Lately I've had this re-occurring question pop up and not far behind has been it's coupled demand...
Question:
"Shouldn't students have a good grasp on multiplication facts before they manipulate with fractions?"
Demand:
"We need to put Multiplication/Division unit before the Fraction unit in the Scope and Sequence. It makes sense that students need to master their facts before they work with fractions!"
I beg to differ and here's why:
3.3F (Equivalent Fractions) TEXAS standard says students are to...
"Represent equivalent fractions with denominators of 2, 3, 4, 6 and 8 using a variety of objects and pictorial models, including number lines."
If we isolate the content (equivalent fractions) from the WHAT or skills students are to do (represent) we get a very concrete and representational approach to instruction.
The CRA (concrete-representational-abstract) process is evident in the progression from 3rd to 4th grade.
Check out the verb difference...
3.3F - Represent...
4.3C - Determine...if two given fractions are equivalent using a variety of methods.
Do you see the progression? Third grade is the place to develop "Fraction Sense" (conceptual and visual foundation of breaking fractions in half) through the lens of the concrete and representational lens. Fourth grade is the place to make connections and build on their fraction sense by using abstract methods to find equivalent fractions.
So perhaps we use 3rd grade as a training ground for exploring with manipulatives and creating visual mental pictures of how to break fractions in half; leaving students with an ability to find methods that make "fraction sense" when they get to 4th!
I do resolve that Multiplication should precede Fractions but so that students have a longer "school year" to master their facts, NOT for the purpose of using the knowledge to master fraction equivalencies.
Here's a quick video to clarify!
