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Advanced Foundations in Fractions 2/5

Once a foundation has been established, students are ready to dive into more nuanced details of fractions. I will be focusing on some of the fraction skills covered in grade 4-6. At this point, fractions are also integrated and combined with other skills. In Fractions 3/5, I will address: adding and subtracting fractions. In Fractions 4/5, I will address converting fractions to decimal numbers. Today I will be addressing advanced foundational skills that students will need to know in order to be successful with fractions.

1. Represent fractions using drawings and standard fractional notation

In grade 4, there is a big shift. We go from mostly hands-on, physical, tangible math tools to representing those fractions using standard fractional notation. At this point, it becomes clear if a child has a solid foundation or if there are cracks in their understanding of fractions.

Standard fractional notation is about shifting from physical manipulatives to numbers and understanding how they relate to each other.


The denominator is the number that is located under the line. It shows how many equal parts are within the whole.


The numerator is the number that is located above the lone. It shows how many parts of the whole.

Home Connection

At home, write a fraction using standard fractional notation like 3/4. Ask your child, which number is the numerator and denominator. Then ask your child to find things in your home that could represent that fraction.

Here are three examples taken directly from the Grade 4 Ontario Mathematics Curriculum:

  • "3 granola bars (3 wholes) are shared equally with 4 people (number of partitions)"

  • "1 granola bar (1 whole) is partitioned into 4 pieces (partitions)... three pieces are three one fourths (3/4) of the granola bar"

  • "a bag has 3 red beads and 2 yellow beads. The fraction 2/3 represents that there are two thirds as many yellow beads as red beads"

  • 3/4 of $100

2. Explore and represent improper fractions and mixed numbers

Improper Fractions

Improper fractions occur when the numerator is larger than the denominator. This happens when you have more than 1 whole. For example, if 1 pizza is a whole and you have 2 and a half pizzas you could write that as: 5/2. Meaning you have 5 half slices of a pizza.

Mixed Fractions

Mixed fractions are another way of representing improper fractions. When we have more than a whole in a fraction we can change 5/2 into 2 1/2. It is a little bit easier to visualize and is another way we represent fractions.

Home Connection

The next time you order pizza or make pizza at home, take out enough pizza that you will have lots of leftovers for the next day. Make sure the pizzas are all the same size and have different toppings. When everyone is finished eating, ask the question, 'how much pizza is left'? When we count up the slices and notice how many slices in each pizza we have two ways we can represent the fraction as an improper fraction and as a mixed fraction.

3. Represent, compare and order fractions up to twelfths

If your child is having difficulty comparing and ordering fractions, have them use drawings or concrete manipulatives. As your child begin to understand the relationship between larger denominators and the size of the part; and as your child understands that the numerator tells us how many parts we have, we can shift increasingly to standard fractional notation.

Home Connection

Using number lines or matching activities activities are a great way to support this understanding. Again, start small, be responsive to what your child can do and build that conceptual understanding to fractions up to twelfths.

4. Count to 10 by halves, thirds, fourths, fifths, sixths, eights, and tenths

This functions, similarly to skip counting. When first learning skip counting, using a hundreds chart is helpful. Likewise, using a number line, is a great way to introduce this concept. Start with fractions that your child is most familiar with (likely halves, fourths and thirds).

Home Connection

While using visuals, like a number line, this skill may come naturally or your child may need a number of repetitions in order to solidify their understanding of fractions. While the repetitions may be necessary, be contentious of how you are doing the repetitions. Try turning it into a song you sing when chopping up food for dinner. Play games with it, like who ever says 10 looses and you can say up to 3 numbers. Keep it light and fun. We want to keep your child engaged and interested.

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