Photomaths was created to address every part of the Grade 4 curriculum while at the same time providing both the student and the teacher with a multitude of tools in tune with the contemporary world, and very often linked to the science curriculum.

The Concept

Photomaths was created based on our desire to educate students to the pervasiveness of mathematics in everyday life and the world in general. The objective is to show them that mathematics, far from being an abstract science, is present in all areas of knowledge and life. Therefore, it is fundamental to the students’ understanding of their surroundings and enriches their general culture.

And what could be more concrete and more expressive than photographs to illustrate the link between mathematics and the real world ? Consequently, we have chosen to support all the concepts covered in this textbook with photos in order to vividly contextualize the proposed problems.

To these diverse pictures, we added two modern and pixilated fictional characters : a robot photographer and his dog with a mouth shaped like a USB drive. In addition to creating a kind of friendly — and often playful — complicity with the student, they also provide an educational role.

The Approach

In accordance with the Grade 4 curriculum, the book covers four broad areas of mathematics with a specific color assigned to each area. This is clearly visible in the table of contents and on the first page of the corresponding lessons, as well as in the shading of the pages that follow. The student immediately understands the nature of the concept that will be studied in a given sequence.

• Red = Algebra and Arithmetic
• Green = Geometry
• Blue = Measurement
• Orange = Statistics

A fifth — more methodological — area was added to the above four. This endeavors to assist the student in problem solving.

• Violet = Problem-Solving Workshops

The textbook consists of 78 lessons divided into 13 groups of six lessons each. Every sequence of 6 lessons ends with an evaluation, Show That You Know, which allows the teacher and the student himself/herself to assess the level of acquisition of the concepts recently studied. Within a group of six lessons, we were careful to alternate the various mathematical areas to avoid boredom and allow the student time to assimilate the new skills. There is a natural progression in the sequence of lessons, and this also helps the integration of new concepts. For example, we have allotted 9 lessons for the mastery of division.

Each lesson begins with a large photo included in the section Discover, where activities are made available to the students, whose role is to discover the concept being tackled be it individually or in groups. These activities help students identify what the main points in each lesson are and what is required for them to understand and remember these points. This is precisely the objective of the next section, Keep in Mind. The following Exercises are to be done directly in the textbook, while those printed on a yellow background, and entitled Train Yourself are to be done in the copybooks. These exercises also follow a logical progression : from direct application exercises to more abstract problems, often referring to all the concepts previously dealt with. The first exercises listed in the Train Yourself section are a general revision of the basic concepts and ensure absolute acquisition. The last exercises in this part often require fluency in mathematics.

Finally, each geometry lesson ends with a Pattern, which seems to be an excellent way of combining precision of movement, logic and art — therefore, students feel they must “ do it well ” ! The other lessons end with a Riddle — a short, entertaining mathematical problem.

The Tools

Photomaths is not just a math book used by students. It is complemented by two other forms of support :

1. The Teacher’s Guide, digital and downloadable, is written for teachers, and clearly explains our pedagogical preferences. It analyzes each lesson in terms of its objectives, the students’ prerequisites, and its anchorage in the curriculum. It offers systematic training in mental calculation; it also provides all the proposed activities (with suggestions for materials to use and possible remediation); moreover, it offers unpublished sets of exercises not available in the student’s textbook.
2. The sequences programmed for classrooms with the IWB (interactive whiteboard) are used by teachers and provide another approach of collective topics by making use of the multimedia resources available to us today.

The authors