To assess prior knowlege, ask students to skip count by 10's. Then ask a volunteer to name a number they said when they skip-counted. Identify this as a product. Ask students to name the numbers that they would multiply together to get that product. Identify these as factors. Repeat with other numbers in the counting sequence.
10, 20, 30, 40, 50, 60, 70, 80, 90, …
30 = 5 × 6, so 5 and 6 are factors of 30.
To begin the lesson, give each student a copy of the 0—99 Chart and a supply of counters or cubes.
Ask students to cover the numbers that are called as you skip count by 2’s. Direct students to observe and report the pattern that results. Note that columns are formed when the numbers are covered in this counting sequence. Engage students in a discussion about this pattern and why it occurs.
Have students clear their 0‑99 chart and ask them to cover the numbers with counters or cubes as you call out the 5’s counting sequence [5, 10, 15, 20, 25, 30, …]. Ask students to describe the resulting pattern. Engage students in a discussion about the comparison between the column pattern created when counting by 2’s and the one created when counting by 5’s. Encourage students to explain their thinking.
Model for students how to count by 3’s and cover the numbers that are included in this sequence. Discuss how the resulting pattern compares with the two previous patterns created when counting by 2’s and 5’s. Invite students to explain how and why the counting pattern for 3’s is different from the others. Then ask students to clear their 0‑99 chart.
Give each student crayons and tell them that they will now color the 0‑99 chart that they used in the previous activity. (To shorten the activity, you may wish to use only the top half of the chart.) When the students are ready, ask them to skip count by 2's in unison, coloring each number that they say with a red crayon. It may be helpful for some students to say 1 softly, 2 loudly, 3 softly, 4 loudly, and so on.
Repeat this same process with counting by 3's and coloring each number with a yellow crayon. Then have students skip count by 5's, coloring each number with a blue crayon. (A portion of the completed chart is shown below.)
Call students' attention to numbers that have been colorded with more than one crayon. For instance, some numbers on their chart are orange (colored both red and yellow), and ask students if these numbers represent a skip-counting pattern. [They will show the pattern of skip counting by 6; each number is divisible by both 2 and 3.] Repeat with the numbers that are colored purple (i.e., colored with both red and blue crayons). [These are products of 10, having both 2 and 5 as factors.] Ask the students why the number 15 is colored green (i.e., colored with both yellow and blue). [It has both 3 and 5 as factors.]
