Detective Cosine McTrig’s Cold Case Mystery Series

As I was reading through the Grade 10 curriculum goals for trig: “except in the case of the ambiguous angle” I some how ended up down the rabbit hole of developing my very own trigonometry mystery series.

Take a look and tell me if it makes any sense! If so, please feel free to use it. I would love feed back in the comments section, or by email: cobblehillCLC@shaw.ca

I showed the three packages to my grade 10 student who struggles with math and she loved it! She wanted to do package C, which is the most difficult, so we dove into McTrig’s Top Secret Field Journal and learned everything from grade 7-10 basic trig so that we could solve the mystery!

Here are the four files:

McTrig’s Private Journal (work book): Detective Cosine McTrig’s Journal

Mystery Level A (grade 8 level): Crossing the River Qwu’atsun

Mystery Level B (grade 9 level): The Ambiguous Case of the man in the Tree

Mystery Level C (grade 10 level): The Great Sapphire Heist

Awesome Factors and Multiples Math Lesson

I recently taught a great math lesson and thought I was would share it with you. Let me know what your think!

Materials:

– iPad or device for Apps

– Apps: FactorSamurai & MiddleSchoolMath HD

– projector or AppleTV (something to connect iPad to projector)

– worksheet or workbook

 

Extension:

– Flocabulary (LCM/ GCF)

– factor tiles

 

Lesson Plan:

1. Begin with a quick brainstorm about multiples and factors. What are they? Where are they useful? How can our understanding of multiples help with factoring and visaversa?

2. What challenges prevent us from understanding of multiples (example: not memorizing multiplication table; difficulty counting on, etc).

3. Help students visualize multiples and factors. Visual tools for multiples: VennDiagram or 100’s chart. Visual tools for factors: factor rainbow or factor tree.

4. Hand out worksheet or workbooks. Help students to visualize problems (work on the board to guide students through the first questions).

5. At this point in the lesson, many students may feel frustration at not understanding multiples or factors. Typical areas of difficulty are multiplication, skip counting and prime/composites…

SOLUTION to frustration: have some fun!

6. Hook up the iPad/device to projector. Begin to play FactorSamurai. Tell students that you only a Grasshopper but really want to become Apprentice and need their help. Students will immediately want to play. Ask them to watch and try to figure out the  pattern. Once students have figured out the pattern, allow several students to try and beat your high score.

7. Soon students should start to see the pattern, even the one’s that were not so sure before. They understand that (yes, this is exactly like fruit ninja!), they are trying to break the numbers into their factors. But you can’t break a prime!

DID YOU KNOW: factor comes from the Latin word “done”. Kind of makes sense!

8. Next, demonstrate the game “sorting multiples” on MiddleSchoolMathHD. Again, ask students to look for the pattern before allowing them to play. The crabs should be sorted into three bins: numbers that 2 goes into, 3, or both, for example. Soon, students should start to see another pattern: some numbers have “common multiples”

9. Finally, students will return to their worksheet. Ask students to explain how the game is like the worksheet. This will be their ticket out the door.

 

Hint: factors are what you multiply to get a number. So the App FactorSamurai actually asks players to slice the end product (multiple)  into factors. For example, two times two is four. Four is a multiple of two; two is a factor of four.

Hint: multiples are what you get after your multiply.

 

Extension Lesson:

10. Students watch flocabulary “LCM and GCF”, completing the fill-in0the-blank worksheet

11. debrief on the difference between multiples and factors.

12. Allow students to use factor tiles to visualize how different numbers can be be broken up in various ways. For example: 1×12, 3×4 or 2×6

Links:

Greatest Common Factor

Primes and Composites

factor tiles

factor and multiple classroom game

explanation of factors and multiples

Happy Teaching!

Another Exciting Math Lesson outside

I came across a fantastic BBC documentary for social studies called “What the Greeks Did for Us” which showed the innovations of Archimedes, Pythagoras, and other ancient Greeks. Something that caught my eye was around the 15:00 minute mark of the documentary- a piece on how the Greeks used geometry to drill through a mountain from either side and met perfectly in the middle.

Deciding to put it to the test for ourselves (go cross curricular connections!), I borrowed some clay from the art teacher, dowels, string and straws from the science lab and headed outside with the students.

First I explained the situation: a village of ancient Greeks is worried that they will be cut off from their fresh water supply on the North side of a mountain, if there is an attack from an enemy. They have an idea- drill through the mountain to create a tunnel. This wasn’t a totally crazy idea for the time as many aqueducts and incredibly elaborate irrigation systems had been developed. So off they set with picks and chisels. Soon, as you can imagine, they felt daunted by the task. They decided to send a team to the opposite side of the mountain so that they could double their efforts and complete the task more quickly. But how could they be sure that they would meet in the middle?

I asked the students to stick a dowel through the mountain from both the north and south and try to meet in the middle. Try as we might, no luck.

They played around with the string and dowels for about 5 minutes before I prompted them by sticking 4 of them in the ground at each quadrant around the mountain. This prompted some of them to use the knowledge of angles and degrees. They were on the right track by still needed prompting. I asked them to consider what we had learned previously about bisecting angles.

Finally, they had a square (ABCD) set up around the mountain (with string) and used point A and C as starting points for drilling. They used a square set to enter the dowel into the mountain (45 degree angle from corner post) and VOILA! they met in the middle! We “drilled”  a hole through the mountain, stuck in the straws and poured water through the straws. Much to our astonishment, water came all the way through!

All in all, this was a complete success and an incredible way to show the importance of circumference, perimeter, angles and bisecting angle. Not to mention a great activity for outdoors!

Tactile math (chalk and string and a little bi-secting)

I loved the kids enthusiasm about our latest out of class math lesson- come rain or shine!

As we are learning about Ancient Greece, I decided to do as the ancients did. Using only sting and chalk, students worked on their own, trying to figure out how to bisect line segments, create perpendicular lines and parallel lines. In their first attempt, many simply used guess work to find parallel lines; in a second attempt we went through three basic steps:

1. create a straight line by holding the string down at point A and B and tracing the chalk along it.
2. bisect the line by folding the string in half to find the midpoint
3. Extend the string to its full length again and place one end on point A. Draw a semi-circle from the midpoint in a rainbow/ arch above the line. Do the same from point B.
4. If you have done this correctly, you will have creates an X which is perpendicular to line segment AB if you connect X to the midpoint.

 

1.