Serving advanced learners (and their teachers) since 2012.
Students will analyze examples and non-examples to deduce the topic: shapes with 180º rotational symmetry
First, students get a set of shapes categorized in two groups.
Then they get a set of ungrouped shapes. Which columns will they go in?
Finally, I reveal the topic: 180º rotational symmetry
Students will analyze examples and non-examples to deduce the topic: regular and irregular polygons.
First, students get a set of items categorized in two groups.
Then they get a set of ungrouped items. Which columns will they go in?
Finally, I reveal the topic: regular vs irregular polygons.
Students will spot the number of parallel and perpendicular lines in shapes and then form groups of shapes.
First, students will identify the number of sets of parallel and perpendicular sides in various shapes.
Next, they create three or four groups based on their findings in step one.
Finally, students venture to the third dimension and look for parallel and perpendicular lines in a cube. For the final question: there are 18 sets of parallel lines in a cube and 24 sets of perpendicular lines. Although technically, we’d call them “edges” instead of lines.
Students will group letters by their type of reflective symmetry and then form symmetrical words and sentences.
First, students will find the lines of symmetry for the capital letters.
Next, they put them in categories based on their lines of symmetry.
Then, students will form words with symmetry.
Finally, they’ll create the longest sentences they can using only symmetrical words.
Students will analyze the shapes and determine the pattern: we’ve got trapezoids!
First, students guess the topic by looking at examples and non-examples, and then discuss their ideas with peers.
Next, students will decide which of three items are examples and which are non-examples of the given topic.
Finally, students identified and classified three shapes based on their parallel sides to distinguish between trapezoids and non-examples.
Students will inductively discover the rules of a triangle’s angles.
Students try to create the biggest possible angle inside of a triangle.
They look for triangles with one or more right angles.
Then they add up three angles, trying to find the largest and smallest sums possible.
Students try to create triangles with two and three congruent angles.
We close by posing the question: how are angles and sides related? (Larger/smaller angles mean longer/shorter sides. Same sized angles? Same size sides. )
Students analyze the similarities and differences of several quadrilaterals.
Students note that living things, as well as quadrilaterals, can be grouped in a variety of different sized categories. They consider how one quadrilateral is similar to and different from two others.
Students learn several criteria for grouping quadrilaterals (right angles, parallel sides, and congruent sides), then revisit their worksheet to increase their level of precision.
Students develop a hierarchy using the criteria from the previous video.
Students debate which is longer: a ray or a line.
I introduce students to lines, line segments, and rays. Finally, I pose the delicious question: “Which is the longest?”
Now we ponder: “Which has more points on it?”
Finally, students explore an idea such as: “What would a ray think about a line?” or “If a line wrote a poem to a line segment, what would it be like?” They can then create a mini-story, a comic, a play, or whatever you see fit!
Students will inductively determine the formula for the area of a triangle. Then we apply it to other, more complex shapes.
Using examples, students will attempt to deduce the formula for the area of a triangle.
We reveal the rule.
Students attempt to decompose more complex shapes into triangles.
Students explore the big idea: Shapes can have the same perimeter, but very different areas.
Students create at least five different rectangles with 16m of perimeter.
They organize their information and look for a pattern between the shape’s dimensions and its area.
Students create three ways to use three of their different rectangles. I give an Alien Zoo example.
Students will inductively determine the formula for the area of a triangle. Then we apply it to other, more complex shapes.
Using examples, students will attempt to deduce the formula for the area of a triangle.
We reveal the rule.
Students attempt to decompose more complex shapes into triangles.
Students will experiment with sticky notes to find the area of a circle and, along the way, discover pi!
First, students will cut up post-it notes, trying to see how many they can fit inside of a circle.
Then, you can reveal that (if you had perfect precision) you could fit exactly π post-its into the circle.
Students will determine how the diameter and circumference of circles are related.
First, students make a guess about how many times they’d need to go across a circle in order to equal the distance around.
Next, they’ll measure across printouts of famous circles.
Then, using string, they’ll measure around.
Now, students will look for a relationship between the diameter and circumference.
We reveal that the relationship is π.
I explain a bit more about π.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students explore the properties of angles, search city maps for intersecting streets, and then design their own street intersection.
Explore how a lone angle creates a second angle. And the two angles always add up to 360º.
Explore how 2, 4, 6, or even 8 intersecting angles still add up to 360º.
Browse online city maps (Google Maps, Open Street Maps, etc) to find an interesting intersection of streets. Measure these angles and check that they also add up to 360º.
Create their own intersection of streets. They’ll label the street names, mark interesting sights, and measure each angle, ensuring that they add up to 360º.
Students will inductively discover the rules of a triangle’s angles.
Students try to create the biggest possible angle inside of a triangle.
They look for triangles with one or more right angles.
Then they add up three angles, trying to find the largest and smallest sums possible.
Students try to create triangles with two and three congruent angles.
We close by posing the question: how are angles and sides related? (Larger/smaller angles mean longer/shorter sides. Same sized angles? Same size sides. )
Students debate which is longer: a ray or a line.
I introduce students to lines, line segments, and rays. Finally, I pose the delicious question: “Which is the longest?”
Now we ponder: “Which has more points on it?”
Finally, students explore an idea such as: “What would a ray think about a line?” or “If a line wrote a poem to a line segment, what would it be like?” They can then create a mini-story, a comic, a play, or whatever you see fit!
Students will analyze examples and non-examples to deduce the topic: regular and irregular polygons.
First, students get a set of items categorized in two groups.
Then they get a set of ungrouped items. Which columns will they go in?
Finally, I reveal the topic: regular vs irregular polygons.
Students will spot the number of parallel and perpendicular lines in shapes and then form groups of shapes.
First, students will identify the number of sets of parallel and perpendicular sides in various shapes.
Next, they create three or four groups based on their findings in step one.
Finally, students venture to the third dimension and look for parallel and perpendicular lines in a cube. For the final question: there are 18 sets of parallel lines in a cube and 24 sets of perpendicular lines. Although technically, we’d call them “edges” instead of lines.
Students will analyze the shapes and determine the pattern: we’ve got trapezoids!
First, students guess the topic by looking at examples and non-examples, and then discuss their ideas with peers.
Next, students will decide which of three items are examples and which are non-examples of the given topic.
Finally, students identified and classified three shapes based on their parallel sides to distinguish between trapezoids and non-examples.
Students analyze the similarities and differences of several quadrilaterals.
Students note that living things, as well as quadrilaterals, can be grouped in a variety of different sized categories. They consider how one quadrilateral is similar to and different from two others.
Students learn several criteria for grouping quadrilaterals (right angles, parallel sides, and congruent sides), then revisit their worksheet to increase their level of precision.
Students develop a hierarchy using the criteria from the previous video.
Students divide equilateral triangles over and over to create a Sierpinski Triangle.
Students learn to create their own Sierpinski Triangle by starting with an equilateral triangle.
Then, they create Sierpinski Carpets by starting with a square.
Finally, they experiment with three-dimensional versions, perhaps creating a Menger Sponge using Lego or in Minecraft.
Students will create a fractal known as The Koch Snowflake.
Students first create a Koch Curve – a simplified version of the Koch Snowflake.
They’ll take their curve from step 1 and extend it to become a snowflake.
Finally, students will create new versions of the Koch Snowflake by experimenting with different starting shapes.
Students will analyze examples and non-examples to deduce the topic: shapes with 180º rotational symmetry
First, students get a set of shapes categorized in two groups.
Then they get a set of ungrouped shapes. Which columns will they go in?
Finally, I reveal the topic: 180º rotational symmetry
Students will group letters by their type of reflective symmetry and then form symmetrical words and sentences.
First, students will find the lines of symmetry for the capital letters.
Next, they put them in categories based on their lines of symmetry.
Then, students will form words with symmetry.
Finally, they’ll create the longest sentences they can using only symmetrical words.
Students will find the information to calculate how many times we could fill up a jet plane using the fuel that would fit in an olympic-sized pool.
First, students will need to figure out how much water is in an olympic-sized pool, pick a plane, and determine much fuel that plane can hold.
I’ll reveal how many times I could fill up my jet plane.
Students will figure out much pasta they can cook using the water in an olympic-sized pool.
First, students will need to figure out how much water is in an olympic-sized pool and how much water you need for a pound of pasta.
I reveal my calculations – which may or may not be the same as what students arrived at. And that’s ok!
Students will find the information they need to calculate how many 2 liter bottles they could fill up using the water in an olympic-sized pool.
First, students will need to figure out how much water is in an olympic-sized pool.
I reveal my calculations – which may or may not be the same as what students arrived at. And that’s ok!
Students will balance various requirements in order to find the perfect gifts for their very special friends.
Students look for gifts that have a large volume while balancing a low price.
Next, they find gifts that are heavy, but don’t take up much space. And also are as cheap as possible.
For the third gift, students are looking for something long – maximizing one dimension while minimizing the other two. They’ll also want to save money.
Use this step whenever you’d like. Students can write a letter explaining their thought process behind the gift(s) they chose.
Students will calculate the volume of laptops throughout history using the formula for the volume of a rectangular prism.
Find five laptops from across history (this Wikipedia page is a nice starting point) and jot down essential information..
Calculate the volume of their five laptops, estimating them as rectangular prisms.
Pick their two favorite laptops and sketch them using this triangular dot grid paper to create accurate, 3d scaled drawings.
Explore shapes with equivalent volumes. They will redistribute the volume of one of their laptops into a new, 3D shape. Same volume but different dimensions.
Finally, students will build two of their sketches: the laptop’s original dimensions and then a model of the reconfigured dimensions with an equivalent volume. Naturally, they can continue extending this idea by finding equivalent volumes of other items or building on the marketing of their “new laptop design.”