When I first started using Thinking Routines, I was teaching Trigonometry to my IB grade 11 class in Shanghai. I used the thinking routine Connect-Extend-Challenge to frame the vector activity.

CONNECT: |
How are the ideas and information presented
CONNECTED to what you already knew? |

EXTEND: |
What new ideas did you get that EXTENDED or pushed your thinking in new directions? |

CHALLENGE: |
What is still CHALLENGING or confusing for you to get your mind around? What questions, wonderings or puzzles do you now have? |

Materials:

- String cut in varying sizes under 30cm,
- masking tape,
- rules,
- meter sticks,
- erasable markers
- 4 pieces of poster board paper if your classroom does not have a floor you can write on with erasable markers.

Activity Instructions:

Part 1: Naming your line segment

- As each walked in the classroom s/he received a piece of yarn of varying lengths under 30cm with two pieces of tape.
- Have each student tape his/her string on the floor in a designated area. (At the time I have tiles in my classroom, I used 4 pieces of poster board when the classroom had carpet, or a surface we could not write on).
- Use erasable markers for students to name their strings (a, x, or Harry… anything they want)

Start the lesson saying that the students already know everything that we are going to go through but in a different form, so our objective for the lesson is to have an overview of vectors, some notation and where we will be going through the unit. After the students label the strings ask them to describe their string to a partner. You can cycle through the CONNECT-EXTEND-CHALLENGE questions. They might measure their string, or talk about a slope. When you bring them back together as a group, point out to them the math vocabulary they were using. Ask the group what would help them describe their line segments more accurately. Most likely they will put an x-axis and a y-axis and decide on a scale. If the students don’t suggest, the coordinate plane do that for them.

Next, have students determine a more precise description of their line segment. Including the end points, and slope. Ask if anything else can be measured with the lines, distance or magnitude.

Part 2: Direction is important

You can discuss with them the differences between lines, line segments, and rays. Have them make their line segments into rays. With this discussion, I like to include direction being important to vectors and start talking more about vectors and the notation.

- Students need to identify (and write on the floor) the starting point of their vector.
- Introduce the directional vector to the class- have the students write out their directional vectors.

Part 3: Vector addition

Partner up the students that have vectors of different directions. One partner will need to move his/her vector to the terminating point of the vector. It is important to remind students that the direction of the vector needs to be maintained.

Once that is done, you can go through the CONNECT-EXTEND-CHALLENGE questions to bring out concepts. Students will want to complete the triangle, find the angles of the triangle, possibly the area. Cosine Rule, Sine Rule, and the area formula will come up in the discussion.

Depending on the time you have you can continue the discussion. Again this lesson is designed to show the students where the unit is going with vectors, and also allow them to connect with the material in a different way. It is fun to write on the floor. The next lesson we summarize what we did and more formally go through the vector notation. If I did this on the poster board, I hang it on the wall for the rest of the unit.

To wrap up the lesson we revise what we discussed and put up questions for the CHALLENGE part of the lesson, “where and how are we going to use this information?” “Why is it important?”

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