Tania_Colligan_17818782_Assignment 2_EDP243_SP3_2023
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Tania Colligan 17818782 Assignment 2
What are fractions?
Fractions are a mathematical way of showing parts of things. Learning and understanding the importance of its work with whole numbers (Booker et al., 2023. pg. 348).
The early understanding is that fractions represent parts of a whole. Finding and exploring the terms numerator and denominator shows how many parts are in the whole and how many have been removed (Clarke et al., 2008.pg. 375). It is important that students are shown and taught that fractions are more than shaded parts of a shape. Fractions can represent many constructs to help develop other meanings needed for a deeper understanding of them (A. et al., 2019. Pg 344).
Constructs for fractions are ways to connect to different meanings of fractions. They are part-whole, measure, quotient, operator, and ratio. The first construct, part-whole is taught in earlier years in school to introduce fractions (Resolve, 2017. pg. 2). It focuses on the equal parts in the whole number or group of things. For example, ‘½ is one of 2 equal parts’ (Booker et al., 2023 pg. 356). An activity that can be presented in class is money fractions.
(Mathgeekmama)
Image adapted from Maths geek Mama
2023
Tania Colligan 17818782 Assignment 2
The money is shown to students, the change that makes a dollar. Discussion is looking at the dollar as a whole and different ways to break the dollar into equal parts. Then, students were given a worksheet to complete after exploring as a class. When introducing fractions, they show parts of a region, e.g., a circle or rectangle. The disadvantage is that students find it hard to see fractions as parts of collections or objects. Doing this money activity can allow the students to explore fractions as a part of the collection of coins (Booker et al., 2023 pg 358).
Measurement is another fraction construct, focusing on how much rather than parts.
A way to model it is through points on a number line (Clarke et al., 2008. pg 374.). When the line is successfully portioned in equal parts, it allows better precision when measuring (Resolve, 2017). After modelling, students engage in various number lines from 0- 1 in which
the parts determine the distance. If there are five equal points on the line, it is fifths. (Booker et al., 2023. pg 387). Then, the students can move on to a game to become more confident in the concept. It’s called a ‘Common fractions number lines game’; the students pick a card and match it to the game board.
Image from Booker et al., 2023. pg 388
Image from Booker et al., 2023. pg 388
Tania Colligan 17818782 Assignment 2
(Booker et al., 2023)
The misconception that 1/5 is smaller than 1/10 is a common mistake by students because 5 is less than 10. If the students do this, it shows a lack of understanding of fractions
and thinking more about whole numbers. The number line activity can help show that 1/5
th
is bigger than 1/10
th
(A. et al., 2019. Pg 345).
Fractions can be represented as division, or another name is quotient and is not often thought about when talking about fractions. Students need to understand that fractions can be thought of as sharing equal amounts (Resolve, 2017 pg.4). For example, if you had three people and two chocolate bars, how much would each person get is “2/3, which is two divided by 3” (Clarke et al., 2008. Pg. 35).
Activities involving sharing are good for helping develop quotient constructs with fractions. Give the students coins enough to make $2, then get into a group of 3 and ask them to show how they can share the $ 2 equally between the 3 of them and then work out the fraction.
Once the group grasped this amount, task them to grab coins, try other amounts and work out the fractions.
A misconception is that the numbers are separate identities, not that the top and bottom numbers are as one single value. Using a variety of visuals and materials will help show the representation of the fraction.
20c, 20c,20c, ?
20c, 20c,20c,?
20c, 20c,20c,?
Fraction Show 2/3
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Tania Colligan 17818782 Assignment 2
Fractions as an operator can enlarge or reduce the number. It indicates the fraction of a whole number. Operator construct is important for students to learn how to operate fractions, not represent them. For example, 2/3 of the crowd were clapping. Students need to think multiplicatively rather than adding. Fraction as operator task sheet
It will start simply to build on the understanding of the students.
1 a) work out 1/3 x $6 1/3 X $6 = ______ = 3 The students can colour each box to represent 6, so 6 /3 = $2
After a few sums, the students would move on to just calculating it using visual representation.
4 a) 5/6 x $12 = _____ of $12 = (
https://www.colindale.barnet.sch.uk/wp-content/uploads/Year-5-Maths-Lesson-4-Activity-
and-Answers-1st-June-2020.pdf
)
Many students could work out half or a quarter of the amounts. Students need to be exposed to various strategies and fractions to show operations.
An incorrect understanding of the denominator and numerator causes students to recognise
the multiplicative relationship between the two numbers.
Fraction as ratios is to compare two related quantities or measures. It can show probability or compare how many boys and girls are in a class (A. et al., 2019. Pg 345). Working with ratios as fractions develops an understanding of equivalent fractions. Ratio tasks are designed more for the year six curriculum. To start the lesson, the teacher would go through the following ratio problem as a class, going through step by step to work it out to ensure they understand how to complete the task.
_
_
_
_
_
Tania Colligan 17818782 Assignment 2
A class 3T have been collecting for charity. They share the $80 they raise in a ratio of 3:5 between the children in need and the RSPCA. How much does each charity get?
https://www.tes.com/teaching-resource/year-6-problem-solving-involving-ratio-and-
simplifying-ratio-11838140
The first step is to find the number of parts in the ratio.
3 + 5= 8 parts
Then, find the value by one part, dividing the total number of parts.
$80 / 8 = $10
Then, the next step will be multiplying each part of the ratio by the value of one part.
3:5 = 3 x 10 and 5 X 10
3:5 = $30:$50
The children in need will get $30 and RSPCA $50
After going through this task as a class, the students pair up and make up a fraction ratio problem themselves and get another pair of students to solve it.
Models of fractions allow students to explore and develop visual representations of fractions. The students gain a deeper understanding when provided with appropriate and different models. The area is used to define the region. Circular fraction pieces are the most common (A. et al., 2019. Pg 347).
Tania Colligan 17818782 Assignment 2
https://www.math-aids.com/Fractions/
Length models are looking at fractions as a measure. It compares length and uses number lines. It helps the students to order the fractions, and a popular task to start with is fraction walls. Some incorrect representations can be from not labelling the strips in the fraction walls correctly. For example, 1/5, 2/5, 3/5, 4/5, and 5/5 instead of each section being 1/5
th
(A. et al., 2019. Pg 349).
(A. et al., 2019. Pg 349).
Who is winning is a good task to explore the length model and provide hands-on experiences for the students. It also provides a better understanding of the relative size of a fraction.
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Tania Colligan 17818782 Assignment 2
The collection/set model is to show that fractions are not just for area models. Fractions can be a set of objects. It refers to the group or sets as a single identity. A common mistake is that the students may think
it has to do with the group size rather than the quantity in the set (A. et al., 2019. Pg 350). https://www.teacherspayteachers.com/browse?search=vcmna190
Teaching fractions is the most complex concept and is important for future mathematical tasks. First, the main knowledge students bring to fractions is related to sharing and measuring. In time, as exposed to varied fraction models and constructs, the students will develop a different meaning of fractions (Clarke et al., 2008. pg. 373 & Resolve, 2017, pg. 8). A misconception about fractions is that it describes the size of the whole. In contrast, it tells us about the relationship between the part and the whole (A. et al., 2019. Pg
351).
Using various representations to teach fractions helps all students and provides opportunities to justify and explain their work. When fractions are not understood meaningfully, it will set students up to continually make the same mistakes (A. et al., 2019. Pg. 346). Addressing common mistakes or misconceptions will help students learn strategies to overcome these and make sense of the operations with fractions (A. et al., 2019. Pg 377). Developing ways to represent fractions in the real world and providing practical applications will further develop mathematics and higher cognitive thinking processes. It is a
Tania Colligan 17818782 Assignment 2
hard concept that is not deeply rooted in the student's world and, therefore, often focuses on the size of the parts rather than the whole (Booker et al., 2023. Pg. 348).
The language of fractions is important for students to develop and use to help them understand parts. Students may call quarters half of a half because they know and can identify with the half language. When teaching or developing the name fourths, they see the
pattern that it is 1 part out of 4 equal parts. Then, it will lead to each fraction name identified and will match when writing the fraction. It also establishes the meaning of the numeration system and extends previous knowledge existing with whole numbers (Booker et al., 2023, pg. 356).
Linking understanding to previous experiences helps support the student's learning of fractions and develop further than fractions are parts of the whole to foster development for further mathematics of algebraic thinking.
Reference
A., V. de W. J., Karp, K. S., Bay-Williams, J. M., Brass, A., Bentley, B., Ferguson, S., Goff, W., Livy, S., Marshman, M., Martin, D., Pearn, C., Prodromou, T., Symons, D., Wilkie, K. J.,
Tania Colligan 17818782 Assignment 2
& Wray, J. A. (2019). Primary and middle years mathematics: Teaching developmentally
. Pearson Australia. Booker, G., Bond, D., & Seah, R. (2023). Teaching primary mathematics
. Pearson Australia. Clarke, D. M., Roche, A., & Mitchell, A. (2008). 10 practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School
, 13
(7), 372–380. https://doi.org/10.5951/mtms.13.7.0372 Mathgeekmama. (n.d.). Money fractions
. Math Geek Mam. Retrieved November 3, 2023, from https://mathgeekmama.com/summer-math-camp-all-about-money/. Resolve. (2017). Fractions - resolve
. Resolve fractions. https://www.resolve.edu.au/sites/default/files/downloads/Fractions%20-%20Learning
%20Progression%20and%20WYNTK.pdf
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