I’m a giant fan of serving to college students to make use of STRATEGIES when approaching math somewhat than mindlessly following steps in an algorithm. Personally, I hardly ever observe order of operations when simplifying a math expression. Having quantity sense means you have a look at the mathematics job and THINK about it and discover methods to interrupt aside and regroup in additional environment friendly methods when it may be performed. Nonetheless, I’ve by no means performed this with fractions.
Commonplace algorithm requires carrying.
Including 19 and 23 utilizing the usual algorithm is certainly slower. once I see this drawback I wish to add one and subtract one.
I used to be capable of EASILY make this transformation in my head. The ensuing expression is considerably simpler so as to add than the primary expression.
What About Fractions?
However what about taking a look at fractions on this method. I noticed this tweet by Jennifer Bay-Williams with an instance of how a pupil added combined fractions. I had an epiphany: How have I by no means considered doing this? It’s virtually like I wanted permission that I can rethink how I strategy fractions.
The problem with instructing college students solely the usual algorithm… and shudder marking them down if they don’t do it precisely how we confirmed them… is that college students usually are not being requested to assume. They’re being requested to REMEMBER.
[Tweet]The primary strategy to a math drawback needs to be THINKING about it. Not competing with a calculator. [/tweet]
Fractions are half of an entire. How do I get an entire?
Utilizing the commutative property I can arrange the fractions and the entire numbers seperately. THINKING in regards to the fractions I can ask, “how do I make an entire?” This helps me to consider the idea of fractions and never simply the steps.
Typically the usual algorithm is quicker and generally it isn’t. College students ought to cease and THINK about math issues earlier than simply diving into the algorithm. Serving to them to be extra versatile with numbers and to use methods when applicable will assist them to be extra assured and proficient at arithmetic.
— Jennifer BayWilliams (@JBayWilliams) November 4, 2022
Graspable Math Whiteboard
To create the pattern math issues I used the Graspable Math Whiteboard.
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As a substitute of diving into the steps of including fractions have college students have a look at how they will break aside the fractions to make it simpler to strategy the mathematics drawback. Have college students decompose fractions as one other mind-set in regards to the numbers.