I may be completely off the mark, but I’m going to share my thoughts anyway and let you decide in the comments if you’d like to challenge my thinking or share an alternative point of view. I think I may finally understand why we have to be careful what we say about the role of context when comparing fractions. At the time, I wondered about it, but I still felt that bringing context to bear was important.įlash forward to now and I have been mulling this idea over all day. As such, 1/2 is always greater than 1/3 regardless of the context. The argument I heard back then was that using contexts to validate the correctness of fraction comparisons ran counter to the fact that fractions are numbers. I let her know I was also challenged about this idea several years ago when I was a digital curriculum developer. My colleague, Hedge, replied about being challenged by a middle school teacher on this very issue. I posted the following picture to Twitter while I read during my daughter’s swim class.

OH NO! No more blood oranges?!? This might make his vacation a bit tougher.Lately I’ve been reading the book Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense by Julie McNamara and Meghan Shaughnessy. Let’s see how Christopher the Vampire is enjoying his vacation. Here a could be greater than b or equal to b. But, when we say ' at least', we mean 'greater than or equal to'. When we say ' as many as' or 'no more than', we mean 'less than or equal to' which means that a could be less than b or equal to b. As we saw earlier, the greater than and less than symbols can also be combined with the equal sign. However, if the mouth opens to the left, it's read: 'a' is greater than 'b'. If the mouth opens to the right, it's read: 'a' is less than 'b'. Since 2 is less than 4, the mouth will eat the 4. The mouth will always eat the larger of the two numbers being compared. A good way to remember which number is greater, is to think of each sign like a mouth. Let's take another look at the different inequality symbols. For inequalities with ' at least', we use the ' greater than or equal to' symbol. He also needs to pack at least 16 capes, one for each day and two, just in case.

For inequalities with 'more than', we use the ' greater than' symbol. Our foodie vampire also needs to pack more than 1 bottle of hair gel, since he ran out during his last vacation. For inequalities like ' less than or equal to' we use this symbol: ≤. Furthermore, for this trip, Chris can't take more than 1000ml of blood orange juice on the plane. For inequailties with 'less than', we use this sign <. Use of inequalitiesĬhristopher the Vampire’s trip will last fewer than 15 days.

But how much of this stuff is he allowed to carry with him on the plane? Let's take a look at the number line. And he has all his supplies laid out in his bed? Capes, check. To help him pack, he uses his knowledge of inequality symbols. He read on Vampedia that blood oranges grow in California, which is perfect because he’s always wanted to visit the underground gardens there. He’s working on a new piece, so he wants to go to a place where his favorite fruit grows: the blood orange. Christopher the Vampire is a foodie and he needs a fresh, new story for his blog: The Vegetarian Vampire.

Less and greater sign