Classroom Activities
Cuisenaire Rods/Manipulatives
Manipulatives will be used daily during lessons. Cuisenaire Rods are the key tool utilized in this topic as they align perfectly to the number line. Cuisenaire Rods are useful because they allow the students to have visual representations of the numbers and their relationships with one another. They are multi-colored for visual conceptualization and help to engage students in the learning. There are ten different types of Cuisenaire Rods.
These rods when lined up along the number line will give the students a deeper understanding of the mathematical properties. Not only will this help with addition and subtraction of whole numbers, I can use the Cuisenaire Rods to represent fractions as well.
The first topic to discuss when using the Cuisenaire Rods is determining the unit value. When we discuss unit value, it will be important that students understand the Cuisenaire Rod sizes and their relative size compared to another rod. It will be important to determine what the value of each color rod is how that will impact our work with the manipulatives. Once this is determined, students will be able to complete addition and subtraction of whole numbers with the Cuisenaire Rods along a number line. (Appendix B)
When I begin work with the addition and subtraction of fractions, we must first model what fractions look like with Cuisenaire Rods. During instruction, students will first use the rods to generate as many models they can for a variety of fractions: ½, ⅓, ¼, 1/10. This will lead us into the conversation about the unit value and determining the value of the varied colored rods according to the unit value. Students will then use their Cuisenaire Rod models to create number lines on paper.
Students can continue this work with the Cuisenaire Rods and with online virtual models (Appendix C) to ensure conceptual understanding before they begin adding and subtracting on the number line.
Field Work
Student fieldwork will occur at the beginning of our learning. On two separate trips, students will be creating number lines from maps of our neighborhood and the local metro system. These maps will be tied into daily lessons when addressing unit value, signed numbers, and the varied operations.
During the first activity, students will be creating a map of 5th Street. When creating the map of 5th Street, students will mark as the 5th & E Street intersection where the school is located as the origin. From that point, each block will be labeled as one unit. During our walk, students will also be required to note the distance from block to block as well as the time it takes to walk from block to block. When mapping, we will note any major landmarks and where they are located. Once all data is collected, students will return to class and share their findings to create one class map of the neighborhood. The map will be linear and have unit markings that we will address when going through problems throughout the unit. The students will complete the same process separately on the metro train. Students will travel the Red Line metro line to create a map, identify distance and speed, mark landmarks, and determine each stop as a unit. We will again create a classroom map that becomes our “real-world” number line.
Once the class maps are created, students will use them as a reference to answer and create real-world application problems. Street blocks and metro stops will be used as units and the unit values will vary depending on if the students are addressing the amount of stops or blocks, the distance between them or the time it takes to travel between points. I will generate example problems for the students but will push the students to do the lift of applying the maps to their addition and subtraction learning.
Discussions
We will engage in Socratic Seminar style conversations when addressing signed numbers with addition and subtraction. Students will sit in a circle to discuss what they have learned about adding and subtracting numbers. Questions to be discussed are not limited to but include:
- What is a number?
- What does it mean to add?
- What does it mean to subtract?
- Where are negative numbers located on a horizontal number line?
- Where are negative numbers located on a vertical number line?
- What is the opposite of 2?
- What is the opposite of 0?
- Describe the relationship between 10 and -10.
Students will be pushed to spend at least one minute discussing each topic. Students additionally will have white boards on their laps in the event they would like to provide a visual to support their comments in the conversation. During the conversations, teachers should be monitoring participation and noting commonalities and unaddressed misconceptions during the conversation. The teacher should attempt to stay silent throughout these conversations allowing students to work through each question using math talk sentence stems. (Appendix D)
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