Getting Started

Back-to-Front Maths is very different to traditional teaching because it is based on asking students questions that develop their own understanding rather than telling them what to think and what steps are needed to solve a problem.  We deliberately ask students questions that are hard rather than easy, to make them think.  Our steps involve:

  1. Pose an unfamiliar problem to students that has new content that they haven’t seen before.  Be aware that around 80% of your class will struggle with this problem at the start as it is designed to make them think really hard.  This is different to a word problem, which generally puts maths that the students already know into a sentence.  An unfamiliar problem is new maths rather than a new context.  Adapt the problem to make it suitable for students requiring support or extension using the tips in the lesson plans.  For grades 1-2 students this is the first of the three-lesson sequence in the Thinking Journal problems.  For grades 3-7, this is the Thinking Journal.
  2. During this lesson, students explore the problem and experiment with ways to work it out.  The teacher watches out for any misconceptions or weird ideas that the students display.
  3. The teacher uses questioning to target misconceptions or weird ideas, trying to lead the student to see that their thinking doesn’t make a lot of sense so that they change their own mind and are ready to try the initial problem again.
  4. The students and the teacher work together to find identify what does work and what does not work to solve the problem, summarising these into more formal findings.
  5. Students search for patterns and make connections.  For grades 3-7 this is done in the Blast lessons.  For grades F-2, this is done in the second lesson in the Thinking Journal.
  6. The teacher helps students to generalise their findings and can then explain the new content once students have found the underlying patterns.  The teacher provides as much practice as he/she feels is appropriate.
  7. Students apply these findings to new questions, adapting and manipulating them as they learn new information.  For grades F-2 this is done in the third lesson in the Thinking Journal.  For grades 3-7 this is done progressively, using the Manipulation and Backwards questions that are contained in both the Thinking Journal and Blast activities.

Click on your year level below to get started on planning a unit of work using the Australian Curriculum and the Back-to-Front Maths resources.


YEARS 1 AND 2

Step 1: Curriculum choices and time frames

Download the term planner for your grade here,  then use the steps below to plan your term.  If you are a website subscriber, you can download an example workprogram ready to adapt.

Firstly, choose which content you would like to cover in each term, and how long you would like to spend working on that content. Use the alignment table section to see the content from the Australian Curriculum: Mathematics aligned with Back to Front Maths within a developmental sequence.

Back-to-Front Maths has divided this content into 12 different common topics for ease of alignment. Each of these sections is listed on the contents page and has the appropriate lesson plans for each Journal problem. These sections are in the Lessons Bank, which is accessible for subscribers:

A: Number and Place Value
B: Money and Financial Mathematics
C: Fractions
D: Operations
E: Length, Mass, Area and Volume
F: Time
GH: Number Patterns and Algebra
I: Chance
J: Data Representation and Interpretation
K: Geometry
L: Symmetry, Transformations and Tessellations
M: Location, Direction and Movement

Step 2: Journal choices for each week

Once you have decided on your content and time frame, the next job is to choose which Journal problems you would like to cover and assign these to weeks. Each journal problem has three lessons, all to be completed within the same week, and a selection of hands on activities and games. To complete your week you will need to plan two other lessons. Make sure that you include time for explicit teaching, hands-on activities (such as those listed in the second lesson plan for each problem), regular consolidation activities (see the Term Planners for a list of other regular activities to complete), skill-and-drill tasks and some work on using mathematics in different contexts (see the Fluency section for some examples to download).  Another option for these two lessons is to include journal problems from a lower grade level, particularly if you find persistent misconceptions occurring in your class.  You can access all lessons, plans and activities from each grade within the Lessons Bank.

Plan your program to make sure that you cover all of the content, not so that you cover all of the activities in Back-to-Front Maths. There is no need to do them all as long as you are covering the curriculum. Make sure that you monitor student understanding regularly and adjust your program as needed. Please also make sure that you emphasise mental mathematics each day.

Step 3: Moderating tasks and assessment

For website subscribers, download and read the criteria sheet that is appropriate for your grade.

For website subscribers, a useful initial step is to complete the moderating tasks provided for your grade.  We suggest that you do the task in week 1, working with one group at a time on the task during rotation group time.  The initial task is not summative, so just use it to get an idea.  Also, make sure that you try the task yourself first as these are remarkably difficult even though they have fairly simple content.  Similar tasks have been provided for mid-year and end of year assessment in order to help you determine whether you are using the Journals problems to grade appropriately.

Step 4: Assessment for report cards

For website subscribers, grading judgements for report cards should be make using the criteria sheets.

In each semester, the last 3-4 Journal problems completed should form the basis for your grading of Problem Solving and Understanding. They count more highly than those completed earlier in the semester because they show the latest student work and this is the most reflective of the student’s current achievement and growth. The grades from these should be compared with those from the moderating tasks (completed at the end of each semester) to check that they align. If they do not align then more assessment may be needed before a final grade can be given. This means that in term 1 you shouldn’t focus too heavily on assessment using the Journals. Instead, focus on developing a problem-based teaching approach as this is pivotal to your students’ later performance.

Reasoning can be graded using application questions or problem solving as it does not require “Insightfulness”. Make sure that you check out when and how to assess. Refer especially to the “Sharing Time Sheet” found in the assessment section.

You will need to write your own assessment for Fluency as none has been included in this series. Your choices for this will depend on what you have covered with your class and the depth that you have gone into.  Use the criteria sheets as guidelines for grading these.

Additional things to consider:

Please be aware that problem-solving skills take time to develop, and Journal problems are designed to show student misconceptions.

In the first year of use make sure that you do not try to hurry through the program, but instead take the time to help students realise for themselves that their ideas are not viable. Plan a lighter than normal first term, and only aim to cover only around 6-8 Journal problems as the added time will be needed to help deal with student misconceptions. If dealt with properly, misconceptions are unlikely to recur, which means that you can plan for more learning in terms 3 and 4.

Deep understanding of mathematical principles and patterns develop when emphasis is placed on understanding rather than the development of procedural skills. Algorithms and formulae should be used to summarise student thinking rather than as procedures to be memorised and applied.

Consider using the following in your class in order to help improve student learning:

A large poster on your classroom wall which has problem-solving strategies listed. Add to this as you develop new ways of solving problems. In lower primary a box with pictures to represent these strategies is a great idea to help with sharing time.

A “word wall” with explanations that you develop as a class to explain the mathematical terms that you come across. Use this each time there is a word in a Journal or Blast activity that your class is unfamiliar with.

A “challenge table”: place a spare table somewhere in your room with 3-4 chairs at it. Use this space to work with students that you miss out on observing in normal lessons for 5 minutes at a time (e.g. all of the quiet students who tend not to share).

Year 1 Term Planner

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Year 2 Term Planner
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YEARS 3-7

Download the term planner to use with your grade for the following steps.  If you are a website subscriber, you can download an example workprogram ready to adapt.

Step 1: Curriculum choices and time frames

Firstly, choose which content you would like to cover in each term, and how long you would like to spend working on that content. Use the alignment table section to see the content from the Australian Curriculum: Mathematics (produced by ACARA).

Back-to-Front Maths has divided this content into 12 different common topics for ease of alignment. These sections are in the Lessons Bank, which is accessible for subscribers:

A: Number and Place Value
B: Money and Financial Mathematics
C: Fractions
D: Operations
E: Length, Mass, Area and Volume
F: Time
GH: Number Patterns and Algebra
I: Chance
J: Data Representation and Interpretation
K: Geometry
L: Symmetry, Transformations and Tessellations
M: Location, Direction and Movement

Step 2: Journal and Blast choices

Once you have decided on your content and time frame, the next job is to use the developmental sequence to examine how the Journal problems and Blast activities work together to cover the content in the sections. If you are a website subscriber, use the lessons in the Lessons Bank in the order that they appear rather than jumping all over the place. You may not need to do all of these as it depends on the prior understanding of the students, so be selective. On average, you should plan to cover approximately one journal problem and two Blast activities each week. These should be on a related topic in order to consolidate learning.  This decision should be based on the needs of your class.

Plan your program to make sure that you cover all of the content, not so that you cover all of the activities in Back-to-Front Maths. There is no need to do them all as long as you are covering the curriculum, and it is unlikely that a class will get through all of the activities in the first year because of the need to deal with student misconceptions. These often only become apparent when asking students to solve insightful problems. Make sure that you monitor student understanding regularly and adjust your program as needed. Two lessons per week should be left free to consolidate learning, practice skills (including from other content areas, such as the examples in the Fluency section) and do larger investigations. Please also make sure that you emphasise mental mathematics each week.

Another option for these two lessons is to include journal problems from a lower grade level, particularly if you find persistent misconceptions occuring in your class.  You can access all lessons, plans and activities from each grade within the Lessons Bank.

Step 3: Moderating tasks and assessment

For website subscribers, download and read the criteria sheet that is appropriate for your grade.

A useful initial step is to complete the moderating tasks provided for each grade. These take approximately one hour to complete with a whole class. Please make sure that you use these to determine students’ Problem Solving, Reasoning and Understanding levels before beginning the program. Similar tasks have been provided for mid-year and end of year assessment in order to help you determine whether you are using the Journals problems and Blast activities to grade appropriately.

The last 3-4 Journal problems completed each semester should form the basis for your grading of Problem Solving and Understanding. They count more highly because they show the latest student work and this is the most reflective of the student’s current achievement. The grades from these should be compared with those from the moderating tasks to check that they align. If they do not align then more assessment may be needed before a final grade can be given.

Reasoning can be graded using application questions or problem solving questions as it does not require “Insightfulness”. Further help for this can be found in the Assessment section.

You will need to write your own assessment for Fluency as none has been included in this series. Your choices over this will depend on what you have covered with your class and the depth that you have gone into.  Read the descriptions in the criteria sheets to help you decide which grade is appropriate.

Step 4: Investigations

Eight larger scale investigations have been included for each grade as well as those that make up every Journal problem. Before you start using these please make sure that your class is confident with problem-based approaches to teaching. This often takes 6-12 months to achieve and it is important not to rush the process.

Things to consider:

Please be aware that problem-solving skills take time to develop, and Journal problems are designed to show student misconceptions.

In the first year of use make sure that you do not try to hurry through the program, but instead take the time to help students realise for themselves that their ideas are not viable. Plan a lighter than normal first term, and only aim to cover only around 6-8 Journal problems as the added time will be needed to help deal with student misconceptions. If dealt with properly, misconceptions are unlikely to recur, which means that you can plan for more learning in terms 3 and 4.

Deep understanding of mathematical principles and patterns develop when emphasis is placed on understanding rather than the development of procedural skills. Algorithms and formulae should be used to summarise student thinking rather than as procedures to be memorised and applied.

Consider using the following in your class in order to help improve student learning:

  • A large poster on your classroom wall which has problem-solving strategies listed. Add to this as you develop new ways of solving problems. In lower primary a box with pictures to represent these strategies is a great idea to help with sharing time.
  • A “word wall” with explanations that you develop as a class to explain the mathematical terms that you come across. Use this each time there is a word in a Journal or Blast activity that your class is unfamiliar with.

Year 3 Term Planner

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Year 4 Term Planner
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Year 5 Term Planner
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Year 6 Term Planner
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Year 7 Term Planner
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