Question

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1. a. plot the following points on the number line without measuring.

i. $\frac{1}{3}$
ii. $\frac{5}{6}$
iii. $\frac{7}{12}$
(number line with 0, $\frac{1}{3}$, $\frac{1}{2}$, $\frac{7}{12}$, $\frac{5}{6}$, 1 marked)
b. use the number line in part (a) to compare the fractions by writing >, <, or = on the lines.
i. $\frac{7}{12}$ ____ $\frac{1}{2}$
ii. $\frac{7}{12}$ ____ $\frac{5}{6}$

1. a. plot the following points on the number line without measuring.

i. $\frac{11}{12}$
ii. $\frac{1}{4}$
iii. $\frac{3}{8}$
(number line with 0, some marked points, $\frac{1}{2}$ marked)
b. select two fractions from part (a), and use the given number line to compare them by writing >, <, or =.
explain how you plotted the points in part (a).
lesson 12: reason using benchmarks to compare two fractions on the number line.
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Explanation:

for plotting: Convert fractions to common denominators or use benchmarks like $\frac{1}{2}$ to estimate positions on the number line.

For 1.b.i: $\frac{1}{2} = \frac{6}{12}$, so $\frac{7}{12} > \frac{6}{12}$. For 1.b.ii: $\frac{5}{6} = \frac{10}{12}$, so $\frac{7}{12} < \frac{10}{12}$. For 2.b, $\frac{1}{4} = \frac{2}{8}$ which is less than $\frac{3}{8}$. Plotting uses common denominators/benchmarks to estimate relative positions on the number line.

Answer:

1. b. i. $\frac{7}{12} > \frac{1}{2}$; ii. $\frac{7}{12} < \frac{5}{6}$
2. b. Example: $\frac{1}{4} < \frac{3}{8}$