Math Across the Curriculum: Geometry and Measurement Paraprofessional Training August 24 th – August 28th

Naming and Describing 2D Shapes Regular or irregular? The number of sides The number of angles The size of the angles

Naming and Describing 3D Shapes The number of edges The number of vertices The number of faces The shape of the faces

Angles All angles have a vertex 360° forms a full circle 180° forms a straight line 90° forms a right angle or the angle formed by two perpendicular lines The angles of a triangle add up to 180° The angles of a quadrilateral always add up to 360°

Name the angles (in degrees°)

Activity Cards Use the pattern blocks to fill in the activity cards. Discuss what mathematical concepts or understanding are being developed by doing activities like these. Assign one person to share out one purpose or value found in doing these.

Tessellations Tessellations are defined as “tiling” with shapes that cover the plane in a regularly repeating pattern without gaps or overlaps Example:

Tessellation Assignments “Odd” Tables Work together to create a regular tessellation using three blocks that are different “Even” Tables Work together to create a regular tessellation using four blocks that are different Use extra time to explore a bit with finding one and two block tessellations.

Fun to create and color…

Gallery Walk and Break Which shapes seem to fit together easily and which shapes do not seem to fit together with the others? Which shapes fit together to make a pattern using only one block? Which shapes fit together to make a pattern using two blocks?

Hexagon Cookie Game This game can be found in our Investigations at grade 3 but is appropriate for all ages working with fractional amounts. Modifying the game a bit to fit the materials we have… 1: one whole cookie (hexagon) 2: one half of a cookie 3: one third of a cookie 6: one sixth of a cookie 4: roll again 5: lose a turn

Trading is allowed… M M M M M

Coordinate Geometry (x,y) (x,-y) (-x,y) (-x,-y) x y

Pi

Pi (π) C = πd Cherry pie delicious! C = Circumference of the circle d = the diameter of the circle So how could I determine the value of π with my students?

Measurement Pre-test A traditional unit of distance called a “hand” is equal to one half of a foot?T or F The formula for converting Celsius to Fahrenheit is roughly x2 plus 32°?T or F A ton of bricks weighs more than a ton of feathers. T or F A 12oz can of soda weighs 12 ounces. T or F Peter picked two gallons of pickled peppers.T or F The inch was created to avoid using fractional parts of a foot.T or F

Would you ever ask an 8 year old… 1 ÷ ¼ ? How about one dollar divided into quarters? 3 ÷ ½ ? How many half-hour shows can you watch in 3 hours? 2 ÷ 1/12 ? How many inches are in 2 feet?

Flip and Multiply 1 ÷ ¼ (just flip and multiply!) ¼ or “1 over 4” becomes “4 over 1” which equals 4 Now just multiply… 1 x 4 So 1 ÷ ¼ = 1 x 4 because both produce a value of 4 and 4 = 4 Does this make sense?

Same numeric value, but… 1 ÷ ¼ = 1 x 4 One dollar divided into quarters (1/4) produces 4 quarters One dollar multiply by 4 produces 4 dollars 3 ÷ ½ = 3 x 2 2 ÷ 1/12 = 2 x 12

Let’s try one… 3 ÷ ¼ = ? Try explaining it with money…  twelve quarters Try explaining it with clocks…  Twelve 15 minute sessions Try explaining it with rulers…  Twelve 3 inch sections

Let’s try a harder one… 2 ÷ 2/3 Two divided by two thirds Money?  Money doesn’t work well with thirds Clocks?  Three 40 minute session Rulers?  Three 8 inch sections

One more… 1 ½ ÷ ¼ One and one-half divided by one fourth Money?  6 quarters Clocks?  Six 15 minute sessions Rulers?  Six three inch sections

Money Good for exploring with…  Fourths (quarters)  Tenths (dime $0.10 or 0.1)  Twentieths (nickel)  Hundredths (penny $0.01)  Havles ? (half – dollar)

Clocks Good for exploring with…  Halves (half hour – 30 minutes)  Fourths (quarter of an hour - 15 minutes)  Thirds (20 minutes)  Sixths (10 minutes)  Twelvths (5 minutes)  Fifths (12 minutes)  Tenths (6 minutes)

Rulers or “one foot” Good for exploring with…  Halves (6 inches)  Thirds (4 inches)  Fourths (3 inches)  Twelvths (one inch)

Metric system Good for exploring with our base ten system…  1 kilogram = 1,000 grams  10 kilograms = 10,000 grams  100 kilograms = 100,000 grams  1 centimeter = 0.01 meters  10 centimeters = 0.1 meters  100 centimeters = 1 meter

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