income tax concept unit 6

We are going to keep things light this week and go with questions that are found in week's readings. Please use thoughtful answers, not just one or two sentences. Choose TWO of the following questions to answer. As you post your response label it with your name and the question # such as AppelQ3. Please respond two two peers after completing your own initial posting. When responding to a peer, the same expectation from posting is applied. Be thoughtful, don't just respond with "I agree." 1. List a few different ways how the numbers "6" and "8" are alike and different. What are the benefits of using an activity like this in a classroom? Would you use this? Why or why not? 2. One of the main differences between a walk-on number line or number path (e.g. , see page 1 04) and a standard number line, is that instead of using numbers to mark points on the number line, the numbers in the walk-on line occupy spaces. What are the advantages of a number line where spaces are marked? What are the disadvantages? 3. Manipulatives are a great way to help students make sense of how many of an item there are. Can anything be used as a manipulative? What do you need to consider when choosing items to help young learners understand number sense? 4. Looking at the counting principles on page 90, which one do you think is most important and why?

Replies to peers with paragraph

Matt - Q2:

One of the main differences between a walk-on number line or number path (e.g. , see page 104) and a standard number line is that instead of using numbers to mark points on the number line, the numbers in the walk-on line occupy spaces. What are the advantages of a number line where spaces are marked? What are the disadvantages?

From my perspective, space-marked number paths are most effective as an introductory tool for early elementary students. One of their main advantages is that they support kinesthetic learning. When students physically move along the numbered spaces, they develop a stronger understanding of magnitude and quantity, making abstract number concepts easier to grasp (Small, 2019). Teachers can also use these number paths to practice skip counting by 2s, 3s, or 5s. In addition, some numbers can be omitted so that students must determine the counting pattern themselves, reinforcing their understanding of number sequences and one-to-one counting. As students become more comfortable with the number path, it can also support addition and subtraction. For example, a student can move from space 5 to space 7 and visually see the change of two units, which makes counting and computation easier to understand. However, there are also some disadvantages. Sometimes in some classrooms, physical walk-on number paths may not be practical when working with larger numbers because classrooms may lack the space or materials needed to create them. In addition, representing decimals and fractions on a space-marked number path can be more challenging, since these concepts require greater precision and more subdivisions between whole numbers. As a result, space-marked number paths are most useful for developing foundational number sense but may become less effective as mathematical concepts grow more advanced.

Q3:

Manipulatives are a great way to help students make sense of how many of an item there are. Can anything be used as a manipulative? What do you need to consider when choosing items to help young learners understand number sense?

Manipulatives are important tools for helping students develop number sense because they allow learners to represent quantities in a concrete and meaningful way (Small, 2019). Almost any object can be used as a manipulative, especially when schools have limited budgets and cannot purchase specialized materials. Teachers can use everyday items such as bottle caps, plastic straws, colored beans, paper clips, or pieces of colored paper cut into different shapes (Best Start, n.d.). These materials are inexpensive, accessible, and can also be used by students at home to continue practicing mathematical concepts.

When selecting manipulatives, it is important to consider whether they are safe, age-appropriate, and easy for young children to handle. The materials should also support the learning objective and help students make clear connections between physical objects and mathematical ideas (Small, 2019). For example, colors can be used to represent different numbers or groups. Students can combine colored objects to model addition, separate them to demonstrate subtraction, or organize them into equal groups to explore multiplication and division.

Manipulatives can also vary in size and color to reinforce number patterns and relationships. For example, blue squares could represent multiples of two. A larger blue square might represent 4, 6, or 8, allowing students to visually recognize the pattern of multiples while maintaining a consistent color connection. By using different sizes, colors, and shapes, teachers can help students identify mathematical relationships more easily and build a deeper understanding of number concepts. Overall, effective manipulatives should be meaningful, accessible, and designed to help students connect concrete experiences with abstract mathematical thinking.

Odell - Q2

One of the main differences between a walk-on number line or number path (e.g. , see page 104) and a standard number line, is that instead of using numbers to mark points on the number line, the numbers in the walk-on line occupy spaces. What are the advantages of a number line where spaces are marked? What are the disadvantages?

One of the advantages of a number line where a student marks the space is that it provides a visual for numbers and depending on how it is done students are further manipulated by the number line. As students progress through school it can be used to recognize patterns. It also helps “visualize and reinforce the magnitude” of numbers so students can understand the value of numbers on the number line (Tamayo, 2026). It can help with other concepts such as distance, time, fractions, and decimals by providing visuals and providing more real world concepts beyond a basic number line (Tamayo, 2026). One of the disadvantages is that for a number line to work students need a foundation to build on and if they don’t have that then the use of the line could be confusing (Fuson, 2018). The use of the number line to mark spaces relies on the student having the foundational knowledge of the value of a number in relation to other numbers and how to add and subtract at a foundational level. Typically students move from a number path to a number line. Moving from the path to the line too quickly could result in confusion and possibly lead to the development of math anxiety.

Q3

Manipulatives are a great way to help students make sense of how many of an item there are. Can anything be used as a manipulative? What do you need to consider when choosing items to help young learners understand number sense?

More or less yes, anything can be used as manipulative. If a student can hold it and move it from one space to another and count with it then it would work. That said it needs to be within reason for a classroom. It would be rather ridiculous if you used laundry hampers as a manipulative in a classroom, but it could work at home. There are many common manipulatives used in the classroom such as, dice, base ten blocks, counters, numicon, multilink cubes, tooth picks, crayons, etc (Lanigan, 2024). When considering items to help students understand number sense is considering what is the goal of the activity. If the goal is adding or subtracting then counters would work well or linking cubes for grouping or pan balance for determining the magnitude of numbers (Small, 2019).