Fractions
What is a fraction?
Take a piece of paper. Divide in to four equal parts as shown in the given diagram. Shade one part blue.
Now this shaded part is one out of four parts. We say here that the shaded part is one fourth of the total.
Fractions with the same denominators are called like fractions. Otherwise, they are called unlike fractions.
A fraction is said to be in its lowest terms if its numerator and denominator have no common factor other than 1.
1.fourths or not fourths.pdf2. brownie sharing cards.pdf3. which is greater.pdf4. equivalent fractions missing number equivalencies.pdf5. fraction value fraction find.pdfAddition & Subtraction
6. Adding Fractions.mp47. Subtracting Fractions Visually.mp48. Finding the GCF.mp4How we teach multiplication of fractions:
It is important to connect knowledge of fraction multiplication back to the learners' understanding of whole-number multiplication.
To transition to multiplication of a whole number by a fraction, it is important to connect the concept to something that is contextual; for example Alice in Wonderland.
An example is shown below:
We continue our exploration by looking at multiplying a fraction by a fraction.
We revisit the idea of the area model and a whole number by a whole number.
Again, we use visual representation to show our understanding of fractions.
We then multiply the two fractions together (the green is meant to show where yellow and blue overlap - it is much easier to see when learners are colouring). We discuss together (small groups and as a whole class), what this means if we compare it to what we noticed previously in the area model of multiplying whole numbers.
How we teach division of fractions:
Again, it is important to connect knowledge of fraction division back to the learners' understanding of whole-number division.
How many sets or groups of the red blocks will fit into the green blocks?
To divide a whole number by a fraction, we first ask a question within a context without introducing division of fractions. We use our problem-solving skills.
To introduce the concept of dividing a fraction by another fraction, we might begin with a problem like this.
Many learners see the relationship between comparing two-thirds and one-sixth immediately while others prefer to have equal parts in both fractions and redraw the visual representations:
Below is a redrawing of the visual using equal parts (denominators)
Four green rectangles are needed.
Learners are applying their knowledge of whole-number division to a fraction divided by a fraction.
We then approach more challenging problems, but use the same ideas as previously.
For this problem, learners recognize the need to have equal parts in both fractions and redraw the visual representations in order to better compare the fractions.
We then have the following problem:
Learners recognise that we need one whole set of red squares plus one more part of the red (which is made of three parts).
Written mathematically, this means:
After time exploring different problems of fractions being divided by a fraction using visual representations, we are ready to transfer our understanding to methods involving equivalent fractions and finding common denominators.
The Common Denominator Method
We spend a lot of time discussing and sharing with what it means that the denominator of the fraction now equals one.
What does it mean to divide by one? Why is dividing by one an important mathematical concept?
Using our understanding, we look at other ways we can have a denominator equal to one. Through exploration, this leads to using the reciprocal.
We do not teach learners to multiply by the reciprocal without this understanding first. We ask learners to show all these steps, if they want to use that method.
The trick of "flip and multiply" is strongly discouraged.
Dividing fractions.mp4