They will come to the conclusion that 1 white is half of a red, which is half of the purple. Probing questions such as ‘How many more white rods will I need to place down to be equivalent to a red rod?’ can be asked to move thinking forward. The teacher could then place a white rod under the red and ask for the relationship between the white and the red. Without difficulty students will be able to find another red rod and place it down. They will quickly identify that red is half of the purple rod and place it like this, underneath the purple.Īsk them to find the other half of purple. You could ask students to find half the purple rod. Cuisenaire rods provide an excellent means of doing this. Introduction to Part and Whole of NumbersĪ key step in students’ understanding of fractions is that they know early on that a fraction is not bound by a whole and has its own sense of ‘numberness’. The cycle continues.Īs professionals, we should be seeking out the opportunities available to us to improve our practice and break this cycle. When students in the second category become teachers, they end up teaching these concepts to their students in a similar manner to how they were originally taught by their teachers. This is usually the way the teacher was taught fractions and they would either understand the abstract immediately or be left to flounder and merely encode a procedure, with very little meaning, to long term memory. Low pedagogical content knowledge (how to teach a concept) can also be low for some teachers so they end up resorting to quick tricks and gimmicks (I am looking at you KCF – “keep it, change it, flip it”) to teach difficult concepts such as dividing fractions.Subject knowledge of fractions can be weak for some teachers who feel less confident due to their own experiences as a learner when grappling with fractions.It does not matter how many times a piece of paper is folded in half or into quarters, some students struggle to retain even this basic understanding. Fractions can be a difficult concept for the students to understand.I believe this to be because of three reasons: If students are unable to do the above, then it is unlikely they will be able to grasp fractions in 4th and 5th grade.įractions is usually a topic that fills some teachers with dread. Finally, they must be aware that ²⁄₄, and ½ are equivalent.Īs stressed in all the other blogs in this series, test the prerequisites and start from there. Students compare simple fractions that have the same numerator or denominator by reasoning about their size. ![]() In 3rd grade, expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8. The teaching of fractions begins in 3rd grade where students are expected to find fractions of shapes and appropriate quantities. This is especially important for children in 3rd grade to grasp as much of the fraction work done in that year group is the breaking of wholes into parts.įractions are a core part of the common core, being introduced in 3rd grade with simple fractions of amounts and comparing fractions.Īs they move into 4th and 5th grades, however, students will be asked to use fractions in ever more complex ways, from learning to divide and multiply fractions to completing fraction word problems.Īs anyone who has gone through the curriculum for math will know, the objectives related to fractions make up a large portion of the entire curriculum. ![]() I would suggest that students are explicitly taught this as it helps to provide a mental model as to what we mean by ‘a fraction’ – a break in a whole. The word fraction comes from the Latin ‘fractio’ which means ‘a break’ especially into pieces. ![]() ![]() Scroll down the page for more examples and solutions on using unit fractions for comparing fractions.The word fraction has very little meaning to students. The following diagram shows some examples of unit fractions. Therefore with a unit fraction, the larger the denominator the smaller the fraction part. When fractions have the same denominator, the one with the larger numerator is greater.Ī unit fraction has a numerator 1. Scroll down the page for more examples and solutions about fractions.įractions can only be compared if the whole is known in each situation. The following diagram shows a sample Frayer Model of a fraction. equal parts of a set have the same number of objects.equal parts of a region have the same size but not necessarily the same shape.the denominator divides the whole into equal parts.Videos, examples, solutions, worksheets, songs, and activities to help Grade 4 students understand fractions.Ī proper fraction is a number that represents part of a whole region, set or length.
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