Describe how you would help your learners in a primary class to multiply the following using number line: 7 x 1/3, 10 x 2/5, 2 x 4/5, 3 x 1/3, 4 x 2/4.

A. $7 \times \frac{1}{3}$

Divide the number line segment from 0 to 1 into 3 equal parts. Each part is $\frac{1}{3}$.

Start at 0 and add $\frac{1}{3}$ seven times:

Jump 1: $0 + \frac{1}{3} = \frac{1}{3}$

Jump 2: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

Jump 3: $\frac{2}{3} + \frac{1}{3} = 1$

Jump 4: $1 + \frac{1}{3} = \frac{4}{3}$

Jump 5: $\frac{4}{3} + \frac{1}{3} = \frac{5}{3}$

Jump 6: $\frac{5}{3} + \frac{1}{3} = 2$

Jump 7: $2 + \frac{1}{3} = \frac{7}{3}$

$\boxed{\dfrac{7}{3}}$

B. $3 \times \frac{1}{5}$

Divide the number line segment from 0 to 1 into 5 equal parts. Each part is $\frac{1}{5}$.

Start at 0 and add $\frac{1}{5}$ three times:

Jump 1: $0 + \frac{1}{5} = \frac{1}{5}$

Jump 2: $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$

Jump 3: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$

$\boxed{\dfrac{3}{5}}$

C. $2 \times \frac{1}{4}$

Divide the number line segment from 0 to 1 into 4 equal parts. Each part is $\frac{1}{4}$.

Start at 0 and add $\frac{1}{4}$ two times:

Jump 1: $0 + \frac{1}{4} = \frac{1}{4}$

Jump 2: $\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

$\boxed{\dfrac{1}{2}}$

D. $4 \times \frac{1}{5}$

Divide the number line segment from 0 to 1 into 5 equal parts. Each part is $\frac{1}{5}$.

Start at 0 and add $\frac{1}{5}$ four times:

Jump 1: $0 + \frac{1}{5} = \frac{1}{5}$

Jump 2: $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$

Jump 3: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$

Jump 4: $\frac{3}{5} + \frac{1}{5} = \frac{4}{5}$

$\boxed{\dfrac{4}{5}}$

2. To help primary class learners multiply a whole number $n$ by a unit fraction $\frac{1}{d}$ using a number line, first draw a number line and mark 0 and 1. Divide the segment from 0 to 1 into $d$ equal parts and label each small segment as $\frac{1}{d}$. Start at 0 and make $n$ equal jumps, each of length $\frac{1}{d}$, along the number line. The point where you land after the last jump is the product $n \times \frac{1}{d}$. This shows that multiplying by a fraction is repeated addition of the fraction.