tried problems. These can be called insightful or novel problems.  They are completely new to the students, not word problems written from what they have already been taught, or applications of their pre-existing content and skills to a real-life context.  These t... READ MORE

#### Simple Ideas for Teaching Volume and Capacity

This week I have enjoyed thinking about creative ways to look at volume and capacity.  I couldn’t resist snapping a picture of a great example of a right prism (the pallet of toilet paper) when visiting a shopping centre.  Check out your local supermarket for lots more ideas!  Large volumes: Using this pict... READ MORE

#### Assessing for Understanding rather than Fluency

In classrooms around the country gifted mathematics students are hiding in support maths.  They have been overlooked by our current Fluency assessment - left back, seeming to struggle and falling behind. Here are some simple questions that I use as a very quick diagnostic tool for students working in different grades: Prep:  C... READ MORE

#### Timely thoughts on analogue time

It is not all that often these days that I meet someone in the course of running Professional Development who seriously challenges my thinking.  I love it when it happens.  I crave that moment when my brain speeds up and everything around seems to come to a stand-still.  This week, ha... READ MORE

#### Workprogram for one and two teacher schools now available

One and two teacher schools face significant challenges in implementing the Australian Curriculum.  With this in mind, Tierney Kennedy has designed a work program that utilises Back-to-Front Maths web access to meet all of the requirements for each grade in an integrated program.  The idea is to group students and w... READ MORE

#### Startling NAPLAN trends for Queensland

Queensland and South Australian NAPLAN data from the past four years reveals that we are very good at content teaching, but comparatively poor at developing deep understanding and the ability to solve unfamiliar problems.  See the link below for how the data reveals these startling trends. Startling NAPLAN trends for QLD  ... READ MORE

#### Review of C2C Mathematics – Leah O’Neill

Having read what is currently available of the C2C/Scribbly Gum Mathematics materials, I believe there are a number of issues that need to be addressed before the program truly reflects the intent of the new Australian curriculum. My concern is predominantly with the implementation of the ACARA proficiency strands.  These strands ... READ MORE

#### Australian Curriculum Preparation Pack

How ready are you to make the changes the Australian Curriculum requires? Learn what the changes entail, assess your school's readiness to meet them and start taking steps to implement the changes in 2012. Your free ACARA preparation pack contains: Auditing tool: 17 questions to help assess your staff's readiness to adopt ACARA,... READ MORE

#### NAPLAN secrets and how to get prepared in the last few weeks.

NAPLAN should not be nearly as scary for teachers as most seem to think.  Great teaching should result in improvements.  If you aren't seeing growth, please check out this recorded webinar and read through the information below to work out why. Leaders - you may wish to download these instructions on <... READ MORE

#### Multistep with money

Money is a common multistep problem that tends to pop up regularly on NAPLAN. It is also a very easy way to introduce algebra or fractions in a meaningful way. Here’s a problem that I enjoy using with anyone from years 3-9. It is really easy to vary to create c... READ MORE

#### Place Value and Base Ten

What comes after 100? 101, 102, 103… 109, 200!! We often use hundreds charts to help children understand place value, but these generally stop at 100. Many students think that after 100 the numbers are counted: 101, 102, 103, 104, 105, 106, 107, 108, 109, 200. In this problem we try t... READ MORE

#### Which half is the biggest?

Take an A4 sheet of paper and hold it up in front of the class. Ask them if they could fold it to make one half. Ask for as many different halves as possible. You can use quarters for grades 5-7 if you think halves will be too easy,... READ MORE

Classroom Tips

#### Problem Solving with Pam

Our thanks to Pamela Barritt of Woodcroft Primary School for sharing this Blog post with us!  It was originally posted on March 14, 2017 During maths lessons we focus on four different parts of learning: Problem Solving, Fluency, Reasoning and Understanding. Each are equally important. At the beginning of every week we work o... READ MORE

#### The power of confronting questions

When kids have persistent misconceptions it can be really hard to help them change their minds.  Try thinking of teaching like doing a science experiment, where they have to disprove their own hypothesis before they will listen to yours. Here are a few steps to help: Ask slightly unusual questions to ... READ MORE

#### What to do when kids already know everything - serious maths extension

Sometimes when teaching, we come across a student who blows our mind. It seems like they either already know everything that we are trying to teach, or are so fast at making connections that we can’t keep up. In th... READ MORE

#### 10 Maths Hacks All Teachers Should Know

With the year just beginning, it’s worth investing a few minutes putting together these simple maths hacks to save you time for the rest of the year. Phone time for rotation groups:  Did you know you can set the timer function on your phone by just holding in the button and ta... READ MORE

#### Why being wrong in maths is better than being right

We could solve the STEM crisis in this country within five years if we could get all parents and teachers to stop saying one thing: “It’s ok to be wrong”. Failure is not “ok”, it’s critical. When we learn, we grow new neural pathways in our brain. The more pathways we grow, the more in... READ MORE

#### Introducing two-digit numbers

It can be tricky for a lot of students to see the need for bundling.  Often students in early primary (and sometimes later than that) will have an understanding of one to one correspondence for relatively large numbers without also developing the concept of "tens".  Here is a fun task t... READ MORE

#### 25% of primary teachers have not developed Multiplicative thinking - check your staff

Multiplicative thinking is one of the concepts that I have found about 1 in 4 primary teachers across the country are missing... and I have tried the diagnostic tasks below with several thousand of them.  Along with Place Value and Proportional Reasoning, Multiplicative thinking is one of the most important ... READ MORE

#### Making Extension Manageable

Key 1: Make the maths weirder rather than making the numbers harder Give the starting and ending numbers and ask, “What happened?” Work backwards from the end point to the start. Have a gap in the question. Ask “What if...?” and then make a change to the circumstances. See what happens to the answer. Look fo... READ MORE

#### Time-saving solutions for rotation groups

Balancing time in rotation groups can be especially tricky:  we need enough time to be able to work in depth with a small group, but not so much that behaviour management becomes a problem as kids get bored. The Back-to-Front Maths authors created a really simple system for rotation groups that ... READ MORE

#### Using Rotation Groups Successfully

By Tierney Kennedy Activities are at this link. Watch a free video explanation here Buy convenient, pre-made cards here Almost every lower primary classroom that I have been into has used rotation groups for literacy.  Yet when this same approach is used for numeracy the effectiveness tends to be pretty variable.  This month I w... READ MORE

#### My favourite maths teaching moment wasn't in maths!

By Tierney Kennedy

What is your favourite maths teaching moment?

One where you know that you made a life-changing difference?

My all-time favourite maths teaching moment was with a boy named “Rick”, and wasn’t actually in a maths class at all, but in a year 8 science lesson.  It was in fourth term and ... READ MORE

#### Critical number concepts >>> The first three years

Download the PDF of this article here:  Critical number concepts - the first three years Check out a video for my Top 5 Diagnostic Tasks in Lower Primary here Watch our free full-length recorded webinar on Key number concepts for F-3 here.

It would be lovely if we had time to teach every ... READ MORE

#### My top ten rotation group activities:

I find that having a bank of regularly-used, highly-motivating and quick rotation group activities saves me a lot of time and headaches when using rotation groups.  Here are my top ten activities.  If you are a member of the Back-to-Front Maths website then you can download most of the resources f... READ MORE

#### The time crunch: buying yourself an extra hour every week

By Tierney Kennedy

I firmly believe that the most important and most effective thing that we can do with our classes is problem-solving.  And yet far and away the biggest complaint that I hear teachers express on Professional Development sessions is their lack of time.  So here is my proposition to y... READ MORE

#### Improving student reasoning

Sometimes kids who are seemingly brilliant at maths have a great deal of trouble showing or explaining how they solved a problem.  Try these suggestions: Try asking these questions instead of "How did you get your answer?" What operations did you use? With which numbers? What did you do first? Then what did ... READ MORE

#### Misconceptions in Maths

This article explains, with examples, the best process to address misconceptions and links you with resources to resolve the specific misconceptions found in your class.  It takes 2 minutes to read and 30 minutes to implement.

Are you looking for Interventions Resources to diagnose and fix misconceptions?  C... READ MORE

#### Supply teacher maths - instant lessons that develop mathematical thinking

As the new year starts many new teachers begin the year on contract or as supply teachers.  Often this means having to run a whole day in a classroom on very short notice, with no planning left for you.  Here are a few ideas that can be used to develop m... READ MORE

#### Horizontal algorithms and negative numbers from year 1

Often we spend an inordinate amount of time in primary schools practicing vertical algorithms.  I have to wonder if there isn't perhaps a better way to spend our time.  Here are a few of the ideas that I have had about using horizontal algorithms instead and introducing students earlier to t... READ MORE

#### Simple Ideas for Teaching Volume and Capacity

This week I have enjoyed thinking about creative ways to look at volume and capacity.  I couldn’t resist snapping a picture of a great example of a right prism (the pallet of toilet paper) when visiting a shopping centre.  Check out your local supermarket for lots more ideas!  Large volumes: Using this pict... READ MORE

#### National numeracy week activities to do at home with your kids

By Tierney Kennedy author of Back-to-Front Maths National literacy and numeracy week is a great way to reflect on what we as parents can do at home to help our kids.  Mathematics is often the subject that most parents tend to shy away from, so here are a few simple suggestions for ... READ MORE

#### The three best things that I have said all year...

This year in all of my Professional Development sessions three statements seem to have made the biggest difference to teachers.  I would like to share these truths with you as well. 1.  Understanding cannot be diagnosed with Fluency questions, because when asked routine questions students give only routine answers.  To find ou... READ MORE

#### Rapid growth in understanding for Emilie in year 2

Today I was working with a year two class on understanding tens and ones.  We used a hundreds chart as a tool to help the students develop deep understanding of two digit numbers.  Key questions included "what is missing?" and "how are the numbers kind of the same?" The four photographs b... READ MORE

#### Timely thoughts on analogue time

It is not all that often these days that I meet someone in the course of running Professional Development who seriously challenges my thinking.  I love it when it happens.  I crave that moment when my brain speeds up and everything around seems to come to a stand-still.  This week, ha... READ MORE

#### Kids who just want worksheets so that they can get all the answers right...

In every class of students there is usually someone who considers themselves very good at maths.  They are highly successful at getting the right answers to routine questions and are often very quick at answering mental maths questions.  They consider problem-based teaching as "not real maths" and want to get o... READ MORE

#### Differentiation and how to really cater for kids working at very different levels... without driving yourself nuts

The reality of classroom teaching nowadays is that no teacher has a class of students who are all working at the one level. Teachers who aim their maths lesson at only one or two groups of learners are choosing to believe in a myth that this type of class... READ MORE

Differentiation

#### What to do when kids already know everything - serious maths extension

Sometimes when teaching, we come across a student who blows our mind. It seems like they either already know everything that we are trying to teach, or are so fast at making connections that we can’t keep up. In th... READ MORE

#### Making Extension Manageable

Key 1: Make the maths weirder rather than making the numbers harder Give the starting and ending numbers and ask, “What happened?” Work backwards from the end point to the start. Have a gap in the question. Ask “What if...?” and then make a change to the circumstances. See what happens to the answer. Look fo... READ MORE

#### Using Rotation Groups Successfully

By Tierney Kennedy Activities are at this link. Watch a free video explanation here Buy convenient, pre-made cards here Almost every lower primary classroom that I have been into has used rotation groups for literacy.  Yet when this same approach is used for numeracy the effectiveness tends to be pretty variable.  This month I w... READ MORE

#### Rapid growth in understanding for Emilie in year 2

Today I was working with a year two class on understanding tens and ones.  We used a hundreds chart as a tool to help the students develop deep understanding of two digit numbers.  Key questions included "what is missing?" and "how are the numbers kind of the same?" The four photographs b... READ MORE

#### Why do some kids put themselves in the “support” category when they are gifted at maths?

This question has been plaguing me a lot lately. In the last week two students have been playing on my mind.  Today I taught a year eight girl who thought she was really bad at maths.  She proceeded to make some of the most creative thirds that I have ever seen.  Ch... READ MORE

#### Differentiation and how to really cater for kids working at very different levels... without driving yourself nuts

The reality of classroom teaching nowadays is that no teacher has a class of students who are all working at the one level. Teachers who aim their maths lesson at only one or two groups of learners are choosing to believe in a myth that this type of class... READ MORE

Miscellaneous

#### My favourite maths teaching moment wasn't in maths!

By Tierney Kennedy

What is your favourite maths teaching moment?

One where you know that you made a life-changing difference?

My all-time favourite maths teaching moment was with a boy named “Rick”, and wasn’t actually in a maths class at all, but in a year 8 science lesson.  It was in fourth term and ... READ MORE

#### DVDs showing Tierney teaching in real classrooms now available!

In our most exciting news yet, we now have a DVD set showing Tierney Kennedy teaching eight Back to Front Maths lessons in real classrooms!

See how to use problem-based teaching to diagnose and confront misconceptions, leading the students to develop deep understanding, generalise mathematical principles and really develop understanding.  Watch ... READ MORE

#### Newly trained Facilitators

Hi to all newly trained Facilitators!  It has been exciting to train so many of you over the past few months.  This page has been designed especially for you, to put together some of the things that we went through in the training course. Things to do: If you are on F... READ MORE

#### Testimonials and Feedback

We have been fortunate to work with a vast number of schools and individual teachers over the years as we have developed our resources and professional development services. The extremely positive feedback we have received has been most encouraging. Here is a small sample of what teachers and administrators (including MASA and... READ MORE

#### Startling NAPLAN trends for Queensland

Queensland and South Australian NAPLAN data from the past four years reveals that we are very good at content teaching, but comparatively poor at developing deep understanding and the ability to solve unfamiliar problems.  See the link below for how the data reveals these startling trends. Startling NAPLAN trends for QLD  ... READ MORE

Parents

#### How to teach Addition and Subtraction free flipbook

Addition and subtraction of small numbers is a very big part of lower-primary teaching, and one that kids can struggle with still in their teens. Download this FREE flip book containing developmentally sequenced strategies for introducing addition and subtraction for all your staff and remember to give it to your support... READ MORE

#### Awesomely cool maths ideas for parents

Would you like to be able to help your kids to understand maths better?  Why not try implementing some of these really simple ideas to make maths part of your everyday life?  There's nothing tricky on this list... just ideas about how to include maths in your normal activities- when y... READ MORE

#### Great ideas for parents

Are you a bit scared of maths yourself?  Try these ideas: Mathematics is often the subject that most parents tend to shy away from, so here are a few simple suggestions for things that you can do at home to improve your child's understanding of maths. 1. Maths at breakfast: Instead of ... READ MORE

#### iPad Apps for parents to help with Maths

iPads and iPhones are everywhere now, and we have every expectation of kids playing with them for hours over the Christmas holidays.  With this in mind, we would like to extend a big thank you to Tabitha Jos from Kingston State School in QLD for her list of iPad apps ... READ MORE

Technology

#### iPad Apps for parents to help with Maths

iPads and iPhones are everywhere now, and we have every expectation of kids playing with them for hours over the Christmas holidays.  With this in mind, we would like to extend a big thank you to Tabitha Jos from Kingston State School in QLD for her list of iPad apps ... READ MORE