Find unit fractions of sets using addition facts.
Number Framework Stage 5
Using Materials
Problem: “Here is a farm (draw a farm cut in two fields on a piece of paper). Thefarmer uses an electric fence to make her farm into two paddocks. She has 10 animals. (Get a student to count out 10 animals). She wants to put one-half of the animals in one paddock and one-half in the other.How many animals do you think will be in each paddock?”
Allow the students access to the animal counters to work out one-half of 10. Look to see if the students can use a dealing strategy to find equal parts. Ask, “Could we have worked out the number of animals in each paddock without sharing them out?” Some students may realise that they could apply their doubles knowledge (5 + 5 = 10).
Pose similar problems and allow the students to use equipment to solve them. For example: “The farmer fences her farm into four paddocks.
She has 12 animals. Put one-quarter (a fourth) of the animals in each paddock.”
Using Imaging
Prediction:
Set up an animals and paddocks problem, such as “On this farm, there are nine animals and three paddocks. One-third of the animals have to be put in each paddock. How many animals will be in each paddock?”
“How many animals are in the paddocks at the moment?”
“How many animals are left to be put in the paddocks?”
“If you put one more in each paddock, how many animals will you have left outside the paddocks?”
“How many animals do you think will be in each paddock when you have finished sharing out the animals?”
Record the final result using symbols, i.e., 1/3 of 9 is 3 (in full language, one-third of
nine is three).
Pose similar problems, such as:
“Twenty animals. One-fi fth in each paddock (five paddocks).”
“Eight animals. One-quarter in each paddock (four paddocks).”
Using Number Properties
The number size is increased to promote generalisation.
“The farmer has 40 animals and 10 paddocks. She wants to put the same number
of animals in each paddock. What fraction will that be?” (one-tenth) “How many
animals will be in each paddock and why?”
Look for responses like:
“There will be four in each paddock. One in each paddock is 10, two is 20, three is
30, four is 40.”
“If you put two animals in each paddock, that would be 10 and 10. That’s 20, so four in each paddock must be 40.”
Note that the students’ application of strategies will be dependent on their skip counting and addition knowledge. Restrict the examples used to numbers for which students will have counting sequences, like twos, fives, and tens, or doubles knowledge, in the case of halves and quarters.
For example:
"One hundred animals. Two paddocks."
"Thirty-five animals. Five paddocks. "