Grade Students Knowledge Of Fractions

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

Students will be able to read story problems that include division problems and read vocabulary words that pertain to the lesson.

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

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

As a class, students identify the fractions on the rest of the five cards and determine to which box each card belongs. The teacher discusses with the students the possible reasons for their

This is one unit in a yearlong 6th grade math course. In this unit, the students will learn about expressions and equations. Students will learn how letters stand for numbers, and be able to read, write, and evaluate expressions in which these letters take the place of numbers. In this unit, students will learn how to identify parts of an expression using various new terms. They will learn to solve both one- and two-step equations. Students will be able to distinguish between dependent and independent variables. They will be able to identify the dependent and independent variables of equations and in turn, be able to graph them. Various activities to be completed inside and outside of the classroom will be used to show

It is important to teach children numeracy to suit their age and use appropriate techniques to suit their age and ability because sometimes too much emphasis on formal recording of 'sum' if introduced to early to children could make it difficult for them to understand. The learning style of numeracy is given more emphasis today to make them understand it much better. In the early years emphasis is made on how to make children understand different methods of working out to be able to arrive to an answer. Working with children the aim is to give children solid ground on

Answer- To demonstrate ability to solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, students will complete 5 addition problems with like denominators and 3 word problems, when asked to do so with the rest of the class, on a paper-pencil teacher-made fractions quiz, with 80% accuracy, at the end of the unit.

In the chapter, “Equal Sharing Problems and Children’s Strategies for Solving them” the authors recommend fractions be introduced to students through equal sharing problems that use countable quantities because they can be shared by people or other groupings. In other words, quantities can be split, cut, or divided. Additionally, equal sharing problems assist children to create “rich mental models “for fractions (p.10).

In a fifth-grade math classroom, the standard of the lesson of the day was 5NF 1 because the lesson covered the learning of addition and subtraction fractions. In the lesson, students learned to add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (a/b + c/d= (ad + bc)/

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

I would start with a visual representation of the topic. To try an engage a visual learning style I would present the subject with some pie. I would start by having 2 pies each cut into eight pieces. We would talk about how each pie is composed of eight pieces and so one piece would be 1/8. We would then compare the following that 1 pie is the same as 8/8. We would then add in the second pie. We would have 2 whole pies and we would then link in that if 1 pie is 8/8 then 2 pies would be 8/8 + 8/8, and thus 2 pies = 16/8. Once this concept is grasped I would take away half a pie. Like she described in her interview we would start by describing our situation as a compound fraction. We would now have 1 and ½ pies. With that we would then count the number of slices we have, remembering that each slice is 1/8th of a whole. So we would have 8/8 + 4/8 = 12/8th. This is an improper fraction. I would hold off for now on simplifying the

Students in 4th grade used ‘an additive strategy’. They would find the difference of two quantities to compare two quantities. Tourniaire and Pulos(1995) indicates that they often use difference or additive strategies in solving problems where multiplicative reasoning is more appropriate. Students in 4th grade don’t fully develop the proportional reasoning.

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.