Teaching Equivalence in Fractions with Unlike Denominators to 4th Graders

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 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

When students finish the whole set of the fraction cards, the teacher will provide them with an answer sheet and they will flip box by box and self-check their work.

First, I did some research about appropriate math activities for 3-year-old children. At the beginning of the semester the preschool class I oversee had a week where pizzeria was the focus in our dramatic play. Many of the children spent most of their self-selected time making pizzas and severing them to one another, so I decided to make my activity pizza related. I gathered a baking pan, colored containers, pizza crusts, and pizza toppings for the activity. Then I placed the supplies neatly on a child-sized table for the children to play and create their own

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).

I know that students learn best by hands on activities and creating. I choice to have the students use cheerios as part of the hands on activity and to create their own arrays, equations and story problems. They were free to pick numbers of their choosing with in my parameters of numbers. This supported the rigor because I asked them to create from scratch but also gave them to freedom to choose their own numbers and stories. As a teacher this was a great lesson to visually see who understand the standards and goals and who needs more practice. Most of the students who struggled with this lesson struggle with addition. I gathered the struggling student into a small group the following day to work on those skills. The learning outcome for this

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)/

First teachers have to be sure students understand that a/b multiplied by c is the same as saying a/b groups of c. This is similar to interpreting fractions as implied concepts. Possible ways of teaching this is threw visual aids. One visual aid is using a number line. Have students explain how the fractions are located within numbers on the number line. Or you can have them do this by filling in squares to represent the fractions being multiplied. Multiplying fractions to describe area is another subject they cover in this grade. The students should already know how to calculate area so all they have to do is apply previous learned concepts about multiplying fractions to do this.

They had us bring in objects (such as buttons, marshmallows, M&M’s… etc.) Coming from a potential teacher’s point of view, this should have been done in elementary school. (That is beside the point.) I remember using white boards to help prove that I knew the answer. The way my school was scheduled, there were four classes a day and you would have new classes half way through the year. You were only required to take one math class per year. With that being said, I enjoyed math so much that I took math every semester except the second half of my senior year! By the first half of my senior year, I took a class called, “college math”. It introduced me to the basic concepts of college math. For example, I learned about sets, intermediate algebra, and more. By the time I graduated high school, I loved

The child from my video is my niece Adriana. Adriana is eight years old and she is in second grade. Since, she is my niece my brother gave me permission to include her in the video. As I went through the activity I tried not to do any modifications in the instruction, I just made up the division problems as I went through the video. The only thing I change was the counters for the cubes. The student learned how to do simple division using equal grouping. I know that she learned because she worked out few problems by herself at the end of the video. She was able to recognize dividing by equal grouping is just having the same number of units in each group. Example she was able to solve six divided by two by drawing a circle for each group and

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

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.

Lesson. During pre-test one, I had assumed that all of the students could pass a simple fractions quiz, but I assumed incorrectly. Many of the students did not pass the quiz, and I had to go back and readjust my use of fractions. The pre-test also showed their teacher that she needed to step back and teach the very basic fraction concepts when the new school year starts. I also found that many students just hurried through the quiz so that they could play with the recorders, which could be the reason why so many did poorly on the pre-test. During the lesson, I focused more on the basics of fractions before I let them play the recorders, and I found that many of them responded positively when called on to answer a question. My experience in administering post-test 1 was a bit better but not much. The students were still hyped from getting to play music during math class that they had a hard time calming down enough to do their best on the test.

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.