Fractions, proportional and multiplicative thinking can grow out of linear measurement activities if we plan accordingly.
There are three types of fractions that need to be dealt with in early and middle primary, they are:
- the area model (think pizzas and chocolate – usually done to death)
- a linear or measurement model (usually rarely and poorly done)
- the quantity model (think equal-sized groups again often neglected and not well connected to division).
We need to get better at connecting atomized aspects of the curriculum to ensure that students see relationships between mathematical ideas. I was watching a clip of a measurement activity a couple of days ago and was shocked by the low level of activity. But it did prompt me to share my take on what using a measuring strip could look like and how it could be differentiated for a broad ability range.
Before moving on though we need to consider that when we measure distance or length, we need to create visual memories of what has been measured so that in turn we will develop good estimation skills.
|Step 1||Choose a measuring strip, take it with you to find something: the same length as it that it will fit into twice, 5 times half as long/twice as long as it ¼, ⅓ … as long as it is.|
|Step 2||As above except the measuring strip is visualized, an object found and brought back for comparison|
|Step 3||A ruler can be used to measure the strip and then used as in Step 2 to go find objects to match the instructions.|
Unifix cubes can tie in the quantity aspect of fractions too.
Take a Unifix stack find and something a quarter/third/4 times its length.
In this case the stack and fraction are visualized, and the stack not used for direct comparison.
I am sure you can extend on this idea and even conclude with a game-like situation.
Present a measuring strip and a number of objects. The students ask you yes/no measurement/fraction questions to find out what your object is, e.g.,
“Is it less than half as long as your strip?”
“Would your strip fit into the object more than three times?”
“Is your object about one and half times as long as your strip?”
NOTE: Our online Mental Routines Course has lots of ideas for creating these flip question games. If you are just beginning an Early Years linear measurement unit, check our Linear Measurement – Level 1 and Linear Measurement – Level 2 publications.