Mathematics Case Study

15, via Goos, Geiger & Dole). The dimensions shown in the above paragraph can be considered to be the important areas of real-life use of mathematics, with most use coming from the functional dimension and the critical dimension - which coincide with the Australian Association of Mathematics Teachers’ definition of being numerate. These ideas reinforce each other to paint a picture that numeracy in it’s real-life form is not an exact science, such as copying notes from a board and working through a set of questions, but rather, it is dynamic. To be numerate is to display confidence in mathematics through all sets of skills, even if those skills are not perfectly formed or are lacking in some areas. For example, a hotel receptionist may never use the Pythagoras theorem in her work of booking rooms or her day-to-day life, and thus does not know or have confidence in performing such numerical tasks. Considering she may never use that particular theorem in her life, it would be unfair to describe her as innumerate, as she does not need to display confidence in that area. This example demonstrates the definition of numeracy in terms that backup and demonstrate the concepts provided by Goos, Geiger & Dole, Frogasz, Paige, Lloyd & Charles - as a dynamically suited

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

2. A month after the classroom teacher completed the review unit for multiplication, we began long division. One student was having a very difficult time with long division. The student hadn't quite mastered their multiplication facts, thus, making the long division unit difficult. I printed out a multiplication chart which listed the multiplication tables from 0-12. The student completed the long division unit with confidence using the chart. Additionally, I created and located

Write 912 ÷ 4 on the board. “We learned about this yesterday. How would we solve this? What do we do with the extra number in the quotient? What is that number called?”

Jazmine was introduced to two digit addition. My first lesson focused on drawing tens and ones to solve two digit addition. This strategy would provide Jazmine with the visuals she needs to solve the problem. First, I did a quick review on how to draw tens and ones to represent a number. She was given three examples ranging from easy to hard. Jazmine showed no signs of difficulty and was able to complete the task. Then, I demonstrated how to use the drawings to add two digit numbers. I explained how she must draw the picture for each addend. Then, I explained that she must count the tens first and then the ones. She smiled and said “that's easy”. We went through a couple of problems together and Jazmine displayed that she understood the strategy of drawing tens and ones to solve two digit

First, the interviewer presented the problem as difficult when reading the problem. Once the child had solved, the interviewer immediately went to the 7 in the hundreds place and questioned what that number represented (i.e. identifying the place of error). The interviewer pushed the child to re-examine place value, and was able to get the child to realize it should be larger numbers that sum to 1000. However, when the child didn’t automatically try to fix the other numbers, the interview pushed the child to fix the other numbers by again prompting towards place value application. Once the child said ten-hundred, the interviewer pointed back to the previous thousand and questioned why they were different—then asked “Really?” when the child showed a

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

If he would have started with it right away, he would have shut down and not want to complete any math. This artifact helped him work on his multiplication fluency, borrowing from the 10’s place, more or less, and word problems. When this student first started working on word problems, he used a note card that had the steps to reading, setting up, and answering word problems. He also used notecard with different words that mean addition and subtraction. When he completed this work, he no longer needed the note cards. He was able to read the problem, set it up, determine if it was addition or subtraction, and solve it all

Today we discussed the different ways we know numbers can be represented. Some great ideas were shared such as using drawings, people, numerals, objects and words. We then read a story called None the Number and recorded all the number words we could find. With our learning partners, we explored a circuit of physical activities and had a go at reading number words on the signs. Bouncing the ball ten times was a fun

For this game, adaptions can be made for students who struggle with thinking quickly when it comes to multiplication and dividions, with different possible selections of flash cards being made. For students who struggle with thinking quickly with multiplication, easier multiplications such as 2, 3, 5 and 10 times tables can be

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.

If the numbers are misrepresented, it is difficult to carry out the correct performance of mathematics. This becomes an issue while solving mathematical word problems. This gives one example of what an ELL student faces and struggles within the everyday classroom.

I chose to incorporate reading as a math warm-up because it is an effective way to explore mathematical concepts, which are both engaging and informative for the students. Integrating elements of literature into the lesson supports problem solving and allows students to be fully immersed in the story, solving themselves the mathematical issues that the characters fall into. Ministry of Education, 2016, endorses this idea stating that applying visual elements of picture books aid in illustrating mathematical concepts, which are difficult to teach with other resources, or challenging for students to comprehend. This particular book introduces properties of place value, discussing the idea that 10 tens is equal to 1 one hundred, which all groups need assisting with.

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.

One of the approaches, which is highly recommended for children to practise, is to do addition calculations mentally (working out calculations in their head) using various strategies, which is the focus of this essay. Tony Cotton (2013, p.109) states that developing mental approaches is more efficient to work out solutions to problems and helps children to become fluent in mental calculation. However, doing mental calculations, such as addition, can be challenging and confusing for some children. Therefore, introducing appropriate strategies (for example counting on, partitioning, bridging through 10) and using them to draw images or mark-making will encourage children to ‘see’ calculations in their heads and will allow them to use the strategy which is the most suited for them (Cotton, 2013, p. 110).