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Measurement & Geometry Hands-on Activities to Inspire Students ~ Ann-Marie Hunter Can you see the baby? TIME MACHINE Telling Time, Writing Dates – Gr. 4 Math curriculum. TIME MACHINE : – a visual tool showing relationships between metric units – interactive, offers regular practice in a fun way – useful for students in other grades Buzz Words of Measurement & Geometry Teachers – check vocabulary for understanding of definitions BEFORE THE UNIT BEGINS! Introduce one set of definitions at a time, not overwhelming your students, Ensure given vocabulary matches the particular activities they are doing. Geometry Guide Book, could be made by each student: - one vocabulary word per page - show examples of each, using materials. - add new vocabulary words as new topics are discussed How many faces? Measurement Activities Allow for weeks of hands-on measuring before introducing formulae. This helps students to get a firm grasp on each concept. Encourage ESTIMATING distance, flat surface area, volume before measuring Ask for 2 different units of measure. (i.e. cm and m) Use rulers, tape measures, graph paper and tiles to measure things that are important to students. Use charts to record class results – making it visual and available for students to benefit from others’ findings. Find class averages. Ask students to make conclusions (reflect on) the results Be open to students creating their own measurement projects. Metric Conversion Chart do not use the chart BEFORE students have lots of practise measuring in 2 units (i.e. cm and mm) make an interactive model of the chart on the board * use magnets and string/yarn to represent the placement of the first and second units, showing the direction and number of moves gives a framework for converting that can be used without the chart after they have used it for a long time builds confidence in students! Metric Conversion Chart Guidelines 1. For each of the questions, put your pencil (the cursor) on the name of the first unit (i.e. km) 2. Move your cursor to the name of the second unit (i.e. mm) and identify how many places and in which direction the cursor moved. 3. That will be how the decimal moves from the original number to give the correct answer! 4. *Remember that whole numbers’ decimals are after the final digit! 45 cm = ? mm, 8.9 km = ? m, 350 g = ? kg Can you see the face? Measurement & Geometry Use clear definitions: Perimeter: measurement of the distance along the outline of a figure – measured in linear units. Area: measurement of the flat surface inside the outline of a figure – measured in square units. Volume: measurement of the space inside a solid – measured in cubic units. Using a protractor properly Protractor use: 1. Place the centre of the ‘sunset’ on the vertex of the angle. 2. Place the zero line (not the edge) of the tool along one of the rays of the angle. 3. Count up from zero along the protractor, until you get to the point where the other ray crosses the edge. 4. The size of the angle, in degrees, is found by seeing where the ray crosses the protractor; check to ensure that you are looking at the correct scale that started from zero. Understanding Angles Teach drawing and measuring angles to have hands-on practice with these Angle Properties: 1. Sum of angles in a triangle is 180° 2. Sum of angles in a quadrilateral is 360° 3. Learn to identify angles as: acute, right, obtuse, straight, or reflex 4. Use a protractor and compass to draw specific triangles and to name them accordingly: acute triangle, obtuse triangle, right triangle, isosceles triangle, equilateral triangle Classifying Shapes When students are comfortable with the names of shapes, they become more confident in their work and are able to think creatively about their learning. I like to call the names of shapes GEOMETRY LANGUAGE, focussing on how Mathematicians have their own language, just as writers and scientists have, to describe the particular aspects of the knowledge. Students add names and examples of shapes, built with materials, to their Geometry Guide Book, Encourage students to find examples of Geometry in the World, relating their Math studies to their lives. Invite adults to speak in your classroom to share how they use Geometry in their professions and/or lives. Classifying Shapes ‘Regular’ polygons are those with equal side lengths: equilateral triangles, squares, regular pentagons, regular hexagons, . . . Encourage proper labelling of sides and angles: measurements, equal side lengths or angle measures. Classifying Shapes Use Venn diagrams (hula hoops or string work well as hands-on tools) to show relationships. Can you see the three women? Examine the Symmetry To identify the symmetry of a figure, draw lines where folding will create exact mirror images, or use MIRAS to show the symmetry on any figure. This activity relates to Transformations later in the unit! Tessellations Tessellations Tessellations Tessellations Tessellations Building Solids Pop-up model of solids – label parts of solids. Have students build solids and display them in the classroom, decorated and labelled with measurements and names of parts: vertex, edge, face. Begin by using nets of rectangular solids or cubes (boxes). Students build open boxes and estimate the volume. Physically fill them with cm3 cubes to find the volume. Use shape riddles to describe solids. Defining DefiningSolids Solids Shape Riddle: I have no curved faces. I have 6 flat faces. I have 12 edges and all the edges are the same size. WHAT AM I? Defining DefiningSolids Solids Shape Riddle: I have 9 edges. I have a total of 5 flat surfaces. Two of my faces are triangles. WHAT AM I? Shapes and Nets Shapes and Nets A Net Project Gould – Rhombicuboctahedron Volume Use nets to show the difference between prisms and pyramids. Use the definition of Volume as: the measurement of space inside a solid. Surface Area Nets allow students to SEE what is meant by Surface Area - measure the area of the flat nets and then label the faces of the built boxes GEOMETRIC SHAPES COMPARED TO NETS: http://www.learningresources.com/text/pdf/Exclusive/092 1FoldingShapes.pdf - this website is listed on the last page of your handout TRANSFORMATIONS Translations - slides A Translation means: Every point of the shape must move: o the same distance o in the same direction o the shape would be shown before and after the translation to show the transformation Rotations – turns A Rotation means: a figure is turned around a point – not necessarily on the shape or the outline of the shape. use tacks to press into a shape, turning the shape held by the tack. The shape is traced before and after turning it. When the point of rotation is not on the shape at all, measurements can be made to ensure that all points are equidistant from the point of rotation. Reflections – flips a reflection is a flip over a line when a reflection is made, every point on the shape must be the same distance from the central line, or mirror line the reflection is the same size as the original shape Measurement & Geometry I have included a sheet with the formulae needed for Perimeter, Area, and Volume calculations. I know that your students will enjoy having the opportunity to play with Measurement and Geometry before the formulae are used! Have FUN with it! Help your students to enjoy hands-on activities of Geometric explorations while building confidence with Geometry Language! Find ways to refer to this knowledge and these skills using terms: Perimeter, Area, and Volume, plus measurement terms throughout the year – not just during the unit! Can you see the couple?