Equivalent Fractions. What do Students Need to Know. A quick look for Montessori Classrooms

Equivalent Fractions are an important area of learning for Montessori students. This learning can start around the age of 7-8 for students who are progressing at a usual level of development.

What to work on first.  Equivalents of a whole

You will need the red Montessori fraction circles.

Find fractions that are equivalent to a whole.

This can be done by taking out the whole fraction circle and then having the child start with halves and placing the correct number of halves onto the whole to find out what is 'equal' to the whole, in this case 2. Then repeating the process through to 10. 

On another day the child can repeat, this time drawing the fraction pieces into their notebook

After that, perhaps on a different day, the child can repeat the process this time writing the fractions down as the do each equivalence e.g. 2/2, 3/3, 4/4, 5/5 and so on. 

Simple problems can be done too that also gently link to addition for example "I want to make a whole, I have 4/5ths how many more 5ths do I need?" or "I need to make 6/6 which is a whole, I have 3/6ths how many more 6ths do I need?"

Different children work at different paces. However this stage should not be rushed as it is a key foundation for being able to work on high concepts such as improper fractions or converting fractions.

Equivalents for amounts less than a whole.

You will need the red Montessori fraction circles.

Find fractions that are equivalent to a given amount through exploration.

Talk to the child about how equivalents can be to a whole but they can also be to a different fraction too.

Get out half of a fraction circle and then ask them to find equivalents of it. Like the earlier lessons students can explore first, then later draw, then last write what they find. This process can take a while and again shouldn't be rushed. After repeated practice many students will start to see patterns however if a child is struggling and we notice that effort they are putting in isn't matching the output it is important we sit alongside them and share the patterns and how to solve such fraction problems.

Equivalents in traditional equations

After the student has had a lot of practise with the above we can introduce the way equivalent fractions are written with the = sign. For example 1/2 = 3/6. 

Students can be given an equation with a missing number and asked to find out what number is missing. 

My equivalence task cards, pictured in all of the examples above work very well for helping your teaching of this concept. You can get them here