Activity 1: Comparing Fractions (October 12, 2016) The learning objective of the lesson Comparing Fractions was to demonstrate to students that fractions are everywhere we go and the importance of being able to identify fractions with greater or less value when comparing fractions.
Engage
During this activity students were very engaged, they created their own figures using the pattern blocks. Below there are some of the examples of the figures that students come up with (see fig.1&2). After creating these figures, they realized that they could have use tringles to make their figures instead of the different shapes. So, I ask them “Could you show me how this could work?” Some students started to make the same figures but this time only using tringles. However, I noticed that David, one of the students was not doing the same as his classmates. Instead, he was writing a key, he wrote how many triangles were in a Hexagon, a rhombus, and in a trapezoid. Then he said “I think that I need 21 triangles.” I thought that was very impressive for him to completely do something different than his classmates. Then, I saw the opportunity to allow him to continue with the lesson while the others were still figuring out how many triangles were needed to create the same figure. After everyone was done with counting how many triangles were needed for their figures, I asked them to create fractions to represent the different shapes in their figures. In order for students to see from an
Also, we had some posters about the shapes and I used them to demonstrate to them. With showing the illustration and let them to touch the colourful shapes I engaged them and I let them to discuss between themselves. I asked them for this activity you should all work as a team and should look at the shapes carefully and according the sides you must put in one circle. For example, in circle 1 we have all shape with 4 sides that we call quadrilateral.
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
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.
Even thou, geometry involve shapes, nature, conjectures, proofs, angles, formulas and patty paper, one needs the common language to express attributes. She was able to tell the number of sides a triangle, pentagon, and rectangles. She could not complete parallel line task because she did not know what parallel meant, which affected the parallelogram activity. I know that we were not supposed to give instruction, but what a great learning moment we shared. We found lines and shapes in the classroom environment and talk about where the lines started and ended. We addressed corners and where two lines met. We traced tile lines on the floor. She came to the conclusions that “top and bottom don’t touch.” We marked parallel lines and talked about what parallel meant. She remembered parallel the next day so it did make sense in her mind. In fact, she remembered the words from the warm-up. Many activities had a rubric that made it clear on how to analysis the
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
The author explains how many students, especially those in the focused-upon second grade class, have difficulty explaining their “mathematical thinking process”. While they may provide correct answers using memorized calculations, they are unable to demonstrate their conceptual understandings or explain how they achieved the right results. As stated by the researcher, “it is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos & Shin, 2010, p.223).
Students were highly engaged and actively participated in mathematical discourse. Consequently, students employed counting to identify and describe patterns in the natural and designed world(s), created algorithms, and used and developed new simulations of designed systems (Next Generation Science Standards, 2013). Although the lesson was successful, the lesson may have a greater impact on the setting if students extended the challenge to investigate growing patterns.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds,
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.) ]
providing opportunities to develop facility with finger-pattern counting, so that 5 fingers and 10 fingers become anchors for the other numbers. Thus, students will recognize that they do not have to recount the 5 fingers on one hand in order to show 6 fingers; instead, they can automatically show the 5 fingers, say “five”, and then count on an additional finger from the other hand to make 6 (A Guide to effective instruction in mathematics, kindergarten to grade 3 : number sense and numeration, 2003).
Before I had the chance to introduce this activity, Jonathan sat down at the table and said, “It looks like a rectangle clump of dirt.” “It does look like dirt but it is called clay” I said, “Or dirt” Jonathan insisted. “You can make things with clay” I continued “like zombies, Minecraft figures and even a scary octopus like these” I explained, pointing to the pictures. “I want to make Minecraft” Jonathan says excitedly. “That’s a good idea, have a look at this picture. What shapes did they use? How many shapes can you see?” I asked. “Squares and rectangles and one, two, three,” he counts “four, five six! he exclaimed” “To make a Minecraft figure what would you need to do first?” I asked. “Umm……Cut it in four pieces” he replied. With this idea, he touched the clay for the first time.
I would with one students on how to make equivalent fractions, She was very confused and did not know how. So I demonstrated the example that was written on the board. I wrote 3/6 and then wrote the division character by the numerator and denominator and then wrote 3. So then I said 3/3=1 and 6/3=2, then wrote 1/2. Then we tried to reduce 25/100, so I said, “What can you divide by 25 and 100.” She said 5 so she followed the example that I had written. So I said, what’s 100/5, she said, 20. So we knew the denominator was 20. Then I said whats 25/5, she said 5. So then I said the equivalent fraction is 5/20. She wrote done all that we had discussed above as we were finding the answer. I still think she was a little confused after, but it was time for discussion. For next time, I think I would try multiplying as another example, which I think could help the student see both. what I would have done was try multiplying instead of
One connection between Lesson 2 and Lesson 3 is the belief that God will reward those who are good and punish those who are wicked. Lesson 3 states, God may “manifest the work of his Spirit” on to the “wicked in moderating and restraining them” (19). The same theme is shown in Lesson 2 when the Pilgrims believed that it was “a special Providence of God” the Native Americans “got seed to plant them corn” and that “the Lord is never wanting unto His in their greatest needs” (10). The Puritans strongly believed in God and how he punished and rewarded them depending one how good they were.
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.
Markworth (2012) suggests ways students can learn algebraic concepts and geometric patterns by developing an understanding of functional thinking. Growing patterns are a useful counting method that allows students to engage with algebra. Geometric growing patterns best support student’s ability to develop functional thinking which is essential. This article outlines three teaching strategies for using geometric growing patterns, these are: