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The linear model is a basic vehicle for understanding fractions. We see that students trying to measure objects with an inch ruler have trouble making sense of fractional parts on a number line. Fraction Towers, as a linear representation of fractions, can help with this.
The crucial skill and discipline is for students to acquire the habit of counting the number of parts into which a line is divided (the denominator), and then count the units included for the numerator.
Students begin by writing fractions illustrated on a number line, then locate fractional points, and find equal fractions. The teacher can decide at what point students can put away the Fraction Towers and calculate equivalent fractions mathematically.
There is a two-page exercise on paper folding included which clearly shows how and why the mathematical steps for finding equal fractions work. The steps are written out and then used in conjunction with Fraction Towers to find and model equal fractions.
Common Core Standards:
3.NF.2: “Understand a fraction as a number on the number line; represent fractions on a number line diagram...”
3.NF.3.a: “Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.”
4.NF.1: “Explain why a fraction a/b is equivalent to a fraction...by using visual fraction models...”
Subject: Math, Fractions
Level: Grades 3 – 4
Length/Duration: 12 pages of student work, 3-4 days