Drawing a picture is one way to envision a fraction problem, but it certainly isn't the only way. Another strategy for dealing with fractions is to utilize a number line.
A number line is really the school version of a tape measure - and every carpenter or contractor knows their tape measure fractions! If we expose students to the number line early and often, then as they start to investigate negative numbers the concept will be clearer. We aim for students to be flexible and nimble in their thinking, so if one pattern or strategy doesn't work they don't give up - instead they have another tool in their tool box (perhaps a tape measure?) to use.
A number line is really the school version of a tape measure - and every carpenter or contractor knows their tape measure fractions! If we expose students to the number line early and often, then as they start to investigate negative numbers the concept will be clearer. We aim for students to be flexible and nimble in their thinking, so if one pattern or strategy doesn't work they don't give up - instead they have another tool in their tool box (perhaps a tape measure?) to use.
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