1 Description Pattern blocks are a type of mathematical manipulatives, developed in the sixties by the Elementary Science Studies[1]. They allow children to see how shapes can be decomposed into other shapes and introduces them to tiling. The standard pattern blocks are divided into two different sets. In the first set, the shapes can all be built out of the green equilateral triangle. This set contains: Equilateral triangle (Green) Regular rhombus (Blue) Trapezoid (Red) Hexagon (Yellow) The second set contains shapes that can't be built of the green triangle, but can still be used in tiling patterns Square (Orange) Small rhombus (Beige) Pattern blocks form the basis of a number of mathematical activities in schools. • • • • • • Polygons and Problem Solving Patterns and Tiling (Tessellations) 1 Perimeter Area Fractions Symmetry and Motion Geometry Pattern Blocks are also available as a virtual manipulative on the web or as learning objects. They provide further enrichment for a student who is struggling with some of the abstract concepts in maths and make it more concrete. 2 Purpose A mathematical manipulative is an object which is designed so that the student can learn some mathematical concept by manipulating it. The use of manipulatives provides a way for children to learn concepts in developmentally appropriate, hands-on ways. Mathematical manipulatives are used in the first step of teaching mathematical concepts, 1 A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. that of concrete representation. The second and third step are representational and abstract, respectively. 2.1 TEACHER: Pattern Blocks by themselves have no inherent meaning. It is important for teachers to make this meaning explicit and help students build connections between the concrete materials and the abstract symbols that they represent. This holds true for both concrete and virtual Pattern Blocks, but virtual Pattern Blocks often have this type of structure built in. For example, many virtual pattern block activities give students hints and feedback, something that the more traditional concrete pattern blocks cannot do without teacher assistance. Students report that virtual pattern blocks are easy to use and as engaging as concrete ones. Although virtual pattern blocks provide some support for individual student use, as with physical pattern blocks, students benefit from teacher guidance to help them use the manipulative correctly and connect to the underlying math. Most virtual pattern blocks include activities and suggestions for teachers (and often parents), as well as ideas for student discussions and sharing. The use of virtual pattern blocks extends the classroom back into the home and parents become involved in their children’s learning. Pattern blocks lend themselves to several types of group learning. Think –pair share, in groups where the students can discover their own information while sharing and reflecting their own discoveries with each other or the teacher. Pattern blocks help identify students who are struggling as the teacher is able to visually identify the student. 2.2 STUDENTS: Pattern blocks help students make concrete, abstract mathematical constructs. There are five specific areas that students can use pattern blocks to concretize their learning. • Polygons – This allows students to fill up pre-defined shapes with pattern blocks. The by walking around the class, they realize that there is more than one solution to the problem. This trial and error manipulation process introduces the idea that there may not be one correct solution but many valid solutions. • Patterns – allow students to create a pattern and then by using flips, slide and turns propagate that initial pattern into a larger tiling. By using pattern blocks flips, slides and turns are kinaesthetically learnt and understood. • Perimeter – as the length of a side of a pattern block is defined as one unit in length, the student is able to lay pattern blocks along the perimeter of a shape and then count up the number of blocks. This process then linked with the lengths of edges of the shape allows student to make a physical connection between the pattern block and the dimensions of a shape. • Area – is another concept that lends itself well to making a physical link to the abstract. Each block has an area of one unit and therefore covering a shape with pattern block then allows a student to make the connection between the dimension and the area. • Symmetry – this is a more advanced use of pattern blocks to relate such concepts as rotation, line and motional symmetry. 3 Sample Activities Activity 1:- Calculating Perimeter (Think – Pair – Share) Let the one edge of a green triangle be one unit of length. Which pattern block has the smallest perimeter? Which pattern block has the largest perimeter? Explain your thinking to your partner. Calculate the perimeter of each pattern block. Use the edge of the green triangle as one unit of length. Green Triangle Blue Rhombus Red Trapezoid Orange Square Beige Rhombus Yellow Hexagon More Discoveries: • • • • Explain to another group member how to calculate the perimeter of any of these polygons Find out the meaning of a regular polygon? Which of the figures above are regular polygons? Write a note about perimeter in your mathematics journal. Activity 2:- Flips and Turns (Think – Pair – Share) Cover this design Complete the design above as a robot. Colour or even dress your robot. • • • • • Make it again so it is standing on its head. Make it again so that it is lying on its side Show your partner how it looks when it is flipped upside down Show your partner how it looks when it is turned on its side Make a rocket. Flip it. Turn it Activity 3:- Equivalent Fractions2 Teacher Notes One of the areas most frustrating for teachers and students alike is the study of fractions, specifically operations with fractions. Year after year, students learn and forget how to add, subtract, multiply and divide with fractions. The main reason students have difficulties with fractions is that they seem to want to memorize formulas or algorithms instead of understanding them. Exercise: Have students work in pairs with the blocks. Have the students discover the relationships between these 4 blocks: ● How many green blocks are equivalent to a blue block, or a red block, or a yellow block? ● how many red blocks are equivalent to a yellow block? ● how many blue blocks are equivalent to a yellow block? ● How many green blocks are equivalent to a yellow block? Teacher Instructions Have the students cover the form with red blocks. What fraction of the whole does 1 red block represent? Write this fraction down on the overhead, the blackboard or chart paper for future reference. Clear the outline. Have them cover the outline with blue blocks. What fraction of the whole does 1 blue block represent? 2 blue blocks? 3 blue blocks? Write these fractions down. Clear the outline. Have the students cover the outline with green blocks. What fraction of the whole does 1 green block represent? 2 green blocks? 3 green blocks? 4 green blocks? 5 green blocks? 6 green blocks? Write these fractions down. 2 Time 5 min (1/2) (1/3) (2/3) (3/3) (1/6) (2/6) (3/6) (4/6) (5/6) (6/6) Modified by me to fit standard pattern blocks Understanding Fractions (Grades 5 to 8); Diane Hanson, Regina Catholic Schools Regina, Saskatchewan Which of these fractions is the same as 1/2? Ask students to show and explain this using their blocks. Which of these fractions is the same as 1/3? 2/3? Ask students to show and explain this using their blocks. Have students list all fractions smaller (but greater than 0) than 1/2. Have students list all fractions greater (but smaller than 1) than 1/2 Have students list from smallest to greatest all the fractions which can be represented by the blocks (up to 1). 4 Black Line Masters Activity 3:- Equivalent Fractions