Jnt2 Task 1

In Video A, Christie Kawalsky (Australian Institute for Teaching and School Leadership [AITSL] (n. d. a)) is the teacher of a Year 3/4 class. In Kawalsky’s class, students are focusing and developing skills based on strand ACMNA058 of the Australian Curriculum (Australian Curriculum and Assessment Reporting Authority [ACARA]. (n.d.b)). The content descriptor for ACMNA058 states that students can “model and represent unit fractions including 1/2, 1/3, 1/4, 1/5 and their multiples to a complete whole” [ACARA, n.d. b). This content descriptor is being met, as evident in Video A because Kawalsky presents concrete-based examples of chocolate bars to her class as a visual cue to determine multiples of a whole. The chocolate bar photocopy is a flexible resource that can become segmented into an array of unit fractions. This reflects the elaboration of ACMNA058 as students are actively folding and cutting out illustrations of fractions to represent halves, thirds, quarters and fifths (ACARA, n.d. b.). Students are also fortunate to meet the elaboration outcome of comparing the number of

When Dustin is asked to identify numbers from 11-20, he is able to accurately identify numbers 11-14. When Dustin is presented with manipulatives and asked to answer “How Many?”, he is able to count manipulatives 1-5 with about 75% accuracy. When Dustin is shown a coin and asked to find it on his communication device, he is able to find the coin with about 75% accuracy. He also has been working on stating the correct values for each coin.

This essay will explore how I would teach a group of 10 first grade students to count rationally to 15 assuming that all of them are already able to count rationally to 10. I shall explain how I would ensure that students understand each of the four rational counting principles of one-to-one correspondence, the stable order rule, the order irrelevance rule, and the cardinality rule. I shall present an assessment I would use to evaluate student mastery of rational counting to 15. Finally, I shall discuss how I would adapt my instruction to accommodate English Language Learners (ELL) and students with learning exceptionalities.

There were some small changes made to the original numbers in the word problems so that the numbers in the math word problems reflected single and double-digit addition and subtraction facts without regrouping. The planning of the segment includes Alejandra’s strengths in math to solve single and double-digit addition problems with 70 % accuracy and creating problems that she can easily read, solve, participate and help her take ownership of her learning. Concepts that Alejandra is unable to understand will be reviewed and repeated through direct instructions, and modeling with the teacher. In addition, lessons 1 through 4 include guided practice. Alejandra along with other student will be asked questions during the instructions to make sure they are correctly following and understanding each segment. For example – why did you choose these operations (addition and subtraction)? How does the large and small part fit in to the equation? Modeling was done to describe Alejandra’s thoughts of the choices she makes on selecting operations and components in the word problems in familiar

The book addressed several Mathematical Practices (MP). MP 4 addressed that apply what they know in math to attempt to solve the problem (The California Department of Education, 2013, p.7). The book describes an everyday problem of having enough money for t-shirts and thought the story they are raising money. The book applies an every day situation to how to count money. Another

Numbers have transformed throughout time. Initially numbers were written in one- to- one correspondence through slashes or tallies in cave walls or bones. Once this number system was considered to be too tedious, different regions sought to find an easier way to count objects. Ropes and a series of knots and beads were used, then symbols to represent the groupings of thousands, hundreds, tens, fives, and ones. Finally, the number system we currently use was developed, which took hundreds of years to understand place values to make numbers more easily understood. In society today, after years of working with numbers as adults the system of place value is understood, but for children, “developing an understanding of

My classroom is consisted of 8 kindergarten students. Their parents have written out skills from Reading and Math that they would like for them to work on during the summer. One of the Math skills that they have as a common goal to learn is to count objects. This mathematic skill coincides with the Kindergarten Math standard: CCSS:Math.Content.K,CC.B.4. This standard wants the students to understand the relationship between numbers and quantities. To put in a kid friendly term, this standard is asking the students to count and tell how many.

1.0A.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.Use strategies such as counting on; making ten (e.g., 8+6=8+2+4=14); decomposing a number leading to a ten (e.g.13-4=13-3-1=10-1=9): using the relationship between addition and subtraction (e.g., knowing that 8+4=12, one knows 12-8=4); and creating equivalent but easier or known sums (e.g., adding 6+7 by creating the known equivalent 6+6+1=12+1=13) DOK 1,2

At the end of the session the child was given a challenge to multiply 8 656 by 1 000 000 [see appendix B] and could successfully do so. He was also able to explain that multiplying 8 656 by 1 000 000 made 8 656 groups of 1 000 000 and this push 8 656 up six places on the place value chart which added six zeros to the end of the number. This demonstrated that he achieved a conceptual understanding of multiplying by powers of 10.

Developing fluency requires a balance and connection between conceptual understanding and computation proficiency. Computational methods that are over-practiced without understanding are forgotten or remembered incorrectly. Understanding without fluency can inhibit the problem solving process. (NCTM, Principles and Standards for School Mathematics, 2000). Adding It Up (National Research Council, 2001), and influential research review on how children learn mathematics, identifies the following five strands of mathematical proficiency as indicators that someone understands (an can do) mathematics (Van de Walle, Lovin, Karp, & Bay-Williams, 2014, p. 2). The five strands the National Research Council (2001) identified are: Conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. These five strands are interdependent and interwoven, as the development of one strand aids the development of the other strands.

Did I miss one? Did I count one twice? All the things that go through your head… ‘But, but, but, bu-’ one might think. There is algebra, and calculus, and… and… and…! Yes, but there is also counting in other base systems. Ever heard of that? This is page 10 of this chapter! You can count in any base system at all. Almost everyone uses base system ten. Hypothetically speaking, if you were to say ‘I want to count in base system three!’ You tell you friend you are going to count to seven so they know when to start the race. The number seven in base system three is twenty-one. So you would count like this: ‘1, 2, 10, 11, 12, 20, 21!’ When you are about to say three, the tens digit goes up one. The only possible units digits when counting in base three are 0, 1, and 2. Here is how you figure it out using a quick shortcut. Three goes into seven twice (2_) with one remainder, so it turns into 21. It seems pretty simple, but in reality, it is not.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and

Place value is essential to developing number sense and without it students would not be able to give meaning to numbers. Place value underpins important mathematical concepts, such as part-part-whole knowledge, estimations, mental strategies, flexible partitioning, and knowledge of multi-digit operations (Dawson, 2013; Hurst & Hurrell 2014). Frequent hands-on counting experiences with concrete materials, models, resources and activities are mandatory to progress students understanding of place value (Appendix A). Ross (2002, p. 420) states when students are provided with conceptual problem-solving activities rather than procedural activities, a greater understanding of place value is developed. Moreover, multiple embodiment experiences allow students to work flexibly with numbers. Research shows students’ ability to work flexibly with numbers in different contexts are limited if they are not provided with “…perceptually different models” (Reys et al., 2012, pg. 28). Hence, students’ development of place value relies heavily on conceptual learning with explicit multi-embodiment experiences and tasks using concrete resources. However, before students can develop base-ten number and place value systems, educators must introduce pre-number concepts including classifications, patterns, conservation, comparisons and one to one correspondence, group recognition (subitising), and counting strategies (Rey et al., 2012). These concepts are

A few days before I taught my lesson, Ms. Bell introduced the standard of adding and subtracting to one million. So, I taught my lesson on the fifth day of a seven-day unit. I incorporated both large group and small group to maximize my students’ learning. I focused my lesson on the goal of fluently adding and subtracting multi-digit numbers using the standard algorithm. The learning goal in simpler terms was to add and subtract to one million. This concept was selected for me based on where my lesson fell in Ms. Bell’s planning.

It could be answered incorrectly due to generalisations being used to identify the sequence (Haylock & Manning, 2014), for example, as the question is adding four to each number, the child may only see the fours in the other sequences. Not understanding a number line can cause problems as children do not always understand which number start the counting on (Reys et al., 2016), for example, counting from 12 to 15 would be incorrect as the number 12 had already been used. Understanding that the stepping out action to the next number (13) is the action to be counted not 12 (Reys et al.,