Lesson 2 of 9
Objective: SWBAT use the transitivity principle to measure indirectly
I like to start this lesson by playing the following game: Measuring
This game allows students to indirectly measure two items. I project the game onto the SmartBoard and call on random students to come to the board and answer the question. Some times, if the game permits, I hand out white boards and markers to students and put them in pairs and allow the pairs to answer the question using their white board. I then call on random pairs of students to come to the board and answer the question.
I then draw a red line, a blue line and a yellow line on the board/chart paper so that the yellow line is the longest and the blue line is the shortest. I ask the students:
- Which is longer, the red line or the blue line? (the red line)
- How does the length of the yellow line compare to the length of the red line? (The yellow line is longer)
- How would you put the lines in order from shortest to longest? (I would put the blue line first, the red line next and then the yellow line.)
The idea of this activating strategy is to get the students to begin to compare the lengths of the objects to each other. To indirectly compare lengths of three objects, children need to be able to attend to the precision in making sure that they begin at the starting points of the object being measured. (MP6)
I like to write the following clues on the board/chart paper, along with a drawing of an orange pencil:
Clue 1: A green pencil is longer than the orange pencil.
Clue 2: The orange pencil is longer than a brown pencil
So the green pencil is _______________ than the brown pencil.
Ask the students:
- What does Clue 1 tell you about the pencils? (that the green pencil is longer than orange pencil) I then draw a green pencil on the board/chart paper that is longer than the orange pencil.
- What does Clue 2 tell you about the brown pencil? (That it is shorter than the orange pencil) I then draw a brown pencil that is shorter than the orange pencil.
- What does it mean to prove your answer? (The drawings should match the clues to show that the green pencil is the longest.)
I then explain how my drawing proves my answer that the green pencil is longer than the brown pencil.
The standard MD.A.1 students are asked to compare the lengths of two objects indirectly by using a third object. By using clues to have them determine which object is longer or shorter, they are required to indirectly compare lengths of three objects. This provides an opportunity for children to reason abstractly about the relationships among the objects (MP2). In this lesson, children use the Transitivity Principle for indirect measurement as they compare the lengths of the objects to each other. To represent this situation symbolically, given a, b, and c, if a<b, and b< c, then a<c.
For the independent practice portion of this lesson students will practice reading clues about lines of different lengths and write shorter or longer to complete the sentences.
For struggling students, I give them groups of red, blue and green connecting cubes, making sure they have more green cubes. Then direct the students to make a red cube train and a blue cube train that is shorter than the red cube train. I then have the students make a green cube train that is longer than the red cube train. Have students put their cube trains in order from the shortest to the longest to compare their lengths. I then ask:
- Which cube train is shorter, the blue or the red cube train? (blue cube train)
- Which cube train is shorter, the red or green cube train? (red cube train)
- Which cube train is shorter, the blue or green cube train? (blue cube train)
By having students use concrete models, it will help them transition from concrete to abstract thinking when working on the independent portion of this lesson.
To close out the lesson, I instruct students to use different colors to draw 3 lines that are different lengths in their math journal. They then write 3 sentences comparing their lengths.