Stage 3 Fractions T4 2020
We will be focusing on Fractions, in small groups 3x per week with students from Pukeko and Piwakawaka. Add/Sub and Mult/Div were covered in Terms 1 - 3.
Students will also work on Stage 3 Number Knowledge and complete Basic Facts activities based on these alongside their fractions learning, as well as completing fractions follow-up activities 3x per week.
Students must come to know common vocabulary for fractions, particularly halves, thirds, quarters (fourths), fifths, and tenths.
The language for the most common fractions does not necessarily indicate how many pieces, e.g., while the connection between tenths and ten is evident, this is not the case with halves and two or quarters and four.
Initially, the emphasis is on unit fractions, such as 1 2 (one-half) and 1 4 (one quarter), that have one as a numerator.
However, it is important to introduce non-unit fractions, such as 3/4 (three-quarters) and 2/5 (two-fifths), when learning opportunities present themselves. At this stage, students are introduced to the symbols and words related to models of fractions, e.g., the word one-half is recorded as well as the symbol 1 2 .
Students need to understand what the numbers represent in a fraction symbol.
The bottom number (denominator) indicates how many pieces make up the whole. The top number (numerator) tells us how many pieces there are. It counts the number of pieces.
Students need to read fractions such as 1/4 as one-quarter and not as one out of four or one over four.
This helps students to see the numerator (top number) as a count and the denominator (bottom number) as the size of the units.
Students need to experience both continuous models, e.g., length and regions (shapes), and discrete models, e.g., using sets of objects.
Students need to understand that fractional parts are equal shares or equal-sized portions of a whole.
Students need to have experiences with finding both a part of a whole, e.g., 1 2 (one-half) of 12 or half of a region, and determining the whole, given a part of it, e.g., “If □ □ □ is one-half of my set, how many □s are in the whole set?”
The students must come to know common vocabulary for fractions, particularly halves, thirds, quarters (fourths), fifths, and tenths.Initially, the emphasis is on unit fractions, like 1/2 and 1/4, that have one as the numerator. However, it is important to introduce non-unit fractions, like 3/4 and 2/5, when learning opportunities permit.
It is important to expose the students to both continuous models, such as lengths and regions, and discrete models, using sets of objects. A significant development for the students is to use their whole number strategies to anticipate the result of equal sharing. This is easier with halves and quarters than with thirds and fifths, as halving is linked to doubles addition and subtraction facts.