Transcript Geometry & Measurement

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?