On
the overhead projector or chalkboard, display a large number line and
demonstrate with a counter how hops of 5 can be taken on the number
line. You may wish to encourage students to count aloud as the hops are
made. You might choose to introduce the equation notation 4 × 5 = 20,
informally reading it as "Four hops of 5, and you land on 20." After
several examples with 5 as a factor, ask the students to determine what
size hop to use next. Encourage the students to predict the products
and to verify their predictions by moving a counter on the large number line. You may wish to provide children with a counter and
individual number lines at their desks.

Number Lines

After allowing time of exploration, ask the students to predict
the answers to questions such as "If I take 4 hops of 3, where will I
land?"

Now give each student a piece of paper and ask them to make up 2
similar problems and trade them with a friend to solve using the number
line. When the pairs have finished, call them together to discuss what
they did. Encourage them to use the number line in their explanation.

Be sure students have the opportunity to explore different factors, such as:

2 × 3

4 × 4

3 × 6

7 × 2

and so on....

Then ask: "If I take 5 hops of 3, where will I land? How about if I
take 3 hops of 5? Will this work every time?" Encourage them to explore
the order property and state their findings. [In each case, the student
should land on 15, because of the commutative property of
multiplication.]

As a concluding activity, you may wish to pose puzzles such as
"I am a number between 20 and 30. You say my name when you hop by 5's.
Who am I?" and encourage students to create and share similar problems.