Common Core Standards: Relationship Between Multiplication And Division

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

It also requires the student to understand approaches to problem solutions utilized by other students and being able to provide peer feedback. Students should be introduced to the use of mathematics to: organize data, solve problems applicable to their life, and understand the world around them. This approach makes the subject both interesting and enjoyable. The use of these strategies is addressed in the next standard “#4 Model with mathematics” (Academics), which helps the student to make connections, surpass procedural knowledge and gain a conceptual understanding of a

Van de Walle, J, Karp, K. S. & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics Teaching Developmentally. (9th ed.). England: Pearson Education Limited.

Students will be able to listen to my questions about division and listen as I explain how to solve different division problems and place the quotient in the correct place value position.

Students had previously covered the topic of developing fluency in multiplication by 2-digit numbers. After that topic students moved on to cover number sense, dividing by 1-digit divisors using mental math to prepare them for the following topic of my learning segment. The topic of my learning segment consists of developing fluency, dividing by 1-digit divisors. I designed my lesson as a three-day unit focusing on long division by modeling division with place-value blocks, dividing 2-digit by 1-digit numbers, and dividing 3-digit by 1-digit numbers. Students were introduced to division prior to my learning segment but the struggled to understand and comprehend division because students were only introduced to the division algorithm and were not provided with a mnemonic to help them recall the steps. Students also weren’t introduced to division with manipulatives or drawings. Therefore, I

This program is appropriate in a diverse, 4th grade general education classroom. The modules are made up of “Topics” and “Lessons” that are aligned to Common Core State Standards (CCSS). Each module provides the foundational standards needed for the lessons (i.e. CCSS from the previous grade), as well as the focus grade level standards. The first module introduces concepts which are then spiraled within the next module’s focus. While the modules are thematic and based on each mathematics domain (base ten numbers, geometry, fractions, data, algebraic thinking), some standards are seen across topics and lessons. Each lesson has allocated time to four major components: fluency practice, concept development, application problems, and student debrief.

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

What preparations have you made to anticipate students’ prior mathematics knowledge, students’ differentiated responses and knowledge, and their evolving mathematical thinking throughout the lessons?

By far the most confusing thing to me in this lesson was factoring numbers. I understood the concept and how to do them, but I wasn’t able to completely get them right every time. It was easier when factoring quadratics, but I still had some trouble with them. I consulted this internet to find out more on factoring polynomials which ended up helping a bit. I still did not have the best understanding of them, but I was able to solve most problems without having much trouble.

Many students get confused when learning about fractions. At our grade level we teach about parts of a whole, equal shares, and partitioning.

By twelfth grade U.S. was near the bottom in international rankings. Bill Schmidt is not the first to identify the “mile wide, inch deep” character of the American mathematics curriculum. A standard-setting process could be a powerful tool in narrowing and deepening the curriculum. (Haycock, 2002). It has been found that students will learn more mathematics when they are exposed to college-preparatory mathematics curriculum; even if they are not college bound. The Common Core standards emphasize critical thinking, creativity. and analysis over rote memorization. This curriculum makes a huge difference in student achievement (2014). The Common Core standards will also help build long-term abilities for our schools to deliver rigorous. meaningful

Within the teaching of mathematics, it is essential that the tutor plans a Scheme of Work and individual lesson plans. Within the context of numeracy this involves different Schemes of Work depending on the

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.

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.

The lack of adopted curriculum also means that most, if not all, teachers are supplementing both materials and instructional routines. These students need to pass the state-mandated Smarter Balanced Assessment (SBA) which requires completion of a problem-solving performance task. Students need to know which operation(s) to use (addition, subtraction, multiplication, and/or division) and how to apply them appropriately. This problem has