IDM - Institut für Didaktik der Mathematik
Lesson Plan Description
Grade 6 Topics (Australia and Germany)
Topic LP1: (Introduction to) Fractions
In this game, students play against a partner, rolling two special dice and shading a part of a fraction wall, which matches their roll, with the aim of being the first player to completely shade their fraction wall. The activity helps students to understand more clearly the role of the numerator and denominator in a fraction, the meaning of improper fractions, equivalence and the relative size of fractions. The activity comes with a very brief pre- and post-test, as an easy measure of growth in understanding over the course of the lesson.
Topic LP2: Area of Polygons
Students produce closed polygons on square dot paper by joining the dots in any way they like. Their task then is to determine if there is any rule that can be found to connect the area of their shape, with the number of dots on the border of their shape and the number of dots inside the shape. Through exploring the problem and generating data, students notice patterns leading to generalisations. This problem was solved by a famous mathematician (Georg Pick) who published it in 1899. Students are invited to be a mathematician as they work through this investigation.
Topic LP3: Transformation of Figures
In this investigation, students are invited to identify and name two congruent figures embedded inside eight provided polygons. For each pair of congruent shapes, they also determine the type of transformation(s) required for one half to fit exactly over the other half, after the polygon is split. They also name each original shape and the twonew congruent shapes by their properties. It can be quite challenging to find the embedded congruent halves in some polygons, and students are encouraged to cut out and test the congruency of their determined halves, if proof is needed, or they are unsure.
Grade 5 Topics (China)
Topic LP1: (Introduction to) Fractions
The main learning goal of this lesson is to perceive a more intuitive understanding of fractions and the partitioning of one whole. The lesson starts with a historical introduction to fractions to motivate its necessity. Students then find representations of 1/4 by folding a piece of paper or drawing it. The activity helps students to understand the role of the numerator and denominator in a fraction. Students are then asked to divide pictures of different objects like fruits and geometric shapes to strengthen their understanding of fractions and the meaning of one whole. They discuss the meaning of fractions, of the numerator and denominator, and their order. At the end, the students are assigned exercises to apply their new knowledge about fractions.
Topic LP2: Area of Polygons (Parallelograms)
The learning goal of this lesson is to realise that a rectangle and a parallelogram have the same area when the length of the rectangle equals the base of the parallelogram and the widthof the rectangle equals the height of the parallelogram. Students calculate and compare the area of parallelograms and rectangles by counting the number of squares. Since calculating the area of parallelogramsby just counting squares is in general not possible, students transform the parallelograms into rectangles by cutting them. The students then solve exercises to apply their understanding and knowledge. At the end of the class the teacher assigns homework.
Topic LP3: Transformation of Figures (Rotations)
The main goal of the lesson is that students learn how to draw the rotation of a segment (e.g. by 90°). The lesson starts with students observing GIF images of daily life objects (e.g. the movement of a windmill). They are then asked to describethe rotations they observed regarding rotation direction and rotation centre. The students explore rotations of different figures using a triangle ruler and paper. At the end of the class the students are assigned exercises to practice what they learned.
