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Getting a Foundation in Fractions 1/5

Let's dive into what fractions are, how to introduce them to kids, and what they need to know to have a strong foundation.

First, I want to look at the Ontario Mathematics Curriculum so that you can see grade level expectations for fractions. This helps you keep an eye on what your child will be expected to know at school by the end of each grade.

These are the expectations related to fractions for Grade 1-3 in Ontario.

Summary of Skills:

While students do not yet need to know specific vocabulary, like numerator and denominator, students will need to know the concept or idea of 'whole' and 'equal parts'. From there students will explore these four concepts from grade 1 to grade 3.

1. Represent and Solve Fair-Share-Problems

Students will be exploring how a group of objects can be "fairly-shared". Students will learn how each person must receive the same amount and that sometimes there is one or two of the objects left over, called the remainder.

Home Connection:

This is a really fun skill because it is super practical. The next time you make cookies, set up two containers and ask your little one to put the same amount in each container. When setting the table, ask your little one to put two ice cubes in each cup. When playing, see if your little one can share the blocks equally with a sibling (very practical!). Remember to start small. Increase the number of objects as your child builds up confidence in the skill. Note that by grade 3, your child will be expected to work with up to 20 items. Be responsive to your child; they might not be ready for 20 items even if they are past grade 3 or they might be ready for 20 items in grade 1.

2. Represent Fair-Share-Problems using Drawings

Students will also be expected to create or interact with drawings as a way of demonstrating their understanding of fair-share problems. For example, the question may be, "Jim and John are sharing 8 cookies. Draw a circle around the cookies that Jim will get". It is important that students come to understand the purpose behind fair-share problems and can represent the problem using real objects, words, and pictures.

Home Connection:

I love using bingo-dabbers! Have your child dab 12 dots onto a piece of paper. Then have your child divide the dots into two groups, three groups or four groups. Experiment with different numbers of sharers and different amounts of dots. Encourage your child to notice remainders and compare how many cookies each person gets when sharing with two people vs sharing with six people.

3. Recognize Equivalent Fractions in a Fair-Share-Context

This is a fun concept to explore! Start with comparing 1/2 and 1/4; then 1/3 and 1/6; and then finally explore a variety of equivalent fractions to ten. Students are often surprised when fractions with different numbers can be used to represent the exact same thing.

Home Connection:

Posing questions like, 'would you rather have 1/2 a pizza or 2/4 of the pizza?' are a fun way to get students thinking about equivalent fractions. The next time you are cutting a cake, sharing a chocolate bar, slicing an apple... consider offering the snack/treat as a fraction question.

4. Compare and Order Fraction Drawings

Students are often surprised when they learn that as the bottom number increases, the individual portion becomes smaller. Even as adults, we can be prone to this common misconception. Look at this internet meme:

Home Connection:

The next time you slice a cake, slice it in half first. Talk about how it can be represented as '1 over 2' and then slice the piece in half again and call it '1 over 4' and then slice it in half again and call it '1 over 8'. This casual yet concrete practice will support your child's conceptual understanding of fractions.

The next time you are baking, take out the measuring cups and look at the 1/3 cup and the 1/4 cup. Ask, "Which one is bigger?" Then prove it. Scoop three 1/3 scoops into a measuring cup. Then scoop 4 1/4 scoops into a measuring cup. These little home connections can go a long way in developing your child's understanding of fractions.

Moving From Concrete to Abstract

Anecdotally, students tend to do well with these concepts. In grade 1-3, these concepts are explored in a very concrete context (lots of hands-on-learning). However, concrete manipulatives will be mostly removed in the coming grades so it's critical that your child has mastered the conceptual understanding in order for them to smoothly transition to a more abstract exploration of fractions. If you are noticing your child is struggling with these concepts, we are happy to support your family in the form of math tutoring.

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