The Distributive Property of Algebraic Expressions

Algebra is a critical aspect of mathematics which provides the means to calculate unknown values. According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and functional situations. The understanding of these concepts by children will have an enormous bearing on their future mathematical capacity. However, conveying these algebraic concepts to children can be difficult due to the abstract symbolic nature of the math that will initially be foreign to the children. Furthermore, each child’s ability to recall learned numerical laws is vital to their proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic concepts is of significant importance to allow all

This question is linked to the Australian Curriculum’s ‘Patterns and Algebra’ content descriptor (ACMNA176) which requires children to “create algebraic expressions and evaluate them by substituting a given value for each variable” (ACARA, n.d.). Algebra is essentially the study of mathematical symbols and the rules for manipulating these symbols. Thus, by converting written sentences in symbolic numerical expressions, algebra has been utilised. More specifically, an algorithm has been followed. Algorithms are step by step guides on how to do something. Thus, the series of clear steps listed in this question creates an

Today we will be learning about place value. When we divide numbers with three and four digits by a one digit number, the quotient doesn’t always go about the first number in the dividend like we saw yesterday. This is important to know because if you had to split $100 with your sister and you divided $100 by 2 and placed the 5 above the 1, then added two zeros, you would have to pay your sister $500. That’s not dividing, or fair. Remember we need to know how to divide so you can evenly split something, like money.”

Construct viable arguments and critique the reasoning of others- it’s important for students to be able to explain and be able to discuss the process into which they believe a problem should be solved this demonstrates the students understanding on the concept. They should be able to clarify and answer any questions that arise about the problem once again displaying a deeper understanding then just being able to memorize formulas/steps and solving a problem.

When you are multiplying fractions you multiply the numbers on top as well as the numbers on the bottom. For example:

The teacher will explain to students the meaning of why they need to know numbers.

The two ways that enhanced my experience of taking this class are learning to get all the facts of

Remember being taught something new in a mathematics class and thinking to yourself, “when am I ever going to use this in life?” Sure, not every mathematical theory taught in class will be used in your career, but from my experience, many of the skills learned in mathematics are frequently utilized each day. While mathematics may not be everyone’s favorite subject, I found it to be not only the subject I use the most outside of school, but the one that I enjoy the most, which is why mathematics is my favorite subject.

that would allow students to explore multiplication as equal groups through a familiar context” (Ex. Lines 4 and 5 provide evidence of established a mathematical goal to focus learning). The teacher also reminded the students of the initial goal,” ‘So, tell me about your picture. How does it show the setup 28 of the chairs for the band concert?’" (Ex. Lines 28 and 29 provide evidence of established a mathematical goal to focus learning).

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Symbolic representation using base-ten and expanded algorithms is a way to show students the written connection to the visual models used. The partial-products algorithm is a more detailed step-by-step process and therefore more advisable to avoid errors in students learning to grasp the procedure (Reys ch.11.4). This process allows students to visualise the distributive property more easily. However, the standard multiplication algorithm is quicker and acceptable for students, if the teacher feels they have complete understanding of the steps in the partial-products algorithm.

What is the most important concept that you learned in this class? Write this for a reader who is unfamiliar with the concept.

Based on several studies, one of the best ways to understand mathematical ideas and apply these ideas is through the use of manipulatives. Students explore these manipulatives, however, it is important that they make their own observations. The teacher then should model and show how to use the materials and explain the link of these materials to the mathematical concept being taught. Schweyer (2000) stated that students learn best when they are active participants in the learning process where they are given the opportunity to explore, assimilate knowledge and discuss their discoveries.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Knowledge must have background facts to be considered true and mathematics must use reason to justify their formulas or methods. For example, memorizing the area under a bell curve is very different from understanding how it is derived. Proofs are useful when proving mathematical concepts although they are not concrete and harder to understand. Creative aspects must be considered when trying to derive a difficult proof.