Materials & Prep
- One 3-by-4 egg carton and 12 counters for the opening.
- Projector or board with grid paper or a 4-by-3 dot array.
- One small set of counters and a 6-by-6 grid mat per pair.
- Copy a one-page recording sheet with four boxes: Expression, Equal Groups, Array, Meaning. Include the independent problems listed below.
- Prepare expression cards: 2 x 5, 3 x 4, 4 x 3, 5 x 2, 3 x 3, 4 x 2.
Notice the Egg Carton
DisplayShow the filled 3-by-4 egg carton without writing a multiplication expression. Ask, “What do you notice? How could we count all of these counters so that we do not lose track?” Students turn and talk, then share ways to count 12 counters. Accept counting by ones, rows, columns, or skip counting.
Ask“If I point to one row, how many counters are there? How many rows are there?” Have students physically trace each row as the class counts 3, 6, 9, 12. This lets students succeed with familiar counting and the egg-carton array they already know.
ConnectExplain that their description, “4 rows with 3 in each row,” is the important idea behind multiplication. Multiplication gives a short way to describe equal-sized groups, especially when counting one by one would be slow.
Modeling Meaning
IntroduceWrite 4 x 3. Read it as “4 groups of 3” or “4 rows of 3.” Explain that the first factor tells how many equal groups or rows, and the second factor tells how many are in each group or row.
ModelPlace 3 counters in each of 4 rows of the egg carton. Say, “I see four equal rows. I check one row: it has three. So 4 x 3 means 4 groups of 3.” Draw the matching array as 4 rows of 3 dots, then write 3 + 3 + 3 + 3 = 12 and 4 x 3 = 12.
Think aloud“I do not begin by chanting ‘3, 6, 9, 12.’ Skip counting can help me find the total, but first I must know what the expression describes. If I built 3 rows of 4, I would have made 3 x 4, not 4 x 3.”
MisconceptionCover the model and ask students to vote with fingers: Does 4 x 3 mean 3 groups of 4, 4 groups of 3, or either one? Reveal the model and have students revise if needed. Clarify that 3 x 4 and 4 x 3 have the same total here, 12, but they describe arrays turned in different directions. The expression tells which description to draw.
Check for understandingDisplay 2 x 5. Ask students to hold up 2 fingers for the number of groups and 5 fingers for the number in each group, then sketch two rows of five on mini whiteboards or in the air. Listen for “2 groups of 5,” not only “10.”
Guided Practice
Worked exampleDraw 3 x 4 together. Prompt, “What do I draw first?” Guide students to make 3 rows, then place 4 dots in every row. Record: 3 groups of 4, 4 + 4 + 4 = 12, and 3 x 4 = 12.
Have studentsComplete 5 x 2 on personal grid mats while the teacher draws it alongside them. Partners use the sentence frame, “ x means groups of .” Ask several students to explain why their array matches the expression.
ScaffoldGive students who are shaky on skip counting a row-by-row counting strip labeled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. They touch and count each counter, then circle the total. They still state the groups and amount in each group before finding the total.
Look forEach row must contain the same number. If a student draws 5 dots in one row and 2 in another for 5 x 2, ask, “Are these equal groups? What must every row have?”
Build, Draw, and Explain
StudentsWork in pairs. Partner A turns over an expression card, reads it, and says its meaning. Both partners build the equal groups with counters on the grid mat, draw the matching array in the recording sheet, and write a sentence explaining the expression. Partner B checks each box before the pair turns over the next card. Switch reader/checker roles each round. Complete at least four cards.
PostChecklist: 1. Read the expression. 2. Say “ groups of .” 3. Build equal rows. 4. Draw the array. 5. Write the total and explanation.
CirculateAsk, “How does your model prove that this is 5 x 2?” and “What would be unreasonable about an array with unequal rows?” Record a quick note on students who can name groups and group size independently.
ExtensionStudents choose one card, rotate its array, and write the turned expression. They explain why the total stays the same while the description changes, for example, 2 x 5 and 5 x 2 both total 10.
Independent Explanation
WriteStudents complete these three items independently on the bottom of the recording sheet.
- Draw an array for 4 x 2. Label the rows and write what 4 x 2 means.
- An array has 3 rows with 5 stars in each row. Write the multiplication expression and explain what it means.
- A student says 3 x 4 means “3 and 4.” Explain what is missing from that statement.
SupportLeave the sentence frame visible: “ x means equal groups of .” Students may use counters or the grid mat for any item.
Closing Check
Exit ticketDisplay 2 x 4. Students draw a quick array and finish the sentence, “2 x 4 means .” Then ask two students to orally justify how the array shows their answer. Sort tickets into: names both groups and group size, has an array but unclear meaning, needs reteaching with counters.