Student 's Mathematical Knowledge ( Fractions, Decimals, And Cpi Essay

Learners may also have difficulty in understanding that a fraction of a group can be found when more than one object is represented, two fractions can be equivalent even with different denominators and that objects that are not the same shape can still be the same fraction. In terms of comparison students may have difficulty in comparing bigger fractions to smaller ones and in associating the size of the fraction to the size of the whole. Furthermore students may have difficulty is grasping all of the representations of fractions and the concept associated with fractions greater than one.

When the denominator is the same he is able to partition and see what fraction is needed to make the whole. When comparing fraction pairs, Adam is using gap thinking of the fractions 5/6 and 7/8 “both need 1 of their fraction to make a whole” understanding that each numerator needs one more part to make it a whole. In saying that, when comparing ¾ to 7/9 that have more than 1 to the whole, Adam said ¾ is larger, “1 more ¼ to make 1. 2 more 9ths to make a whole” He tried to apply gap thinking, incorrectly not understanding the unit of fractions. Adam has limitations surrounding improper fractions, not recognizing that 4/2 is larger than 1 whole and is equal to 2. He has misconceptions when comparing fractions with proportional reasoning is limited. When asked to draw a fraction he automatically swaps the numerator and denominator (6/3 to 3/6) when the numerator is larger than the denominator, when considering improper fractions, rather than converting to a mixed number fraction or whole number.. This displays Adams misconceptions of the understanding of the

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.”

My goal is to assess student’s prior knowledge of division and to teach students how division can be modeled by using place-value blocks so students can see that division consists of arranging items into equal groups. My goal for day one is to help students develop and understanding of division through the use of manipulatives and drawings so when they transfer that knowledge to day two, students will have a better sense that division consists of dividing a large number into equal groups. By using place-value blocks I also want students to visually see what a remainder looks like so they can better understand what a remainder represents. Sometimes students can’t understand the definition of a remainder which is the part that is left over after

He can convert improper fractions to a mixed number with 57% accuracy and convert mixed numbers to improper fractions with 80% accuracy. John can simplify a fraction with 92% accuracy. However, he does not always simplify his answer, instead he stops with his answer rather than seeing if it can be simplified. He can add and subtract fractions with 88% accuracy. He can multiply a fraction by a fraction with 14% accuracy and by a whole number with 90% accuracy. He can divide a fraction by a whole number and a whole number by a fraction with 89% accuracy. He needs to be able to simplify fractions when computing with fractions. He needs to be able to add, subtract, multiply, and divide fractions. He needs to identify the correct operation to solve a word problem. He needs to be able to solve one-step and multi-step word problems involving all 4 operations (addition, subtraction, multiplication, and division) of whole numbers and fractions. John’s weaknesses in math impact his ability to solve multi-step word problems, which is expected in 5th

Objective: Student will inform audience on how to add and subtract decimals with and without regrouping.

For the student interview, I interviewed a 9th-grade boy and used the Algebra Interview questions. When we started the interview the boy was very apprehensive. I assured him it was not a test, and not much writing was required. He slowly started to relax. I read the first question (1a) out loud and had barely finished when he gave me the answer. His mental math was in high gear despite his initial apprehension. I proceeded to the next question (1b) with the same result. He provided an answer quickly to this question as well. I was beginning to wonder if this was going to be too easy for him, so I asked him to write down and explain his thinking so I could understand how he got the answers. For number (1a), he explained that he multiplied 6 by 3 because Alice ate 6 ounces of cake and she grew 3 feet for each ounce of cake that she ate. He then added the product of 36 to her original height of 4 and came up with the answer of 40 feet. For (1b), he modeled a different approach where he started with 16 feet and subtracted 4 increments of 3 until he arrived at Alice’s original height of 4 feet. He told me that he knew that he needed to get to the base height, and that is why he used subtraction. He did it in increments of 3 as he knew that Alice grew 3 feet/ounce of cake.

When it came time to write the answer to problem #8 as a fraction, decimal, and percent, I was pleased to find the majority of the students remembered how to complete this conversion. For this portion of the problem, I disregarded whether the

These samples of student’s work support the standards 3.3 and 3.5. For addition, subtraction, multiplication, more or less, and word problems, the student has learned how to do these methods through visual, audio, modeling, guided practice, and individual practice. When teaching the lessons, I used modeling, visual and audio instructional strategies. Once the methods were taught, the student did guided practice and then individual practice. For this student I start with addition problems because they are something he enjoys doing. Once he has done some, I am able to have him complete less desired tasks such as subtraction and word problems.

Jaclyn’s grade 8 math focused on mixed numbers to improper fractions. Jaclyn’s tone of voice was clear and welcoming to all students. Jaclyn used the Smartboard and OneNote to show examples of dividing fractions and simplifying fractions. Students were engaged and focused on the questions that were given to them as practice questions in OneNote software. Jacqueline also used instructional strategies and classroom management to refocus students on the task by asking students to put down their pencils while she taught certain math steps and she asked for student feedback while proceeding through each step. Jaclyn encouraged students to work in groups of five students at each table and she monitored each group by prompting questions with each

IEPs additionally address other dialect or perusing handicaps that influence a kid's capacity to learn arithmetic. As a result of the wide assortment of issues found under the conclusion of arithmetic issue, arrangements change extensively. For the most part, guideline stresses fundamental numerical ideas, while showing kids critical thinking aptitudes and approaches to dispense with diversions and superfluous data. Solid, hands-on direction is more fruitful than conceptual or hypothetical guideline. The treatment is not an easy task to

[In clip 2 at 0:57 the student explains how she knows that -24 is less than -12. She explains this by saying, “because -24 is farther away from 0 than -12 is.” I responded to her by saying, “Positive 24 is further away from 0 than positive 12 and positive 24 is greater than positive 12. So, how… what’s our difference there?” One student in the group said, “because you’re dealing with negatives and then positives.” The other student in the group said, “Negatives… um… is counting down and for positives it’s counting up.” Through this conversation and their explanations, the two students could deepen and solidify their conceptual understanding. I was able to get the students to connect positive and negative integers and see how they relate and

In this question, the student is demonstrating their knowledge of being able to recognise that the place value system can be extended beyond hundredths (ACMNA104). According to the curriculum, using the child’s place value knowledge and division by 10 will allow the student’s knowledge to extend. A number of researchers have found that some students are confused by the range of symbols that decimals can hold in mathematics (Barmby, Bilsborough, Harries & Higgins, 2009). Therefore incorporating this into the answers will allow the educator to determine who understands the value of decimals. It is highly important for students to understand that the place value system is a multiplicative system where each place shows multiplication by 10 (to

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.