Van De Walle, Karp, And Bay-Williams

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

I was expecting for the student to have a few difficulties solving the harder fraction problems. Angel, however, was having a very difficult time answering addition problems. He continuously solved addition and subtraction problems different ways. There were moments he added numbers starting from the left and other times he started at the right. In the end, Angel almost never got a question correct and when he did, his explanation showed that he did not understand the problem correctly.

The math concepts taught in this lesson are teaching the students how to use certain math formulas, and practice addition and multiplication. It is beneficial for students to know what tools to use for capturing and displaying information that is important to them (Davis, 2011). The science concepts taught in this

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.

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

In a math classroom, the teacher cannot neglect the need for providing a print rich environment. “Word walls are a technique that many classroom teachers use to help students become fluent with the language of mathematics. It is vital that vocabulary be taught as part of a lesson and not be taught as a separate activity” (Draper, 2012). Draper acknowledges the fact that words in mathematics may be confusing for students to study as “words and phrases that mean one thing in the world of mathematics mean another in every day context. For example, the word “similar” means “alike” in everyday usage, whereas in mathematics similar has to have proportionality” (Draper, 2012). Fites (2002) argues that the way a math problem is written drastically will effect a student’s performance, not just in reading the problem, but in solving the math equation as well. There is where the misinterpreting of different word meanings in math comes into play. Fites continues with the importance of understanding vocabulary not just in reading but for math as well with the correlation between improved vocabularies in math yields improvement on verbal problem solving

For the Kidwatching Project Part 1, I found myself interviewing a few students on the concept of multiplication and division. According to Merriam-Webster Dictionary, multiplication is defined as the process of adding a number to itself a certain number of times: the act or process of multiplying numbers. Merriam-Webster Dictionary also defines Division to be the act or process of dividing something into parts: the way that something is divided (Merriam-Webster, 2015). Multiplication and Division is a subject that many different students in early ages can grasp or struggle with because the concept of using different ways to approach these particular problems. Many kindergarten children can solve simple multiplication and division problems

And it connects with the Australian Curriculum areas: Create symmetrical patterns, pictures and shapes with or without digital technologies. The Storytelling strategy engages all students in listening and promotes their imagination, emotions and critical thinking skills while learning the main concept of math. The class discussion along with questioning strategy throughout the lesson promotes students’ exploratory conversations and shared experiences on mathematics. The main theme of this lesson is to enable students to understand Aboriginal symbols in the painting and reinforce the relation of the mathematical concepts behind the symbols.

The magnet board and dots allow the students to interpret problems as the total number of objects in different groups; for example, 5x7 is interpreted as 5 groups of 7 objects each. The math fact table, supplied to Peter, will help build connection between prior learning that is essential for the lesson; furthermore, repetition of concepts over the course of the day will be supplied to the student. For example, the skills practiced will be extended into the other courses throughout the day (i.e. english, science, etc.) ]

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

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 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

A work tray will have been compiled of the necessary resources for the Numeracy task. A student may be working on shape/colour recognition; the resources may contain a tracing card with a square, a circle and a triangle; a pencil and paper. Then the student is asked to trace the shape which may require hand over hand support. Other resources will also be used but using a different approach such as solid shapes in various colours, the student will be shown a shape and asked “what is the shape?” or more simply “it’s a .....” leaving time for the student to respond and complete the sentence. They may be asked to “take the yellow circle” from a choice of two shapes. Progress is then recorded and will aid the teacher to plan for future lessons depending on the progress made or whether the task is achievable and needs adapting to best suit the ability of the

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.