A few years ago I trialed an activity for a project that involved interviewing students as they counted halves and quarters. What I observed really surprised me; many students could not do it. They either had no idea what to do, or counted the number of items. At that moment it dawned on me this was an activity that had been missing from my teaching of fractions. I had spent hours teaching students to count whole numbers, but had failed to realise that counting by fractions forms a foundation for a solid understanding and flexible use of fractional numbers.

When the Australian Curriculum for Mathematics was published, I was excited (yes, I know that sounds a bit sad!) to find that counting by fractions was a skill that threaded its way through the content of a number of year levels.

Number and Algebra: Fractions and Decimals | ||
---|---|---|

Year 3 | Year 4 | Year 5 |

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole ACMNA058 | Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line ACMNA078 | Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator ACMNA103 |

## Year Three

Year three is the first time the idea of counting by fractional amounts is mentioned. Counting by fractions can be taught as students are learning about unit fractions and how many of particular unit fraction makes one whole. The focus is on the whole and how many parts will make a complete whole. Students should be counting by unit fractions that are represented by regions, lengths and collections. This helps them to understand the broad use of fractional language, and that no matter what is being partitioned the same number of pieces make the whole.

**In the classroom this might look like:**

Students partition objects, lengths and collections into halves, thirds, quarter and fifths then counting the parts to show how many make the whole. You want to hear them saying “one quarter, two quarters, three quarters, and four quarters. Four quarters makes one whole”

Progress the verbal counting to written counting. Students should have experience writing both words and symbols.

Count forwards and backwards by fractional amounts.

Decompose fractional amount into their parts. For example four fifths can be broken into 1 fifth and 3 fifths as well as 2 fifths and 2 fifths.

**Some questions you might ask;**

If I am counting by thirds, what comes next?

How many quarters make one whole?

If I have three fifths, how many more do I need to make the whole?

If there is a whole bag of lollies and Dad eats one quarter, how much is left?

What fractions go together to make this fraction?

What does the denominator/numerator tell you?

## Year Four

The content progresses in year four to include mixed numerals. Students need to now go past the whole representing the amount in symbol form. The first step is the process is to keep counting past the whole, writing the count as improper fractions. Once students see that the counting continues you can talk about the alternative ways of writing the fraction amounts using mixed numerals. Doing this also links into the ideas of equivalence also being explored in the year level. The idea of placing the fractions on a number line is also introduced. The introduction of the number line adds another level of complexity, as students must now think about the spacing of the fraction amounts and where the numbers fit in relation to whole numbers.

**In the classroom this might look like:**

Divide paper into fractional amounts, glue to card then write numbers beneath the paper pieces.

Count cards with pictures of fractions on them.

Place fraction cards along a number line that goes past 1.

**Some questions you might ask;**

What number comes next?

How else could we say that number?

If I have 7 thirds, how many wholes is that?

If I have 3 wholes, how many quarters can I cut them into?

How do we write that amount as a number?

## Year Five

The natural progression from counting by fractions is adding and subtracting with them. This is how we work with whole numbers and the same goes for fractions. At this year level, the focus is on fractions with the same denominator. It is important to give students a good amount of experience with addition and subtraction problems using fractions with the same denominator. The main strategies for adding and subtracting fractions with the same denominator are jumping along a number line and the partitioning and shading of shapes.

**In the classroom this might look like:**

Story problems involving addition and subtraction of fractional amounts, with different pieces of information missing.

Physically act out problems with materials.

Move a counter or peg along a number line display to demonstrate moving forwards and backwards between fractional amounts.

Solving problems by shading shapes in different colours showing the parts being added.

** Some questions you might ask;**

How many more thirds do we need to get to five thirds?

How many quarters will be left?

Where do we start counting from? Do we go backwards or forwards?

Why does the denominator stay the same?

## Lots of Fun

Teaching fractions can be a bit of fun if you keep in mind the importance and simplicity of counting by fractions. Use all the great ideas you have for teaching counting by whole numbers and use them to teach students to count by fractions. The content descriptors build nicely across the year three to five year levels. Activities involving dividing different wholes into fractional amounts, then counting backwards and forward through the shapes is engaging. Setting up a whole class display number line is another idea that can support the discussion you have about counting with fractions. This also helps students to see how fractions compare in size. So many of the more advanced concepts involving fractions can be made a bit less painful when students understand how to count forwards and backwards with fractional amounts.

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