Comparing Multiplication Facts (Hey Tocayo!)

Kathryn Gregory
Multiple Subject Teacher

Students will be assigned a number that has various factors and they will find partners with different factors that have the same product.

Grade Level: 3 - 5th

Subject: Math

Length of Time: 30 - 40 Minutes

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Common Core Alignment

CCSS.MATH.CONTENT.4.OA.A.1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

CCSS.MATH.CONTENT.4.OA.B.4 - Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Objectives & Outcomes

Students will interpret a multiplication equation as a comparison and represent verbal statements of multiplicative comparisons as multiplication equations. Students will practice finding factor pairs for a whole number in the range 1-100. Students will recognize that a whole number is a multiple of each of its factors. Students will determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.

Materials Needed

A white board, a white board marker, a multiplication chart (attached if necessary) a teacher-created multiplication worksheet or practice from text book.


Opening to Lesson

  • Teacher explains that in some Spanish speaking countries, when 2 people have the same name, they often greet each other with the word “Tocayo” (Toe-KIE-yo) for a boy, and “Tocaya” (Toe-KIE-ya) for a girl.
    • If you have any kids with the same name in the class, use them as an example. “For example, Alex A and Alex B can greet each other with ‘Hey tocoyo what’s up!’”
    • Let them have time to find their Tocayos and say “Hey Tocayo.” Maybe they will share “my dad is my Tocayo, My Tocaya is in Mrs. Smith’s class…etc…”
  • Settle the class and explain that in many languages a lot of names have many nicknames. For example, the name Kathryn could have a nickname of Kate, Katie, Kathy, Kat, Katrina, etc… but she is still Kathryn. So if a “Kate” meets a “Katie,” she can still say “Hey Tocaya!”
  • Explain that in multiplication, whole numbers often have multiple factor pairs. So if “2 x 10” meets “4 x 5,” they can say “Hey Tocayo,” because they are both actually “20.”

Body of Lesson


  • Show the multiplication chart (attached) on the overhead.
  • Point out to the students that there are many numbers that appear many times as an answer with different factors, for example the number 12 appears 6 times!
  • Have students name the different factor combinations that have a product of 12 using the multiplication chart and write them as follows.
    • 2 times 6, 6 times 2, 1 times 12, 12 times 1, 3 times 4, and 4 times 3

Guided Practice

  • Instruct students to get out their white board and white board markers.
  • Have students write, “Hi, my name is______” at the top of the whiteboard.
  • Tell students to look at the multiplication and find products that appear multiple times on the chart.
  • Tell students to choose two factors from the chart and write them on their whiteboard.
    • Ex. Hi my name is: 2 times 6
  • Once all students have chosen their factor combination, have them stand up and find someone who has a factor combination that has the same product as theirs.
    • Ex. 3 times 4, 6 times 2, 1 times 12 or 12 times 1
  • When they find someone with an equivalent combination, they say “Hey Tocayo/a!” and stand next to each other and raise their boards for you to see.
  • When students are in groups with their Tocayos, point to each group and have them shout out their product one group at a time.
    • Ex. 12
  • Don’t let the students who don’t find a tocayo feel left out, have the entire class solve their factor combination.
    • “Ah looks like ‘4 times 7’ didn’t find her tocaya today, ‘7 times 4’ must be home sick, that’s ok, what’s her product class?” –“28!!!!”
  • Have students return to their seat and choose another factor combination and repeat the process!

Independent Practice

  • Teacher will create a multiplication worksheet for students to complete or do a related lesson from the textbook.


Lead a class discussion and ask if this could also work for addition and subtraction, for related division facts, or for anything else. Call on students to explain what they learned during the lesson.

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