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Category Archives: Geometry

Surface Area of Cylinders

Another 3 Act Math Lesson!

Act 1

I’m starting to make my own videos to match the grade 8 curriculum.

This is Act 2.  Ideally, I would have actually wrapped the Pringles can with paper but….sometimes time is a factor so I have an ongoing goal to keep adding videos when I have time.  🙂

 

Working on it:

 

We discovered all of this!

cylinder images surface area formula

 

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Grade 5 Geometry – Test on Monday, January 27th

The grade fives have been learning about 2-D geometry for the past few weeks.  We have learned about different properties and types of triangles:

 

types of triangles

 

We did this and discovered some types of triangles are impossible:

 

photo (3)

 

images

 

We have learned about angles:

types of angles

We have been learning that angles are measured in units called degrees.  Degrees are wedge shaped units and there are 360 of them in a circle.

degrees-360

I want the students to have a really solid understanding of degrees and angles so we did lots of activities exploring angles before we used a protractor.  They had to determine the angle measures in pattern blocks without using a protractor.    First we determined that the square angles were all 90 degrees.  We  know that a straight angle is 180 degrees so therefore a square angle must be 90 degrees.

photo (1)

and since three triangles fit on a straight 180 degrees then one triangle must be 60 degrees!

photo (2)

Now we can figure out all the rest, just by putting them on the 180 degree straight angle and doing some calculations.

Here is a video from Teacher Tube showing some ways to find the measure of angles

 

Next we learned how to measure angles using a protractor.  A common mistake is reading the wrong set of numbers so I ask the students to label the angle as acute or obtuse first.  If they say the angle is acute, which means less than 90 degrees, and they measure 120 degrees, then they know they have used the wrong set of measures.

Our next step is constructing triangles given the length of one side and one of the angles.

 

Students will have a review package for over the weekend.

 
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Posted by on January 23, 2014 in Geometry, Math

 

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Geometry Grade 4

Both classes are working on Geometry units.

Grade 4

We started off by using a right angle as a benchmark for comparing and naming angles.  I quickly realized that many students didn’t really understand what and angle was so I backtracked and we created a manipulative to model angles.  I cut out strips of bristol board and attached them together at a vertex so that the students could make angles.  We played around with these until everyone was comfortable with what and angle is.

Acute angle 5

Then we worked on what is a benchmark.  All the students lined up according to height (I tried to take a panoramic photo but it didn’t work).   I asked the tallest (Paris), shortest (Ayla) and median (Griffin)  person to step forward and we used their heights as benchmarks for everyone else to compare their own height to.   For example, Bradley was in between Ayla and Griffin.  Then we went back to angles and compared a variety of angles to a right angle and a straight angle.   When the students were ready, we gave the angles names.

Next we tried to measure them.  I didn’t show them how as this was an investigation.  The students tried to measure the distance between the rays (lines) with their rulers and we quickly discovered that the distance was different depending on where you measured.  The closer to the vertex, the smaller the distance.

measuring_angles

The students then named the angles on pattern blocks.  Many of them used the square to determine if the angles were acute or obtuse.  If you put the square on top of the hexagon angles (lining up one side and the vertex)  you can clearly see that the angle is larger so it must be obtuse.

images (1)

Now it was time to try to understand degrees.  We talked about how we couldn’t use rulers for measure them and why that didn’t work.  The kids are great ideas and realized that it was because of the difference between the space near the vertex was smallest and got larger the further away we moved from the vertex.   We talked about what the shape was of an angle (smaller than 180) and decided to call it a wedge shape.  I pulled up the pattern blocks on the SMART board and we used the beige rhombus as a unit of measurement.  We called the units wedges.  We noted that a full circle was 12 wedges and that one of the angles on the blue rhombus was 4 wedges.  Exploring with non-standard units helps the students to develop a deeper understanding of measurement.

IMG_1032

From here we moved onto degrees and looked a protractor.  Individual degrees are so small they are hard to visualize!

download (1)

 
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Posted by on January 15, 2014 in Geometry, Math, Uncategorized

 

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Angles, Polygons, & Triangles – Oh My!

The grade 5s have been learning about polygons, angles and triangles:

 

We looked up the definition of polygon on Etymology Dictionary dot com and foudn out it comes from the Latin and the Greek, with poly meaning many and gonos meaning angles.  Further investigations revealed that polygons are closed 2D shapes with straight sides.  Regular polygons have equal sides. 

polygons

s1eg1angles

 

Constructing & Classifying triangles:

 

TriangleClassification

 

Here is Jenna’s work trying to construct triangles that meet the crieteria in the columns and rows.  We discovered that they aren’t all possible. 

Jenna triangles

Damian figured out that the angles in a triangle add up to 180 degrees so there for there can only be one right angle or one obtuse angle. 

Stay tuned for polyhedra!  Very exciting.  The students were VERY engaged today building different polyhedra:  Here is a teaser of what’s to come!

 

polyhedra

 

 
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Posted by on May 30, 2013 in Geometry, Math

 

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